Sanz-Vicario, José Luis; Pérez-Torres, Jhon Fredy; Moreno-Polo, Germán
2017-08-01
We compute the entanglement between the electronic and vibrational motions in the simplest molecular system, the hydrogen molecular ion, considering the molecule as a bipartite system, electron and vibrational motion. For that purpose we compute an accurate total non-Born-Oppenheimer wave function in terms of a huge expansion using nonorthogonal B-spline basis sets that expand separately the electronic and nuclear wave functions. According to the Schmidt decomposition theorem for bipartite systems, widely used in quantum-information theory, it is possible to find a much shorter but equivalent expansion in terms of the natural orbitals or Schmidt bases for the electronic and nuclear half spaces. Here we extend the Schmidt decomposition theorem to the case in which nonorthogonal bases are used to span the partitioned Hilbert spaces. This extension is first illustrated with two simple coupled systems, the former without an exact solution and the latter exactly solvable. In these model systems of distinguishable coupled particles it is shown that the entanglement content does not increase monotonically with the excitation energy, but only within the manifold of states that belong to an existing excitation mode, if any. In the hydrogen molecular ion the entanglement content for each non-Born-Oppenheimer vibronic state is quantified through the von Neumann and linear entropies and we show that entanglement serves as a witness to distinguish vibronic states related to different Born-Oppenheimer molecular energy curves or electronic excitation modes.
Directory of Open Access Journals (Sweden)
M. Shrivastava
2011-07-01
Full Text Available The Weather Research and Forecasting model coupled with chemistry (WRF-Chem is modified to include a volatility basis set (VBS treatment of secondary organic aerosol formation. The VBS approach, coupled with SAPRC-99 gas-phase chemistry mechanism, is used to model gas-particle partitioning and multiple generations of gas-phase oxidation of organic vapors. In addition to the detailed 9-species VBS, a simplified mechanism using 2 volatility species (2-species VBS is developed and tested for similarity to the 9-species VBS in terms of both mass and oxygen-to-carbon ratios of organic aerosols in the atmosphere. WRF-Chem results are evaluated against field measurements of organic aerosols collected during the MILAGRO 2006 campaign in the vicinity of Mexico City. The simplified 2-species mechanism reduces the computational cost by a factor of 2 as compared to 9-species VBS. Both ground site and aircraft measurements suggest that the 9-species and 2-species VBS predictions of total organic aerosol mass as well as individual organic aerosol components including primary, secondary, and biomass burning are comparable in magnitude. In addition, oxygen-to-carbon ratio predictions from both approaches agree within 25 %, providing evidence that the 2-species VBS is well suited to represent the complex evolution of organic aerosols. Model sensitivity to amount of anthropogenic semi-volatile and intermediate volatility (S/IVOC precursor emissions is also examined by doubling the default emissions. Both the emission cases significantly under-predict primary organic aerosols in the city center and along aircraft flight transects. Secondary organic aerosols are predicted reasonably well along flight tracks surrounding the city, but are consistently over-predicted downwind of the city. Also, oxygen-to-carbon ratio predictions are significantly improved compared to prior studies by adding 15 % oxygen mass per generation of oxidation; however, all modeling cases
Kollmar, Christian; Neese, Frank
2014-10-07
The role of the static Kohn-Sham (KS) response function describing the response of the electron density to a change of the local KS potential is discussed in both the theory of the optimized effective potential (OEP) and the so-called inverse Kohn-Sham problem involving the task to find the local KS potential for a given electron density. In a general discussion of the integral equation to be solved in both cases, it is argued that a unique solution of this equation can be found even in case of finite atomic orbital basis sets. It is shown how a matrix representation of the response function can be obtained if the exchange-correlation potential is expanded in terms of a Schmidt-orthogonalized basis comprising orbitals products of occupied and virtual orbitals. The viability of this approach in both OEP theory and the inverse KS problem is illustrated by numerical examples.
Exact exchange with non-orthogonal generalized Wannier functions
Mountjoy, Jeff; Todd, Michelle; Mosey, Nicholas J.
2017-03-01
The evaluation of exact exchange (EXX) is an important component of quantum chemical calculations performed with ab initio and hybrid density functional methods. While evaluating exact exchange is routine in molecular quantum chemical calculations performed with localized basis sets, the non-local nature of the exchange operator presents a major impediment to the efficient use of exact exchange in calculations that employ planewave basis sets. Non-orthogonal generalized Wannier functions (NGWFs) corresponding to planewave expansions of localized basis functions are an alternative form of basis set that can be used in quantum chemical calculations. The periodic nature of these functions renders them suitable for calculations of periodic systems, while the contraction of sets of planewaves into individual basis functions reduces the number of variational parameters, permitting the construction and direct diagonalization of the Fock matrix. The present study examines how NGWFs corresponding to Fourier series representations of conventional atom-centered basis sets can be used to evaluate exact exchange in periodic systems. Specifically, an approach for constructing the exchange operator with NGWFs is presented and used to perform Hartree-Fock calculations with a series of molecules in periodically repeated simulation cells. The results demonstrate that the NGWF approach is significantly faster than the EXX method, which is a standard approach for evaluating exact exchange in periodic systems.
2012-01-01
We develop a first-principles computational method for investigating the dielectric screening in extended systems using the self-consistent Sternheimer equation and localized non-orthogonal basis sets. Our approach does not require the explicit calculation of unoccupied electronic states, only uses two-center integrals, and has a theoretical scaling of order O(N^3). We demonstrate this method by comparing our calculations for silicon, germanium, diamond, and LiCl with reference planewaves cal...
Hübener, Hannes; Pérez-Osorio, Miguel A.; Ordejón, Pablo; Giustino, Feliciano
2012-06-01
We develop a first-principles computational method for investigating the dielectric screening in extended systems using the self-consistent Sternheimer equation and localized nonorthogonal basis sets. Our approach does not require the explicit calculation of unoccupied electronic states, uses only two-center integrals, and has a theoretical scaling of order O(N3). We demonstrate this method by comparing our calculations for silicon, germanium, diamond, and LiCl with reference plane-wave calculations. We show that accuracy comparable to that of plane-wave calculations can be achieved via a systematic optimization of the basis set.
Spackman, Peter R.; Karton, Amir
2015-05-01
Coupled cluster calculations with all single and double excitations (CCSD) converge exceedingly slowly with the size of the one-particle basis set. We assess the performance of a number of approaches for obtaining CCSD correlation energies close to the complete basis-set limit in conjunction with relatively small DZ and TZ basis sets. These include global and system-dependent extrapolations based on the A + B/Lα two-point extrapolation formula, and the well-known additivity approach that uses an MP2-based basis-set-correction term. We show that the basis set convergence rate can change dramatically between different systems(e.g.it is slower for molecules with polar bonds and/or second-row elements). The system-dependent basis-set extrapolation scheme, in which unique basis-set extrapolation exponents for each system are obtained from lower-cost MP2 calculations, significantly accelerates the basis-set convergence relative to the global extrapolations. Nevertheless, we find that the simple MP2-based basis-set additivity scheme outperforms the extrapolation approaches. For example, the following root-mean-squared deviations are obtained for the 140 basis-set limit CCSD atomization energies in the W4-11 database: 9.1 (global extrapolation), 3.7 (system-dependent extrapolation), and 2.4 (additivity scheme) kJ mol-1. The CCSD energy in these approximations is obtained from basis sets of up to TZ quality and the latter two approaches require additional MP2 calculations with basis sets of up to QZ quality. We also assess the performance of the basis-set extrapolations and additivity schemes for a set of 20 basis-set limit CCSD atomization energies of larger molecules including amino acids, DNA/RNA bases, aromatic compounds, and platonic hydrocarbon cages. We obtain the following RMSDs for the above methods: 10.2 (global extrapolation), 5.7 (system-dependent extrapolation), and 2.9 (additivity scheme) kJ mol-1.
Energy Technology Data Exchange (ETDEWEB)
Spackman, Peter R.; Karton, Amir, E-mail: amir.karton@uwa.edu.au [School of Chemistry and Biochemistry, The University of Western Australia, Perth, WA 6009 (Australia)
2015-05-15
Coupled cluster calculations with all single and double excitations (CCSD) converge exceedingly slowly with the size of the one-particle basis set. We assess the performance of a number of approaches for obtaining CCSD correlation energies close to the complete basis-set limit in conjunction with relatively small DZ and TZ basis sets. These include global and system-dependent extrapolations based on the A + B/L{sup α} two-point extrapolation formula, and the well-known additivity approach that uses an MP2-based basis-set-correction term. We show that the basis set convergence rate can change dramatically between different systems(e.g.it is slower for molecules with polar bonds and/or second-row elements). The system-dependent basis-set extrapolation scheme, in which unique basis-set extrapolation exponents for each system are obtained from lower-cost MP2 calculations, significantly accelerates the basis-set convergence relative to the global extrapolations. Nevertheless, we find that the simple MP2-based basis-set additivity scheme outperforms the extrapolation approaches. For example, the following root-mean-squared deviations are obtained for the 140 basis-set limit CCSD atomization energies in the W4-11 database: 9.1 (global extrapolation), 3.7 (system-dependent extrapolation), and 2.4 (additivity scheme) kJ mol{sup –1}. The CCSD energy in these approximations is obtained from basis sets of up to TZ quality and the latter two approaches require additional MP2 calculations with basis sets of up to QZ quality. We also assess the performance of the basis-set extrapolations and additivity schemes for a set of 20 basis-set limit CCSD atomization energies of larger molecules including amino acids, DNA/RNA bases, aromatic compounds, and platonic hydrocarbon cages. We obtain the following RMSDs for the above methods: 10.2 (global extrapolation), 5.7 (system-dependent extrapolation), and 2.9 (additivity scheme) kJ mol{sup –1}.
Energy Technology Data Exchange (ETDEWEB)
Rossi, Tuomas P., E-mail: tuomas.rossi@alumni.aalto.fi; Sakko, Arto; Puska, Martti J. [COMP Centre of Excellence, Department of Applied Physics, Aalto University School of Science, P.O. Box 11100, FI-00076 Aalto (Finland); Lehtola, Susi, E-mail: susi.lehtola@alumni.helsinki.fi [COMP Centre of Excellence, Department of Applied Physics, Aalto University School of Science, P.O. Box 11100, FI-00076 Aalto (Finland); Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States); Nieminen, Risto M. [COMP Centre of Excellence, Department of Applied Physics, Aalto University School of Science, P.O. Box 11100, FI-00076 Aalto (Finland); Dean’s Office, Aalto University School of Science, P.O. Box 11000, FI-00076 Aalto (Finland)
2015-03-07
We present an approach for generating local numerical basis sets of improving accuracy for first-principles nanoplasmonics simulations within time-dependent density functional theory. The method is demonstrated for copper, silver, and gold nanoparticles that are of experimental interest but computationally demanding due to the semi-core d-electrons that affect their plasmonic response. The basis sets are constructed by augmenting numerical atomic orbital basis sets by truncated Gaussian-type orbitals generated by the completeness-optimization scheme, which is applied to the photoabsorption spectra of homoatomic metal atom dimers. We obtain basis sets of improving accuracy up to the complete basis set limit and demonstrate that the performance of the basis sets transfers to simulations of larger nanoparticles and nanoalloys as well as to calculations with various exchange-correlation functionals. This work promotes the use of the local basis set approach of controllable accuracy in first-principles nanoplasmonics simulations and beyond.
Reuter, Matthew G; Harrison, Robert J
2014-05-01
The thesis of Brandbyge's comment [J. Chem. Phys. 140, 177103 (2014)] is that our operator decoupling condition is immaterial to transport theories, and it appeals to discussions of nonorthogonal basis sets in transport calculations in its arguments. We maintain that the operator condition is to be preferred over the usual matrix conditions and subsequently detail problems in the existing approaches. From this operator perspective, we conclude that nonorthogonal projectors cannot be used and that the projectors must be selected to satisfy the operator decoupling condition. Because these conclusions pertain to operators, the choice of basis set is not germane.
Conductance calculations with a wavelet basis set
DEFF Research Database (Denmark)
Thygesen, Kristian Sommer; Bollinger, Mikkel; Jacobsen, Karsten Wedel
2003-01-01
. The linear-response conductance is calculated from the Green's function which is represented in terms of a system-independent basis set containing wavelets with compact support. This allows us to rigorously separate the central region from the contacts and to test for convergence in a systematic way...
Accurate basis set truncation for wavefunction embedding
Barnes, Taylor A.; Goodpaster, Jason D.; Manby, Frederick R.; Miller, Thomas F.
2013-07-01
Density functional theory (DFT) provides a formally exact framework for performing embedded subsystem electronic structure calculations, including DFT-in-DFT and wavefunction theory-in-DFT descriptions. In the interest of efficiency, it is desirable to truncate the atomic orbital basis set in which the subsystem calculation is performed, thus avoiding high-order scaling with respect to the size of the MO virtual space. In this study, we extend a recently introduced projection-based embedding method [F. R. Manby, M. Stella, J. D. Goodpaster, and T. F. Miller III, J. Chem. Theory Comput. 8, 2564 (2012)], 10.1021/ct300544e to allow for the systematic and accurate truncation of the embedded subsystem basis set. The approach is applied to both covalently and non-covalently bound test cases, including water clusters and polypeptide chains, and it is demonstrated that errors associated with basis set truncation are controllable to well within chemical accuracy. Furthermore, we show that this approach allows for switching between accurate projection-based embedding and DFT embedding with approximate kinetic energy (KE) functionals; in this sense, the approach provides a means of systematically improving upon the use of approximate KE functionals in DFT embedding.
DEFF Research Database (Denmark)
Brandbyge, Mads
2014-01-01
In a recent paper Reuter and Harrison [J. Chem. Phys.139, 114104 (2013)] question the widely used mean-field electron transport theories, which employ nonorthogonal localized basis sets. They claim these can violate an “implicit decoupling assumption,” leading to wrong results for the current...
Basis set independent calculation of molecular polarizabilities
Talman, James D.
2012-08-01
It is shown that e-F, where F is the Hartree-Fock (HF) operator, can be inverted, for molecular systems, in numerical Cartesian coordinates. The method was originally applied to finding corrections to approximate Hartree-Fock orbitals [J. D. Talman, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.82.052518 82, 052518 (2010)]. The approach is applied to determine basis set independent dipole polarizabilities for the water molecule using the Sternheimer method within the uncoupled HF and coupled perturbed HF approximations.
The Role of the Basis Set: Assessing Density Functional Theory
Boese, A D; Handy, N C; Martin, Jan M. L.; Handy, Nicholas C.
2003-01-01
When developing and assessing density functional theory methods, a finite basis set is usually employed. In most cases, however, the issue of basis set dependency is neglected. Here, we assess several basis sets and functionals. In addition, the dependency of the semiempirical fits to a given basis set for a generalised gradient approximation and a hybrid functional is investigated. The resulting functionals are then tested for other basis sets, evaluating their errors and transferability.
On a nonorthogonal polynomial sequence associated with Bessel operator
Loureiro, Ana F; Yakubovich, S
2011-01-01
By means of the Bessel operator a polynomial sequence is constructed to which several properties are given. Among them, its explicit expression, the connection with the Euler numbers, its integral representation via the Kontorovich-Lebedev transform. Despite its non-orthogonality, it is possible to associate to the canonical element of its dual sequence a positive-definite measure as long as certain stronger constraints are imposed.
ORBITAL CONNECTIONS FOR PERTURBATION-DEPENDENT BASIS-SETS
DEFF Research Database (Denmark)
Olsen, Jeppe; Bak, Keld L.; Ruud, K.
1995-01-01
The use of perturbation-dependent basis sets is analysed with emphasis on the connection between the basis sets at different values of the perturbation strength. A particular connection, the natural connection, that minimizes the change of the basis set orbitals is devised and the second quantiza......The use of perturbation-dependent basis sets is analysed with emphasis on the connection between the basis sets at different values of the perturbation strength. A particular connection, the natural connection, that minimizes the change of the basis set orbitals is devised and the second...... quantization realization of this connection is introduced. It is shown that the natural connection is important for the efficient evaluation of molecular properties and for the physical interpretation of the terms entering the calculated properties. For example, in molecular Hessian calculations the natural...
Basis Set Exchange: A Community Database for Computational Sciences
Energy Technology Data Exchange (ETDEWEB)
Schuchardt, Karen L.; Didier, Brett T.; Elsethagen, Todd O.; Sun, Lisong; Gurumoorthi, Vidhya; Chase, Jared M.; Li, Jun; Windus, Theresa L.
2007-05-01
Basis sets are one of the most important input data for computational models in the chemistry, materials, biology and other science domains that utilize computational quantum mechanics methods. Providing a shared, web accessible environment where researchers can not only download basis sets in their required format, but browse the data, contribute new basis sets, and ultimately curate and manage the data as a community will facilitate growth of this resource and encourage sharing both data and knowledge. We describe the Basis Set Exchange (BSE), a web portal that provides advanced browsing and download capabilities, facilities for contributing basis set data, and an environment that incorporates tools to foster development and interaction of communities. The BSE leverages and enables continued development of the basis set library originally assembled at the Environmental Molecular Sciences Laboratory.
Basis set exchange: a community database for computational sciences.
Schuchardt, Karen L; Didier, Brett T; Elsethagen, Todd; Sun, Lisong; Gurumoorthi, Vidhya; Chase, Jared; Li, Jun; Windus, Theresa L
2007-01-01
Basis sets are some of the most important input data for computational models in the chemistry, materials, biology, and other science domains that utilize computational quantum mechanics methods. Providing a shared, Web-accessible environment where researchers can not only download basis sets in their required format but browse the data, contribute new basis sets, and ultimately curate and manage the data as a community will facilitate growth of this resource and encourage sharing both data and knowledge. We describe the Basis Set Exchange (BSE), a Web portal that provides advanced browsing and download capabilities, facilities for contributing basis set data, and an environment that incorporates tools to foster development and interaction of communities. The BSE leverages and enables continued development of the basis set library originally assembled at the Environmental Molecular Sciences Laboratory.
Continuum contributions to dipole oscillator-strength sum rules for hydrogen in finite basis sets
DEFF Research Database (Denmark)
Oddershede, Jens; Ogilvie, John F.; Sauer, Stephan P. A.;
2017-01-01
Calculations of the continuum contributions to dipole oscillator sum rules for hydrogen are performed using both exact and basis-set representations of the stick spectra of the continuum wave function. We show that the same results are obtained for the sum rules in both cases, but that the conver...
Non-orthogonal subband/transform coder
Glover, Daniel R. (Inventor)
1993-01-01
The present invention is directed to a simplified digital subband coder/decoder. In the present invention a signal is fed into a coder. The coder uses a non-orthogonal algorithm that is simply implemented in the coder hardware. The simple non-orthogonal design is then used in the implementation of the decoder to decode the signal.
KINETIC BALANCE IN CONTRACTED BASIS-SETS FOR RELATIVISTIC CALCULATIONS
VISSCHER, L; AERTS, PJC; VISSER, O; NIEUWPOORT, WC
1991-01-01
A demonstration of kinetic balance failure in heavily contracted basis sets is given. Other possible methods of constructing small component basis sets for 4-component relativistic calculations are discussed. The position of the additional negative energy levels in extended balance calculations in s
Reuter, Matthew G; Harrison, Robert J
2013-09-21
We revisit the derivation of electron transport theories with a focus on the projection operators chosen to partition the system. The prevailing choice of assigning each computational basis function to a region causes two problems. First, this choice generally results in oblique projection operators, which are non-Hermitian and violate implicit assumptions in the derivation. Second, these operators are defined with the physically insignificant basis set and, as such, preclude a well-defined basis set limit. We thus advocate for the selection of physically motivated, orthogonal projection operators (which are Hermitian) and present an operator-based derivation of electron transport theories. Unlike the conventional, matrix-based approaches, this derivation requires no knowledge of the computational basis set. In this process, we also find that common transport formalisms for nonorthogonal basis sets improperly decouple the exterior regions, leading to a short circuit through the system. We finally discuss the implications of these results for first-principles calculations of electron transport.
Efficient Diffuse Basis Sets for Density Functional Theory.
Papajak, Ewa; Truhlar, Donald G
2010-03-09
Eliminating all but the s and p diffuse functions on the non-hydrogenic atoms and all diffuse functions on the hydrogen atoms from the aug-cc-pV(x+d)Z basis sets of Dunning and co-workers, where x = D, T, Q, ..., yields the previously proposed "minimally augmented" basis sets, called maug-cc-pV(x+d)Z. Here, we present extensive and systematic tests of these basis sets for density functional calculations of chemical reaction barrier heights, hydrogen bond energies, electron affinities, ionization potentials, and atomization energies. The tests show that the maug-cc-pV(x+d)Z basis sets are as accurate as the aug-cc-pV(x+d)Z ones for density functional calculations, but the computational cost savings are a factor of about two to seven.
Corsetti, Fabiano
2014-01-01
The implementation of the orbital minimization method (OMM) for solving the self-consistent Kohn-Sham (KS) problem for electronic structure calculations in a basis of non-orthogonal numerical atomic orbitals of finite-range is reported. We explore the possibilities for using the OMM as an exact cubic-scaling solver for the KS problem, and compare its performance with that of explicit diagonalization in realistic systems. We analyze the efficiency of the method depending on the choice of line search algorithm and on two free parameters, the scale of the kinetic energy preconditioning and the eigenspectrum shift. The results of several timing tests are then discussed, showing that the OMM can achieve a noticeable speedup with respect to diagonalization even for minimal basis sets for which the number of occupied eigenstates represents a significant fraction of the total basis size (>15%). We investigate the hard and soft parallel scaling of the method on multiple cores, finding a performance equal to or better ...
Gauge origin independence in finite basis sets and perturbation theory
Sørensen, Lasse Kragh; Lindh, Roland; Lundberg, Marcus
2017-09-01
We show that origin independence in finite basis sets for the oscillator strengths is possibly in any gauge contrary to what is stated in literature. This is proved from a discussion of the consequences in perturbation theory when the exact eigenfunctions and eigenvalues to the zeroth order Hamiltonian H0 cannot be found. We demonstrate that the erroneous conclusion for the lack of gauge origin independence in the length gauge stems from not transforming the magnetic terms in the multipole expansion leading to the use of a mixed gauge. Numerical examples of exact origin dependence are shown.
Coupled-cluster based basis sets for valence correlation calculations
Claudino, Daniel; Gargano, Ricardo; Bartlett, Rodney J.
2016-03-01
Novel basis sets are generated that target the description of valence correlation in atoms H through Ar. The new contraction coefficients are obtained according to the Atomic Natural Orbital (ANO) procedure from CCSD(T) (coupled-cluster singles and doubles with perturbative triples correction) density matrices starting from the primitive functions of Dunning et al. [J. Chem. Phys. 90, 1007 (1989); ibid. 98, 1358 (1993); ibid. 100, 2975 (1993)] (correlation consistent polarized valence X-tuple zeta, cc-pVXZ). The exponents of the primitive Gaussian functions are subject to uniform scaling in order to ensure satisfaction of the virial theorem for the corresponding atoms. These new sets, named ANO-VT-XZ (Atomic Natural Orbital Virial Theorem X-tuple Zeta), have the same number of contracted functions as their cc-pVXZ counterparts in each subshell. The performance of these basis sets is assessed by the evaluation of the contraction errors in four distinct computations: correlation energies in atoms, probing the density in different regions of space via (-3 ≤ n ≤ 3) in atoms, correlation energies in diatomic molecules, and the quality of fitting potential energy curves as measured by spectroscopic constants. All energy calculations with ANO-VT-QZ have contraction errors within "chemical accuracy" of 1 kcal/mol, which is not true for cc-pVQZ, suggesting some improvement compared to the correlation consistent series of Dunning and co-workers.
Quiney, H. M.; Glushkov, V. N.; Wilson, S.; Sabin,; Brandas, E
2001-01-01
A comparison is made of the accuracy achieved in finite difference and finite basis set approximations to the Dirac equation for the ground state of the hydrogen molecular ion. The finite basis set calculations are carried out using a distributed basis set of Gaussian functions the exponents and pos
Quiney, H. M.; Glushkov, V. N.; Wilson, S.; Sabin,; Brandas, E
2001-01-01
A comparison is made of the accuracy achieved in finite difference and finite basis set approximations to the Dirac equation for the ground state of the hydrogen molecular ion. The finite basis set calculations are carried out using a distributed basis set of Gaussian functions the exponents and
Finite-basis-set expansion methods for scattering problems
Energy Technology Data Exchange (ETDEWEB)
Ladanyi, K.; Levay, P.; Apagyi, B.
1988-10-01
A wide variety of finite-basis-set expansion methods is applied to electron--hydrogen-atom scattering in the static-exchange approximation. All these methods are based on the Lippmann-Schwinger formalism. A careful analysis of the numerical results is presented with the aim of selecting efficient approaches to the solution of realistic electron-atom (and electron-molecule) scattering problems. The results show that the efficiency of the expansion methods may depend sensitively on the characteristics of the interaction terms. Some difficulties of the simple method of moments are pointed out. A particular least-squares method is proposed to avoid the spurious singularities encountered in applications of the Schwinger variational method to singlet scattering processes.
Localized atomic basis set in the projector augmented wave method
DEFF Research Database (Denmark)
Larsen, Ask Hjorth; Vanin, Marco; Mortensen, Jens Jørgen
2009-01-01
representation. The possibility to switch seamlessly between the two representations implies that simulations employing the local basis can be fine tuned at the end of the calculation by switching to the grid, thereby combining the strength of the two representations for optimal performance. The implementation...... is tested by calculating atomization energies and equilibrium bulk properties of a variety of molecules and solids, comparing to the grid results. Finally, it is demonstrated how a grid-quality structure optimization can be performed with significantly reduced computational effort by switching between...
Plascencia, Cesar; Wang, Jiaqi; Wilson, Angela K.
2017-10-01
The impact of basis set choice has been considered for a series of transition metal (TM) species. The need for higher level correlation consistent basis sets on both the metal and ligand has been investigated, and permutations in the pairings of basis set used for TM's and basis set used for ligands can lead to effective routes to complete basis set (CBS) limit extrapolations of thermochemical energetics with little change in thermochemical predictions as compared to those resulting from the use of traditional basis set pairings, while enabling computational cost savings. Basis set superposition errors (BSSE) that can arise have also been considered.
A nonorthogonal state-interaction approach for matrix product state wave functions
Knecht, Stefan; Autschbach, Jochen; Reiher, Markus
2016-01-01
We present a state-interaction approach for matrix product state (MPS) wave functions in a nonorthogonal molecular orbital basis. Our approach allows us to calculate for example transition and spin-orbit coupling matrix elements between arbitrary electronic states provided that they share the same one-electron basis functions and active orbital space, respectively. The key element is the transformation of the MPS wave functions of different states from a nonorthogonal to a biorthonormal molecular orbital basis representation exploiting a sequence of non-unitary transformations following a proposal by Malmqvist (Int. J. Quantum Chem. 30, 479 (1986)). This is well-known for traditional wave-function parametrizations but has not yet been exploited for MPS wave functions.
Basis set expansion for inverse problems in plasma diagnostic analysis
Jones, B.; Ruiz, C. L.
2013-07-01
A basis set expansion method [V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, Rev. Sci. Instrum. 73, 2634 (2002)], 10.1063/1.1482156 is applied to recover physical information about plasma radiation sources from instrument data, which has been forward transformed due to the nature of the measurement technique. This method provides a general approach for inverse problems, and we discuss two specific examples relevant to diagnosing fast z pinches on the 20-25 MA Z machine [M. E. Savage, L. F. Bennett, D. E. Bliss, W. T. Clark, R. S. Coats, J. M. Elizondo, K. R. LeChien, H. C. Harjes, J. M. Lehr, J. E. Maenchen, D. H. McDaniel, M. F. Pasik, T. D. Pointon, A. C. Owen, D. B. Seidel, D. L. Smith, B. S. Stoltzfus, K. W. Struve, W. A. Stygar, L. K. Warne, J. R. Woodworth, C. W. Mendel, K. R. Prestwich, R. W. Shoup, D. L. Johnson, J. P. Corley, K. C. Hodge, T. C. Wagoner, and P. E. Wakeland, in Proceedings of the Pulsed Power Plasma Sciences Conference (IEEE, 2007), p. 979]. First, Abel inversion of time-gated, self-emission x-ray images from a wire array implosion is studied. Second, we present an approach for unfolding neutron time-of-flight measurements from a deuterium gas puff z pinch to recover information about emission time history and energy distribution. Through these examples, we discuss how noise in the measured data limits the practical resolution of the inversion, and how the method handles discontinuities in the source function and artifacts in the projected image. We add to the method a propagation of errors calculation for estimating uncertainties in the inverted solution.
Basis set expansion for inverse problems in plasma diagnostic analysis
Energy Technology Data Exchange (ETDEWEB)
Jones, B.; Ruiz, C. L. [Sandia National Laboratories, PO Box 5800, Albuquerque, New Mexico 87185 (United States)
2013-07-15
A basis set expansion method [V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, Rev. Sci. Instrum. 73, 2634 (2002)] is applied to recover physical information about plasma radiation sources from instrument data, which has been forward transformed due to the nature of the measurement technique. This method provides a general approach for inverse problems, and we discuss two specific examples relevant to diagnosing fast z pinches on the 20–25 MA Z machine [M. E. Savage, L. F. Bennett, D. E. Bliss, W. T. Clark, R. S. Coats, J. M. Elizondo, K. R. LeChien, H. C. Harjes, J. M. Lehr, J. E. Maenchen, D. H. McDaniel, M. F. Pasik, T. D. Pointon, A. C. Owen, D. B. Seidel, D. L. Smith, B. S. Stoltzfus, K. W. Struve, W. A. Stygar, L. K. Warne, J. R. Woodworth, C. W. Mendel, K. R. Prestwich, R. W. Shoup, D. L. Johnson, J. P. Corley, K. C. Hodge, T. C. Wagoner, and P. E. Wakeland, in Proceedings of the Pulsed Power Plasma Sciences Conference (IEEE, 2007), p. 979]. First, Abel inversion of time-gated, self-emission x-ray images from a wire array implosion is studied. Second, we present an approach for unfolding neutron time-of-flight measurements from a deuterium gas puff z pinch to recover information about emission time history and energy distribution. Through these examples, we discuss how noise in the measured data limits the practical resolution of the inversion, and how the method handles discontinuities in the source function and artifacts in the projected image. We add to the method a propagation of errors calculation for estimating uncertainties in the inverted solution.
Denis, Pablo A
2005-09-01
We have investigated the SX (X = first- or second-row atom), SO2, and SO3 molecules employing the correlation-consistent (cc), the recently developed polarization-consistent (pc), and three Pople-type basis sets, in conjunction with the B3LYP functional. The results confirmed that the aug-pc basis sets represent a great contribution in terms of cost-benefits. In the case of the B3LYP functional, when employing the aug-pc-3 and aug-pc-4 basis sets, it is possible to obtain results that are of aug-cc-pV(5+d)Z and aug-cc-pV(6+d)Z quality, respectively, at a much lower cost. The estimations obtained employing smaller members of the family are of nearly double-ζ quality and do not provide reliable results. There is no basis set of quadruple-ζ quality among the polarized-consistent basis sets, although in terms of composition, the aug-pc-3 basis set is a QZ basis set. A precise estimation of the Kohn-Sham complete basis set (CBS) limit with the aug-pc-X basis sets is too difficult for the B3LYP functional because the ∞(aug-pc-4, aug-pc-3, aug-pc-2) extrapolation gives the same results as those of the aug-pc-4 basis set. This is in contrast with the results observed for ab initio methodologies for which the largest basis sets provided the best estimation of the CBS limit. In our opinion, the closest results to the B3LYP/CBS limit are expected to be those obtained with a two-point extrapolation employing the aug-cc-pV(X+d)Z (X = 5, 6) basis sets. The results obtained with this extrapolation are very close to those predicted by the ∞(aug-pc-3, aug-pc-2, aug-pc-1) extrapolation, and that provides a cheaper but more inaccurate alternative to estimate the CBS limit. Minor problems were found for the aug-pc-X basis sets and the B3LYP functional for molecules in which sulfur is bound to a very electronegative element, such as SO, SF, SO2, and SO3. For these molecules, the cc basis sets were demonstrated to be more useful. The importance of tight d functions was observed
A linear variational exercise with a simple non-orthogonal basis for the particle-in-the-box problem
Energy Technology Data Exchange (ETDEWEB)
Luana, VIctor; Otero-de la Roza, A; Blanco, M A; Recio, J M [Universidad de Oviedo, Departamento de Quimica Fisica y AnalItica, E-33006-Oviedo (Spain)], E-mail: victor@carbono.quimica.uniovi.es
2010-01-15
The particle-in-the-box, with or without an additional potential, is proposed as an excellent laboratory to teach and explore the details of the linear variational method using a non-orthogonal basis. The x{sup n}(a - x){sup n} and x{sup n}(a/2 - x)(a - x){sup n} polynomials are shown to form a complete basis for the even and odd states, respectively, of the particle confined to the x in [0, a] interval. A short and simple Octave code is presented as the natural extension to the hand calculations when the basis set grows in size.
Efficient construction of nonorthogonal localized molecular orbitals in large systems.
Cui, Ganglong; Fang, Weihai; Yang, Weitao
2010-08-26
Localized molecular orbitals (LMOs) are much more compact representations of electronic degrees of freedom than canonical molecular orbitals (CMOs). The most compact representation is provided by nonorthogonal localized molecular orbitals (NOLMOs), which are linearly independent but are not orthogonal. Both LMOs and NOLMOs are thus useful for linear-scaling calculations of electronic structures for large systems. Recently, NOLMOs have been successfully applied to linear-scaling calculations with density functional theory (DFT) and to reformulating time-dependent density functional theory (TDDFT) for calculations of excited states and spectroscopy. However, a challenge remains as NOLMO construction from CMOs is still inefficient for large systems. In this work, we develop an efficient method to accelerate the NOLMO construction by using predefined centroids of the NOLMO and thereby removing the nonlinear equality constraints in the original method ( J. Chem. Phys. 2004 , 120 , 9458 and J. Chem. Phys. 2000 , 112 , 4 ). Thus, NOLMO construction becomes an unconstrained optimization. Its efficiency is demonstrated for the selected saturated and conjugated molecules. Our method for fast NOLMO construction should lead to efficient DFT and NOLMO-TDDFT applications to large systems.
Non-orthogonal approaches to the study of magnetic interactions
Broer-Braam, H.B.; Hozoi, L; Nieuwpoort, WC
2003-01-01
Early theoretical studies of magnetic interactions between paramagnetic centres in solids and molecules are briefly reviewed as an introduction to the main theme of this paper: nonorthogonal CI approaches for the prediction and interpretation of magnetic couplings. In a non-orthogonal CI approach, t
Quantum noise in a laser with nonorthogonal polarization modes
van der Lee, A.M.; Mieremet, A.L.; van Exter, M.P.; van Druten, N.J.; Woerdman, J.P.
2000-01-01
We describe the quantum-noise behavior of a laser that has nonorthogonal polarization modes. The nonorthogonality of the modes leads to excess quantum noise. Theoretically, we derive the excess noise dynamics of the laser, including the saturation of the gain medium. Experimentally, we have measured
Magnetic properties of small Fe clusters: a nonorthogonal Hamiltonian study
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
We calculate the magnetic properties of small FeN clusters(N=2～7,9,13,15) by using a parameterized Hubbard tight-binding sp d-band model Hamiltonian, with the parameters obtained from nonorthogonal Ham il tonian parameters. the average magnetic moments, and the spin-polarized charge distribution within clusters are in agreement with those obtained by first-prin ciple and tight-binding calculations. The effect of the nonorthogonal basis is discussed.
Accurate adapted Gaussian basis sets for the atoms from H through Xe
Energy Technology Data Exchange (ETDEWEB)
Jorge, F.E.; Muniz, E.P. [Univ. Federal do Espirito Santo, Vitoria, Espirito Santo (Brazil). Dept. de Fisica-CCE
1999-02-05
The authors have applied the generator coordinate Hartree-Fock method to generate adapted Gaussian basis sets for the atoms from H through Xe. The Griffin-Hill-Wheeler-Hartree-Fock equations are integrated numerically generating accurate basis sets for these atoms. The atomic wave functions are an improvement over those of Clementi et al. using larger atom-optimized geometrical Gaussian basis sets and Jorge et al. using a universal Gaussian basis set. In all cases, the current wave functions predict total energy results within 6.13 {times} 10{sup {minus}4} hartree of the numerical Hartree-Fock limit.
Hill, J Grant
2011-07-28
Auxiliary basis sets specifically matched to the correlation consistent cc-pVnZ-PP, cc-pwCVnZ-PP, aug-cc-pVnZ-PP, and aug-cc-pwCVnZ-PP orbital basis sets (used in conjunction with pseudopotentials) for the 5d transition metal elements Hf-Pt have been optimized for use in density fitting second-order Møller-Plesset perturbation theory and other correlated ab initio methods. Calculations of the second-order Møller-Plesset perturbation theory correlation energy, for a test set of small to medium sized molecules, indicate that the density fitting error when utilizing these sets is negligible at three to four orders of magnitude smaller than the orbital basis set incompleteness error.
Miliordos, Evangelos; Xantheas, Sotiris S.
2015-03-01
We report the variation of the binding energy of the Formic Acid Dimer with the size of the basis set at the Coupled Cluster with iterative Singles, Doubles and perturbatively connected Triple replacements [CCSD(T)] level of theory, estimate the Complete Basis Set (CBS) limit, and examine the validity of the Basis Set Superposition Error (BSSE)-correction for this quantity that was previously challenged by Kalescky, Kraka, and Cremer (KKC) [J. Chem. Phys. 140, 084315 (2014)]. Our results indicate that the BSSE correction, including terms that account for the substantial geometry change of the monomers due to the formation of two strong hydrogen bonds in the dimer, is indeed valid for obtaining accurate estimates for the binding energy of this system as it exhibits the expected decrease with increasing basis set size. We attribute the discrepancy between our current results and those of KKC to their use of a valence basis set in conjunction with the correlation of all electrons (i.e., including the 1s of C and O). We further show that the use of a core-valence set in conjunction with all electron correlation converges faster to the CBS limit as the BSSE correction is less than half than the valence electron/valence basis set case. The uncorrected and BSSE-corrected binding energies were found to produce the same (within 0.1 kcal/mol) CBS limits. We obtain CCSD(T)/CBS best estimates for De = - 16.1 ± 0.1 kcal/mol and for D0 = - 14.3 ± 0.1 kcal/mol, the later in excellent agreement with the experimental value of -14.22 ± 0.12 kcal/mol.
Benchmarking DFT methods with small basis sets for the calculation of halogen-bond strengths.
Siiskonen, Antti; Priimagi, Arri
2017-02-01
In recent years, halogen bonding has become an important design tool in crystal engineering, supramolecular chemistry and biosciences. The fundamentals of halogen bonding have been studied extensively with high-accuracy computational methods. Due to its non-covalency, the use of triple-zeta (or larger) basis sets is often recommended when studying halogen bonding. However, in the large systems often encountered in supramolecular chemistry and biosciences, large basis sets can make the calculations far too slow. Therefore, small basis sets, which would combine high computational speed and high accuracy, are in great demand. This study focuses on comparing how well density functional theory (DFT) methods employing small, double-zeta basis sets can estimate halogen-bond strengths. Several methods with triple-zeta basis sets are included for comparison. Altogether, 46 DFT methods were tested using two data sets of 18 and 33 halogen-bonded complexes for which the complexation energies have been previously calculated with the high-accuracy CCSD(T)/CBS method. The DGDZVP basis set performed far better than other double-zeta basis sets, and it even outperformed the triple-zeta basis sets. Due to its small size, it is well-suited to studying halogen bonding in large systems.
Boström, Jonas; Delcey, Mickaël G; Aquilante, Francesco; Serrano-Andrés, Luis; Pedersen, Thomas Bondo; Lindh, Roland
2010-03-09
The accuracy of auxiliary basis sets derived from Cholesky decomposition of two-electron integrals is assessed for excitation energies calculated at the state-average complete active space self-consistent field (CASSCF) and multiconfigurational second order perturbation theory (CASPT2) levels of theory using segmented as well as generally contracted atomic orbital basis sets. Based on 196 valence excitations in 26 organic molecules and 72 Rydberg excitations in 3 organic molecules, the results show that Cholesky auxiliary basis sets can be used without compromising the accuracy of the multiconfigurational methods. Specifically, with a decomposition threshold of 10(-4) au, the mean error due to the Cholesky auxiliary basis set is 0.001 eV, or smaller, decreasing with increasing atomic orbital basis set quality.
Non-Orthogonal Opportunistic Beamforming: Performance Analysis and Implementation
Xia, Minghua
2012-04-01
Aiming to achieve the sum-rate capacity in multi-user multi-antenna systems where $N_t$ antennas are implemented at the transmitter, opportunistic beamforming (OBF) generates~$N_t$ orthonormal beams and serves $N_t$ users during each channel use, which results in high scheduling delay over the users, especially in densely populated networks. Non-orthogonal OBF with more than~$N_t$ transmit beams can be exploited to serve more users simultaneously and further decrease scheduling delay. However, the inter-beam interference will inevitably deteriorate the sum-rate. Therefore, there is a tradeoff between sum-rate and scheduling delay for non-orthogonal OBF. In this context, system performance and implementation of non-orthogonal OBF with $N>N_t$ beams are investigated in this paper. Specifically, it is analytically shown that non-orthogonal OBF is an interference-limited system as the number of users $K \\\\to \\\\infty$. When the inter-beam interference reaches its minimum for fixed $N_t$ and~$N$, the sum-rate scales as $N\\\\ln\\\\left(\\\\frac{N}{N-N_t}\\ ight)$ and it degrades monotonically with the number of beams $N$ for fixed $N_t$. On the contrary, the average scheduling delay is shown to scale as $\\\\frac{1}{N}K\\\\ln{K}$ channel uses and it improves monotonically with $N$. Furthermore, two practical non-orthogonal beamforming schemes are explicitly constructed and they are demonstrated to yield the minimum inter-beam interference for fixed $N_t$ and $N$. This study reveals that, if user traffic is light and one user can be successfully served within a single transmission, non-orthogonal OBF can be applied to obtain lower worst-case delay among the users. On the other hand, if user traffic is heavy, non-orthogonal OBF is inferior to orthogonal OBF in terms of sum-rate and packet delay.
Efficient basis sets for non-covalent interactions in XDM-corrected density-functional theory.
Johnson, Erin R; Otero-de-la-Roza, Alberto; Dale, Stephen G; DiLabio, Gino A
2013-12-07
In the development and application of dispersion-corrected density-functional theory, the effects of basis set incompleteness have been largely mitigated through the use of very large, nearly-complete basis sets. However, the use of such large basis sets makes application of these methods inefficient for large systems. In this work, we examine a series of basis sets, including Pople-style, correlation-consistent, and polarization-consistent bases, for their ability to efficiently and accurately predict non-covalent interactions when used in conjunction with the exchange-hole dipole moment (XDM) dispersion model. We find that the polarization-consistent 2 (pc-2) basis sets, and two modifications thereof with some diffuse functions removed, give performance of comparable quality to that obtained with aug-cc-pVTZ basis sets, while being roughly 12 to 23 times faster computationally. The behavior is explained, in part, by the role of diffuse functions in recovering small density changes in the intermolecular region. The general performance of the modified basis sets is tested by application of XDM to standard intermolecular benchmark sets at, and away from, equilibrium.
Dynamical basis sets for algebraic variational calculations in quantum-mechanical scattering theory
Sun, Yan; Kouri, Donald J.; Truhlar, Donald G.; Schwenke, David W.
1990-01-01
New basis sets are proposed for linear algebraic variational calculations of transition amplitudes in quantum-mechanical scattering problems. These basis sets are hybrids of those that yield the Kohn variational principle (KVP) and those that yield the generalized Newton variational principle (GNVP) when substituted in Schlessinger's stationary expression for the T operator. Trial calculations show that efficiencies almost as great as that of the GNVP and much greater than the KVP can be obtained, even for basis sets with the majority of the members independent of energy.
Calaminici, Patrizia; Janetzko, Florian; Köster, Andreas M; Mejia-Olvera, Roberto; Zuniga-Gutierrez, Bernardo
2007-01-28
Density functional theory optimized basis sets for gradient corrected functionals for 3d transition metal atoms are presented. Double zeta valence polarization and triple zeta valence polarization basis sets are optimized with the PW86 functional. The performance of the newly optimized basis sets is tested in atomic and molecular calculations. Excitation energies of 3d transition metal atoms, as well as electronic configurations, structural parameters, dissociation energies, and harmonic vibrational frequencies of a large number of molecules containing 3d transition metal elements, are presented. The obtained results are compared with available experimental data as well as with other theoretical data from the literature.
A Hartree–Fock study of the confined helium atom: Local and global basis set approaches
Energy Technology Data Exchange (ETDEWEB)
Young, Toby D., E-mail: tyoung@ippt.pan.pl [Zakład Metod Komputerowych, Instytut Podstawowych Prolemów Techniki Polskiej Akademia Nauk, ul. Pawińskiego 5b, 02-106 Warszawa (Poland); Vargas, Rubicelia [Universidad Autónoma Metropolitana Iztapalapa, División de Ciencias Básicas e Ingenierías, Departamento de Química, San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, D.F. C.P. 09340, México (Mexico); Garza, Jorge, E-mail: jgo@xanum.uam.mx [Universidad Autónoma Metropolitana Iztapalapa, División de Ciencias Básicas e Ingenierías, Departamento de Química, San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, D.F. C.P. 09340, México (Mexico)
2016-02-15
Two different basis set methods are used to calculate atomic energy within Hartree–Fock theory. The first is a local basis set approach using high-order real-space finite elements and the second is a global basis set approach using modified Slater-type orbitals. These two approaches are applied to the confined helium atom and are compared by calculating one- and two-electron contributions to the total energy. As a measure of the quality of the electron density, the cusp condition is analyzed. - Highlights: • Two different basis set methods for atomic Hartree–Fock theory. • Galerkin finite element method and modified Slater-type orbitals. • Confined atom model (helium) under small-to-extreme confinement radii. • Detailed analysis of the electron wave-function and the cusp condition.
Generation of basis sets with high degree of fulfillment of the Hellmann-Feynman theorem.
Rico, J Fernández; López, R; Ema, I; Ramírez, G
2007-03-01
A direct relationship is established between the degree of fulfillment of the Hellman-Feynman (electrostatic) theorem, measured as the difference between energy derivatives and electrostatic forces, and the stability of the basis set, measured from the indices that characterize the distance of the space generated by the basis functions to the space of their derivatives with respect to the nuclear coordinates. On the basis of this relationship, a criterion for obtaining basis sets of moderate size with a high degree of fulfillment of the theorem is proposed. As an illustrative application, previously reported Slater basis sets are extended by using this criterion. The resulting augmented basis sets are tested on several molecules finding that the differences between energy gradient and electrostatic forces are reduced by at least one order of magnitude.
DEFF Research Database (Denmark)
Hedegård, Erik D.; Jensen, Frank; Kongsted, Jacob
2012-01-01
of the optical rotation to the basis set limits for nine small or medium sized molecules, using basis sets developed specifically for DFT and magnetic properties (aug-pcS-n series). We suggest that assignment of absolute configuration by comparisons between theoretical and experimental optical rotations may......Even for pure substances, the deduction of the absolute configuration is not always straightforward since there is no direct link between the magnitude and sign of the optical rotation and the absolute configuration. It would be very useful to use computations of the optical rotation to link...... experimentally measured optical rotations to an absolute configuration. Such electronic structure calculations of the optical rotation typically employ regular energy optimized basis sets from wave function theory, and especially the aug-cc-pVDZ basis set has been popular. Here, we have carried out extrapolation...
Basis set generation for quantum dynamics simulations using simple trajectory-based methods.
Saller, Maximilian A C; Habershon, Scott
2015-01-13
Methods for solving the time-dependent Schrödinger equation generally employ either a global static basis set, which is fixed at the outset, or a dynamic basis set, which evolves according to classical-like or variational equations of motion; the former approach results in the well-known exponential scaling with system size, while the latter can suffer from challenging numerical problems, such as singular matrices, as well as violation of energy conservation. Here, we suggest a middle road: building a basis set using trajectories to place time-independent basis functions in the regions of phase space relevant to wave function propagation. This simple approach, which potentially circumvents many of the problems traditionally associated with global or dynamic basis sets, is successfully demonstrated for two challenging benchmark problems in quantum dynamics, namely, relaxation dynamics following photoexcitation in pyrazine, and the spin Boson model.
LANL2DZ basis sets recontracted in the framework of density functional theory.
Chiodo, S; Russo, N; Sicilia, E
2006-09-14
In this paper we report recontracted LANL2DZ basis sets for first-row transition metals. The valence-electron shell basis functions were recontracted using the PWP86 generalized gradient approximation functional and the hybrid B3LYP one. Starting from the original LANL2DZ basis sets a cyclic method was used in order to optimize variationally the contraction coefficients, while the contraction scheme was held fixed at the original one of the LANL2DZ basis functions. The performance of the recontracted basis sets was analyzed by direct comparison between calculated and experimental excitation and ionization energies. Results reported here compared with those obtained using the original basis sets show clearly an improvement in the reproduction of the corresponding experimental gaps.
Mackie, Iain D.; DiLabio, Gino A.
2011-10-01
The first-principles calculation of non-covalent (particularly dispersion) interactions between molecules is a considerable challenge. In this work we studied the binding energies for ten small non-covalently bonded dimers with several combinations of correlation methods (MP2, coupled-cluster single double, coupled-cluster single double (triple) (CCSD(T))), correlation-consistent basis sets (aug-cc-pVXZ, X = D, T, Q), two-point complete basis set energy extrapolations, and counterpoise corrections. For this work, complete basis set results were estimated from averaged counterpoise and non-counterpoise-corrected CCSD(T) binding energies obtained from extrapolations with aug-cc-pVQZ and aug-cc-pVTZ basis sets. It is demonstrated that, in almost all cases, binding energies converge more rapidly to the basis set limit by averaging the counterpoise and non-counterpoise corrected values than by using either counterpoise or non-counterpoise methods alone. Examination of the effect of basis set size and electron correlation shows that the triples contribution to the CCSD(T) binding energies is fairly constant with the basis set size, with a slight underestimation with CCSD(T)/aug-cc-pVDZ compared to the value at the (estimated) complete basis set limit, and that contributions to the binding energies obtained by MP2 generally overestimate the analogous CCSD(T) contributions. Taking these factors together, we conclude that the binding energies for non-covalently bonded systems can be accurately determined using a composite method that combines CCSD(T)/aug-cc-pVDZ with energy corrections obtained using basis set extrapolated MP2 (utilizing aug-cc-pVQZ and aug-cc-pVTZ basis sets), if all of the components are obtained by averaging the counterpoise and non-counterpoise energies. With such an approach, binding energies for the set of ten dimers are predicted with a mean absolute deviation of 0.02 kcal/mol, a maximum absolute deviation of 0.05 kcal/mol, and a mean percent
Probing eigenfunction nonorthogonality by parametric shifts of resonance widths
Savin, D V
2013-01-01
Recently, it has been shown that the change of resonance widths in an open system under a perturbation of its interior is a sensitive indicator of the nonorthogonality of resonance states. We apply this measure to quantify parametric motion of the resonances. In particular, a strong redistribution of the widths is linked with the maximal degree of nonorthogonality. Then for weakly open chaotic systems we discuss the role of spectral rigidity on the statistical properties of the parametric width shifts, and derive the distribution of the latter in a picket-fence model with equidistant spectrum.
Unambiguous discrimination of nonorthogonal quantum states in cavity QED
de Assis, R. J.; Sales, J. S.; de Almeida, N. G.
2017-09-01
We propose an oversimplified scheme to unambiguously discriminate nonorthogonal quantum field states inside high-Q cavities. Our scheme, which is based on positive operator-valued measures (POVM) technique, uses a single three-level atom interacting resonantly with a single mode of a cavity-field and selective atomic state detectors. While the single three-level atom takes the role of the ancilla, the single cavity mode field represents the system we want to obtain information. The efficiency of our proposal is analyzed considering the nowadays achievements in the context of cavity QED. We also analyze the effect of a thermal environment to discrimination of nonorthogonal states.
Adapting DFT+U for the Chemically Motivated Correction of Minimal Basis Set Incompleteness.
Kulik, Heather J; Seelam, Natasha; Mar, Brendan D; Martínez, Todd J
2016-07-28
Recent algorithmic and hardware advances have enabled the application of electronic structure methods to the study of large-scale systems such as proteins with O(10(3)) atoms. Most such methods benefit greatly from the use of reduced basis sets to further enhance their speed, but truly minimal basis sets are well-known to suffer from incompleteness error that gives rise to incorrect descriptions of chemical bonding, preventing minimal basis set use in production calculations. We present a strategy for improving these well-known shortcomings in minimal basis sets by selectively tuning the energetics and bonding of nitrogen and oxygen atoms within proteins and small molecules to reproduce polarized double-ζ basis set geometries at minimal basis set cost. We borrow the well-known +U correction from the density functional theory community normally employed for self-interaction errors and demonstrate its power in the context of correcting basis set incompleteness within a formally self-interaction-free Hartree-Fock framework. We tune the Hubbard U parameters for nitrogen and oxygen atoms on small-molecule tautomers (e.g., cytosine), demonstrate the applicability of the approach on a number of amide-containing molecules (e.g., formamide, alanine tripeptide), and test our strategy on a 10 protein test set where anomalous proton transfer events are reduced by 90% from RHF/STO-3G to RHF/STO-3G+U, bringing the latter into quantitative agreement with RHF/6-31G* results. Although developed with the study of biological molecules in mind, this empirically tuned U approach shows promise as an alternative strategy for correction of basis set incompleteness errors.
Haghdani, Shokouh; Åstrand, Per-Olof; Koch, Henrik
2016-02-01
We have calculated the electronic optical rotation of seven molecules using coupled cluster singles-doubles (CCSD) and the second-order approximation (CC2) employing the aug-cc-pVXZ (X = D, T, or Q) basis sets. We have also compared to time-dependent density functional theory (TDDFT) by utilizing two functionals B3LYP and CAM-B3LYP and the same basis sets. Using relative and absolute error schemes, our calculations demonstrate that the CAM-B3LYP functional predicts optical rotation with the minimum deviations compared to CCSD at λ = 355 and 589.3 nm. Furthermore, our results illustrate that the aug-cc-pVDZ basis set provides the optical rotation in good agreement with the larger basis sets for molecules not possessing small-angle optical rotation at λ = 589.3 nm. We have also performed several two-point inverse power extrapolations for the basis set convergence, i.e., OR(∞) + AX(-n), using the CC2 model at λ = 355 and 589.3 nm. Our results reveal that a two-point inverse power extrapolation with the aug-cc-pVTZ and aug-cc-pVQZ basis sets at n = 5 provides optical rotation deviations similar to those of aug-cc-pV5Z with respect to the basis limit.
Improved Segmented All-Electron Relativistically Contracted Basis Sets for the Lanthanides.
Aravena, Daniel; Neese, Frank; Pantazis, Dimitrios A
2016-03-08
Improved versions of the segmented all-electron relativistically contracted (SARC) basis sets for the lanthanides are presented. The second-generation SARC2 basis sets maintain efficient construction of their predecessors and their individual adaptation to the DKH2 and ZORA Hamiltonians, but feature exponents optimized with a completely new orbital shape fitting procedure and a slightly expanded f space that results in sizable improvement in CASSCF energies and in significantly more accurate prediction of spin-orbit coupling parameters. Additionally, an extended set of polarization/correlation functions is constructed that is appropriate for multireference correlated calculations and new auxiliary basis sets for use in resolution-of-identity (density-fitting) approximations in combination with both DFT and wave function based treatments. Thus, the SARC2 basis sets extend the applicability of the first-generation DFT-oriented basis sets to routine all-electron wave function-based treatments of lanthanide complexes. The new basis sets are benchmarked with respect to excitation energies, radial distribution functions, optimized geometries, orbital eigenvalues, ionization potentials, and spin-orbit coupling parameters of lanthanide systems and are shown to be suitable for the description of magnetic and spectroscopic properties using both DFT and multireference wave function-based methods.
Gidofalvi, Gergely
2014-01-01
Molecule-optimized basis sets, based on approximate natural orbitals, are developed for accelerating the convergence of quantum calculations with strongly correlated (multi-referenced) electrons. We use a low-cost approximate solution of the anti-Hermitian contracted Schr{\\"o}dinger equation (ACSE) for the one- and two-electron reduced density matrices (RDMs) to generate an approximate set of natural orbitals for strongly correlated quantum systems. The natural-orbital basis set is truncated to generate a molecule-optimized basis set whose rank matches that of a standard correlation-consistent basis set optimized for the atoms. We show that basis-set truncation by approximate natural orbitals can be viewed as a one-electron unitary transformation of the Hamiltonian operator and suggest an extension of approximate natural-orbital truncations through two-electron unitary transformations of the Hamiltonian operator, such as those employed in the solution of the ACSE. The molecule-optimized basis set from the ACS...
Mazziotti, David A
2007-05-14
Two-electron reduced density matrices (2-RDMs) have recently been directly determined from the solution of the anti-Hermitian contracted Schrodinger equation (ACSE) to obtain 95%-100% of the ground-state correlation energy of atoms and molecules, which significantly improves upon the accuracy of the contracted Schrodinger equation (CSE) [D. A. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006)]. Two subsets of the CSE, the ACSE and the contraction of the CSE onto the one-particle space, known as the 1,3-CSE, have two important properties: (i) dependence upon only the 3-RDM and (ii) inclusion of all second-order terms when the 3-RDM is reconstructed as only a first-order functional of the 2-RDM. The error in the 1,3-CSE has an important role as a stopping criterion in solving the ACSE for the 2-RDM. Using a computationally more efficient implementation of the ACSE, the author treats a variety of molecules, including H2O, NH3, HCN, and HO3-, in larger basis sets such as correlation-consistent polarized double- and triple-zeta. The ground-state energy of neon is also calculated in a polarized quadruple-zeta basis set with extrapolation to the complete basis-set limit, and the equilibrium bond length and harmonic frequency of N2 are computed with comparison to experimental values. The author observes that increasing the basis set enhances the ability of the ACSE to capture correlation effects in ground-state energies and properties. In the triple-zeta basis set, for example, the ACSE yields energies and properties that are closer in accuracy to coupled cluster with single, double, and triple excitations than to coupled cluster with single and double excitations. In all basis sets, the computed 2-RDMs very closely satisfy known N-representability conditions.
A Non-orthogonal STFC-OFDM on Frequency-Selective Fading Channels
Institute of Scientific and Technical Information of China (English)
XUE Yi; JIANG Ling-ge; HE Chen
2005-01-01
A new non-orthogonal space-time-frequency code (STFC) was proposed. In conjunction with orthogonal frequency-division multiplexing (OFDM), it is appropriate for the application on frequency-selective fading channels. On the basis of the existing non-orthogonal STC, frequency diversity is studied and a new non-orthogonal STFC is further designed. Monte-Carlo simulations show that the non-orthogonal STFC-OFDM has the advantage of large diversity order, high bandwidth efficiency and better BER performance when compared with the orthogonal STC/STFC OFDM and non-orthogonal STC-OFDM systems.
New STO(II-3Gmag family basis sets for the calculations of the molecules magnetic properties
Directory of Open Access Journals (Sweden)
Karina Kapusta
2015-10-01
Full Text Available An efficient approach for construction of physically justified STO(II-3Gmag family basis sets for calculation of molecules magnetic properties has been proposed. The procedure of construction based upon the taken into account the second order of perturbation theory in the magnetic field case. Analytical form of correction functions has been obtained using the closed representation of the Green functions by the solution of nonhomogeneous Schrödinger equation for the model problem of "one-electron atom in the external uniform magnetic field". Their performance has been evaluated for the DFT level calculations carried out with a number of functionals. The test calculations of magnetic susceptibility and 1H nuclear magnetic shielding tensors demonstrated a good agreement of the calculated values with the experimental data.
Pseudospectral sampling of Gaussian basis sets as a new avenue to high-dimensional quantum dynamics
Heaps, Charles
This thesis presents a novel approach to modeling quantum molecular dynamics (QMD). Theoretical approaches to QMD are essential to understanding and predicting chemical reactivity and spectroscopy. We implement a method based on a trajectory-guided basis set. In this case, the nuclei are propagated in time using classical mechanics. Each nuclear configuration corresponds to a basis function in the quantum mechanical expansion. Using the time-dependent configurations as a basis set, we are able to evolve in time using relatively little information at each time step. We use a basis set of moving frozen (time-independent width) Gaussian functions that are well-known to provide a simple and efficient basis set for nuclear dynamics. We introduce a new perspective to trajectory-guided Gaussian basis sets based on existing numerical methods. The distinction is based on the Galerkin and collocation methods. In the former, the basis set is tested using basis functions, projecting the solution onto the functional space of the problem and requiring integration over all space. In the collocation method, the Dirac delta function tests the basis set, projecting the solution onto discrete points in space. This effectively reduces the integral evaluation to function evaluation, a fundamental characteristic of pseudospectral methods. We adopt this idea for independent trajectory-guided Gaussian basis functions. We investigate a series of anharmonic vibrational models describing dynamics in up to six dimensions. The pseudospectral sampling is found to be as accurate as full integral evaluation, while the former method is fully general and integration is only possible on very particular model potential energy surfaces. Nonadiabatic dynamics are also investigated in models of photodissociation and collinear triatomic vibronic coupling. Using Ehrenfest trajectories to guide the basis set on multiple surfaces, we observe convergence to exact results using hundreds of basis functions
Magnetic properties with multiwavelets and DFT: the complete basis set limit achieved.
Jensen, Stig Rune; Flå, Tor; Jonsson, Dan; Monstad, Rune Sørland; Ruud, Kenneth; Frediani, Luca
2016-08-01
Multiwavelets are emerging as an attractive alternative to traditional basis sets such as Gaussian-type orbitals and plane waves. One of their distinctive properties is the ability to reach the basis set limit (often a chimera for traditional approaches) reliably and consistently by fixing the desired precision ε. We present our multiwavelet implementation of the linear response formalism, applied to static magnetic properties, at the self-consistent field level of theory (both for Hartree-Fock and density functional theories). We demonstrate that the multiwavelets consistently improve the accuracy of the results when increasing the desired precision, yielding results that have four to five digits precision, thus providing a very useful benchmark which could otherwise only be estimated by extrapolation methods. Our results show that magnetizabilities obtained with the augmented quadruple-ζ basis (aug-cc-pCVQZ) are practically at the basis set limit, whereas absolute nuclear magnetic resonance shielding tensors are more challenging: even by making use of a standard extrapolation method, the accuracy is not substantially improved. In contrast, our results provide a benchmark that: (1) confirms the validity of the extrapolation ansatz; (2) can be used as a reference to achieve a property-specific extrapolation scheme, thus providing a means to obtain much better extrapolated results; (3) allows us to separate functional-specific errors from basis-set ones and thus to assess the level of cancellation between basis set and functional errors often exploited in density functional theory.
Basis set effects on the Hartree-Fock description of confined many-electron atoms
Garza, Jorge; Hernández-Pérez, Julio M.; Ramírez, José-Zeferino; Vargas, Rubicelia
2012-01-01
In this work, the basis sets designed by Clementi, Bunge and Thakkar, for atomic systems, have been used to obtain the electronic structure of confined many-electron atoms by using Roothaan's approach in the Hartree-Fock context with a new code written in C, which uses the message-passing interface library. The confinement was imposed as Ludeña suggested to simulate walls with infinity potential. For closed-shell atoms, the Thakkar basis set functions give the best total energies (TE) as a function of the confinement radius, obtaining the following ordering: TE(Thakkar) Clementi). However, for few open-shell atoms this ordering is not preserved and a trend, for the basis sets, is not observed. Although there are differences between the TE predicted by these basis set functions, the corresponding pressures are similar to each other; it means that changes in the total energy are described almost in the same way by using any of these basis sets. By analysing the total energy as a function of the inverse of the volume we propose an equation of state; for regions of small volumes, this equation predicts that the pressure is inversely proportional to the square of the volume.
An effective scheme for selecting basis sets for ab initio calculations
Institute of Scientific and Technical Information of China (English)
张瑞勤; 黄建华; 步宇翔; 韩克利; 李述汤; 何国钟
2000-01-01
An effective scheme for selecting economical basis sets for ab initio calculations has been proposed for wide-range systems based on the analysis of different functions in the currently used basis sets. Accordingly, the selection of the basis sets should be made according to the different properties and real chemical surrounding of the atoms in the systems. For normal systems, the size and level of the basis sets used for the descriptions of the constituent atoms should be increased from left to right according to the position of the atom in the periodic table. Moreover, the more the atom is negatively charged, the more the basis functions and suitable polarization functions and diffuse functions should be utilized. whereas, for the positively charged atoms, the size of basis set may be reduced. it is not necessary to use the polarization and diffuse functions for the covalently saturated atoms with normal valence states. However, for the system involving hy-drogen-bonding, weak interactions, functional
Behavior of the Sapporo-nZP-2012 basis set family
Weber, Rebecca; Hovda, Benjamin; Schoendorff, George; Wilson, Angela K.
2015-09-01
The behavior of Sapporo-nZP-2012 (n = D, T, Q) basis sets for 3d atoms is investigated. It is shown that total atomic energies obtained using Sapporo sets of increasing quality converge to a limit. Several schemes are used to determine these limits and comparisons are made to numerical Hartree-Fock energies and to limits obtained with correlation consistent sets (cc-pVnZ, n = T, Q, 5). While differences in energy relative to numerical HF are larger for Sapporo-nZP-2012 sets (16-40 mEh) than for correlation consistent basis sets (∼0.005 mEh), the systematic nature of the Sapporo-nZP-2012 sets may provide a reasonable alternative when the correlation consistent basis sets are not available.
Basis set convergence on static electric dipole polarizability calculations of alkali-metal clusters
Energy Technology Data Exchange (ETDEWEB)
Souza, Fabio A. L. de; Jorge, Francisco E., E-mail: jorge@cce.ufes.br [Departamento de Fisica, Universidade Federal do Espirito Santo, 29060-900 Vitoria-ES (Brazil)
2013-07-15
A hierarchical sequence of all-electron segmented contracted basis sets of double, triple and quadruple zeta valence qualities plus polarization functions augmented with diffuse functions for the atoms from H to Ar was constructed. A systematic study of basis sets required to obtain reliable and accurate values of static dipole polarizabilities of lithium and sodium clusters (n = 2, 4, 6 and 8) at their optimized equilibrium geometries is reported. Three methods are examined: Hartree-Fock (HF), second-order Moeller-Plesset perturbation theory (MP2), and density functional theory (DFT). By direct calculations or by fitting the directly calculated values through one extrapolation scheme, estimates of the HF, MP2 and DFT complete basis set limits were obtained. Comparison with experimental and theoretical data reported previously in the literature is done (author)
New basis set for the prediction of the specific rotation in flexible biological molecules
DEFF Research Database (Denmark)
Baranowska-Łaczkowska, Angelika; Z. Łaczkowski, Krzysztof Z. Łaczkowski; Henriksen, Christian
2016-01-01
Using a novel method based on increasingly accurate calculations, we obtain the main conformers of a set of flexible molecules. We then employ the recently developed ORP basis set for calculating the specific rotation of the found set carried out at the TD-DFT level of theory. The results...... presented for the investigated chiral azido alcohols are to our knowledge the first estimations of their specific rotations....... are compared to those obtained with the (d-)aug-cc-pVXZ (X = D, T and Q) basis sets of Dunning et al. The ORP values are in good overall agreement with the aug-cc-pVTZ results making the ORP a good basis set for routine TD-DFT optical rotation calculations of conformationally flexible molecules. The results...
Booth, George H; Alavi, Ali; Tew, David P
2012-01-01
By performing a stochastic dynamic in a space of Slater determinants, the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method has been able to obtain energies which are essentially free from systematic error to the basis set correlation energy, within small and systematically improvable errorbars. However, the weakly exponential scaling with basis size makes converging the energy with respect to basis set costly and in larger systems, impossible. To ameliorate these basis set issues, here we use perturbation theory to couple the FCIQMC wave function to an explicitly correlated strongly orthogonal basis of geminals, following the [2]_{\\textrm{R12}} approach of Valeev {\\em et al.}. The required one- and two-particle density matrices are computed on-the-fly during the FCIQMC dynamic, using a sampling procedure which incurs relatively little additional computation expense. The F12 energy corrections are shown to converge rapidly as a function of sampling, both in imaginary time, and number of walke...
An effective scheme for selecting basis sets for ab initio calculations
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
An effective scheme for selecting economical basis sets for ab initio calculations has been proposed for wide-range systems based on the analysis of different functions in the currently used basis sets. Accordingly, the selection of the basis sets should be made according to the different properties and real chemical surrounding of the atoms in the systems. For normal systems, the size and level of the basis sets used for the descriptions of the constituent atoms should be increased from left to right according to the position of the atom in the periodic table. Moreover, the more the atom is negatively charged, the more the basis functions and suitable polarization functions and diffuse functions should be utilized. Whereas, for the positively charged atoms, the size of basis set may be reduced. It is not necessary to use the polarization and diffuse functions for the covalently saturated atoms with normal valence states. However, for the system involving hydrogen-bonding, weak interactions, functional groups, metallic bonding with zero valence or low positive valence, and other sensitive interactions, the polarization and diffuse functions must be used. With this scheme, reliable calculation results may be obtained with suitable basis sets and smaller computational capability. By detailed analysis of a series of systems, it has been demonstrated that this scheme is very practical and effective. This scheme may be used in Hartree-Fock, M?ller-Plesset and density functional theoretical calculations. It is expected that the scheme would find important applications in the extensive calculations of large systems in chemistry, materials science, and life and biological sciences.
Strategies for reducing basis set superposition error (BSSE) in O/AU and O/Ni
Shuttleworth, I.G.
2015-11-01
© 2015 Elsevier Ltd. All rights reserved. The effect of basis set superposition error (BSSE) and effective strategies for the minimisation have been investigated using the SIESTA-LCAO DFT package. Variation of the energy shift parameter ΔEPAO has been shown to reduce BSSE for bulk Au and Ni and across their oxygenated surfaces. Alternative strategies based on either the expansion or contraction of the basis set have been shown to be ineffective in reducing BSSE. Comparison of the binding energies for the surface systems obtained using LCAO were compared with BSSE-free plane wave energies.
The Bethe Sum Rule and Basis Set Selection in the Calculation of Generalized Oscillator Strengths
DEFF Research Database (Denmark)
Cabrera-Trujillo, Remigio; Sabin, John R.; Oddershede, Jens;
1999-01-01
Fulfillment of the Bethe sum rule may be construed as a measure of basis set quality for atomic and molecular properties involving the generalized oscillator strength distribution. It is first shown that, in the case of a complete basis, the Bethe sum rule is fulfilled exactly in the random phase...
Efficient calculation of integrals in mixed ramp-Gaussian basis sets
Energy Technology Data Exchange (ETDEWEB)
McKemmish, Laura K., E-mail: laura.mckemmish@gmail.com [Department of Physics and Astronomy, University College London, London (United Kingdom); Research School of Chemistry, Australian National University, Canberra (Australia)
2015-04-07
Algorithms for the efficient calculation of two-electron integrals in the newly developed mixed ramp-Gaussian basis sets are presented, alongside a Fortran90 implementation of these algorithms, RAMPITUP. These new basis sets have significant potential to (1) give some speed-up (estimated at up to 20% for large molecules in fully optimised code) to general-purpose Hartree-Fock (HF) and density functional theory quantum chemistry calculations, replacing all-Gaussian basis sets, and (2) give very large speed-ups for calculations of core-dependent properties, such as electron density at the nucleus, NMR parameters, relativistic corrections, and total energies, replacing the current use of Slater basis functions or very large specialised all-Gaussian basis sets for these purposes. This initial implementation already demonstrates roughly 10% speed-ups in HF/R-31G calculations compared to HF/6-31G calculations for large linear molecules, demonstrating the promise of this methodology, particularly for the second application. As well as the reduction in the total primitive number in R-31G compared to 6-31G, this timing advantage can be attributed to the significant reduction in the number of mathematically complex intermediate integrals after modelling each ramp-Gaussian basis-function-pair as a sum of ramps on a single atomic centre.
On the use of Locally Dense Basis Sets in the Calculation of EPR Hyperfine Couplings
DEFF Research Database (Denmark)
Hedegård, Erik D.; Sauer, Stephan P. A.; Milhøj, Birgitte O.
2013-01-01
The usage of locally dense basis sets in the calculation of Electron Paramagnetic Resonance (EPR) hyperne coupling constants is investigated at the level of Density Functional Theory (DFT) for two model systems of biologically important transition metal complexes: One for the active site in the c...
On the use of locally dense basis sets in the calculation of EPR hyperfine couplings
DEFF Research Database (Denmark)
Milhøj, Birgitte Olai; Hedegård, Erik D.; Sauer, Stephan P. A.
2013-01-01
The usage of locally dense basis sets in the calculation of Electron Paramagnetic Resonance (EPR) hyperne coupling constants is investigated at the level of Density Functional Theory (DFT) for two model systems of biologically important transition metal complexes: One for the active site in the c...
On the basis set convergence of electron-electron entanglement measures: helium-like systems.
Hofer, Thomas S
2013-01-01
A systematic investigation of three different electron-electron entanglement measures, namely the von Neumann, the linear and the occupation number entropy at full configuration interaction level has been performed for the four helium-like systems hydride, helium, Li(+) and Be(2+) using a large number of different basis sets. The convergence behavior of the resulting energies and entropies revealed that the latter do in general not show the expected strictly monotonic increase upon increase of the one-electron basis. Overall, the three different entanglement measures show good agreement among each other, the largest deviations being observed for small basis sets. The data clearly demonstrates that it is important to consider the nature of the chemical system when investigating entanglement phenomena in the framework of Gaussian type basis sets: while in case of hydride the use of augmentation functions is crucial, the application of core functions greatly improves the accuracy in case of cationic systems such as Li(+) and Be(2+). In addition, numerical derivatives of the entanglement measures with respect to the nucleic charge have been determined, which proved to be a very sensitive probe of the convergence leading to qualitatively wrong results (i.e., the wrong sign) if too small basis sets are used.
On the basis set convergence of electron-electron entanglement measures: helium-like systems
Directory of Open Access Journals (Sweden)
Thomas S. Hofer
2013-11-01
Full Text Available A systematic investigation of three different electron--electron entanglement measures, namely the von Neumann, the linear and the occupation number entropy at full configuration interaction level has been performed for the four helium-like systems hydride, helium, lithium(I and beryllium(II using a large number of different basis sets. The convergence behaviour of the resulting energies and entropies was revealed that the latter do in general not show monotonic convergence upon increase of the one--electron basis. Overall, the three different entanglement measures show good agreement among each other, the largest deviations being observed for small basis sets. The data clearly demonstrates that it is important to consider the nature of the chemical system when investigating entanglement phenomena in the framework of Gaussian type basis sets: while in case of hydride the use of augmentation functions is crucial, the application of core functions greatly improves the accuracy in case of cationic systems such as lithium(I and beryllium(II.In addition, numerical derivatives of the entanglement measures with respect to the nucleic charge have been determined, which proved to be a very sensitive probe of the convergence leading to qualitatively wrong results if inadequate basis sets are used.
Laury, Marie L; Carlson, Matthew J; Wilson, Angela K
2012-11-15
Calculated harmonic vibrational frequencies systematically deviate from experimental vibrational frequencies. The observed deviation can be corrected by applying a scale factor. Scale factors for: (i) harmonic vibrational frequencies [categorized into low (1000 cm(-1))], (ii) vibrational contributions to enthalpy and entropy, and (iii) zero-point vibrational energies (ZPVEs) have been determined for widely used density functionals in combination with polarization consistent basis sets (pc-n, n = 0,1,2,3,4). The density functionals include pure functionals (BP86, BPW91, BLYP, HCTH93, PBEPBE), hybrid functionals with Hartree-Fock exchange (B3LYP, B3P86, B3PW91, PBE1PBE, mPW1K, BH&HLYP), hybrid meta functionals with the kinetic energy density gradient (M05, M06, M05-2X, M06-2X), a double hybrid functional with Møller-Plesset correlation (B2GP-PLYP), and a dispersion corrected functional (B97-D). The experimental frequencies for calibration were from 41 organic molecules and the ZPVEs for comparison were from 24 small molecules (diatomics, triatomics). For this family of basis sets, the scale factors for each property are more dependent on the functional selection than on basis set level, and thus allow for a suggested scale factor for each density functional when employing polarization consistent basis sets (pc-n, n = 1,2,3,4). A separate scale factor is recommended when the un-polarized basis set, pc-0, is used in combination with the density functionals.
Downlink scheduling using non-orthogonal uplink beams
Eltayeb, Mohammed E.
2014-04-01
Opportunistic schedulers rely on the feedback of the channel state information of users in order to perform user selection and downlink scheduling. This feedback increases with the number of users, and can lead to inefficient use of network resources and scheduling delays. We tackle the problem of feedback design, and propose a novel class of nonorthogonal codes to feed back channel state information. Users with favorable channel conditions simultaneously transmit their channel state information via non-orthogonal beams to the base station. The proposed formulation allows the base station to identify the strong users via a simple correlation process. After deriving the minimum required code length and closed-form expressions for the feedback load and downlink capacity, we show that i) the proposed algorithm reduces the feedback load while matching the achievable rate of full feedback algorithms operating over a noiseless feedback channel, and ii) the proposed codes are superior to the Gaussian codes.
Productivity of Non-Orthogonal Term Rewrite Systems
Raffelsieper, Matthias
2012-01-01
Productivity is the property that finite prefixes of an infinite constructor term can be computed using a given term rewrite system. Hitherto, productivity has only been considered for orthogonal systems, where non-determinism is not allowed. This paper presents techniques to also prove productivity of non-orthogonal term rewrite systems. For such systems, it is desired that one does not have to guess the reduction steps to perform, instead any outermost-fair reduction should compute an infinite constructor term in the limit. As a main result, it is shown that for possibly non-orthogonal term rewrite systems this kind of productivity can be concluded from context-sensitive termination. This result can be applied to prove stabilization of digital circuits, as will be illustrated by means of an example.
Papajak, Ewa; Truhlar, Donald G
2011-01-11
We present sets of convergent, partially augmented basis set levels corresponding to subsets of the augmented "aug-cc-pV(n+d)Z" basis sets of Dunning and co-workers. We show that for many molecular properties a basis set fully augmented with diffuse functions is computationally expensive and almost always unnecessary. On the other hand, unaugmented cc-pV(n+d)Z basis sets are insufficient for many properties that require diffuse functions. Therefore, we propose using intermediate basis sets. We developed an efficient strategy for partial augmentation, and in this article, we test it and validate it. Sequentially deleting diffuse basis functions from the "aug" basis sets yields the "jul", "jun", "may", "apr", etc. basis sets. Tests of these basis sets for Møller-Plesset second-order perturbation theory (MP2) show the advantages of using these partially augmented basis sets and allow us to recommend which basis sets offer the best accuracy for a given number of basis functions for calculations on large systems. Similar truncations in the diffuse space can be performed for the aug-cc-pVxZ, aug-cc-pCVxZ, etc. basis sets.
Lee, Hee-Seung; Tuckerman, Mark E.
2007-04-01
Dynamical properties of liquid water were studied using Car-Parrinello [Phys. Rev. Lett. 55, 2471 (1985)] ab initio molecular dynamics (AIMD) simulations within the Kohn-Sham (KS) density functional theory employing the Becke-Lee-Yang-Parr exchange-correlation functional for the electronic structure. The KS orbitals were expanded in a discrete variable representation basis set, wherein the complete basis set limit can be easily reached and which, therefore, provides complete convergence of ionic forces. In order to minimize possible nonergodic behavior of the simulated water system in a constant energy (NVE) ensemble, a long equilibration run (30ps) preceded a 60ps long production run. The temperature drift during the entire 60ps trajectory was found to be minimal. The diffusion coefficient [0.055Å2/ps] obtained from the present work for 32 D2O molecules is a factor of 4 smaller than the most up to date experimental value, but significantly larger than those of other recent AIMD studies. Adjusting the experimental result so as to match the finite-sized system used in the present study brings the comparison between theory and experiment to within a factor of 3. More importantly, the system is not observed to become "glassy" as has been reported in previous AIMD studies. The computed infrared spectrum is in good agreement with experimental data, especially in the low frequency regime where the translational and librational motions of water are manifested. The long simulation length also made it possible to perform detailed studies of hydrogen bond dynamics. The relaxation dynamics of hydrogen bonds observed in the present AIMD simulation is slower than those of popular force fields, such as the TIP4P potential, but comparable to that of the TIP5P potential.
Anharmonic Vibrational Frequency Calculations Are Not Worthwhile for Small Basis Sets.
Jacobsen, Ruth L; Johnson, Russell D; Irikura, Karl K; Kacker, Raghu N
2013-02-12
Anharmonic calculations using vibrational perturbation theory are known to provide near-spectroscopic accuracy when combined with high-level ab initio potential energy functions. However, performance with economical, popular electronic structure methods is less well characterized. We compare the accuracy of harmonic and anharmonic predictions from Hartree-Fock, second-order perturbation, and density functional theories combined with 6-31G(d) and 6-31+G(d,p) basis sets. As expected, anharmonic frequencies are closer than harmonic frequencies to experimental fundamentals. However, common practice is to correct harmonic predictions using multiplicative scaling. The surprising conclusion is that scaled anharmonic calculations are no more accurate than scaled harmonic calculations for the basis sets we used. The data used are from the Computational Chemistry Comparison and Benchmark Database (CCCBDB), maintained by the National Institute of Standards and Technology, which includes more than 3939 independent vibrations for 358 molecules.
First-principle modelling of forsterite surface properties: Accuracy of methods and basis sets.
Demichelis, Raffaella; Bruno, Marco; Massaro, Francesco R; Prencipe, Mauro; De La Pierre, Marco; Nestola, Fabrizio
2015-07-15
The seven main crystal surfaces of forsterite (Mg2 SiO4 ) were modeled using various Gaussian-type basis sets, and several formulations for the exchange-correlation functional within the density functional theory (DFT). The recently developed pob-TZVP basis set provides the best results for all properties that are strongly dependent on the accuracy of the wavefunction. Convergence on the structure and on the basis set superposition error-corrected surface energy can be reached also with poorer basis sets. The effect of adopting different DFT functionals was assessed. All functionals give the same stability order for the various surfaces. Surfaces do not exhibit any major structural differences when optimized with different functionals, except for higher energy orientations where major rearrangements occur around the Mg sites at the surface or subsurface. When dispersions are not accounted for, all functionals provide similar surface energies. The inclusion of empirical dispersions raises the energy of all surfaces by a nearly systematic value proportional to the scaling factor s of the dispersion formulation. An estimation for the surface energy is provided through adopting C6 coefficients that are more suitable than the standard ones to describe O-O interactions in minerals. A 2 × 2 supercell of the most stable surface (010) was optimized. No surface reconstruction was observed. The resulting structure and surface energy show no difference with respect to those obtained when using the primitive cell. This result validates the (010) surface model here adopted, that will serve as a reference for future studies on adsorption and reactivity of water and carbon dioxide at this interface.
Predicting Pt-195 NMR chemical shift using new relativistic all-electron basis set.
Paschoal, D; Guerra, C Fonseca; de Oliveira, M A L; Ramalho, T C; Dos Santos, H F
2016-10-01
Predicting NMR properties is a valuable tool to assist the experimentalists in the characterization of molecular structure. For heavy metals, such as Pt-195, only a few computational protocols are available. In the present contribution, all-electron Gaussian basis sets, suitable to calculate the Pt-195 NMR chemical shift, are presented for Pt and all elements commonly found as Pt-ligands. The new basis sets identified as NMR-DKH were partially contracted as a triple-zeta doubly polarized scheme with all coefficients obtained from a Douglas-Kroll-Hess (DKH) second-order scalar relativistic calculation. The Pt-195 chemical shift was predicted through empirical models fitted to reproduce experimental data for a set of 183 Pt(II) complexes which NMR sign ranges from -1000 to -6000 ppm. Furthermore, the models were validated using a new set of 75 Pt(II) complexes, not included in the descriptive set. The models were constructed using non-relativistic Hamiltonian at density functional theory (DFT-PBEPBE) level with NMR-DKH basis set for all atoms. For the best model, the mean absolute deviation (MAD) and the mean relative deviation (MRD) were 150 ppm and 6%, respectively, for the validation set (75 Pt-complexes) and 168 ppm (MAD) and 5% (MRD) for all 258 Pt(II) complexes. These results were comparable with relativistic DFT calculation, 200 ppm (MAD) and 6% (MRD). © 2016 Wiley Periodicals, Inc.
Robust Periodic Hartree-Fock Exchange for Large-Scale Simulations Using Gaussian Basis Sets.
Guidon, Manuel; Hutter, Jürg; VandeVondele, Joost
2009-11-10
Hartree-Fock exchange with a truncated Coulomb operator has recently been discussed in the context of periodic plane-waves calculations [Spencer, J.; Alavi, A. Phys. Rev. B: Solid State, 2008, 77, 193110]. In this work, this approach is extended to Gaussian basis sets, leading to a stable and accurate procedure for evaluating Hartree-Fock exchange at the Γ-point. Furthermore, it has been found that standard hybrid functionals can be transformed into short-range functionals without loss of accuracy. The well-defined short-range nature of the truncated exchange operator can naturally be exploited in integral screening procedures and makes this approach interesting for both condensed phase and gas phase systems. The presented Hartree-Fock implementation is massively parallel and scales up to ten thousands of cores. This makes it feasible to perform highly accurate calculations on systems containing thousands of atoms or ten thousands of basis functions. The applicability of this scheme is demonstrated by calculating the cohesive energy of a LiH crystal close to the Hartree-Fock basis set limit and by performing an electronic structure calculation of a complete protein (rubredoxin) in solution with a large and flexible basis set.
A novel Gaussian-Sinc mixed basis set for electronic structure calculations
Jerke, Jonathan L.; Lee, Young; Tymczak, C. J.
2015-08-01
A Gaussian-Sinc basis set methodology is presented for the calculation of the electronic structure of atoms and molecules at the Hartree-Fock level of theory. This methodology has several advantages over previous methods. The all-electron electronic structure in a Gaussian-Sinc mixed basis spans both the "localized" and "delocalized" regions. A basis set for each region is combined to make a new basis methodology—a lattice of orthonormal sinc functions is used to represent the "delocalized" regions and the atom-centered Gaussian functions are used to represent the "localized" regions to any desired accuracy. For this mixed basis, all the Coulomb integrals are definable and can be computed in a dimensional separated methodology. Additionally, the Sinc basis is translationally invariant, which allows for the Coulomb singularity to be placed anywhere including on lattice sites. Finally, boundary conditions are always satisfied with this basis. To demonstrate the utility of this method, we calculated the ground state Hartree-Fock energies for atoms up to neon, the diatomic systems H2, O2, and N2, and the multi-atom system benzene. Together, it is shown that the Gaussian-Sinc mixed basis set is a flexible and accurate method for solving the electronic structure of atomic and molecular species.
Noncovalent Interactions by Quantum Monte Carlo: A Speedup by a Smart Basis Set Reduction
Dubecký, Matúš
2015-01-01
A fixed-node diffusion Monte Carlo (FN-DMC) method provides a promising alternative to the commonly used coupled-cluster (CC) methods, in the domain of benchmark noncovalent interaction energy calculations. This is mainly true for a low-order polynomial CPU cost scaling of FN-DMC and favorable FN error cancellation leading to benchmark interaction energies accurate to 0.1 kcal/mol. While it is empirically accepted that the FN-DMC results depend weakly on the one-particle basis sets used to expand the guiding functions, limits of this assumption remain elusive. Our recent work indicates that augmented triple zeta basis sets are sufficient to achieve a benchmark level of 0.1 kcal/mol. Here we report on a possibility of significant truncation of the one-particle basis sets without any visible bias on the overall accuracy of the final FN-DMC energy differences. The approach is tested on a set of seven small noncovalent closed-shell complexes including a water dimer. The reported findings enable cheaper high-quali...
Accurate calculation of the intensity dependence of the refractive index using polarized basis sets
Baranowska-Łączkowska, Angelika; Łączkowski, Krzysztof Z.; Fernández, Berta
2012-01-01
Using the single and double excitation coupled cluster level of theory (CCSD) and the density functional theory/Becke 3-parameter Lee-Yang and Parr (DFT/B3LYP) methods, we test the performance of the Pol, ZPol, and LPol-n (n = ds, dl, fs, fl) basis sets in the accurate description of the intensity dependence of the refractive index in the Ne atom, and the N2 and the CO molecules. Additionally, we test the aug-pc-n (n = 1, 2) basis sets of Jensen, and the SVPD, TZVPD, and QZVPD bases by Rappoport and Furche. Tests involve calculations of dynamic polarizabilities and frequency dependent second hyperpolarizabilities. The results are interpreted in terms of the medium constants entering the expressions for optically induced birefringences. In all achiral systems, the performance of the LPol-n sets is very good. Also the aug-pc-2 set yields promising results. Accurate CCSD results available in the literature allow us to select the best basis sets in order to carry out DFT/B3LYP calculations of medium constants in larger molecules. As applications, we show results for (R)-fluoro-oxirane and (R)-methyloxirane.
Tesch, Carmen M; de Vivie-Riedle, Regina
2004-12-22
The phase of quantum gates is one key issue for the implementation of quantum algorithms. In this paper we first investigate the phase evolution of global molecular quantum gates, which are realized by optimally shaped femtosecond laser pulses. The specific laser fields are calculated using the multitarget optimal control algorithm, our modification of the optimal control theory relevant for application in quantum computing. As qubit system we use vibrational modes of polyatomic molecules, here the two IR-active modes of acetylene. Exemplarily, we present our results for a Pi gate, which shows a strong dependence on the phase, leading to a significant decrease in quantum yield. To correct for this unwanted behavior we include pressure on the quantum phase in our multitarget approach. In addition the accuracy of these phase corrected global quantum gates is enhanced. Furthermore we could show that in our molecular approach phase corrected quantum gates and basis set independence are directly linked. Basis set independence is also another property highly required for the performance of quantum algorithms. By realizing the Deutsch-Jozsa algorithm in our two qubit molecular model system, we demonstrate the good performance of our phase corrected and basis set independent quantum gates.
Geminal embedding scheme for optimal atomic basis set construction in correlated calculations
Energy Technology Data Exchange (ETDEWEB)
Sorella, S., E-mail: sorella@sissa.it [International School for Advanced Studies (SISSA), Via Beirut 2-4, 34014 Trieste, Italy and INFM Democritos National Simulation Center, Trieste (Italy); Devaux, N.; Dagrada, M., E-mail: mario.dagrada@impmc.upmc.fr [Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Université Pierre et Marie Curie, Case 115, 4 Place Jussieu, 75252 Paris Cedex 05 (France); Mazzola, G., E-mail: gmazzola@phys.ethz.ch [Theoretische Physik, ETH Zurich, 8093 Zurich (Switzerland); Casula, M., E-mail: michele.casula@impmc.upmc.fr [CNRS and Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Université Pierre et Marie Curie, Case 115, 4 Place Jussieu, 75252 Paris Cedex 05 (France)
2015-12-28
We introduce an efficient method to construct optimal and system adaptive basis sets for use in electronic structure and quantum Monte Carlo calculations. The method is based on an embedding scheme in which a reference atom is singled out from its environment, while the entire system (atom and environment) is described by a Slater determinant or its antisymmetrized geminal power (AGP) extension. The embedding procedure described here allows for the systematic and consistent contraction of the primitive basis set into geminal embedded orbitals (GEOs), with a dramatic reduction of the number of variational parameters necessary to represent the many-body wave function, for a chosen target accuracy. Within the variational Monte Carlo method, the Slater or AGP part is determined by a variational minimization of the energy of the whole system in presence of a flexible and accurate Jastrow factor, representing most of the dynamical electronic correlation. The resulting GEO basis set opens the way for a fully controlled optimization of many-body wave functions in electronic structure calculation of bulk materials, namely, containing a large number of electrons and atoms. We present applications on the water molecule, the volume collapse transition in cerium, and the high-pressure liquid hydrogen.
DEFF Research Database (Denmark)
Silva-Junior, Mario R.; Sauer, Stephan P. A.; Schreiber, Marko;
2010-01-01
to those obtained previously with the smaller TZVP basis set. For each of the three coupled cluster methods, a correlation coefficient greater than 0.994 is found between the vertical excitation energies computed with the two basis sets. The deviations of the CC2 and CCSDR(3) results from the CC3 reference...... strengths and excited-state dipole moments, CC2 calculations with the aug-cc-pVTZ and TZVP basis sets give correlation coefficients of 0.966 and 0.833, respectively, implying that basis set convergence is slower for these one-electron properties....
Velocity field calculation for non-orthogonal numerical grids
Energy Technology Data Exchange (ETDEWEB)
Flach, G. P. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL)
2015-03-01
Computational grids containing cell faces that do not align with an orthogonal (e.g. Cartesian, cylindrical) coordinate system are routinely encountered in porous-medium numerical simulations. Such grids are referred to in this study as non-orthogonal grids because some cell faces are not orthogonal to a coordinate system plane (e.g. xy, yz or xz plane in Cartesian coordinates). Non-orthogonal grids are routinely encountered at the Savannah River Site in porous-medium flow simulations for Performance Assessments and groundwater flow modeling. Examples include grid lines that conform to the sloping roof of a waste tank or disposal unit in a 2D Performance Assessment simulation, and grid surfaces that conform to undulating stratigraphic surfaces in a 3D groundwater flow model. Particle tracking is routinely performed after a porous-medium numerical flow simulation to better understand the dynamics of the flow field and/or as an approximate indication of the trajectory and timing of advective solute transport. Particle tracks are computed by integrating the velocity field from cell to cell starting from designated seed (starting) positions. An accurate velocity field is required to attain accurate particle tracks. However, many numerical simulation codes report only the volumetric flowrate (e.g. PORFLOW) and/or flux (flowrate divided by area) crossing cell faces. For an orthogonal grid, the normal flux at a cell face is a component of the Darcy velocity vector in the coordinate system, and the pore velocity for particle tracking is attained by dividing by water content. For a non-orthogonal grid, the flux normal to a cell face that lies outside a coordinate plane is not a true component of velocity with respect to the coordinate system. Nonetheless, normal fluxes are often taken as Darcy velocity components, either naively or with accepted approximation. To enable accurate particle tracking or otherwise present an accurate depiction of the velocity field for a non-orthogonal
Laser Doppler anemometer measurements using nonorthogonal velocity components: error estimates.
Orloff, K L; Snyder, P K
1982-01-15
Laser Doppler anemometers (LDAs) that are arranged to measure nonorthogonal velocity components (from which orthogonal components are computed through transformation equations) are more susceptible to calibration and sampling errors than are systems with uncoupled channels. In this paper uncertainty methods and estimation theory are used to evaluate, respectively, the systematic and statistical errors that are present when such devices are applied to the measurement of mean velocities in turbulent flows. Statistical errors are estimated for two-channel LDA data that are either correlated or uncorrelated. For uncorrelated data the directional uncertainty of the measured velocity vector is considered for applications where mean streamline patterns are desired.
Optimal linear detectors for nonorthogonal amplify-and-forward protocol
Ahmed, Qasim Zeeshan
2013-06-01
In this paper, we propose optimal linear detectors for non-orthogonal amplify-and-forward cooperative protocol when considering a single-relay scenario. Two types of detectors are proposed based on the principles of minimum mean square error (MMSE) and minimum bit error rate (MBER). The MMSE detector minimizes the mean square error, while the MBER minimizes the system bit error rate (BER). Both detectors exhibit excellent BER performance with relatively low complexity as compared to the maximal likelihood (ML) detector. The BER performance of both detectors is superior to the channel inversion, the maximal ratio combining, and the biased ML detectors. © 2013 IEEE.
Gidopoulos, Nikitas I.; Lathiotakis, Nektarios N.
2013-10-01
The Comment by Friedrich does not dispute the central result of our paper [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.85.052508 85, 052508 (2012)] that nonanalytic behavior is present in long-established mathematical pathologies arising in the solution of finite basis optimized effective potential (OEP) equations. In the Comment, the terms “balancing of basis sets” and “basis-set convergence” imply a particular order towards the limit of a large orbital basis sets where the large-orbital-base limit is always taken first, before the large-auxiliary-base limit, until overall convergence is achieved, at a high computational cost. The authors claim that, on physical grounds, this order of limits is not only sufficient, but also necessary in order to avoid the mathematical pathologies. In response to the Comment, we remark that it is already written in our paper that the nonanalyticity trivially disappears with large orbital basis sets. We point out that the authors of the Comment give an incorrect proof of this statement. We also show that the order of limits towards convergence of the potential is immaterial. A recent paper by the authors of the Comment proposes a partial correction for the incomplete orbital basis error in the full-potential linearized augmented-plane-wave method. Similar to the correction developed in our paper, this correction also benefits from an effectively complete orbital basis, even though only a finite orbital basis is employed in the calculation. This shows that it is unnecessary to take, in practice, the limit of an infinite orbital basis in order to avoid mathematical pathologies in the OEP. Our paper is a significant contribution in that direction with general applicability to any choice of basis sets. Finally, contrary to an allusion in the abstract and assertions in the main text of the Comment that unphysical oscillations of the OEP are supposedly attributed to the common energy denominator approximation, in fact, such
Basis set limit geometries for ammonia at the SCF and MP2 levels of theory
Defrees, D. J.; Mclean, A. D.
1984-01-01
The controversy over the Hartree-Fock bond angle of NH3 is resolved and the convergence of the geometry for the molecule as the basis set is systematically improved with both SCF and correlated MP2 wave functions. The results of the geometrical optimizations, carried out in four stages with a series of uncontracted bases sets, are shown. The obtained structure for NH3 supports the results of Radom and Rodwell (1980) that the Hartree-Fock limit angle is significantly greater than was previously believed.
Correlation consistent basis sets for lanthanides: The atoms La-Lu.
Lu, Qing; Peterson, Kirk A
2016-08-07
Using the 3rd-order Douglas-Kroll-Hess (DKH3) Hamiltonian, all-electron correlation consistent basis sets of double-, triple-, and quadruple-zeta quality have been developed for the lanthanide elements La through Lu. Basis sets designed for the recovery of valence correlation (defined here as 4f5s5p5d6s), cc-pVnZ-DK3, and outer-core correlation (valence + 4s4p4d), cc-pwCVnZ-DK3, are reported (n = D, T, and Q). Systematic convergence of both Hartree-Fock and correlation energies towards their respective complete basis set (CBS) limits are observed. Benchmark calculations of the first three ionization potentials (IPs) of La through Lu are reported at the DKH3 coupled cluster singles and doubles with perturbative triples, CCSD(T), level of theory, including effects of correlation down through the 4s electrons. Spin-orbit coupling is treated at the 2-component HF level. After extrapolation to the CBS limit, the average errors with respect to experiment were just 0.52, 1.14, and 4.24 kcal/mol for the 1st, 2nd, and 3rd IPs, respectively, compared to the average experimental uncertainties of 0.03, 1.78, and 2.65 kcal/mol, respectively. The new basis sets are also used in CCSD(T) benchmark calculations of the equilibrium geometries, atomization energies, and heats of formation for Gd2, GdF, and GdF3. Except for the equilibrium geometry and harmonic frequency of GdF, which are accurately known from experiment, all other calculated quantities represent significant improvements compared to the existing experimental quantities. With estimated uncertainties of about ±3 kcal/mol, the 0 K atomization energies (298 K heats of formation) are calculated to be (all in kcal/mol): 33.2 (160.1) for Gd2, 151.7 (-36.6) for GdF, and 447.1 (-295.2) for GdF3.
Correlation consistent basis sets for actinides. II. The atoms Ac and Np-Lr
Feng, Rulin; Peterson, Kirk A.
2017-08-01
New correlation consistent basis sets optimized using the all-electron third-order Douglas-Kroll-Hess (DKH3) scalar relativistic Hamiltonian are reported for the actinide elements Ac and Np through Lr. These complete the series of sets reported previously for Th-U [K. A. Peterson, J. Chem. Phys. 142, 074105 (2015); M. Vasiliu et al., J. Phys. Chem. A 119, 11422 (2015)]. The new sets range in size from double- to quadruple-zeta and encompass both those optimized for valence (6s6p5f7s6d) and outer-core electron correlations (valence + 5s5p5d). The final sets have been contracted for both the DKH3 and eXact 2-component (X2C) Hamiltonians, yielding cc-pVnZ-DK3/cc-pVnZ-X2C sets for valence correlation and cc-pwCVnZ-DK3/cc-pwCVnZ-X2C sets for outer-core correlation (n = D, T, Q in each case). In order to test the effectiveness of the new basis sets, both atomic and molecular benchmark calculations have been carried out. In the first case, the first three atomic ionization potentials (IPs) of all the actinide elements Ac-Lr have been calculated using the Feller-Peterson-Dixon (FPD) composite approach, primarily with the multireference configuration interaction (MRCI) method. Excellent convergence towards the respective complete basis set (CBS) limits is achieved with the new sets, leading to good agreement with experiment, where these exist, after accurately accounting for spin-orbit effects using the 4-component Dirac-Hartree-Fock method. For a molecular test, the IP and atomization energy (AE) of PuO2 have been calculated also using the FPD method but using a coupled cluster approach with spin-orbit coupling accounted for using the 4-component MRCI. The present calculations yield an IP0 for PuO2 of 159.8 kcal/mol, which is in excellent agreement with the experimental electron transfer bracketing value of 162 ± 3 kcal/mol. Likewise, the calculated 0 K AE of 305.6 kcal/mol is in very good agreement with the currently accepted experimental value of 303.1 ± 5 kcal
Grimme, Stefan; Brandenburg, Jan Gerit; Bannwarth, Christoph; Hansen, Andreas
2015-08-01
A density functional theory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chemical systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approximation in a modified global hybrid functional with a relatively large amount of non-local Fock-exchange. The orbitals are expanded in Ahlrichs-type valence-double zeta atomic orbital (AO) Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold corrected (3c) Hartree-Fock method, the new composite scheme (termed PBEh-3c) represents the next member in a hierarchy of "low-cost" electronic structure approaches. They are mainly free of BSSE and account for most interactions in a physically sound and asymptotically correct manner. PBEh-3c yields good results for thermochemical properties in the huge GMTKN30 energy database. Furthermore, the method shows excellent performance for non-covalent interaction energies in small and large complexes. For evaluating its performance on equilibrium structures, a new compilation of standard test sets is suggested. These consist of small (light) molecules, partially flexible, medium-sized organic molecules, molecules comprising heavy main group elements, larger systems with long bonds, 3d-transition metal systems, non-covalently bound complexes (S22 and S66×8 sets), and peptide conformations. For these sets, overall deviations from accurate reference data are smaller than for various other tested DFT methods
Grimme, Stefan; Brandenburg, Jan Gerit; Bannwarth, Christoph; Hansen, Andreas
2015-08-07
A density functional theory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chemical systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approximation in a modified global hybrid functional with a relatively large amount of non-local Fock-exchange. The orbitals are expanded in Ahlrichs-type valence-double zeta atomic orbital (AO) Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold corrected (3c) Hartree-Fock method, the new composite scheme (termed PBEh-3c) represents the next member in a hierarchy of "low-cost" electronic structure approaches. They are mainly free of BSSE and account for most interactions in a physically sound and asymptotically correct manner. PBEh-3c yields good results for thermochemical properties in the huge GMTKN30 energy database. Furthermore, the method shows excellent performance for non-covalent interaction energies in small and large complexes. For evaluating its performance on equilibrium structures, a new compilation of standard test sets is suggested. These consist of small (light) molecules, partially flexible, medium-sized organic molecules, molecules comprising heavy main group elements, larger systems with long bonds, 3d-transition metal systems, non-covalently bound complexes (S22 and S66×8 sets), and peptide conformations. For these sets, overall deviations from accurate reference data are smaller than for various other tested DFT methods
Energy Technology Data Exchange (ETDEWEB)
Grimme, Stefan, E-mail: grimme@thch.uni-bonn.de; Brandenburg, Jan Gerit; Bannwarth, Christoph; Hansen, Andreas [Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie, Rheinische Friedrich-Wilhelms Universität Bonn, Beringstraße 4, 53115 Bonn (Germany)
2015-08-07
A density functional theory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chemical systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approximation in a modified global hybrid functional with a relatively large amount of non-local Fock-exchange. The orbitals are expanded in Ahlrichs-type valence-double zeta atomic orbital (AO) Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold corrected (3c) Hartree-Fock method, the new composite scheme (termed PBEh-3c) represents the next member in a hierarchy of “low-cost” electronic structure approaches. They are mainly free of BSSE and account for most interactions in a physically sound and asymptotically correct manner. PBEh-3c yields good results for thermochemical properties in the huge GMTKN30 energy database. Furthermore, the method shows excellent performance for non-covalent interaction energies in small and large complexes. For evaluating its performance on equilibrium structures, a new compilation of standard test sets is suggested. These consist of small (light) molecules, partially flexible, medium-sized organic molecules, molecules comprising heavy main group elements, larger systems with long bonds, 3d-transition metal systems, non-covalently bound complexes (S22 and S66×8 sets), and peptide conformations. For these sets, overall deviations from accurate reference data are smaller than for various other tested DFT
Kawashima, Yukio; Hirao, Kimihiko
2017-02-24
We introduced two methods to correct the singularity in the calculation of long-range Hartree-Fock (HF) exchange for long-range-corrected density functional theory (LC-DFT) calculations in plane-wave basis sets. The first method introduces an auxiliary function to cancel out the singularity. The second method introduces a truncated long-range Coulomb potential, which has no singularity. We assessed the introduced methods using the LC-BLYP functional by applying it to isolated systems of naphthalene and pyridine. We first compared the total energies and the HOMO energies of the singularity-corrected and uncorrected calculations and confirmed that singularity correction is essential for LC-DFT calculations using plane-wave basis sets. The LC-DFT calculation results converged rapidly with respect to the cell size as the other functionals, and their results were in good agreement with the calculated results obtained using Gaussian basis sets. LC-DFT succeeded in obtaining accurate orbital energies and excitation energies. We next applied LC-DFT with singularity correction methods to the electronic structure calculations of the extended systems, Si and SiC. We confirmed that singularity correction is important for calculations of extended systems as well. The calculation results of the valence and conduction bands by LC-BLYP showed good convergence with respect to the number of k points sampled. The introduced methods succeeded in overcoming the singularity problem in HF exchange calculation. We investigated the effect of the singularity correction on the excitation state calculation and found that careful treatment of the singularities is required compared to ground-state calculations. We finally examined the excitonic effect on the band gap of the extended systems. We calculated the excitation energies to the first excited state of the extended systems using a supercell model at the Γ point and found that the excitonic binding energy, supposed to be small for
Gaspari, Roberto; Rapallo, Arnaldo
2008-06-28
In this work a new method is proposed for the choice of basis functions in diffusion theory (DT) calculations. This method, named hybrid basis approach (HBA), combines the two previously adopted long time sorting procedure (LTSP) and maximum correlation approximation (MCA) techniques; the first emphasizing contributions from the long time dynamics, the latter being based on the local correlations along the chain. In order to fulfill this task, the HBA procedure employs a first order basis set corresponding to a high order MCA one and generates upper order approximations according to LTSP. A test of the method is made first on a melt of cis-1,4-polyisoprene decamers where HBA and LTSP are compared in terms of efficiency. Both convergence properties and numerical stability are improved by the use of the HBA basis set whose performance is evaluated on local dynamics, by computing the correlation times of selected bond vectors along the chain, and on global ones, through the eigenvalues of the diffusion operator L. Further use of the DT with a HBA basis set has been made on a 71-mer of syndiotactic trans-1,2-polypentadiene in toluene solution, whose dynamical properties have been computed with a high order calculation and compared to the "numerical experiment" provided by the molecular dynamics (MD) simulation in explicit solvent. The necessary equilibrium averages have been obtained by a vacuum trajectory of the chain where solvent effects on conformational properties have been reproduced with a proper screening of the nonbonded interactions, corresponding to a definite value of the mean radius of gyration of the polymer in vacuum. Results show a very good agreement between DT calculations and the MD numerical experiment. This suggests a further use of DT methods with the necessary input quantities obtained by the only knowledge of some experimental values, i.e., the mean radius of gyration of the chain and the viscosity of the solution, and by a suitable vacuum
A two-dimensional volatility basis set – Part 3: Prognostic modeling and NOx dependence
Directory of Open Access Journals (Sweden)
W. K. Chuang
2015-06-01
Full Text Available When NOx is introduced to organic emissions, aerosol production is sometimes, but not always, reduced. Under certain conditions, these interactions will instead increase aerosol concentrations. We expanded the two-dimensional volatility basis set (2-D-VBS to include the effects of NOx on aerosol formation. This includes the formation of organonitrates, where the addition of a nitrate group contributes to a decrease of 2.5 orders of magnitude in volatility. With this refinement, we model outputs from experimental results, such as the atomic N : C ratio, organonitrate mass, and nitrate fragments in AMS measurements. We also discuss the mathematical methods underlying the implementation of the 2-D-VBS and provide the complete code in the Supplemental material. A developer version is available on Bitbucket, an online community repository.
Phosgene at the complete basis set limit of CCSDT(Q): Molecular structure and rovibrational analysis
Murphy, Kevin V.; Schaefer, Henry F.; Agarwal, Jay
2017-09-01
The ground-state (X∼1A″) equilibrium geometry of phosgene is examined with coupled-cluster theory, using derivatives extrapolated to the complete basis set (CBS) limit of CCSDT(Q). The C-O and C-Cl bond lengths are predicted to be 1.1768 Å and 1.7374 Å, respectively; the Cl-C-Cl bond angle is 124.03° and the O-C-Cl bond angle is 111.93°. Anharmonic frequencies are determined with VPT2, using CCSD(T)/cc-pCVQZ cubic and quartic force-fields and a CCSDT(Q)/CBS quadratic force field: ν1 = 1832.9 ; ν2 = 570.5 ; ν3 = 301.2 ; ν4 = 576.3 ; ν5 = 849.4 ; and ν6 = 438.9 cm-1.
Accurate Hartree-Fock energy of extended systems using large Gaussian basis sets
Paier, Joachim; Diaconu, Cristian V.; Scuseria, Gustavo E.; Guidon, Manuel; Vandevondele, Joost; Hutter, Jürg
2009-11-01
Calculating highly accurate thermochemical properties of condensed matter via wave-function-based approaches (such as, e.g., Hartree-Fock or hybrid functionals) has recently attracted much interest. We here present two strategies providing accurate Hartree-Fock energies for solid LiH in a large Gaussian basis set and applying periodic boundary conditions. The total energies were obtained using two different approaches, namely, a supercell evaluation of Hartree-Fock exchange using a truncated Coulomb operator and an extrapolation toward the full-range Hartree-Fock limit of a Padé fit to a series of short-range screened Hartree-Fock calculations. These two techniques agreed to significant precision. We also present the Hartree-Fock cohesive energy of LiH (converged to within sub-millielectron volt) at the experimental equilibrium volume as well as the Hartree-Fock equilibrium lattice constant and bulk modulus.
Rohmer, Jeremy
2016-04-01
Predicting the temporal evolution of landslides is typically supported by numerical modelling. Dynamic sensitivity analysis aims at assessing the influence of the landslide properties on the time-dependent predictions (e.g., time series of landslide displacements). Yet two major difficulties arise: 1. Global sensitivity analysis require running the landslide model a high number of times (> 1000), which may become impracticable when the landslide model has a high computation time cost (> several hours); 2. Landslide model outputs are not scalar, but function of time, i.e. they are n-dimensional vectors with n usually ranging from 100 to 1000. In this article, I explore the use of a basis set expansion, such as principal component analysis, to reduce the output dimensionality to a few components, each of them being interpreted as a dominant mode of variation in the overall structure of the temporal evolution. The computationally intensive calculation of the Sobol' indices for each of these components are then achieved through meta-modelling, i.e. by replacing the landslide model by a "costless-to-evaluate" approximation (e.g., a projection pursuit regression model). The methodology combining "basis set expansion - meta-model - Sobol' indices" is then applied to the La Frasse landslide to investigate the dynamic sensitivity analysis of the surface horizontal displacements to the slip surface properties during the pore pressure changes. I show how to extract information on the sensitivity of each main modes of temporal behaviour using a limited number (a few tens) of long running simulations. In particular, I identify the parameters, which trigger the occurrence of a turning point marking a shift between a regime of low values of landslide displacements and one of high values.
Mackie, Iain D; Dilabio, Gino A
2010-06-21
B971, PBE and PBE1 density functionals with 6-31G(d) basis sets are shown to accurately describe the binding in dispersion bound dimers. This is achieved through the use of dispersion-correcting potentials (DCPs) in conjunction with counterpoise corrections. DCPs resemble and are applied like conventional effective core potentials that can be used with most computational chemistry programs without code modification. Rather, DCPs are implemented by simple appendage to the input files for these types of programs. Binding energies are predicted to within ca. 11% and monomer separations to within ca. 0.06 A of high-level wavefunction data using B971/6-31G(d)-DCP. Similar results are obtained for PBE and PBE1 with the 6-31G(d) basis sets and DCPs. Although results found using the 3-21G(d) are not as impressive, they never-the-less show promise as a means of initial study for a wide variety of dimers, including those dominated by dispersion, hydrogen-bonding and a mixture of interactions. Notable improvement is found in comparison to M06-2X/6-31G(d) data, e.g., mean absolute deviations for the S22-set of dimers of ca. 13.6 and 16.5% for B971/6-31G(d)-DCP and M06-2X, respectively. However, it should be pointed out that the latter data were obtained using a larger integration grid size since a smaller grid results in different binding energies and geometries for simple dispersion-bound dimers such as methane and ethene.
Roscioni, Otello M; Lee, Edmond P F; Dyke, John M
2012-10-05
We present a set of effective core potential (ECP) basis sets for rhodium atoms which are of reasonable size for use in electronic structure calculations. In these ECP basis sets, the Los Alamos ECP is used to simulate the effect of the core electrons while an optimized set of Gaussian functions, which includes polarization and diffuse functions, is used to describe the valence electrons. These basis sets were optimized to reproduce the ionization energy and electron affinity of atomic rhodium. They were also tested by computing the electronic ground state geometry and harmonic frequencies of [Rh(CO)(2) μ-Cl](2) , Rh(CO)(2) ClPy, and RhCO (neutral and its positive, and negative ions) as well as the enthalpy of the reaction of [Rh(CO)(2) μ-Cl](2) with pyridine (Py) to give Rh(CO)(2) ClPy, at different levels of theory. Good agreement with experimental values was obtained. Although the number of basis functions used in our ECP basis sets is smaller than those of other ECP basis sets of comparable quality, we show that the newly developed ECP basis sets provide the flexibility and precision required to reproduce a wide range of chemical and physical properties of rhodium compounds. Therefore, we recommend the use of these compact yet accurate ECP basis sets for electronic structure calculations on molecules involving rhodium atoms. Copyright © 2012 Wiley Periodicals, Inc.
Dziedzic, J; Hill, Q; Skylaris, C-K
2013-12-07
We present a method for the calculation of four-centre two-electron repulsion integrals in terms of localised non-orthogonal generalised Wannier functions (NGWFs). Our method has been implemented in the ONETEP program and is used to compute the Hartree-Fock exchange energy component of Hartree-Fock and Density Functional Theory (DFT) calculations with hybrid exchange-correlation functionals. As the NGWFs are optimised in situ in terms of a systematically improvable basis set which is equivalent to plane waves, it is possible to achieve large basis set accuracy in routine calculations. The spatial localisation of the NGWFs allows us to exploit the exponential decay of the density matrix in systems with a band gap in order to compute the exchange energy with a computational effort that increases linearly with the number of atoms. We describe the implementation of this approach in the ONETEP program for linear-scaling first principles quantum mechanical calculations. We present extensive numerical validation of all the steps in our method. Furthermore, we find excellent agreement in energies and structures for a wide variety of molecules when comparing with other codes. We use our method to perform calculations with the B3LYP exchange-correlation functional for models of myoglobin systems bound with O2 and CO ligands and confirm that the same qualitative behaviour is obtained as when the same myoglobin models are studied with the DFT+U approach which is also available in ONETEP. Finally, we confirm the linear-scaling capability of our method by performing calculations on polyethylene and polyacetylene chains of increasing length.
Quantum Walks with Non-Orthogonal Position States
Matjeschk, R; Enderlein, M; Cedzich, Ch; Werner, A H; Keyl, M; Schaetz, T; Werner, R F
2012-01-01
Quantum walks have by now been realized in a large variety of different physical settings. In some of these, particularly with trapped ions, the walk is implemented in phase space, where the corresponding position states are not orthogonal. We develop a general description of such a quantum walk and show how to map it into a standard one with orthogonal states, thereby making available all the tools developed for the latter. This enables a variety of experiments, which can be implemented with smaller step sizes and more steps. Tuning the non-orthogonality allows for an easy preparation of extended states such as momentum eigenstates, which travel at a well-defined speed with low dispersion. We introduce a method to adjust their velocity by momentum shifts, which allows to investigate intriguing effects such as the analog of Bloch oscillations.
European air quality modelled by CAMx including the volatility basis set scheme
Directory of Open Access Journals (Sweden)
G. Ciarelli
2015-12-01
Full Text Available Four periods of EMEP (European Monitoring and Evaluation Programme intensive measurement campaigns (June 2006, January 2007, September–October 2008 and February–March 2009 were modelled using the regional air quality model CAMx with VBS (Volatility Basis Set approach for the first time in Europe within the framework of the EURODELTA-III model intercomparison exercise. More detailed analysis and sensitivity tests were performed for the period of February–March 2009 and June 2006 to investigate the uncertainties in emissions as well as to improve the modelling of organic aerosols (OA. Model performance for selected gas phase species and PM2.5 was evaluated using the European air quality database Airbase. Sulfur dioxide (SO2 and ozone (O3 were found to be overestimated for all the four periods with O3 having the largest mean bias during June 2006 and January–February 2007 periods (8.93 and 12.30 ppb mean biases, respectively. In contrast, nitrogen dioxide (NO2 and carbon monoxide (CO were found to be underestimated for all the four periods. CAMx reproduced both total concentrations and monthly variations of PM2.5 very well for all the four periods with average biases ranging from −2.13 to 1.04 μg m-3. Comparisons with AMS (Aerosol Mass Spectrometer measurements at different sites in Europe during February–March 2009, showed that in general the model over-predicts the inorganic aerosol fraction and under-predicts the organic one, such that the good agreement for PM2.5 is partly due to compensation of errors. The effect of the choice of volatility basis set scheme (VBS on OA was investigated as well. Two sensitivity tests with volatility distributions based on previous chamber and ambient measurements data were performed. For February–March 2009 the chamber-case reduced the total OA concentrations by about 43 % on average. On the other hand, a test based on ambient measurement data increased OA concentrations by about 47 % for the same
Hsu, Po Jen; Lai, S K; Rapallo, Arnaldo
2014-03-14
Improved basis sets for the study of polymer dynamics by means of the diffusion theory, and tests on a melt of cis-1,4-polyisoprene decamers, and a toluene solution of a 71-mer syndiotactic trans-1,2-polypentadiene were presented recently [R. Gaspari and A. Rapallo, J. Chem. Phys. 128, 244109 (2008)]. The proposed hybrid basis approach (HBA) combined two techniques, the long time sorting procedure and the maximum correlation approximation. The HBA takes advantage of the strength of these two techniques, and its basis sets proved to be very effective and computationally convenient in describing both local and global dynamics in cases of flexible synthetic polymers where the repeating unit is a unique type of monomer. The question then arises if the same efficacy continues when the HBA is applied to polymers of different monomers, variable local stiffness along the chain and with longer persistence length, which have different local and global dynamical properties against the above-mentioned systems. Important examples of this kind of molecular chains are the proteins, so that a fragment of the protein transthyretin is chosen as the system of the present study. This peptide corresponds to a sequence that is structured in β-sheets of the protein and is located on the surface of the channel with thyroxin. The protein transthyretin forms amyloid fibrils in vivo, whereas the peptide fragment has been shown [C. P. Jaroniec, C. E. MacPhee, N. S. Astrof, C. M. Dobson, and R. G. Griffin, Proc. Natl. Acad. Sci. U.S.A. 99, 16748 (2002)] to form amyloid fibrils in vitro in extended β-sheet conformations. For these reasons the latter is given considerable attention in the literature and studied also as an isolated fragment in water solution where both experimental and theoretical efforts have indicated the propensity of the system to form β turns or α helices, but is otherwise predominantly unstructured. Differing from previous computational studies that employed implicit
Energy Technology Data Exchange (ETDEWEB)
Holden, Zachary C.; Richard, Ryan M.; Herbert, John M., E-mail: herbert@chemistry.ohio-state.edu [Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210 (United States)
2013-12-28
An implementation of Ewald summation for use in mixed quantum mechanics/molecular mechanics (QM/MM) calculations is presented, which builds upon previous work by others that was limited to semi-empirical electronic structure for the QM region. Unlike previous work, our implementation describes the wave function's periodic images using “ChElPG” atomic charges, which are determined by fitting to the QM electrostatic potential evaluated on a real-space grid. This implementation is stable even for large Gaussian basis sets with diffuse exponents, and is thus appropriate when the QM region is described by a correlated wave function. Derivatives of the ChElPG charges with respect to the QM density matrix are a potentially serious bottleneck in this approach, so we introduce a ChElPG algorithm based on atom-centered Lebedev grids. The ChElPG charges thus obtained exhibit good rotational invariance even for sparse grids, enabling significant cost savings. Detailed analysis of the optimal choice of user-selected Ewald parameters, as well as timing breakdowns, is presented.
Culpitt, Tanner; Brorsen, Kurt R.; Hammes-Schiffer, Sharon
2017-06-01
Density functional theory (DFT) embedding approaches have generated considerable interest in the field of computational chemistry because they enable calculations on larger systems by treating subsystems at different levels of theory. To circumvent the calculation of the non-additive kinetic potential, various projector methods have been developed to ensure the orthogonality of molecular orbitals between subsystems. Herein the orthogonality constrained basis set expansion (OCBSE) procedure is implemented to enforce this subsystem orbital orthogonality without requiring a level shifting parameter. This scheme is a simple alternative to existing parameter-free projector-based schemes, such as the Huzinaga equation. The main advantage of the OCBSE procedure is that excellent convergence behavior is attained for DFT-in-DFT embedding without freezing any of the subsystem densities. For the three chemical systems studied, the level of accuracy is comparable to or higher than that obtained with the Huzinaga scheme with frozen subsystem densities. Allowing both the high-level and low-level DFT densities to respond to each other during DFT-in-DFT embedding calculations provides more flexibility and renders this approach more generally applicable to chemical systems. It could also be useful for future extensions to embedding approaches combining wavefunction theories and DFT.
Entanglement Patterns in Mutually Unbiased Basis Sets for N Prime-state Particles
Lawrence, Jay
2011-01-01
A few simply-stated rules govern the entanglement patterns that can occur in mutually unbiased basis sets (MUBs), and constrain the combinations of such patterns that can coexist (ie, the stoichiometry) in full complements of p^N+1 MUBs. We consider Hilbert spaces of prime power dimension (as realized by systems of N prime-state particles, or qupits), where full complements are known to exist, and we assume only that MUBs are eigenbases of Pauli operators, without using a particular construction. The general rules include the following: 1) In any MUB, a particular qupit appears either in a pure state, or totally entangled, and 2) in any full MUB complement, each qupit is pure in p+1 bases (not necessarily the same ones), and totally entangled in the remaining p^N-p. It follows that the maximum number of product bases is p+1, and when this number is realized, all remaining p^N-p bases in the complement are characterized by the total entanglement of every qupit. This "standard distribution" is inescapable for t...
Solving One-Electron Systems in a Novel Gaussian-Sinc Mixed Basis Set
Jerke, Jonathan L; Tymczak, C J
2014-01-01
We introduce a novel Gaussian-Sinc mixed basis set for the calculation of the electronic structure of one-electron systems within a uniform magnetic field in three dimensions. As opposed to traditional grid based methods, the Sinc basis is unbiased and invariant to the choice of the grids origin. This is shown to be due to the transformation properties of the Sinc basis functions under translations. The entire method is translational invariant and the potentials are properly calculated and are necessarily off diagonal, as well as variationally bounded. With this method, it was generally found that under arbitrary configurations of the protons that four to six significant digits in the ground state energy accuracy was achievable. This technology was then applied to calculate the ground state energy of H, $H_{2}^{+}$ ion and $H_{3}^{2+}$ ion in magnetic fields up to a magnetic field strength of 1.18x$10^9$ T (5000 au). From this it can be shown that $H_{3}^(2+}$ ion is unstable up to the maximum magnetic field ...
Trail-Needs pseudopotentials in quantum Monte Carlo calculations with plane-wave/blip basis sets
Drummond, N. D.; Trail, J. R.; Needs, R. J.
2016-10-01
We report a systematic analysis of the performance of a widely used set of Dirac-Fock pseudopotentials for quantum Monte Carlo (QMC) calculations. We study each atom in the periodic table from hydrogen (Z =1 ) to mercury (Z =80 ), with the exception of the 4 f elements (57 ≤Z ≤70 ). We demonstrate that ghost states are a potentially serious problem when plane-wave basis sets are used in density functional theory (DFT) orbital-generation calculations, but that this problem can be almost entirely eliminated by choosing the s channel to be local in the DFT calculation; the d channel can then be chosen to be local in subsequent QMC calculations, which generally leads to more accurate results. We investigate the achievable energy variance per electron with different levels of trial wave function and we determine appropriate plane-wave cutoff energies for DFT calculations for each pseudopotential. We demonstrate that the so-called "T-move" scheme in diffusion Monte Carlo is essential for many elements. We investigate the optimal choice of spherical integration rule for pseudopotential projectors in QMC calculations. The information reported here will prove crucial in the planning and execution of QMC projects involving beyond-first-row elements.
Spackman, Peter R; Jayatilaka, Dylan; Karton, Amir
2016-09-14
We examine the basis set convergence of the CCSD(T) method for obtaining the structures of the 108 neutral first- and second-row species in the W4-11 database (with up to five non-hydrogen atoms). This set includes a total of 181 unique bonds: 75 H-X, 49 X-Y, 43 X=Y, and 14 X≡Y bonds (where X and Y are first- and second-row atoms). As reference values, geometries optimized at the CCSD(T)/aug'-cc-pV(6+d)Z level of theory are used. We consider the basis set convergence of the CCSD(T) method with the correlation consistent basis sets cc-pV(n+d)Z and aug'-cc-pV(n+d)Z (n = D, T, Q, 5) and the Weigend-Ahlrichs def2-n ZVPP basis sets (n = T, Q). For each increase in the highest angular momentum present in the basis set, the root-mean-square deviation (RMSD) over the bond distances is decreased by a factor of ∼4. For example, the following RMSDs are obtained for the cc-pV(n+d)Z basis sets 0.0196 (D), 0.0050 (T), 0.0015 (Q), and 0.0004 (5) Å. Similar results are obtained for the aug'-cc-pV(n+d)Z and def2-n ZVPP basis sets. The double-zeta and triple-zeta quality basis sets systematically and significantly overestimate the bond distances. A simple and cost-effective way to improve the performance of these basis sets is to scale the bond distances by an empirical scaling factor of 0.9865 (cc-pV(D+d)Z) and 0.9969 (cc-pV(T+d)Z). This results in RMSDs of 0.0080 (scaled cc-pV(D+d)Z) and 0.0029 (scaled cc-pV(T+d)Z) Å. The basis set convergence of larger basis sets can be accelerated via standard basis-set extrapolations. In addition, the basis set convergence of explicitly correlated CCSD(T)-F12 calculations is investigated in conjunction with the cc-pVnZ-F12 basis sets (n = D, T). Typically, one "gains" two angular momenta in the explicitly correlated calculations. That is, the CCSD(T)-F12/cc-pVnZ-F12 level of theory shows similar performance to the CCSD(T)/cc-pV(n+2)Z level of theory. In particular, the following RMSDs are obtained for the cc-pVnZ-F12 basis sets 0.0019 (D
Spackman, Peter R.; Jayatilaka, Dylan; Karton, Amir
2016-09-01
We examine the basis set convergence of the CCSD(T) method for obtaining the structures of the 108 neutral first- and second-row species in the W4-11 database (with up to five non-hydrogen atoms). This set includes a total of 181 unique bonds: 75 H—X, 49 X—Y, 43 X=Y, and 14 X≡Y bonds (where X and Y are first- and second-row atoms). As reference values, geometries optimized at the CCSD(T)/aug'-cc-pV(6+d)Z level of theory are used. We consider the basis set convergence of the CCSD(T) method with the correlation consistent basis sets cc-pV(n+d)Z and aug'-cc-pV(n+d)Z (n = D, T, Q, 5) and the Weigend-Ahlrichs def2-n ZVPP basis sets (n = T, Q). For each increase in the highest angular momentum present in the basis set, the root-mean-square deviation (RMSD) over the bond distances is decreased by a factor of ˜4. For example, the following RMSDs are obtained for the cc-pV(n+d)Z basis sets 0.0196 (D), 0.0050 (T), 0.0015 (Q), and 0.0004 (5) Å. Similar results are obtained for the aug'-cc-pV(n+d)Z and def2-n ZVPP basis sets. The double-zeta and triple-zeta quality basis sets systematically and significantly overestimate the bond distances. A simple and cost-effective way to improve the performance of these basis sets is to scale the bond distances by an empirical scaling factor of 0.9865 (cc-pV(D+d)Z) and 0.9969 (cc-pV(T+d)Z). This results in RMSDs of 0.0080 (scaled cc-pV(D+d)Z) and 0.0029 (scaled cc-pV(T+d)Z) Å. The basis set convergence of larger basis sets can be accelerated via standard basis-set extrapolations. In addition, the basis set convergence of explicitly correlated CCSD(T)-F12 calculations is investigated in conjunction with the cc-pVnZ-F12 basis sets (n = D, T). Typically, one "gains" two angular momenta in the explicitly correlated calculations. That is, the CCSD(T)-F12/cc-pVnZ-F12 level of theory shows similar performance to the CCSD(T)/cc-pV(n+2)Z level of theory. In particular, the following RMSDs are obtained for the cc-pVnZ-F12 basis sets 0
The radar cross section of non-orthogonal corner reflectors, symmetrically illuminated
Williams, J. M.
The monostatic radar cross section of a nonorthogonal corner reflector, for symmetrical illumination, is shown to be a function of a single dimensionless group at high frequency. The function is calculated for the triangular and square trihedrals and the dihedral.
Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism
Alam, Aftab; Khan, Suffian N.; Smirnov, A. V.; Nicholson, D. M.; Johnson, Duane D.
2014-11-01
The Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an efficient site-centered, electronic-structure technique for addressing an assembly of N scatterers. Wave functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number Lmax=(l,mmax), while scattering matrices, which determine spectral properties, are truncated at Lt r=(l,mt r) where phase shifts δl >ltr are negligible. Historically, Lmax is set equal to Lt r, which is correct for large enough Lmax but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for Lmax>Lt r with δl >ltr set to zero [X.-G. Zhang and W. H. Butler, Phys. Rev. B 46, 7433 (1992), 10.1103/PhysRevB.46.7433]. We present a numerically efficient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R3 process with rank N (ltr+1 ) 2 ] and includes higher-L contributions via linear algebra [R2 process with rank N (lmax+1) 2 ]. The augmented-KKR approach yields properly normalized wave functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe, and L 1 0 CoPt and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus Lmax for a given Lt r.
The Raman Spectrum of the Squarate (C4O4-2 Anion: An Ab Initio Basis Set Dependence Study
Directory of Open Access Journals (Sweden)
Miranda Sandro G. de
2002-01-01
Full Text Available The Raman excitation profile of the squarate anion, C4O4-2 , was calculated using ab initio methods at the Hartree-Fock using Linear Response Theory (LRT for six excitation frequencies: 632.5, 514.5, 488.0, 457.9, 363.8 and 337.1 nm. Five basis set functions (6-31G*, 6-31+G*, cc-pVDZ, aug-cc-pVDZ and Sadlej's polarizability basis set were investigated aiming to evaluate the performance of the 6-31G* set for numerical convergence and computational cost in relation to the larger basis sets. All basis sets reproduce the main spectroscopic features of the Raman spectrum of this anion for the excitation interval investigated. The 6-31G* basis set presented, on average, the same accuracy of numerical results as the larger sets but at a fraction of the computational cost showing that it is suitable for the theoretical investigation of the squarate dianion and its complexes and derivatives.
The study of basis sets for the calculation of the structure and dynamics of the benzene-Kr complex
Energy Technology Data Exchange (ETDEWEB)
Shirkov, Leonid; Makarewicz, Jan, E-mail: jama@amu.edu.pl [Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań (Poland)
2015-05-28
An ab initio intermolecular potential energy surface (PES) has been constructed for the benzene-krypton (BKr) van der Waals (vdW) complex. The interaction energy has been calculated at the coupled cluster level of theory with single, double, and perturbatively included triple excitations using different basis sets. As a result, a few analytical PESs of the complex have been determined. They allowed a prediction of the complex structure and its vibrational vdW states. The vibrational energy level pattern exhibits a distinct polyad structure. Comparison of the equilibrium structure, the dipole moment, and vibrational levels of BKr with their experimental counterparts has allowed us to design an optimal basis set composed of a small Dunning’s basis set for the benzene monomer, a larger effective core potential adapted basis set for Kr and additional midbond functions. Such a basis set yields vibrational energy levels that agree very well with the experimental ones as well as with those calculated from the available empirical PES derived from the microwave spectra of the BKr complex. The basis proposed can be applied to larger complexes including Kr because of a reasonable computational cost and accurate results.
The study of basis sets for the calculation of the structure and dynamics of the benzene-Kr complex.
Shirkov, Leonid; Makarewicz, Jan
2015-05-28
An ab initio intermolecular potential energy surface (PES) has been constructed for the benzene-krypton (BKr) van der Waals (vdW) complex. The interaction energy has been calculated at the coupled cluster level of theory with single, double, and perturbatively included triple excitations using different basis sets. As a result, a few analytical PESs of the complex have been determined. They allowed a prediction of the complex structure and its vibrational vdW states. The vibrational energy level pattern exhibits a distinct polyad structure. Comparison of the equilibrium structure, the dipole moment, and vibrational levels of BKr with their experimental counterparts has allowed us to design an optimal basis set composed of a small Dunning's basis set for the benzene monomer, a larger effective core potential adapted basis set for Kr and additional midbond functions. Such a basis set yields vibrational energy levels that agree very well with the experimental ones as well as with those calculated from the available empirical PES derived from the microwave spectra of the BKr complex. The basis proposed can be applied to larger complexes including Kr because of a reasonable computational cost and accurate results.
Study on the construction of satisfactory nonorthogonal localized molecular orbitals
Institute of Scientific and Technical Information of China (English)
FENG; Huasheng; BIAN; Jiang; LI; Lemin
2004-01-01
Comparing to orthogonal localized molecular orbitals (OLMO), the nonorthogonal localized molecular orbitals (NOLMO) exhibit bonding pictures more accordant with those in the traditional chemistry. They are more contracted, so that they have a better transferability and better performances for the calculation of election correlation energies and for the linear scaling algorithms of large systems. The satisfactory NOLMOs should be as contracted as possible while their shapes and spatial distribution keep in accordance with the traditional chemical bonding picture. It is found that the spread of NOLMOs is a monotonic decreasing function of their orthogonality, and it may reduce to any extent as the orthogonality descends. However, when the orthogonality descends to some point, the shapes and spatial distribution of the NOLMOs deviate drastically from the traditional chemical bonding picture, and finally the NOLMOs tend to linear dependence. Without the requirement of orthogonalization, some other constraints have to be imposed for constructing satisfactory NOLMOs by minimizing their spread functional. It is shown that satisfactory results can be generated by coupling the minimization of orbital spread functionals with the maximization of the distances between orbital centroids.
An optimal nonorthogonal separation of the anisotropic Gaussian convolution filter.
Lampert, Christoph H; Wirjadi, Oliver
2006-11-01
We give an analytical and geometrical treatment of what it means to separate a Gaussian kernel along arbitrary axes in R(n), and we present a separation scheme that allows us to efficiently implement anisotropic Gaussian convolution filters for data of arbitrary dimensionality. Based on our previous analysis we show that this scheme is optimal with regard to the number of memory accesses and interpolation operations needed. The proposed method relies on nonorthogonal convolution axes and works completely in image space. Thus, it avoids the need for a fast Fourier transform (FFT)-subroutine. Depending on the accuracy and speed requirements, different interpolation schemes and methods to implement the one-dimensional Gaussian (finite impulse response and infinite impulse response) can be integrated. Special emphasis is put on analyzing the performance and accuracy of the new method. In particular, we show that without any special optimization of the source code, it can perform anisotropic Gaussian filtering faster than methods relying on the FFT.
Simulating the oxygen content of ambient organic aerosol with the 2D volatility basis set
Murphy, B. N.; Donahue, N. M.; Fountoukis, C.; Pandis, S. N.
2011-08-01
A module predicting the oxidation state of organic aerosol (OA) has been developed using the two-dimensional volatility basis set (2D-VBS) framework. This model is an extension of the 1D-VBS framework and tracks saturation concentration and oxygen content of organic species during their atmospheric lifetime. The host model, a one-dimensional Lagrangian transport model, is used to simulate air parcels arriving at Finokalia, Greece during the Finokalia Aerosol Measurement Experiment in May 2008 (FAME-08). Extensive observations were collected during this campaign using an aerosol mass spectrometer (AMS) and a thermodenuder to determine the chemical composition and volatility, respectively, of the ambient OA. Although there are several uncertain model parameters, the consistently high oxygen content of OA measured during FAME-08 (O:C = 0.8) can help constrain these parameters and elucidate OA formation and aging processes that are necessary for achieving the high degree of oxygenation observed. The base-case model reproduces observed OA mass concentrations (measured mean = 3.1 μg m-3, predicted mean = 3.3 μg m-3) and O:C (predicted O:C = 0.78) accurately. A suite of sensitivity studies explore uncertainties due to (1) the anthropogenic secondary OA (SOA) aging rate constant, (2) assumed enthalpies of vaporization, (3) the volatility change and number of oxygen atoms added for each generation of aging, (4) heterogeneous chemistry, (5) the oxidation state of the first generation of compounds formed from SOA precursor oxidation, and (6) biogenic SOA aging. Perturbations in most of these parameters do impact the ability of the model to predict O:C well throughout the simulation period. By comparing measurements of the O:C from FAME-08, several sensitivity cases including a high oxygenation case, a low oxygenation case, and biogenic SOA aging case are found to unreasonably depict OA aging, keeping in mind that this study does not consider possibly important processes
Friese, Daniel H; Ringholm, Magnus; Gao, Bin; Ruud, Kenneth
2015-10-13
We present theory, implementation, and applications of a recursive scheme for the calculation of single residues of response functions that can treat perturbations that affect the basis set. This scheme enables the calculation of nonlinear light absorption properties to arbitrary order for other perturbations than an electric field. We apply this scheme for the first treatment of two-photon circular dichroism (TPCD) using London orbitals at the Hartree-Fock level of theory. In general, TPCD calculations suffer from the problem of origin dependence, which has so far been solved by using the velocity gauge for the electric dipole operator. This work now enables comparison of results from London orbital and velocity gauge based TPCD calculations. We find that the results from the two approaches both exhibit strong basis set dependence but that they are very similar with respect to their basis set convergence.
Energy Technology Data Exchange (ETDEWEB)
Caravaca, M A [Facultad de Ingenieria, Universidad Nacional del Nordeste, Avenida Las Heras 727, 3500-Resistencia (Argentina); Casali, R A [Facultad de Ciencias Exactas y Naturales y Agrimensura, Universidad Nacional del Nordeste, Avenida Libertad, 5600-Corrientes (Argentina)
2005-09-21
The SIESTA approach based on pseudopotentials and a localized basis set is used to calculate the electronic, elastic and equilibrium properties of P 2{sub 1}/c, Pbca, Pnma, Fm3m, P4{sub 2}nmc and Pa3 phases of HfO{sub 2}. Using separable Troullier-Martins norm-conserving pseudopotentials which include partial core corrections for Hf, we tested important physical properties as a function of the basis set size, grid size and cut-off ratio of the pseudo-atomic orbitals (PAOs). We found that calculations in this oxide with the LDA approach and using a minimal basis set (simple zeta, SZ) improve calculated phase transition pressures with respect to the double-zeta basis set and LDA (DZ-LDA), and show similar accuracy to that determined with the PPPW and GGA approach. Still, the equilibrium volumes and structural properties calculated with SZ-LDA compare better with experiments than the GGA approach. The bandgaps and elastic and structural properties calculated with DZ-LDA are accurate in agreement with previous state of the art ab initio calculations and experimental evidence and cannot be improved with a polarized basis set. These calculated properties show low sensitivity to the PAO localization parameter range between 40 and 100 meV. However, this is not true for the relative energy, which improves upon decrease of the mentioned parameter. We found a non-linear behaviour in the lattice parameters with pressure in the P 2{sub 1}/c phase, showing a discontinuity of the derivative of the a lattice parameter with respect to external pressure, as found in experiments. The common enthalpy values calculated with the minimal basis set give pressure transitions of 3.3 and 10.8?GPa for P2{sub 1}/c {yields} Pbca and Pbca {yields} Pnma, respectively, in accordance with different high pressure experimental values.
Basis set dependence using DFT/B3LYP calculations to model the Raman spectrum of thymine.
Bielecki, Jakub; Lipiec, Ewelina
2016-02-01
Raman spectroscopy (including surface enhanced Raman spectroscopy (SERS) and tip enhanced Raman spectroscopy (TERS)) is a highly promising experimental method for investigations of biomolecule damage induced by ionizing radiation. However, proper interpretation of changes in experimental spectra for complex systems is often difficult or impossible, thus Raman spectra calculations based on density functional theory (DFT) provide an invaluable tool as an additional layer of understanding of underlying processes. There are many works that address the problem of basis set dependence for energy and bond length consideration, nevertheless there is still lack of consistent research on basis set influence on Raman spectra intensities for biomolecules. This study fills this gap by investigating of the influence of basis set choice for the interpretation of Raman spectra of the thymine molecule calculated using the DFT/B3LYP framework and comparing these results with experimental spectra. Among 19 selected Pople's basis sets, the best agreement was achieved using 6-31[Formula: see text](d,p), 6-31[Formula: see text](d,p) and 6-11[Formula: see text]G(d,p) sets. Adding diffuse functions or polarized functions for small basis set or use of a medium or large basis set without diffuse or polarized functions is not sufficient to reproduce Raman intensities correctly. The introduction of the diffuse functions ([Formula: see text]) on hydrogen atoms is not necessary for gas phase calculations. This work serves as a benchmark for further research on the interaction of ionizing radiation with DNA molecules by means of ab initio calculations and Raman spectroscopy. Moreover, this work provides a set of new scaling factors for Raman spectra calculation in the framework of DFT/B3LYP method.
On the Use of a Mixed Gaussian/Finite-Element Basis Set for the Calculation of Rydberg States
Thuemmel, Helmar T.; Langhoff, Stephen (Technical Monitor)
1996-01-01
Configuration-interaction studies are reported for the Rydberg states of the helium atom using mixed Gaussian/finite-element (GTO/FE) one particle basis sets. Standard Gaussian valence basis sets are employed, like those, used extensively in quantum chemistry calculations. It is shown that the term values for high-lying Rydberg states of the helium atom can be obtained accurately (within 1 cm -1), even for a small GTO set, by augmenting the n-particle space with configurations, where orthonormalized interpolation polynomials are singly occupied.
Directory of Open Access Journals (Sweden)
CASTRO EUSTÁQUIO V. R. DE
2001-01-01
Full Text Available The generator coordinate Hartree-Fock method is used to generate adapted Gaussian basis sets for the atoms from Li (Z=3 through Xe (Z=54. In this method the Griffin-Hill-Wheeler-Hartree-Fock equations are integrated through the integral discretization technique. The wave functions generated in this work are compared with the widely used Roothaan-Hartree-Fock wave functions of Clementi and Roetti (1974, and with other basis sets reported in the literature. For all atoms studied, the errors in our total energy values relatively to the numerical Hartree-Fock limits are always less than 7.426 mhartree.
Hill, J Grant
2013-09-30
Auxiliary basis sets (ABS) specifically matched to the cc-pwCVnZ-PP and aug-cc-pwCVnZ-PP orbital basis sets (OBS) have been developed and optimized for the 4d elements Y-Pd at the second-order Møller-Plesset perturbation theory level. Calculation of the core-valence electron correlation energies for small to medium sized transition metal complexes demonstrates that the error due to the use of these new sets in density fitting is three to four orders of magnitude smaller than that due to the OBS incompleteness, and hence is considered negligible. Utilizing the ABSs in the resolution-of-the-identity component of explicitly correlated calculations is also investigated, where it is shown that i-type functions are important to produce well-controlled errors in both integrals and correlation energy. Benchmarking at the explicitly correlated coupled cluster with single, double, and perturbative triple excitations level indicates impressive convergence with respect to basis set size for the spectroscopic constants of 4d monofluorides; explicitly correlated double-ζ calculations produce results close to conventional quadruple-ζ, and triple-ζ is within chemical accuracy of the complete basis set limit.
Simulating the oxygen content of ambient organic aerosol with the 2D volatility basis set
Directory of Open Access Journals (Sweden)
B. N. Murphy
2011-08-01
Full Text Available A module predicting the oxidation state of organic aerosol (OA has been developed using the two-dimensional volatility basis set (2D-VBS framework. This model is an extension of the 1D-VBS framework and tracks saturation concentration and oxygen content of organic species during their atmospheric lifetime. The host model, a one-dimensional Lagrangian transport model, is used to simulate air parcels arriving at Finokalia, Greece during the Finokalia Aerosol Measurement Experiment in May 2008 (FAME-08. Extensive observations were collected during this campaign using an aerosol mass spectrometer (AMS and a thermodenuder to determine the chemical composition and volatility, respectively, of the ambient OA. Although there are several uncertain model parameters, the consistently high oxygen content of OA measured during FAME-08 (O:C = 0.8 can help constrain these parameters and elucidate OA formation and aging processes that are necessary for achieving the high degree of oxygenation observed. The base-case model reproduces observed OA mass concentrations (measured mean = 3.1 μg m^{−3}, predicted mean = 3.3 μg m^{−3} and O:C (predicted O:C = 0.78 accurately. A suite of sensitivity studies explore uncertainties due to (1 the anthropogenic secondary OA (SOA aging rate constant, (2 assumed enthalpies of vaporization, (3 the volatility change and number of oxygen atoms added for each generation of aging, (4 heterogeneous chemistry, (5 the oxidation state of the first generation of compounds formed from SOA precursor oxidation, and (6 biogenic SOA aging. Perturbations in most of these parameters do impact the ability of the model to predict O:C well throughout the simulation period. By comparing measurements of the O:C from FAME-08, several sensitivity cases including a high oxygenation case, a low oxygenation case, and biogenic SOA aging case are found to unreasonably depict OA aging, keeping in mind that this study does not consider
Heaps, Charles W
2016-01-01
Quantum molecular dynamics requires an accurate representation of the molecular potential energy surface from a minimal number of electronic structure calculations, particularly for nonadiabatic dynamics where excited states are required. In this paper, we employ pseudospectral sampling of time-dependent Gaussian basis functions for the simulation of non-adiabatic dynamics. Unlike other methods, the pseudospectral Gaussian molecular dynamics tests the Schr\\"{o}dinger equation with $N$ Dirac delta functions located at the centers of the Gaussian functions reducing the scaling of potential energy evaluations from $\\mathcal{O}(N^2)$ to $\\mathcal{O}(N)$. By projecting the Gaussian basis onto discrete points in space, the method is capable of efficiently and quantitatively describing nonadiabatic population transfer and intra-surface quantum coherence. We investigate three model systems; the photodissociation of three coupled Morse oscillators, the bound state dynamics of two coupled Morse oscillators, and a two-d...
Nikolaev, A. V.; Lamoen, D.; Partoens, B.
2016-07-01
In order to increase the accuracy of the linearized augmented plane wave (LAPW) method, we present a new approach where the plane wave basis function is augmented by two different atomic radial components constructed at two different linearization energies corresponding to two different electron bands (or energy windows). We demonstrate that this case can be reduced to the standard treatment within the LAPW paradigm where the usual basis set is enriched by the basis functions of the tight binding type, which go to zero with zero derivative at the sphere boundary. We show that the task is closely related with the problem of extended core states which is currently solved by applying the LAPW method with local orbitals (LAPW+LO). In comparison with LAPW+LO, the number of supplemented basis functions in our approach is doubled, which opens up a new channel for the extension of the LAPW and LAPW+LO basis sets. The appearance of new supplemented basis functions absent in the LAPW+LO treatment is closely related with the existence of the u ˙ l -component in the canonical LAPW method. We discuss properties of additional tight binding basis functions and apply the extended basis set for computation of electron energy bands of lanthanum (face and body centered structures) and hexagonal close packed lattice of cadmium. We demonstrate that the new treatment gives lower total energies in comparison with both canonical LAPW and LAPW+LO, with the energy difference more pronounced for intermediate and poor LAPW basis sets.
Brorsen, Kurt R.; Sirjoosingh, Andrew; Pak, Michael V.; Hammes-Schiffer, Sharon
2015-06-01
The nuclear electronic orbital (NEO) reduced explicitly correlated Hartree-Fock (RXCHF) approach couples select electronic orbitals to the nuclear orbital via Gaussian-type geminal functions. This approach is extended to enable the use of a restricted basis set for the explicitly correlated electronic orbitals and an open-shell treatment for the other electronic orbitals. The working equations are derived and the implementation is discussed for both extensions. The RXCHF method with a restricted basis set is applied to HCN and FHF- and is shown to agree quantitatively with results from RXCHF calculations with a full basis set. The number of many-particle integrals that must be calculated for these two molecules is reduced by over an order of magnitude with essentially no loss in accuracy, and the reduction factor will increase substantially for larger systems. Typically, the computational cost of RXCHF calculations with restricted basis sets will scale in terms of the number of basis functions centered on the quantum nucleus and the covalently bonded neighbor(s). In addition, the RXCHF method with an odd number of electrons that are not explicitly correlated to the nuclear orbital is implemented using a restricted open-shell formalism for these electrons. This method is applied to HCN+, and the nuclear densities are in qualitative agreement with grid-based calculations. Future work will focus on the significance of nonadiabatic effects in molecular systems and the further enhancement of the NEO-RXCHF approach to accurately describe such effects.
Duke, Brian J.; Havenith, Remco W. A.
2016-01-01
The use of larger basis sets to approach the complete basis limit, now common in quantum chemistry, is applied for the first time to a range of valence bond functions for the simplest case of molecular hydrogen. Good convergence of the energy is slow due to difficulty in getting a correct cusp near
Swart, M; Snijders, JG
The geometries of a set of small molecules were optimized using eight different exchange-correlation (xc) potentials in a few different basis sets of Slater-type orbitals, ranging from a minimal basis (I) to a triple-zeta valence basis plus double polarization functions (VII). This enables a
Wang, Nick X; Wilson, Angela K
2005-08-18
The HSO and HOS isomers have been revisited using the DFT functionals, B3LYP, B3PW91, and PBE, in combination with tight d-augmented correlation consistent basis sets, cc-pV(x+d)Z and aug-cc-pV(x+d)Z for second-row atoms. Structures, vibrationally averaged structures, relative energies, harmonic and anharmonic frequencies, enthalpies of formation of HSO and HOS, and the barrier for the HSO/HOS isomerization have been determined. These results were compared with results from previous DFT and ab initio studies in which the standard correlation consistent basis sets were used. The relative energies of the two isomers converge more rapidly and smoothly with respect to increasing basis set size for the tight d-augmented sets than for the standard basis sets. Our best calculations, B3PW91/aug-cc-pV(5+d)Z, for the relative energy of the isomers are in excellent agreement with previous CCSD(T) results given by Wilson and Dunning.
Which are more accurate, orthogonal or non-orthogonal sonic anemometers?
Massman, W. J.; Frank, J. M.; Swiatek, E.; Zimmerman, H.; Ewers, B. E.
2013-12-01
Sonic anemometry is fundamental to all eddy-covariance studies of surface energy, ecosystem carbon, and water balance. Recent studies have shown the potential underestimation of the vertical wind fluctuations among the most commonly encountered anemometer models, but thus far testing has been focused on non-orthogonal sonic anemometer designs. We hypothesize that these underestimates are systematic to the non-orthogonal design and not attributable to a single manufacturer. If so, orthogonal measurements of vertical wind should be more accurate. We tested this by conducting an experiment to measure the relative consistency between vertical and horizontal wind measurements for three sonic anemometer designs: orthogonal, non-orthogonal, and quasi-orthogonal. Both the orthogonal and non-orthogonal models were from a single manufacturer (K-probe and A-probe, Applied Technologies, Inc.) while the quasi-orthogonal design featured non-orthogonal u- and v-axes but with an orthogonal w-axis (CSAT3V, Campbell Scientific, Inc.). We conducted a 12-week experiment, testing four sonic anemometers relative to a control (CSAT3, Campbell Scientific, Inc.), each week randomly selecting at least one of each model from a pool of twelve instruments (three of each model) and randomly locating the test anemometers around the control. Half-way through the week the test anemometers were re-mounted in a horizontal position. Work was done at the GLEES AmeriFlux site (southeastern Wyoming, USA) which experiences large, uni-directional wind and turbulence. Results are discussed.
Sun, Y; Bergou, J A; Sun, Yuqing; Hillery, Mark; Bergou, Janos
2000-01-01
The problem of unambiguously distinguishing among nonorthogonal but linearly independent quantum states can be solved by mapping the set of nonorthogonal quantum states onto a set of orthogonal ones, which can then be distinguished without error. Such nonunitary transformations can be performed conditionally on quantum systems; a unitary transformation is carried out on a larger system of which the system of interest is a subsytem, a measurement is performed, and if the proper result is obtained, the desired nonunitary transformation will have been performed on the subsystem. We show how to construct generalized interferometers (multiports), which when combined with measurements on some of the output ports, implement nonunitary transformations of this type. The input states are single-photon states in which the photon is divided among several modes. A number of explicit examples of distinguishing among three nonorthogonal states are discussed, and the networks that optimally distinguish among these states are...
Non-orthogonal multiple-relaxation-time lattice Boltzmann method for incompressible thermal flows
Liu, Qing; Li, Dong
2015-01-01
In this paper, a non-orthogonal multiple-relaxation-time (MRT) lattice Boltzmann (LB) method for simulating incompressible thermal flows is presented. In the method, the incompressible Navier-Stokes equations and temperature equation (or convection-diffusion equation) are solved separately by two different MRT-LB models, which are proposed based on non-orthogonal transformation matrices constructed in terms of some proper non-orthogonal basis vectors obtained from the combinations of the lattice velocity components. The macroscopic equations for incompressible thermal flows can be recovered from the present method through the Chapman-Enskog analysis in the incompressible limit. Numerical simulations of several typical two-dimensional problems are carried out to validate the present method. It is found that the present numerical results are in good agreement with the analytical solutions or other numerical results of previous studies. Furthermore, the grid convergence tests indicate that the present MRT-LB met...
Chan, Bun; Radom, Leo
2011-09-13
A variety of combinations of B-LYP-based double-hybrid density functional theory (DHDFT) procedures and basis sets have been examined. A general observation is that the optimal combination of exchange contributions is in the proximity of 30% Becke 1988 (B88) exchange and 70% Hartree-Fock (HF) exchange, while for the correlation contributions, the use of independently optimized spin-component-scaled Møller-Plesset second-order perturbation theory (SCS-MP2) parameters (MP2OS and MP2SS) is beneficial. The triple-ζ Dunning aug'-cc-pVTZ+d and Pople 6-311+G(3df,2p)+d basis sets are found to be cost-effective for DHDFT methods. As a result, we have formulated the DuT-D3 DHDFT procedure, which employs the aug'-cc-pVTZ+d basis set and includes 30% B88 and 70% HF exchange energies, 59% LYP, 47% MP2OS, and 36% MP2SS correlation energies, and a D3 dispersion correction with the parameters s6 = 0.5, sr,6 = 1.569, and s8 = 0.35. Likewise, the PoT-D3 DHDFT procedure was formulated with the 6-311+G(3df,2p)+d basis set and has 32% B88 and 68% HF exchange energies, 63% LYP, 46% MP2OS, and 27% MP2SS correlation energies, and the D3 parameters s6 = 0.5, sr,6 = 1.569, and s8 = 0.30. Testing using the large E3 set of 740 energies demonstrates the robustness of these methods. Further comparisons show that the performance of these methods, particularly DuT-D3, compares favorably with the previously reported DSD-B-LYP and DSD-B-LYP-D3 methods used in conjunction with quadruple-ζ aug'-pc3+d and aug'-def2-QZVP basis sets but at lower computational expense. The previously reported ωB97X-(LP)/6-311++G(3df,3pd) procedure also performs very well. Our findings highlight the cost-effectiveness of appropriate- and moderate-sized triple-ζ basis sets in the application of DHDFT procedures.
Real-time detection and elimination of nonorthogonality error in interference fringe processing.
Hu, Haijiang; Zhang, Fengdeng
2011-05-20
In the measurement system of interference fringe, the nonorthogonality error is a main error source that influences the precision and accuracy of the measurement system. The detection and elimination of the error has been an important target. A novel method that only uses the cross-zero detection and the counting is proposed to detect and eliminate the nonorthogonality error in real time. This method can be simply realized by means of the digital logic device, because it does not invoke trigonometric functions and inverse trigonometric functions. And it can be widely used in the bidirectional subdivision systems of a Moiré fringe and other optical instruments.
Liquid Water through Density-Functional Molecular Dynamics: Plane-Wave vs Atomic-Orbital Basis Sets
Miceli, Giacomo; Pasquarello, Alfredo
2016-01-01
We determine and compare structural, dynamical, and electronic properties of liquid water at near ambient conditions through density-functional molecular dynamics simulations, when using either plane-wave or atomic-orbital basis sets. In both frameworks, the electronic structure and the atomic forces are self-consistently determined within the same theoretical scheme based on a nonlocal density functional accounting for van der Waals interactions. The overall properties of liquid water achieved within the two frameworks are in excellent agreement with each other. Thus, our study supports that implementations with plane-wave or atomic-orbital basis sets yield equivalent results and can be used indiscriminately in study of liquid water or aqueous solutions.
Salvador, P; Mayer, I
2004-04-01
The basis set superposition error-free second-order Møller-Plesset perturbation theory of intermolecular interactions, based on the "chemical Hamiltonian approach," which has been introduced in Part I, is applied here to open-shell systems by using a new, effective computer realization. The results of the numerical examples considered (CH(4) em leader HO, NO em leader HF) showed again the perfect performance of the method. Striking agreement has again been found with the results of the a posteriori counterpoise correction (CP) scheme in the case of large, well-balanced basis sets, which is also in agreement with a most recent formal theoretical analysis. The difficulties of the CP correction in open-shell systems are also discussed.
Bjornsson, Ragnar; Bühl, Michael
2010-06-14
Electric field gradients (EFGs) were computed for the first-row transition metal nuclei in Cr(C(6)H(6))(CO)(3), MnO(3)F, Mn(CO)(5)H, MnCp(CO)(3), Co(CO)(4)H, Co(CO)(3)(NO) and VCp(CO)(4), for which experimental gas-phase data (in form of nuclear quadrupole coupling constants) are available from microwave spectroscopy. A variety of exchange-correlation functionals were assessed, among which range-separated hybrids (such as CAM-B3LYP or LC-omegaPBE) perform best, followed by global hybrids (such as B3LYP and PBE0) and gradient-corrected functionals (such as BP86). While large basis sets are required on the metal atom for converged EFGs, smaller basis sets can be employed on the ligands. In most cases, EFGs show little sensitivity toward the geometrical parameters.
Buimaga-Iarinca, Luiza
2014-01-01
We compare the density functional theory (DFT) results on the adsorption of small aromatic molecules (benzene, pyridine and thiophene) on gold surfaces obtained by using three types of van der Waals exchange-correlation functionals and localized basis set calculations. We show that the value of the molecule surface binding energy depends on the interplay between the BSSE effect and the tendency of the exchange-correlation functionals to overestimate both the molecule-surface as well as the gold-gold distances within the relaxed systems. Consequently, we find that by using different types of LCAO basis sets or geometric models for the adsorption of the molecules on the surface, the binding energy can vary up to 100 %. A critical analysis of the physical parameters resulting from the calculations is presented for each exchange-correlation functional.
Brandenburg, Jan Gerit; Alessio, Maristella; Civalleri, Bartolomeo; Peintinger, Michael F; Bredow, Thomas; Grimme, Stefan
2013-09-26
We extend the previously developed geometrical correction for the inter- and intramolecular basis set superposition error (gCP) to periodic density functional theory (DFT) calculations. We report gCP results compared to those from the standard Boys-Bernardi counterpoise correction scheme and large basis set calculations. The applicability of the method to molecular crystals as the main target is tested for the benchmark set X23. It consists of 23 noncovalently bound crystals as introduced by Johnson et al. (J. Chem. Phys. 2012, 137, 054103) and refined by Tkatchenko et al. (J. Chem. Phys. 2013, 139, 024705). In order to accurately describe long-range electron correlation effects, we use the standard atom-pairwise dispersion correction scheme DFT-D3. We show that a combination of DFT energies with small atom-centered basis sets, the D3 dispersion correction, and the gCP correction can accurately describe van der Waals and hydrogen-bonded crystals. Mean absolute deviations of the X23 sublimation energies can be reduced by more than 70% and 80% for the standard functionals PBE and B3LYP, respectively, to small residual mean absolute deviations of about 2 kcal/mol (corresponding to 13% of the average sublimation energy). As a further test, we compute the interlayer interaction of graphite for varying distances and obtain a good equilibrium distance and interaction energy of 6.75 Å and -43.0 meV/atom at the PBE-D3-gCP/SVP level. We fit the gCP scheme for a recently developed pob-TZVP solid-state basis set and obtain reasonable results for the X23 benchmark set and the potential energy curve for water adsorption on a nickel (110) surface.
2012-01-01
We present a systematic study of the performance of numerical pseudo-atomic orbital basis sets in the calculation of dielectric matrices of extended systems using the self-consistent Sternheimer approach of [F. Giustino et al., Phys. Rev. B 81 (11), 115105 (2010)]. In order to cover a range of systems, from more insulating to more metallic character, we discuss results for the three semiconductors diamond, silicon, and germanium. Dielectric matrices calculated using our method fall within 1-3...
Homeier, H. H. H.; Neef, M. D.
2000-01-01
The performance of the recently introduced $\\Pi$2 method [1] is investigated for some diatomic molecules. For this end, ground state energies are calculated at the MP4 level for various basis sets of increasing size. With negligible extra effort, the $\\Pi$2, F4, and [2/2] estimators are obtained, together with information on the reliability of the basic perturbation series [1]. The results are compared to more expensive CCSD(T) results. Also, electronic energy hypersurfaces are calculated at ...
Witte, Jonathon; Neaton, Jeffrey B.; Head-Gordon, Martin
2016-05-01
With the aim of systematically characterizing the convergence of common families of basis sets such that general recommendations for basis sets can be made, we have tested a wide variety of basis sets against complete-basis binding energies across the S22 set of intermolecular interactions—noncovalent interactions of small and medium-sized molecules consisting of first- and second-row atoms—with three distinct density functional approximations: SPW92, a form of local-density approximation; B3LYP, a global hybrid generalized gradient approximation; and B97M-V, a meta-generalized gradient approximation with nonlocal correlation. We have found that it is remarkably difficult to reach the basis set limit; for the methods and systems examined, the most complete basis is Jensen's pc-4. The Dunning correlation-consistent sequence of basis sets converges slowly relative to the Jensen sequence. The Karlsruhe basis sets are quite cost effective, particularly when a correction for basis set superposition error is applied: counterpoise-corrected def2-SVPD binding energies are better than corresponding energies computed in comparably sized Dunning and Jensen bases, and on par with uncorrected results in basis sets 3-4 times larger. These trends are exhibited regardless of the level of density functional approximation employed. A sense of the magnitude of the intrinsic incompleteness error of each basis set not only provides a foundation for guiding basis set choice in future studies but also facilitates quantitative comparison of existing studies on similar types of systems.
Witte, Jonathon; Neaton, Jeffrey B; Head-Gordon, Martin
2016-05-21
With the aim of systematically characterizing the convergence of common families of basis sets such that general recommendations for basis sets can be made, we have tested a wide variety of basis sets against complete-basis binding energies across the S22 set of intermolecular interactions-noncovalent interactions of small and medium-sized molecules consisting of first- and second-row atoms-with three distinct density functional approximations: SPW92, a form of local-density approximation; B3LYP, a global hybrid generalized gradient approximation; and B97M-V, a meta-generalized gradient approximation with nonlocal correlation. We have found that it is remarkably difficult to reach the basis set limit; for the methods and systems examined, the most complete basis is Jensen's pc-4. The Dunning correlation-consistent sequence of basis sets converges slowly relative to the Jensen sequence. The Karlsruhe basis sets are quite cost effective, particularly when a correction for basis set superposition error is applied: counterpoise-corrected def2-SVPD binding energies are better than corresponding energies computed in comparably sized Dunning and Jensen bases, and on par with uncorrected results in basis sets 3-4 times larger. These trends are exhibited regardless of the level of density functional approximation employed. A sense of the magnitude of the intrinsic incompleteness error of each basis set not only provides a foundation for guiding basis set choice in future studies but also facilitates quantitative comparison of existing studies on similar types of systems.
Kolmann, Stephen J; Jordan, Meredith J T
2010-02-07
One of the largest remaining errors in thermochemical calculations is the determination of the zero-point energy (ZPE). The fully coupled, anharmonic ZPE and ground state nuclear wave function of the SSSH radical are calculated using quantum diffusion Monte Carlo on interpolated potential energy surfaces (PESs) constructed using a variety of method and basis set combinations. The ZPE of SSSH, which is approximately 29 kJ mol(-1) at the CCSD(T)/6-31G* level of theory, has a 4 kJ mol(-1) dependence on the treatment of electron correlation. The anharmonic ZPEs are consistently 0.3 kJ mol(-1) lower in energy than the harmonic ZPEs calculated at the Hartree-Fock and MP2 levels of theory, and 0.7 kJ mol(-1) lower in energy at the CCSD(T)/6-31G* level of theory. Ideally, for sub-kJ mol(-1) thermochemical accuracy, ZPEs should be calculated using correlated methods with as big a basis set as practicable. The ground state nuclear wave function of SSSH also has significant method and basis set dependence. The analysis of the nuclear wave function indicates that SSSH is localized to a single symmetry equivalent global minimum, despite having sufficient ZPE to be delocalized over both minima. As part of this work, modifications to the interpolated PES construction scheme of Collins and co-workers are presented.
On the Analytical Solution of Non-Orthogonal Stagnation Point Flow towards a Stretching Sheet
DEFF Research Database (Denmark)
Kimiaeifar, Amin; Bagheri, G. H.; Barari, Amin
2011-01-01
An analytical solution for non-orthogonal stagnation point for the steady flow of a viscous and incompressible fluid is presented. The governing nonlinear partial differential equations for the flow field are reduced to ordinary differential equations by using similarity transformations existed i...
Teleportation of a qubit using entangled non-orthogonal states: a comparative study
Sisodia, Mitali; Verma, Vikram; Thapliyal, Kishore; Pathak, Anirban
2017-03-01
The effect of non-orthogonality of an entangled non-orthogonal state-based quantum channel is investigated in detail in the context of the teleportation of a qubit. Specifically, average fidelity, minimum fidelity and minimum assured fidelity (MASFI) are obtained for teleportation of a single-qubit state using all the Bell-type entangled non-orthogonal states known as quasi-Bell states. Using Horodecki criterion, it is shown that the teleportation scheme obtained by replacing the quantum channel (Bell state) of the usual teleportation scheme by a quasi-Bell state is optimal. Further, the performance of various quasi-Bell states as teleportation channel is compared in an ideal situation (i.e., in the absence of noise) and under different noise models (e.g., amplitude and phase damping channels). It is observed that the best choice of the quasi-Bell state depends on the amount non-orthogonality, both in noisy and noiseless case. A specific quasi-Bell state, which was found to be maximally entangled in the ideal conditions, is shown to be less efficient as a teleportation channel compared to other quasi-Bell states in particular cases when subjected to noisy channels. It has also been observed that usually the value of average fidelity falls with an increase in the number of qubits exposed to noisy channels (viz., Alice's, Bob's and to be teleported qubits), but the converse may be observed in some particular cases.
DEFF Research Database (Denmark)
Kupka, Teobald; Stachów, Michal; Kaminsky, Jakub
2013-01-01
A linear correlation between isotropic nuclear magnetic shielding constants for seven model molecules (CH2O, H2O, HF, F2, HCN, SiH4 and H2S) calculated with 37 methods (34 density functionals, RHF, MP2 and CCSD(T) ), with affordable pcS-2 basis set and corresponding complete basis set results......, estimated from calculations with the family of polarizationconsistent pcS-n basis sets is reported. This dependence was also supported by inspection of profiles of deviation between CBS estimated nuclear shieldings and obtained with significantly smaller basis sets pcS-2 and aug-cc-pVTZ-J for the selected...
Thorvaldsen, Andreas J.; Ruud, Kenneth; Kristensen, Kasper; Jørgensen, Poul; Coriani, Sonia
2008-12-01
A general method is presented for the calculation of molecular properties to arbitrary order at the Kohn-Sham density functional level of theory. The quasienergy and Lagrangian formalisms are combined to derive response functions and their residues by straightforward differentiation of the quasienergy derivative Lagrangian using the elements of the density matrix in the atomic orbital representation as variational parameters. Response functions and response equations are expressed in the atomic orbital basis, allowing recent advances in the field of linear-scaling methodology to be used. Time-dependent and static perturbations are treated on an equal footing, and atomic basis sets that depend on the applied frequency-dependent perturbations may be used, e.g., frequency-dependent London atomic orbitals. The 2n+1 rule may be applied if computationally favorable, but alternative formulations using higher-order perturbed density matrices are also derived. These may be advantageous in order to minimize the number of response equations that needs to be solved, for instance, when one of the perturbations has many components, as is the case for the first-order geometrical derivative of the hyperpolarizability.
Thorvaldsen, Andreas J; Ruud, Kenneth; Kristensen, Kasper; Jørgensen, Poul; Coriani, Sonia
2008-12-07
A general method is presented for the calculation of molecular properties to arbitrary order at the Kohn-Sham density functional level of theory. The quasienergy and Lagrangian formalisms are combined to derive response functions and their residues by straightforward differentiation of the quasienergy derivative Lagrangian using the elements of the density matrix in the atomic orbital representation as variational parameters. Response functions and response equations are expressed in the atomic orbital basis, allowing recent advances in the field of linear-scaling methodology to be used. Time-dependent and static perturbations are treated on an equal footing, and atomic basis sets that depend on the applied frequency-dependent perturbations may be used, e.g., frequency-dependent London atomic orbitals. The 2n+1 rule may be applied if computationally favorable, but alternative formulations using higher-order perturbed density matrices are also derived. These may be advantageous in order to minimize the number of response equations that needs to be solved, for instance, when one of the perturbations has many components, as is the case for the first-order geometrical derivative of the hyperpolarizability.
Simon, Sílvia; Duran, Miquel
1997-08-01
Quantum molecular similarity (QMS) techniques are used to assess the response of the electron density of various small molecules to application of a static, uniform electric field. Likewise, QMS is used to analyze the changes in electron density generated by the process of floating a basis set. The results obtained show an interrelation between the floating process, the optimum geometry, and the presence of an external field. Cases involving the Le Chatelier principle are discussed, and an insight on the changes of bond critical point properties, self-similarity values and density differences is performed.
Institute of Scientific and Technical Information of China (English)
Zhang Yue-Xia; Meng Hui-Yan; Shi Ting-Yun
2008-01-01
The B-spline basis set plus complex scaling method is applied to the numerical calculation of the exact resonance parameters Er and I/2 of a hydrogen atom in parallel electric and magnetic fields.The method can calculate the ground and higher excited resonances accurately and efficiently.The resonance parameters with accuracies of 10-9 - 10-12 for hydrogen atom in parallel fields with different field strengths and symmetries are presented and compared with previous ones.Extension to the calculation of Rydberg atom in crossed electric and magnetic fields and of atomic double excited states in external electric fields is discussed.
Tekarli, Sammer M; Drummond, Michael L; Williams, T Gavin; Cundari, Thomas R; Wilson, Angela K
2009-07-30
The performance of 44 density functionals used in conjunction with the correlation consistent basis sets (cc-pVnZ where n = T and Q) has been assessed for the gas-phase enthalpies of formation at 298.15 K of 3d transition metal (TM) containing systems. Nineteen molecules were examined: ScS, VO, VO(2), Cr(CO)(6), MnS, MnCl(2), Mn(CO)(5)Cl, FeCl(3), Fe(CO)(5), CoH(CO)(4), NiCl(2), Ni(CO)(4), CuH, CuF, CuCl, ZnH, ZnO, ZnCl, and Zn(CH(3))(2). Of the functionals examined, the functionals that resulted in the smallest mean absolute deviation (MAD, in parentheses, kcal mol(-1)) from experiment were B97-1 (6.9), PBE1KCIS (8.1), TPSS1KCIS (9.6), B97-2 (9.7), and B98 (10.7). All five of these functionals include some degree of Hartree-Fock (HF) exchange. The impact of increasing the basis set from cc-pVTZ to cc-pVQZ was found to be slight for the generalized gradient approximation (GGA) and meta-GGA (MGGA) functionals studied, indicating basis set saturation at the triple-zeta level. By contrast, for most of the generalized gradient exchange (GGE), hybrid GGA (HGGA), and hybrid meta-GGA (HMGGA) functionals considered, improvements in the average MAD of 2-3 kcal mol(-1) were seen upon progressing to a quadruple-zeta level basis set. Overall, it was found that the functionals that include Hartree-Fock exchange performed best overall, but those with greater than 40% HF exchange exhibit significantly poor performance for the prediction of enthalpies of formation for 3d TM complexes. Carbonyl-containing complexes, a mainstay in organometallic TM chemistry, are demonstrated to be exceedingly difficult to describe accurately with all but 2 of the 44 functionals considered. The most accurate functional, for both CO-containing and CO-free compounds, is B97-1/cc-pVQZ, which is shown to be capable of yielding results within 1 kcal mol(-1) of high-level ab initio composite methodologies.
DEFF Research Database (Denmark)
Avery, John Scales; Rettrup, Sten; Avery, James Emil
In theoretical physics, theoretical chemistry and engineering, one often wishes to solve partial differential equations subject to a set of boundary conditions. This gives rise to eigenvalue problems of which some solutions may be very difficult to find. For example, the problem of finding...... eigenfunctions and eigenvalues for the Hamiltonian of a many-particle system is usually so difficult that it requires approximate methods, the most common of which is expansion of the eigenfunctions in terms of basis functions that obey the boundary conditions of the problem. The computational effort needed...
Energy Technology Data Exchange (ETDEWEB)
Kupka, T.; Ruscic, B.; Botto, R. E.; Chemistry
2003-05-01
The nuclear shielding anisotropy and shielding tensor components calculated using the hybrid density functional B3PW91 are reported for a model set of compounds comprised of N{sub 2}, NH{sub 3}, CH{sub 4}, C{sub 2}H{sub 4}, HCN and CH{sub 3}CN. An estimation of density functional theory (DFT) and Hartree-Fock complete basis-set limit (CBS) parameters from a 2 (3) point exact fit vs. least-squares fit was obtained with the cc-pVxZ and aug-cc-pVxZ basis sets (x=D, T, Q, 5, 6). Both Hartree-Fock- and DFT-predicted CBS shielding anisotropies and shielding tensor components of the model molecules were in reasonable agreement with available experimental data. The utility of using a limited CBS approach for calculating accurate anisotropic shielding parameters of larger molecules as complementary methods to solid-state NMR is proposed.
Indian Academy of Sciences (India)
Sarvesh Kumar Pandey; Prasanta Das; Puspendu K Das; Elangannan Arunan; Sadasivam Manogaran
2015-06-01
It has been shown earlier1 that the relaxed force constants (RFCs) could be used as a measure of bond strength only when the bonds form a part of the complete valence internal coordinates (VIC) basis. However, if the bond is not a part of the complete VIC basis, its RFC is not necessarily a measure of bond strength. Sometimes, it is possible to have a complete VIC basis that does not contain the intramolecular hydrogen bond (IMHB) as part of the basis. This means the RFC of IMHB is not necessarily a measure of bond strength. However, we know that IMHB is a weak bond and hence its RFC has to be a measure of bond strength. We resolve this problem of IMHB not being part of the complete basis by postulating `equivalent’ basis sets where IMHB is part of the basis at least in one of the equivalent sets of VIC. As long as a given IMHB appears in one of the equivalent complete VIC basis sets, its RFC could be used as a measure of bond strength parameter.
Hübener, H.; Pérez-Osorio, M. A.; Ordejón, P.; Giustino, F.
2012-09-01
We present a systematic study of the performance of numerical pseudo-atomic orbital basis sets in the calculation of dielectric matrices of extended systems using the self-consistent Sternheimer approach of [F. Giustino et al., Phys. Rev. B 81, 115105 (2010)]. In order to cover a range of systems, from more insulating to more metallic character, we discuss results for the three semiconductors diamond, silicon, and germanium. Dielectric matrices of silicon and diamond calculated using our method fall within 1% of reference planewaves calculations, demonstrating that this method is promising. We find that polarization orbitals are critical for achieving good agreement with planewaves calculations, and that only a few additional ζ's are required for obtaining converged results, provided the split norm is properly optimized. Our present work establishes the validity of local orbital basis sets and the self-consistent Sternheimer approach for the calculation of dielectric matrices in extended systems, and prepares the ground for future studies of electronic excitations using these methods.
Zhang, Gaigong; Hu, Wei; Yang, Chao; Pask, John E
2015-01-01
Recently, we have proposed the adaptive local basis set for electronic structure calculations based on Kohn-Sham density functional theory in a pseudopotential framework. The adaptive local basis set is efficient and systematically improvable for total energy calculations. In this paper, we present the calculation of atomic forces, which can be used for a range of applications such as geometry optimization and molecular dynamics simulation. We demonstrate that, under mild assumptions, the computation of atomic forces can scale nearly linearly with the number of atoms in the system using the adaptive local basis set. We quantify the accuracy of the Hellmann-Feynman forces for a range of physical systems, benchmarked against converged planewave calculations, and find that the adaptive local basis set is efficient for both force and energy calculations, requiring at most a few tens of basis functions per atom to attain accuracy required in practice. Since the adaptive local basis set has implicit dependence on a...
Structure and binding energy of the H2S dimer at the CCSD(T) complete basis set limit
Lemke, Kono H.
2017-06-01
This study presents results for the binding energy and geometry of the H2S dimer which have been computed using Møller-Plesset perturbation theory (MP2, MP4) and coupled cluster (CCSD, CCSD(T)) calculations with basis sets up to aug-cc-pV5Z. Estimates of De, EZPE, Do, and dimer geometry have been obtained at each level of theory by taking advantage of the systematic convergence behavior toward the complete basis set (CBS) limit. The CBS limit binding energy values of De are 1.91 (MP2), 1.75 (MP4), 1.41 (CCSD), and 1.69 kcal/mol (CCSD[T]). The most accurate values for the equilibrium S-S distance rSS (without counterpoise correction) are 4.080 (MP2/aug-cc-pV5Z), 4.131 (MP4/aug-cc-pVQZ), 4.225 (CCSD/aug-cc-pVQZ), and 4.146 Å (CCSD(T)/aug-cc-pVQZ). This study also evaluates the effect of counterpoise correction on the H2S dimer geometry and binding energy. As regards the structure of (H2S)2, MPn, CCSD, and CCSD(T) level values of rSS, obtained by performing geometry optimizations on the counterpoise-corrected potential energy surface, converge systematically to CBS limit values of 4.099 (MP2), 4.146 (MP4), 4.233 (CCSD), and 4.167 Å (CCSD(T)). The corresponding CBS limit values of the equilibrium binding energy De are 1.88 (MP2), 1.76 (MP4), 1.41 (CCSD), and 1.69 kcal/mol (CCSD(T)), the latter in excellent agreement with the measured binding energy value of 1.68 ± 0.02 kcal/mol reported by Ciaffoni et al. [Appl. Phys. B 92, 627 (2008)]. Combining CBS electronic binding energies De with EZPE predicted by CCSD(T) vibrational second-order perturbation theory calculations yields Do = 1.08 kcal/mol, which is around 0.6 kcal/mol smaller than the measured value of 1.7 ± 0.3 kcal/mol. Overall, the results presented here demonstrate that the application of high level calculations, in particular CCSD(T), in combination with augmented correlation consistent basis sets provides valuable insight into the structure and energetics of the hydrogen sulfide dimer.
Andrade, Xavier
2013-01-01
We discuss the application of graphical processing units (GPUs) to accelerate real-space density functional theory (DFT) calculations. To make our implementation efficient, we have developed a scheme to expose the data parallelism available in the DFT approach; this is applied to the different procedures required for a real-space DFT calculation. We present results for current-generation GPUs from AMD and Nvidia, which show that our scheme, implemented in the free code OCTOPUS, can reach a sustained performance of up to 90 GFlops for a single GPU, representing an important speed-up when compared to the CPU version of the code. Moreover, for some systems our implementation can outperform a GPU Gaussian basis set code, showing that the real-space approach is a competitive alternative for DFT simulations on GPUs.
Andrade, Xavier; Aspuru-Guzik, Alán
2013-10-01
We discuss the application of graphical processing units (GPUs) to accelerate real-space density functional theory (DFT) calculations. To make our implementation efficient, we have developed a scheme to expose the data parallelism available in the DFT approach; this is applied to the different procedures required for a real-space DFT calculation. We present results for current-generation GPUs from AMD and Nvidia, which show that our scheme, implemented in the free code Octopus, can reach a sustained performance of up to 90 GFlops for a single GPU, representing a significant speed-up when compared to the CPU version of the code. Moreover, for some systems, our implementation can outperform a GPU Gaussian basis set code, showing that the real-space approach is a competitive alternative for DFT simulations on GPUs.
Guan, Qingze; Blume, Doerte
2016-05-01
The explicit correlated Gaussian (ECG) basis set expansion approach is a variational approach that has been used in various areas, including molecular, nuclear, atomic, and chemical physics. In the world of cold atoms, e.g., the ECG approach has been used to calculate the eigenenergies and eigenstates of few-body systems governed by Efimov physics. Since the first experimental realization of synthesized gauge fields, few-body systems with spin-orbit coupling have attracted a great deal of attention. Here, the ECG approach is customized to few-body systems with both short-range interactions and spin-orbit couplings. Benchmark tests and a performance analysis will be presented. Support by the NSF is gratefully acknowledged.
Many-body basis-set reduction applied to the two-dimensional t-Jz model
Riera, J.; Dagotto, E.
1993-06-01
A simple variation of the Lanczos method is discussed. The technique is based on a systematic reduction of the size of the Hilbert space of the model under consideration, and it has many similarities with the basis-set-reduction approach recently introduced by Wenzel and Wilson in the context of quantum chemistry. As an example, the two-dimensional t-Jz model of strongly correlated electrons is studied. Accurate results for the ground-state energy can be obtained on clusters of up to 50 sites, which are unreachable by conventional Lanczos approaches. In particular, the energy of one and two holes is analyzed as a function of Jz/t. In the bulk limit, the numerical results suggest that a finite coupling Jz/t]c~0.18 is necessary to induce ``binding'' of holes in the model.
Daramola, Damilola A; Muthuvel, Madhivanan; Botte, Gerardine G
2010-07-29
Geometry and vibration properties for monoclinic zirconium oxide were studied using Gaussian basis sets and LDA, GGA, and B3LYP functionals. Bond angles, bond lengths, lattice parameters, and Raman frequencies were calculated and compared to experimental values. Bond angles and lengths were found to agree within experimental standard deviations. The B3LYP gave the best performance of all three functionals with a percent error of 1.35% for the lattice parameters while the average difference between experimental and calculated Raman frequency values was -3 cm(-1). The B3LYP functional was then used to assign the atomic vibrations causing each frequency mode using isotopic substitution of (93.40)Zr for (91.22)Zr and (18.00)O for (16.00)O. This resulted in seven modes assigned to the Zr atom, ten modes to the O atom, and one mode being a mixture of both.
Power allocation for non-orthogonal decode-and-forward cooperation protocol
Institute of Scientific and Technical Information of China (English)
ZHANG Yong; XU YouYun; CAI YueMing
2009-01-01
This paper studies the power allocation problem for the non-orthogonal decode-and-forward (NDF) cooperation protocol with selection relaying. With the availability of the magnitudes of all channel gains at the source, the power allocation is explored that maximizes the mutual information between the source and destination subject to a total power constraint. The minimum power that avoids the outage of the relay is set as a condition, under which the power allocation problem becomes one of selecting the optimal one from several allocation factor triplets. It is shown that the power allocation scheme can provide considerable performance gain, and the non-orthogonal cooperation protocol is superior to the orthogonal protocol and direct transmission.
Directory of Open Access Journals (Sweden)
Thiago Prudêncio
2017-01-01
Full Text Available We discuss the modified Maxwell action of a KF-type Lorentz symmetry breaking theory and present a solution of Maxwell equations derived in the cases of linear and elliptically polarized electromagnetic waves in the vacuum of CPT-even Lorentz violation. We show in this case that the Lorentz violation has the effect of changing the amplitude of one component of the magnetic field, while leaving the electric field unchanged, leading to nonorthogonal propagation of electromagnetic fields and dependence of the eccentricity on κ-term. Further, we exhibit numerically the consequences of this effect in the cases of linear and elliptical polarization, in particular, the regimes of nonorthogonality of the electromagnetic wave fields and the eccentricity of the elliptical polarization of the magnetic field with dependence on the κ-term.
Distinguishing between non-orthogonal quantum states of a single spin
Waldherr, Gerald; Neumann, Philipp; Jelezko, Fedor; Andersson, Erika; Wrachtrup, Jorg
2012-01-01
An important task for quantum information processing is optimal discrimination between two non-orthogonal quantum states, which until now has only been realized optically. Here, we present and compare experimental realizations of optimal quantum measurements for distinguishing between two non-orthogonal quantum states encoded in a single ^14 N nuclear spin. Implemented measurement schemes are the minimum-error measurement (known as Helstrom measurement), unambiguous state discrimination using a standard projective mea-surement, and optimal unambiguous state discrimination (known as IDP measurement), which utilizes a three-dimensional Hilbert space. Measurement efficiencies are found to be above 80% for all schemes and reach a value of 90% for the IDP measurement
Practical non-orthogonal decoy state quantum key distribution with heralded single photon source
Institute of Scientific and Technical Information of China (English)
Mi Jing-Long; Wang Fa-Qiang; Lin Qing-Qun; Liang Rui-Sheng
2008-01-01
Recently the performance of the quantum key distribution (QKD) is substantially improved by the decoy state method and the non-orthogonal encoding protocol, separately. In this paper, a practical non-orthogonal decoy state protocol with a heralded single photon source (HSPS) for QKD is presented. The protocol is based on 4 states with different intensities, i.e. one signal state and three decoy states. The signal state is for generating keys; the decoy states arc for detecting the eavesdropping and estimating the fraction of single-photon and two-photon pulses. We have discussed three cases of this protocol, i.e. the general case, the optimal case and the special case. Moreover, the final key rate over transmission distance is simulated. For the low dark count of the HSPS and the utilization of the two-photon pulses, our protocol has a higher key rate and a longer transmission distance than any other decoy state protocol.
Oberhofer, Harald; Blumberger, Jochen
2010-12-01
We present a plane wave basis set implementation for the calculation of electronic coupling matrix elements of electron transfer reactions within the framework of constrained density functional theory (CDFT). Following the work of Wu and Van Voorhis [J. Chem. Phys. 125, 164105 (2006)], the diabatic wavefunctions are approximated by the Kohn-Sham determinants obtained from CDFT calculations, and the coupling matrix element calculated by an efficient integration scheme. Our results for intermolecular electron transfer in small systems agree very well with high-level ab initio calculations based on generalized Mulliken-Hush theory, and with previous local basis set CDFT calculations. The effect of thermal fluctuations on the coupling matrix element is demonstrated for intramolecular electron transfer in the tetrathiafulvalene-diquinone (Q-TTF-Q-) anion. Sampling the electronic coupling along density functional based molecular dynamics trajectories, we find that thermal fluctuations, in particular the slow bending motion of the molecule, can lead to changes in the instantaneous electron transfer rate by more than an order of magnitude. The thermal average, ( { } )^{1/2} = 6.7 {mH}, is significantly higher than the value obtained for the minimum energy structure, | {H_ab } | = 3.8 {mH}. While CDFT in combination with generalized gradient approximation (GGA) functionals describes the intermolecular electron transfer in the studied systems well, exact exchange is required for Q-TTF-Q- in order to obtain coupling matrix elements in agreement with experiment (3.9 mH). The implementation presented opens up the possibility to compute electronic coupling matrix elements for extended systems where donor, acceptor, and the environment are treated at the quantum mechanical (QM) level.
Non-orthogonal optical multicarrier access based on filter bank and SCMA.
Liu, Bo; Zhang, Lijia; Xin, Xiangjun
2015-10-19
This paper proposes a novel non-orthogonal optical multicarrier access system based on filter bank and sparse code multiple access (SCMA). It offers released frequency offset and better spectral efficiency for multicarrier access. An experiment of 73.68 Gb/s filter bank-based multicarrier (FBMC) SCMA system with 60 km single mode fiber link is performed to demonstrate the feasibility. The comparison between fast Fourier transform (FFT) based multicarrier and the proposed scheme is also investigated in the experiment.
Hill, J. Grant; Mazumder, Shivnath; Peterson, Kirk A.
2010-02-01
Correlation consistent basis sets have been optimized for accurately describing core-core and core-valence correlation effects with explicitly correlated F12 methods. The new sets, denoted cc-pCVnZ-F12 (n =D, T, Q) and aug-cc-pCF12VnZ (n =D, T, Q, 5), were developed by augmenting the cc-pVnZ-F12 and aug-cc-pVnZ families of basis sets with additional functions whose exponents were optimized based on the difference between all-electron and valence-electron correlation energies. The number of augmented functions added is fewer, in general, than in the standard cc-pCVnZ and cc-pwCVnZ families of basis sets. Optimal values of the geminal Slater exponent for use with these basis sets in MP2-F12 calculations are presented and are also recommended for CCSD-F12b calculations. Auxiliary basis sets for use in the resolution of the identity approximation in explicitly correlated calculations have also been optimized and matched to the new cc-pCVnZ-F12 series of orbital basis sets. The cc-pCVnZ-F12 basis sets, along with the new auxiliary sets, were benchmarked in CCSD(T)-F12b calculations of spectroscopic properties on a series of homo- and heteronuclear first and second row diatomic molecules. Comparing the effects of correlating the outer core electrons in these molecules with those from conventional CCSD(T) at the complete basis set limit, which involved calculations with new cc-pCV6Z basis sets for the second row elements that were also developed in the course of this work, it is observed that the F12 values are reasonably well converged already at just the triple-ζ level.
Non-orthogonal transmission in multi-user systems with Grassmannian beamforming
Xia, Minghua
2011-06-01
Aiming to achieve the sum-rate capacity in multiuser multi-input multi-output (MIMO) channels with N t antennas implemented at the transmitter, opportunistic beamforming (OBF) generates N t orthonormal beams and serves N t users during each transmission, which results in high scheduling delay over the users, especially in densely populated wireless networks. Non-orthogonal OBF with more than N t transmit beams can be exploited to serve more users simultaneously and further decreases scheduling delay. However, the inter-beam interference will inevitably deteriorate the sum-rate. Therefore, there is a tradeoff between the sum-rate and the increasing number of transmit beams. In this context, the sum-rate of non-orthogonal OBF with N > N t beams are studied, where the transmitter is based on the Grassmannian beamforming. Our results show that non-orthogonal OBF is an interference-limited system. Moreover, when the inter-beam interference reaches its minimum for fixed N t and N, the sum-rate scales as N ln (N/N-N t) and it decreases monotonically with N for fixed N t. Numerical results corroborate the accuracy of our analyses. © 2011 IEEE.
Mao, Yuezhi; Horn, Paul R.; Mardirossian, Narbe; Head-Gordon, Teresa; Skylaris, Chris-Kriton; Head-Gordon, Martin
2016-07-01
Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large atomic orbital basis sets are used. To approach the basis set limit with potentially lower computational cost, a new self-consistent field (SCF) scheme is presented that employs minimal adaptive basis (MAB) functions. The MAB functions are optimized on each atomic site by minimizing a surrogate function. High accuracy is obtained by applying a perturbative correction (PC) to the MAB calculation, similar to dual basis approaches. Compared to exact SCF results, using this MAB-SCF (PC) approach with the same large target basis set produces modern density functionals.
Khvostichenko, Daria; Choi, Andrew; Boulatov, Roman
2008-04-24
We investigated the effect of several computational variables, including the choice of the basis set, application of symmetry constraints, and zero-point energy (ZPE) corrections, on the structural parameters and predicted ground electronic state of model 5-coordinate hemes (iron(II) porphines axially coordinated by a single imidazole or 2-methylimidazole). We studied the performance of B3LYP and B3PW91 with eight Pople-style basis sets (up to 6-311+G*) and B97-1, OLYP, and TPSS functionals with 6-31G and 6-31G* basis sets. Only hybrid functionals B3LYP, B3PW91, and B97-1 reproduced the quintet ground state of the model hemes. With a given functional, the choice of the basis set caused up to 2.7 kcal/mol variation of the quintet-triplet electronic energy gap (DeltaEel), in several cases, resulting in the inversion of the sign of DeltaEel. Single-point energy calculations with triple-zeta basis sets of the Pople (up to 6-311G++(2d,2p)), Ahlrichs (TZVP and TZVPP), and Dunning (cc-pVTZ) families showed the same trend. The zero-point energy of the quintet state was approximately 1 kcal/mol lower than that of the triplet, and accounting for ZPE corrections was crucial for establishing the ground state if the electronic energy of the triplet state was approximately 1 kcal/mol less than that of the quintet. Within a given model chemistry, effects of symmetry constraints and of a "tense" structure of the iron porphine fragment coordinated to 2-methylimidazole on DeltaEel were limited to 0.3 kcal/mol. For both model hemes the best agreement with crystallographic structural data was achieved with small 6-31G and 6-31G* basis sets. Deviation of the computed frequency of the Fe-Im stretching mode from the experimental value with the basis set decreased in the order: nonaugmented basis sets, basis sets with polarization functions, and basis sets with polarization and diffuse functions. Contraction of Pople-style basis sets (double-zeta or triple-zeta) affected the results
Dunn, Meghan E; Pokon, Emma K; Shields, George C
2004-03-03
The Gaussian-2, Gaussian-3, complete basis set- (CBS-) QB3, and CBS-APNO methods have been used to calculate Delta H degrees and Delta G degrees values for neutral clusters of water, (H(2)O)(n), where n = 2-6. The structures are similar to those determined from experiment and from previous high-level calculations. The thermodynamic calculations by the G2, G3, and CBS-APNO methods compare well against the estimated MP2(CBS) limit. The cyclic pentamer and hexamer structures release the most heat per hydrogen bond formed of any of the clusters. While the cage and prism forms of the hexamer are the lowest energy structures at very low temperatures, as temperature is increased the cyclic structure is favored. The free energies of cluster formation at different temperatures reveal interesting insights, the most striking being that the cyclic trimer, cyclic tetramer, and cyclic pentamer, like the dimer, should be detectable in the lower troposphere. We predict water dimer concentrations of 9 x 10(14) molecules/cm(3), water trimer concentrations of 2.6 x 10(12) molecules/cm(3), tetramer concentrations of approximately 5.8 x 10(11) molecules/cm(3), and pentamer concentrations of approximately 3.5 x 10(10) molecules/cm(3) in saturated air at 298 K. These results have important implications for understanding the gas-phase chemistry of the lower troposphere.
DEFF Research Database (Denmark)
Faber, Rasmus; Buczek, Aneta; Kupka, Teobald;
2016-01-01
convergence of the vibrational corrections is not monotonic and that very large basis sets are needed before a reasonable extrapolation to the basis set limit can be performed. Furthermore, our results suggest that coupled cluster methods and a decent basis set are required before the error of the electronic......The method and basis set dependence of zero-point vibrational corrections (ZPVC) to NMR shielding constants and anisotropies has been investigated using water as a test system. A systematic comparison has been made using the Hartree-Fock (HF), second-order Møller-Plesset perturbation theory (MP2......), coupled cluster singles and doubles (CCSD), coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)) and Kohn-Sham density functional theory (DFT) with the B3LYP exchange-correlation functional methods in combination with the second order vibrational perturbation theory (VPT2...
Mao, Yuezhi; Horn, Paul R; Mardirossian, Narbe; Head-Gordon, Teresa; Skylaris, Chris-Kriton; Head-Gordon, Martin
2016-07-28
Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large atomic orbital basis sets are used. To approach the basis set limit with potentially lower computational cost, a new self-consistent field (SCF) scheme is presented that employs minimal adaptive basis (MAB) functions. The MAB functions are optimized on each atomic site by minimizing a surrogate function. High accuracy is obtained by applying a perturbative correction (PC) to the MAB calculation, similar to dual basis approaches. Compared to exact SCF results, using this MAB-SCF (PC) approach with the same large target basis set produces set limit can be even better reproduced. With further improvement to its implementation, MAB-SCF (PC) is a promising lower-cost substitute for conventional large-basis calculations as a method to approach the basis set limit of modern density functionals.
Petit, Laurence; Maldivi, Pascale; Adamo, Carlo
2005-09-01
The calculation of the absorption spectra of four families of transition-metal complexes (Ni(CO)4, MnO4(-), MF6 (M = Cr, Mo, W) and CpM(CO)2 (M = Rh, Ir)) has been undertaken to unravel the influence of basis sets onto excitation energies, oscillator strengths, and assignments. Three among the most common pseudopotentials, with the corresponding valence basis sets, and two all-electron basis sets have been used for the metal center description in the framework of the time dependent Density Functional Theory (TD-DFT). Our results show that this approach does not particularly depend on the basis set used on the metal atoms. Furthermore, the chosen functional PBE0 provides transitions in good agreement with experiments, and it provides an accuracy of about 0.3 eV, comparable to that of refined post-Hartree-Fock methods.
Teodoro, Tiago Quevedo; Visscher, Lucas; da Silva, Albérico Borges Ferreira; Haiduke, Roberto Luiz Andrade
2017-01-06
The f-block elements are addressed in this third part of a series of prolapse-free basis sets of quadruple-ζ quality (RPF-4Z). Relativistic adapted Gaussian basis sets (RAGBSs) are used as primitive sets of functions while correlating/polarization (C/P) functions are chosen by analyzing energy lowerings upon basis set increments in Dirac-Coulomb multireference configuration interaction calculations with single and double excitations of the valence spinors. These function exponents are obtained by applying the RAGBS parameters in a polynomial expression. Moreover, through the choice of C/P characteristic exponents from functions of lower angular momentum spaces, a reduction in the computational demand is attained in relativistic calculations based on the kinetic balance condition. The present study thus complements the RPF-4Z sets for the whole periodic table (Z ≤ 118). The sets are available as Supporting Information and can also be found at http://basis-sets.iqsc.usp.br .
Buczek, Aneta; Kupka, Teobald; Broda, Małgorzata A; Żyła, Adriana
2016-01-01
In this work, regular convergence patterns of the structural, harmonic, and VPT2-calculated anharmonic vibrational parameters of ethylene towards the Kohn-Sham complete basis set (KS CBS) limit are demonstrated for the first time. The performance of the VPT2 scheme implemented using density functional theory (DFT-BLYP and DFT-B3LYP) in combination with two Pople basis sets (6-311++G** and 6-311++G(3df,2pd)), the polarization-consistent basis sets pc-n, aug-pc-n, and pcseg-n (n = 0, 1, 2, 3, 4), and the correlation-consistent basis sets cc-pVXZ and aug-cc-pVXZ (X = D, T, Q, 5, 6) was tested.The BLYP-calculated harmonic frequencies were found to be markedly closer than the B3LYP-calculated harmonic frequencies to the experimentally derived values, while the calculated anharmonic frequencies consistently underestimated the observed wavenumbers. The different basis set families gave very similar estimated values for the CBS parameters. The anharmonic frequencies calculated with B3LYP/aug-pc-3 were consistently significantly higher than those obtained with the pc-3 basis set; applying the aug-pcseg-n basis set family alleviated this problem. Utilization of B3LYP/aug-pcseg-n basis sets instead of B3LYP/aug-cc-pVXZ, which is computationally less expensive, is suggested for medium-sized molecules. Harmonic BLYP/pc-2 calculations produced fairly accurate ethylene frequencies. Graphical Abstract In this study, the performance of the VPT2 scheme implemented using density functional theory (DFT-BLYP and DFT-B3LYP) in combination with the polarization-consistent basis sets pc-n, aug-pc-n, and pcseg-n (n = 0, 1, 2, 3, 4), and the correlation-consistent basis sets cc-pVXZ and aug-cc-pVXZ (X = D, T, Q, 5, and 6) was tested. For the first time, we demonstrated regular convergence patterns of the structural, harmonic, and VPT2-calculated anharmonic vibrational parameters of ethylene towards the Kohn-Sham complete basis set (KS CBS) limit.
Directory of Open Access Journals (Sweden)
Claudio Amovilli
2016-02-01
Full Text Available In this work, we present a simple decomposition scheme of the Kohn-Sham optimized orbitals which is able to provide a reduced basis set, made of localized polycentric orbitals, specifically designed for Quantum Monte Carlo. The decomposition follows a standard Density functional theory (DFT calculation and is based on atomic connectivity and shell structure. The new orbitals are used to construct a compact correlated wave function of the Slater–Jastrow form which is optimized at the Variational Monte Carlo level and then used as the trial wave function for a final Diffusion Monte Carlo accurate energy calculation. We are able, in this way, to capture the basic information on the real system brought by the Kohn-Sham orbitals and use it for the calculation of the ground state energy within a strictly variational method. Here, we show test calculations performed on some small selected systems to assess the validity of the proposed approach in a molecular fragmentation, in the calculation of a barrier height of a chemical reaction and in the determination of intermolecular potentials. The final Diffusion Monte Carlo energies are in very good agreement with the best literature data within chemical accuracy.
Wang, Yang; Liu, Qingzhu; Qiu, Ling; Wang, Tengfei; Yuan, Haoliang; Lin, Jianguo; Luo, Shineng
2015-01-01
Three different density functional theory (DFT) methods were employed to study the molecular structures of cis-diamminedichloroplatinum(II) (CDDP) and trans-diamminedichloroplatinum(II) (TDDP). The basis set effect on the structure was also investigated. By comparing the optimized structures with the experimental data, a relatively more accurate method was chosen for further study of the IR spectra and other properties as well as the solvent effect. Nineteen characteristic vibrational bands of the title compounds were assigned and compared with available experimental data. The number of characteristic peaks for the asymmetric stretching and deformation vibrations of N-H can serve as a judgment for the isomer between CDDP and TDDP. Significant solvent effect was observed on the molecular structures and IR spectra. The reduced density gradient analysis was performed to study the intramolecular interactions of CDDP and TDDP, and the nature of changes in the structures caused by the solvent was illustrated. Several descriptors determined from the energies of frontier molecular orbitals (HOMO and LUMO) were applied to describe the chemical reactivity of the title compounds. The molecular electrostatic potential (MESP) surfaces showed that the amino groups were the most favorable sites that nucleophilic reagents tend to attack, and CDDP was easier to be attacked by nucleophilic reagents than TDDP.
Berski, Slawomir; Latajka, Zdzislaw; Gordon, Agnieszka J
2010-11-15
The article focus on the isomerization of nitrous acid HONO to hydrogen nitryl HNO(2). Density functional (B3LYP) and MP2 methods, and a wide variety of basis sets, have been chosen to investigate the mechanism of this reaction. The results clearly show that there are two possible paths: 1) Uncatalysed isomerisation, trans-HONO --> HNO(2), involving 1,2-hydrogen shift and characterized by a large energetic barrier 49.7 divided by 58.9 kcal/mol, 2) Catalysed double hydrogen transfer process, trans-HONO + cis-HONO --> HNO(2) + cis-HONO, which displays a significantly lower energetic barrier in a range of 11.6 divided by 18.9 kcal/mol. Topological analysis of the Electron Localization Function (ELF) shows that the hydrogen transfer for both studied reactions takes place through the formation of a 'dressed' proton along the reaction path. Use of a wide variety of basis sets demonstrates a clear basis set dependence on the ELF topology of HNO(2). Less saturated basis sets yield two lone pair basins, V(1)(N), V(2)(N), whereas more saturated ones (for example aug-cc-pVTZ and aug-cc-pVQZ) do not indicate a lone pair on the nitrogen atom. Topological analysis of the Electron Localizability Indication (ELI-D) at the CASSCF (12,10) confirms these findings, showing the existence of the lone pair basins but with decreasing populations as the basis set becomes more saturated (0.35e for the cc-pVDZ basis set to 0.06e for the aug-cc-pVTZ). This confirms that the choice of basis set not only can influence the value of the electron population at the particular atom, but can also lead to different ELF topology. 2010 Wiley Periodicals, Inc.
Directory of Open Access Journals (Sweden)
Fabien Cignetti
2016-07-01
Full Text Available Conventional analysis of functional magnetic resonance imaging (fMRI data using the general linear model (GLM employs a neural model convolved with a canonical hemodynamic response function (HRF peaking 5s after stimulation. Incorporation of a further basis function, namely the canonical HRF temporal derivative, accounts for delays in the hemodynamic response to neural activity. A population that may benefit from this flexible approach is children whose hemodynamic response is not yet mature. Here, we examined the effects of using the set based on the canonical HRF plus its temporal derivative on both first- and second-level GLM analyses, through simulations and using developmental data (an fMRI dataset on proprioceptive mapping in children and adults. Simulations of delayed fMRI first-level data emphasized the benefit of carrying forward to the second-level a derivative boost that combines derivative and nonderivative beta estimates. In the experimental data, second-level analysis using a paired t-test showed increased mean amplitude estimate (i.e., increased group contrast mean in several brain regions related to proprioceptive processing when using the derivative boost compared to using only the nonderivative term. This was true especially in children. However, carrying forward to the second-level the individual derivative boosts had adverse consequences on random-effects analysis that implemented one-sample t-test, yielding increased between-subject variance, thus affecting group-level statistic. Boosted data also presented a lower level of smoothness that had implication for the detection of group average activation. Imposing soft constraints on the derivative boost by limiting the time-to-peak range of the modelled response within a specified range (i.e., 4-6s mitigated these issues. These findings support the notion that there are pros and cons to using the informed basis set with developmental data.
Li, Ji-Lai; Mata, Ricardo A; Ryde, Ulf
2013-03-12
The oxygen-atom transfer reaction catalyzed by the mononuclear molybdenum enzyme dimethyl sulfoxide reductase (DMSOR) has attracted considerable attention through both experimental and theoretical studies. We show here that this reaction is more sensitive to details of quantum mechanical calculations than what has previously been appreciated. Basis sets of at least triple-ζ quality are needed to obtain qualitatively correct results. Dispersion has an appreciable effect on the reaction, in particular the binding of the substrate or the dissociation of the product (up to 34 kJ/mol). Polar and nonpolar solvation effects are also significant, especially if the enzyme can avoid cavitation effects by using a preformed active-site cavity. Relativistic effects are considerable (up to 22 kJ/mol), but they are reasonably well treated by a relativistic effective core potential. Various density-functional methods give widely different results for the activation and reaction energy (differences of over 100 kJ/mol), mainly reflecting the amount of exact exchange in the functional, owing to the oxidation of Mo from +IV to +VI. By calibration toward local CCSD(T0) calculations, we show that none of eight tested functionals (TPSS, BP86, BLYP, B97-D, TPSSH, B3LYP, PBE0, and BHLYP) give accurate energies for all states in the reaction. Instead, B3LYP gives the best activation barrier, whereas pure functionals give more accurate energies for the other states. Our best results indicate that the enzyme follows a two-step associative reaction mechanism with an overall activation enthalpy of 63 kJ/mol, which is in excellent agreement with the experimental results.
Cignetti, Fabien; Salvia, Emilie; Anton, Jean-Luc; Grosbras, Marie-Hélène; Assaiante, Christine
2016-01-01
Conventional analysis of functional magnetic resonance imaging (fMRI) data using the general linear model (GLM) employs a neural model convolved with a canonical hemodynamic response function (HRF) peaking 5 s after stimulation. Incorporation of a further basis function, namely the canonical HRF temporal derivative, accounts for delays in the hemodynamic response to neural activity. A population that may benefit from this flexible approach is children whose hemodynamic response is not yet mature. Here, we examined the effects of using the set based on the canonical HRF plus its temporal derivative on both first- and second-level GLM analyses, through simulations and using developmental data (an fMRI dataset on proprioceptive mapping in children and adults). Simulations of delayed fMRI first-level data emphasized the benefit of carrying forward to the second-level a derivative boost that combines derivative and nonderivative beta estimates. In the experimental data, second-level analysis using a paired t-test showed increased mean amplitude estimate (i.e., increased group contrast mean) in several brain regions related to proprioceptive processing when using the derivative boost compared to using only the nonderivative term. This was true especially in children. However, carrying forward to the second-level the individual derivative boosts had adverse consequences on random-effects analysis that implemented one-sample t-test, yielding increased between-subject variance, thus affecting group-level statistic. Boosted data also presented a lower level of smoothness that had implication for the detection of group average activation. Imposing soft constraints on the derivative boost by limiting the time-to-peak range of the modeled response within a specified range (i.e., 4-6 s) mitigated these issues. These findings support the notion that there are pros and cons to using the informed basis set with developmental data.
PO Analysis for RCS of Nonorthogonal Dihedral Corner Reflectors Coated by RAM
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The backscattering radar cross section (RCS) of nonorthogonal dihedral corner reflectors coated by RAM (radar absorbing materials) is formulated by the method of PO (physical optics), where singly, doubly, and triply reflected contributions are considered. The final expressions are analytical and allow for the incidence nonperpendicular to the fold axis of the reflector. The results are compared with ones of MoM (method of moment), which shows that the trend of backscatter patterr of the dihedral corner reflector can be well predicted by this method.
Non-orthogonal configuration interaction for the calculation of multielectron excited states
Sundstrom, Eric J.; Head-Gordon, Martin
2014-03-01
We apply Non-orthogonal Configuration Interaction (NOCI) to molecular systems where multielectron excitations, in this case double excitations, play a substantial role: the linear polyenes and β-carotene. We demonstrate that NOCI when applied to systems with extended conjugation, provides a qualitatively correct wavefunction at a fraction of the cost of many other multireference treatments. We also present a new extension to this method allowing for purification of higher-order spin states by utilizing Generalized Hartree-Fock Slater determinants and the details for computing ⟨S2⟩ for the ground and excited states.
Non-orthogonal configuration interaction for the calculation of multielectron excited states
Energy Technology Data Exchange (ETDEWEB)
Sundstrom, Eric J., E-mail: eric.jon.sundstrom@berkeley.edu; Head-Gordon, Martin [Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)
2014-03-21
We apply Non-orthogonal Configuration Interaction (NOCI) to molecular systems where multielectron excitations, in this case double excitations, play a substantial role: the linear polyenes and β-carotene. We demonstrate that NOCI when applied to systems with extended conjugation, provides a qualitatively correct wavefunction at a fraction of the cost of many other multireference treatments. We also present a new extension to this method allowing for purification of higher-order spin states by utilizing Generalized Hartree-Fock Slater determinants and the details for computing 〈S{sup 2}〉 for the ground and excited states.
Fairness for Non-Orthogonal Multiple Access in 5G Systems
Timotheou, Stelios; Krikidis, Ioannis
2015-10-01
In non-orthogonal multiple access (NOMA) downlink, multiple data flows are superimposed in the power domain and user decoding is based on successive interference cancellation. NOMA's performance highly depends on the power split among the data flows and the associated power allocation (PA) problem. In this letter, we study NOMA from a fairness standpoint and we investigate PA techniques that ensure fairness for the downlink users under i) instantaneous channel state information (CSI) at the transmitter, and ii) average CSI. Although the formulated problems are non-convex, we have developed low-complexity polynomial algorithms that yield the optimal solution in both cases considered.
Paschoal, Diego; Marcial, Bruna L; Lopes, Juliana Fedoce; De Almeida, Wagner B; Dos Santos, Hélio F
2012-11-05
In this article, we conducted an extensive ab initio study on the importance of the level of theory and the basis set for theoretical predictions of the structure and reactivity of cisplatin [cis-diamminedichloroplatinum(II) (cDDP)]. Initially, the role of the basis set for the Pt atom was assessed using 24 different basis sets, including three all-electron basis sets (ABS). In addition, a modified all-electron double zeta polarized basis set (mDZP) was proposed by adding a set of diffuse d functions onto the existing DZP basis set. The energy barrier and the rate constant for the first chloride/water exchange ligand process, namely, the aquation reaction, were taken as benchmarks for which reliable experimental data are available. At the B3LYP/mDZP/6-31+G(d) level (the first basis set is for Pt and the last set is for all of the light atoms), the energy barrier was 22.8 kcal mol(-1), which is in agreement with the average experimental value, 22.9 ± 0.4 kcal mol(-1). For the other accessible ABS (DZP and ADZP), the corresponding values were 15.4 and 24.5 kcal mol(-1), respectively. The ADZP and mDZP are notably similar, raising the importance of diffuse d functions for the prediction of the kinetic properties of cDDP. In this article, we also analyze the ligand basis set and the level of theory effects by considering 36 basis sets at distinct levels of theory, namely, Hartree-Fock, MP2, and several DFT functionals. From a survey of the data, we recommend the mPW1PW91/mDZP/6-31+G(d) or B3PW91/mDZP/6-31+G(d) levels to describe the structure and reactivity of cDDP and its small derivatives. Conversely, for large molecules containing a cisplatin motif (for example, the cDDP-DNA complex), the lower levels B3LYP/LANL2DZ/6-31+G(d) and B3LYP/SBKJC-VDZ/6-31+G(d) are suggested. At these levels of theory, the predicted energy barrier was 26.0 and 25.9 kcal mol(-1), respectively, which is only 13% higher than the actual value.
Martin, J M L; Martin, Jan M.L.; Sundermann, Andreas
2001-01-01
We propose large-core correlation-consistent pseudopotential basis sets for the heavy p-block elements Ga-Kr and In-Xe. The basis sets are of cc-pVTZ and cc-pVQZ quality, and have been optimized for use with the large-core (valence-electrons only) Stuttgart-Dresden-Bonn relativistic pseudopotentials. Validation calculations on a variety of third-row and fourth-row diatomics suggest them to be comparable in quality to the all-electron cc-pVTZ and cc-pVQZ basis sets for lighter elements. Especially the SDB-cc-pVQZ basis set in conjunction with a core polarization potential (CPP) yields excellent agreement with experiment for compounds of the later heavy p-block elements. For accurate calculations on Ga (and, to a lesser extent, Ge) compounds, explicit treatment of 13 valence electrons appears to be desirable, while it seems inevitable for In compounds. For Ga and Ge, we propose correlation consistent basis sets extended for (3d) correlation. For accurate calculations on organometallic complexes of interest to h...
Boström, Jonas; Pitoňák, Michal; Aquilante, Francesco; Neogrády, Pavel; Pedersen, Thomas Bondo; Lindh, Roland
2012-06-12
We compute noncovalent intermolecular interaction energies for the S22 test set [Phys. Chem. Chem. Phys.2006, 8, 1985-1993] of molecules at the Møller-Plesset and coupled cluster levels of supermolecular theory using density fitting (DF) to approximate all two-electron integrals. The error due to the DF approximation is analyzed for a range of auxiliary basis sets derived from Cholesky decomposition (CD) in conjunction with correlation consistent and atomic natural orbital valence basis sets. A Cholesky decomposition threshold of 10(-4)Eh for full molecular CD and its one-center approximation (1C-CD) generally yields errors below 0.03 kcal/mol, whereas 10(-3)Eh is sufficient to obtain the same level of accuracy or better with the atomic CD (aCD) and atomic compact CD (acCD) auxiliary basis sets. Comparing to commonly used predefined auxiliary basis sets, we find that while the aCD and acCD sets are larger by a factor of 2-4 with triple-ζ AO basis sets, they provide results 1-2 orders of magnitude more accurate.
Orthogonal functions, discrete variable representation, and generalized gauss quadratures
DEFF Research Database (Denmark)
Schneider, B. I.; Nygaard, Nicolai
2002-01-01
The numerical solution of most problems in theoretical chemistry involve either the use of a basis set expansion (spectral method) or a numerical grid. For many basis sets, there is an intimate connection between the spectral form and numerical quadrature. When this connection exists, the distinc......The numerical solution of most problems in theoretical chemistry involve either the use of a basis set expansion (spectral method) or a numerical grid. For many basis sets, there is an intimate connection between the spectral form and numerical quadrature. When this connection exists...... in the original representation. This has been exploited in bound-state, scattering, and time-dependent problems using the so-called, discrete variable representation (DVR). At the core of this approach is the mathematical three-term recursion relationship satisfied by the classical orthogonal functions...
López Arvizu, Gregorio; Calaminici, Patrizia
2007-05-21
Density functional calculations have been performed for small nickel clusters, Ni(n), Ni(n) (+), and Ni(n)(-) (ntheory approach. Newly developed nickel all-electron basis sets optimized for generalized gradient approximation (GGA) as well as an all-electron basis set optimized for the local density approximation were employed. For both neutral and charged systems, several isomers and different multiplicities were studied in order to determine the lowest energy structures. A vibrational analysis was performed in order to characterize these isomers. Structural parameters, harmonic frequencies, binding energies, ionization potentials, and electron affinities are reported. This work shows that the employed GGA basis sets for the nickel atom are important for the correct prediction of the ground state structures of small nickel clusters and that the structural assignment of these systems can be performed, with a good resolution, over the ionization potential.
Study on the SVPWM algorithm of N-level Inverter in the context of non-orthogonal coordinates
Institute of Scientific and Technical Information of China (English)
XIAO Xiang-ning; JIANG Xu; LIU Hao; LIU Hui-wei; KONG Sheng-li
2006-01-01
In this paper,the authors propose a new space vector pulse width modulation (SVPWM) algorithm based on non-orthogonal coordinates for N-level inverters.First,it is pointed out that classical aft coordinates-based SVPWM has many shortcomings because of improper coordinate choice.Then,a non-orthogonal coordinates-based SVPWM is proposed to solve these problems.The proposed algorithm can easily identify which sector the reference space vector falls in and conduct simple operations to find the duty cycle of each vector.Finally,it is verified that the proposed SVPWM is actually a pulse-width modulation (PWM) technology based on line voltages.
A novel calibration method for non-orthogonal shaft laser theodolite measurement system
Energy Technology Data Exchange (ETDEWEB)
Wu, Bin, E-mail: wubin@tju.edu.cn, E-mail: xueting@tju.edu.cn; Yang, Fengting; Ding, Wen [State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 300072 (China); Xue, Ting, E-mail: wubin@tju.edu.cn, E-mail: xueting@tju.edu.cn [College of Electrical Engineering and Automation, Tianjin Key Laboratory of Process Measurement and Control, Tianjin University, Tianjin 300072 (China)
2016-03-15
Non-orthogonal shaft laser theodolite (N-theodolite) is a new kind of large-scale metrological instrument made up by two rotary tables and one collimated laser. There are three axes for an N-theodolite. According to naming conventions in traditional theodolite, rotary axes of two rotary tables are called as horizontal axis and vertical axis, respectively, and the collimated laser beam is named as sight axis. And the difference between N-theodolite and traditional theodolite is obvious, since the former one with no orthogonal and intersecting accuracy requirements. So the calibration method for traditional theodolite is no longer suitable for N-theodolite, while the calibration method applied currently is really complicated. Thus this paper introduces a novel calibration method for non-orthogonal shaft laser theodolite measurement system to simplify the procedure and to improve the calibration accuracy. A simple two-step process, calibration for intrinsic parameters and for extrinsic parameters, is proposed by the novel method. And experiments have shown its efficiency and accuracy.
A novel calibration method for non-orthogonal shaft laser theodolite measurement system
Wu, Bin; Yang, Fengting; Ding, Wen; Xue, Ting
2016-03-01
Non-orthogonal shaft laser theodolite (N-theodolite) is a new kind of large-scale metrological instrument made up by two rotary tables and one collimated laser. There are three axes for an N-theodolite. According to naming conventions in traditional theodolite, rotary axes of two rotary tables are called as horizontal axis and vertical axis, respectively, and the collimated laser beam is named as sight axis. And the difference between N-theodolite and traditional theodolite is obvious, since the former one with no orthogonal and intersecting accuracy requirements. So the calibration method for traditional theodolite is no longer suitable for N-theodolite, while the calibration method applied currently is really complicated. Thus this paper introduces a novel calibration method for non-orthogonal shaft laser theodolite measurement system to simplify the procedure and to improve the calibration accuracy. A simple two-step process, calibration for intrinsic parameters and for extrinsic parameters, is proposed by the novel method. And experiments have shown its efficiency and accuracy.
Institute of Scientific and Technical Information of China (English)
G(U)M(U)(S), Sedat; (O)ZDO(G)AN, Telhat
2004-01-01
Hartree-Fock-Roothaan (HFR) calculations for ground states of some atoms, i.e. He, Be, Ne, Ar, and Kr have been performed using minimal basis sets of Slater type orbitals (STOs) with integer and noninteger principal quantum numbers (integer n-STOs and noninteger n-STOs). The obtained total energies for these atoms using minimal basis sets of integer n-STOs are in good agreement with those in the previous literature. On the other hand, for the case of minimal basis sets of noninteger n-STOs, although the calculated total energies of these atoms agree well with the results in literature, some striking results have been obtained for atoms Ar and Kr. Our computational results for the energies of atoms Ar and Kr are slightly better than those in literature, by amount of 0.00222 and 0.000054 a.u., respectively. The improvement in the energies of atoms Ar and Kr may result from the efficient calculations of one-center two-electron integrals over noninteger n-STOs. For some atomic ions in their ground state,HFR calculations have been carried out using minimal basis sets of noninteger n-STOs. The obtained total energies for these atomic ions are substantially lower than those available in literature.
Energy Technology Data Exchange (ETDEWEB)
Alam, T.M.
1998-09-01
The influence of changes in the contracted Gaussian basis set used for ab initio calculations of nuclear magnetic resonance (NMR) phosphorous chemical shift anisotropy (CSA) tensors was investigated. The isotropic chemical shitl and chemical shift anisotropy were found to converge with increasing complexity of the basis set at the Hartree-Fock @IF) level. The addition of d polarization function on the phosphorous nucIei was found to have a major impact of the calculated chemical shi~ but diminished with increasing number of polarization fimctions. At least 2 d polarization fimctions are required for accurate calculations of the isotropic phosphorous chemical shift. The introduction of density fictional theory (DFT) techniques through tie use of hybrid B3LYP methods for the calculation of the phosphorous chemical shift tensor resulted in a poorer estimation of the NMR values, even though DFT techniques result in improved energy and force constant calculations. The convergence of the W parametem with increasing basis set complexity was also observed for the DFT calculations, but produced results with consistent large deviations from experiment. The use of a HF 6-31 l++G(242p) basis set represents a good compromise between accuracy of the simulation and the complexity of the calculation for future ab initio calculations of 31P NMR parameters in larger complexes.
Champagne, Benoı̂t; Botek, Edith; Nakano, Masayoshi; Nitta, Tomoshige; Yamaguchi, Kizashi
2005-03-01
The basis set and electron correlation effects on the static polarizability (α) and second hyperpolarizability (γ) are investigated ab initio for two model open-shell π-conjugated systems, the C5H7 radical and the C6H8 radical cation in their doublet state. Basis set investigations evidence that the linear and nonlinear responses of the radical cation necessitate the use of a less extended basis set than its neutral analog. Indeed, double-zeta-type basis sets supplemented by a set of d polarization functions but no diffuse functions already provide accurate (hyper)polarizabilities for C6H8 whereas diffuse functions are compulsory for C5H7, in particular, p diffuse functions. In addition to the 6-31G*+pd basis set, basis sets resulting from removing not necessary diffuse functions from the augmented correlation consistent polarized valence double zeta basis set have been shown to provide (hyper)polarizability values of similar quality as more extended basis sets such as augmented correlation consistent polarized valence triple zeta and doubly augmented correlation consistent polarized valence double zeta. Using the selected atomic basis sets, the (hyper)polarizabilities of these two model compounds are calculated at different levels of approximation in order to assess the impact of including electron correlation. As a function of the method of calculation antiparallel and parallel variations have been demonstrated for α and γ of the two model compounds, respectively. For the polarizability, the unrestricted Hartree-Fock and unrestricted second-order Møller-Plesset methods bracket the reference value obtained at the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples level whereas the projected unrestricted second-order Møller-Plesset results are in much closer agreement with the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples values than the projected unrestricted Hartree
Duguet, T
2003-01-01
The Goldstone-Brueckner perturbation theory is extended to incorporate in a simple way correlations associated with large amplitude collective motions in nuclei. The new energy expansion making use of non-orthogonal vacua still allows to remove the divergences originating from the hard-core of the bare interaction. This is done through the definition of a new Brueckner matrix summing generalized Brueckner ladders. At the lowest-order, this formalism motivates variational calculations beyond the mean-field such as the Generator Coordinate Method (GCM) and the Projected Mean-Field Method from a perturbative point of view for the first time. Going to higher orders amounts to incorporate diabatic effects in the GCM and to extend the projection technique from product states to well-defined correlated states.
Efficient computation of Hamiltonian matrix elements between non-orthogonal Slater determinants
Utsuno, Yutaka; Otsuka, Takaharu; Abe, Takashi
2012-01-01
We present an efficient numerical method for computing Hamiltonian matrix elements between non-orthogonal Slater determinants, focusing on the most time-consuming component of the calculation that involves a sparse array. In the usual case where many matrix elements should be calculated, this computation can be transformed into a multiplication of dense matrices. It is demonstrated that the present method based on the matrix-matrix multiplication attains $\\sim$80\\% of the theoretical peak performance measured on systems equipped with modern microprocessors, a factor of 5-10 better than the normal method using indirectly indexed arrays to treat a sparse array. The reason for such different performances is discussed from the viewpoint of memory access.
Time-dependent density functional theory quantum transport simulation in non-orthogonal basis.
Kwok, Yan Ho; Xie, Hang; Yam, Chi Yung; Zheng, Xiao; Chen, Guan Hua
2013-12-14
Basing on the earlier works on the hierarchical equations of motion for quantum transport, we present in this paper a first principles scheme for time-dependent quantum transport by combining time-dependent density functional theory (TDDFT) and Keldysh's non-equilibrium Green's function formalism. This scheme is beyond the wide band limit approximation and is directly applicable to the case of non-orthogonal basis without the need of basis transformation. The overlap between the basis in the lead and the device region is treated properly by including it in the self-energy and it can be shown that this approach is equivalent to a lead-device orthogonalization. This scheme has been implemented at both TDDFT and density functional tight-binding level. Simulation results are presented to demonstrate our method and comparison with wide band limit approximation is made. Finally, the sparsity of the matrices and computational complexity of this method are analyzed.
Chen, Y. S.
1986-03-01
In this report, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BFC) systems has been developed. The equations of motion are transformed to a generalized curvilinear coordinate system from which the transformed equations are discretized using finite difference approximations in the transformed domain. The hybrid scheme is used to approximate the convection terms in the governing equations. Solutions of the finite difference equations are obtained iteratively by using a pressure-velocity correction algorithm (SIMPLE-C). Numerical examples of two- and three-dimensional, laminar and turbulent flow problems are employed to evaluate the accuracy and efficiency of the present computer code. The user's guide and computer program listing of the present code are also included.
Energy Technology Data Exchange (ETDEWEB)
Kedgley, Angela E.; Jenkyn, Thomas R. [Department of Mechanical and Materials Engineering, Faculty of Engineering, University of Western Ontario, London, Ontario N6A 5B9 (Canada); Wolf Orthopaedic Biomechanics Laboratory, Fowler Kennedy Sport Medicine Clinic, London, Ontario N6A 5B9 (Canada); Department of Mechanical and Materials Engineering, Faculty of Engineering, University of Western Ontario, London, Ontario N6A 5B9 (Canada) and School of Kinesiology, Faculty of Health Sciences, University of Western Ontario, London, Ontario N6A 5B9 (Canada)
2009-07-15
When performing radiostereometric analysis (RSA) in a clinical setting it may be desirable to orient the two imaging devices nonorthogonally to obtain the best views of an anatomical structure. In this study, a calibration frame was constructed that allowed the relative angles of fiducial and control planes to be adjusted. Precision and accuracy were quantified across multiple trials and orientations. The 90 deg. frame was always of equivalent or greater accuracy than a calibration frame with the fiducial and control planes aligned parallel to the image intensifiers. This study also showed that RSA may be performed with imaging devices at relative angles other than 90 deg. without compromising accuracy. This allows researchers greater freedom in positioning equipment.
Rocca, Dario
2014-05-14
A new ab initio approach is introduced to compute the correlation energy within the adiabatic connection fluctuation dissipation theorem in the random phase approximation. First, an optimally small basis set to represent the response functions is obtained by diagonalizing an approximate dielectric matrix containing the kinetic energy contribution only. Then, the Lanczos algorithm is used to compute the full dynamical dielectric matrix and the correlation energy. The convergence issues with respect to the number of empty states or the dimension of the basis set are avoided and the dynamical effects are easily kept into account. To demonstrate the accuracy and efficiency of this approach the binding curves for three different configurations of the benzene dimer are computed: T-shaped, sandwich, and slipped parallel.
Sure, Rebecca; Brandenburg, Jan Gerit; Grimme, Stefan
2016-04-01
In quantum chemical computations the combination of Hartree-Fock or a density functional theory (DFT) approximation with relatively small atomic orbital basis sets of double-zeta quality is still widely used, for example, in the popular B3LYP/6-31G* approach. In this Review, we critically analyze the two main sources of error in such computations, that is, the basis set superposition error on the one hand and the missing London dispersion interactions on the other. We review various strategies to correct those errors and present exemplary calculations on mainly noncovalently bound systems of widely varying size. Energies and geometries of small dimers, large supramolecular complexes, and molecular crystals are covered. We conclude that it is not justified to rely on fortunate error compensation, as the main inconsistencies can be cured by modern correction schemes which clearly outperform the plain mean-field methods.
Al-Saidi, W A; Krakauer, Henry; Zhang, Shiwei
2007-05-21
The authors present phaseless auxiliary-field (AF) quantum Monte Carlo (QMC) calculations of the ground states of some hydrogen-bonded systems. These systems were selected to test and benchmark different aspects of the new phaseless AF QMC method. They include the transition state of H+H(2) near the equilibrium geometry and in the van der Walls limit, as well as the H(2)O, OH, and H(2)O(2) molecules. Most of these systems present significant challenges for traditional independent-particle electronic structure approaches, and many also have exact results available. The phaseless AF QMC method is used either with a plane wave basis with pseudopotentials or with all-electron Gaussian basis sets. For some systems, calculations are done with both to compare and characterize the performance of AF QMC under different basis sets and different Hubbard-Stratonovich decompositions. Excellent results are obtained using as input single Slater determinant wave functions taken from independent-particle calculations. Comparisons of the Gaussian based AF QMC results with exact full configuration interaction show that the errors from controlling the phase problem with the phaseless approximation are small. At the large basis-size limit, the AF QMC results using both types of basis sets are in good agreement with each other and with experimental values.
Witte, Jonathon; Neaton, Jeffrey B.; Head-Gordon, Martin
2017-06-01
With the aim of mitigating the basis set error in density functional theory (DFT) calculations employing local basis sets, we herein develop two empirical corrections for basis set superposition error (BSSE) in the def2-SVPD basis, a basis which—when stripped of BSSE—is capable of providing near-complete-basis DFT results for non-covalent interactions. Specifically, we adapt the existing pairwise geometrical counterpoise (gCP) approach to the def2-SVPD basis, and we develop a beyond-pairwise approach, DFT-C, which we parameterize across a small set of intermolecular interactions. Both gCP and DFT-C are evaluated against the traditional Boys-Bernardi counterpoise correction across a set of 3402 non-covalent binding energies and isomerization energies. We find that the DFT-C method represents a significant improvement over gCP, particularly for non-covalently-interacting molecular clusters. Moreover, DFT-C is transferable among density functionals and can be combined with existing functionals—such as B97M-V—to recover large-basis results at a fraction of the cost.
Maschio, Lorenzo; Usvyat, Denis; Schütz, Martin; Civalleri, Bartolomeo
2010-04-07
We have calculated the equilibrium geometry, formation energy, and bulk modulus of two molecular bulk crystals, NH(3) and CO(2), at the periodic post-Hartree-Fock correlated level. The dependence of the results on the basis set has been analyzed, by employing basis sets up to aug-cc-pVQZ quality. In the calculations, we used the periodic local Møller-Plesset second order perturbation theory (LMP2), implemented in the CRYSCOR program. Multipolar expansion techniques, as well as density fitting, are employed in this code to reduce the number of and to factorize the required electron repulsion integrals; as a consequence of that, the computational cost for the correlation part of the calculations is comparable to that of the Hartree-Fock. Auxiliary calculations performed on molecular dimers are also reported to verify the accuracy of the LMP2 approach and of the basis sets used. Furthermore, the effect of spin-component scaling has been investigated for the two crystals. One intention of the present paper is also to lay out and specify the computational setup, which is generally applicable for accurate CRYSCOR calculations on molecular crystals.
Prudencio, Thiago
2016-01-01
We discuss the modified Maxwell action of a $K_{F}$-type Lorentz symmetry breaking theory and present a solution of Maxwell equations derived in the cases of linear and elliptically polarized electromagnetic waves in the vacuum of CPT-even Lorentz violation. We show in this case the Lorentz violation has the effect of changing the amplitude of one component of the magnetic field, while leaving the electric field unchanged, leading to non-orthogonal propagation of eletromagnetic fields and dependence of the eccentricity on $\\kappa$-term. Further, we exhibit numerically the consequences of this effect in the cases of linear and elliptical polarization, in particular, the regimes of non-orthogonality of the electromagnetic wave fields and the eccentricity of the elliptical polarization of the magnetic field with dependence on the $\\kappa$-term.
Matthews, Devin A.; Stanton, John F.
2015-02-01
The theory of non-orthogonal spin-adaptation for closed-shell molecular systems is applied to coupled cluster methods with quadruple excitations (CCSDTQ). Calculations at this level of detail are of critical importance in describing the properties of molecular systems to an accuracy which can meet or exceed modern experimental techniques. Such calculations are of significant (and growing) importance in such fields as thermodynamics, kinetics, and atomic and molecular spectroscopies. With respect to the implementation of CCSDTQ and related methods, we show that there are significant advantages to non-orthogonal spin-adaption with respect to simplification and factorization of the working equations and to creating an efficient implementation. The resulting algorithm is implemented in the CFOUR program suite for CCSDT, CCSDTQ, and various approximate methods (CCSD(T), CC3, CCSDT-n, and CCSDT(Q)).
Chan, Garnet Kin-Lic; Van Voorhis, Troy
2005-05-22
We describe the theory and implementation of two extensions to the density-matrix renormalization-group (DMRG) algorithm in quantum chemistry: (i) to work with an underlying nonorthogonal one-particle basis (using a biorthogonal formulation) and (ii) to use non-Hermitian and complex operators and complex wave functions, which occur naturally in biorthogonal formulations. Using these developments, we carry out ground-state calculations on ethene, butadiene, and hexatriene, in a polarized atomic-orbital basis. The description of correlation in these systems using a localized nonorthogonal basis is improved over molecular-orbital DMRG calculations, and comparable to or better than coupled-cluster calculations, although we encountered numerical problems associated with non-Hermiticity. We believe that the non-Hermitian DMRG algorithm may further become useful in conjunction with other non-Hermitian Hamiltonians, for example, similarity-transformed coupled-cluster Hamiltonians.
Lei, Lei; Yuan, Di; Ho, Chin Keong; Sun, Sumei
2016-01-01
Network capacity calls for significant increase for 5G cellular systems. A promising multi-user access scheme, non-orthogonal multiple access (NOMA) with successive interference cancellation (SIC), is currently under consideration. In NOMA, spectrum efficiency is improved by allowing more than one user to simultaneously access the same frequency-time resource and separating multi-user signals by SIC at the receiver. These render resource allocation and optimization in NOMA different from orth...
Legler, C R; Brown, N R; Dunbar, R A; Harness, M D; Nguyen, K; Oyewole, O; Collier, W B
2015-06-15
The Scaled Quantum Mechanical (SQM) method of scaling calculated force constants to predict theoretically calculated vibrational frequencies is expanded to include a broad array of polarized and augmented basis sets based on the split valence 6-31G and 6-311G basis sets with the B3LYP density functional. Pulay's original choice of a single polarized 6-31G(d) basis coupled with a B3LYP functional remains the most computationally economical choice for scaled frequency calculations. But it can be improved upon with additional polarization functions and added diffuse functions for complex molecular systems. The new scale factors for the B3LYP density functional and the 6-31G, 6-31G(d), 6-31G(d,p), 6-31G+(d,p), 6-31G++(d,p), 6-311G, 6-311G(d), 6-311G(d,p), 6-311G+(d,p), 6-311G++(d,p), 6-311G(2d,p), 6-311G++(2d,p), 6-311G++(df,p) basis sets are shown. The double d polarized models did not perform as well and the source of the decreased accuracy was investigated. An alternate system of generating internal coordinates that uses the out-of plane wagging coordinate whenever it is possible; makes vibrational assignments via potential energy distributions more meaningful. Automated software to produce SQM scaled vibrational calculations from different molecular orbital packages is presented.
Rangel, T.; Caliste, D.; Genovese, L.; Torrent, M.
2016-11-01
We present a Projector Augmented-Wave (PAW) method based on a wavelet basis set. We implemented our wavelet-PAW method as a PAW library in the ABINIT package [http://www.abinit.org] and into BigDFT [http://www.bigdft.org]. We test our implementation in prototypical systems to illustrate the potential usage of our code. By using the wavelet-PAW method, we can simulate charged and special boundary condition systems with frozen-core all-electron precision. Furthermore, our work paves the way to large-scale and potentially order- N simulations within a PAW method.
Indian Academy of Sciences (India)
M Talebian; E Talebian; A Abdi
2012-05-01
We obtained an approximation of the force ﬁeld of -quartz crystal using a new idea of applying density functional theory [J Purton, R Jones, C R A Catlow and M Leslie, Phys. Chem. Minerals 19, 392 (1993)]. Our calculations were based on B3LYP Hamiltonian [A N Lazarev and A P Mirgorodsky, Phys. Chem. Minerals 18, 231 (1991)] in 6−311+G(2d) basis set for H16Si7O6 cluster and included a unit cell of the lattice. The advantage of our method is the increase in the speed of calculations and the better adaption of simulation results with the experimental data.
Rangel, Tonatiuh; Genovese, Luigi; Torrent, Marc
2016-01-01
We present a Projector Augmented-Wave~(PAW) method based on a wavelet basis set. We implemented our wavelet-PAW method as a PAW library in the ABINIT package [http://www.abinit.org] and into BigDFT [http://www.bigdft.org]. We test our implementation in prototypical systems to illustrate the potential usage of our code. By using the wavelet-PAW method, we can simulate charged and special boundary condition systems with frozen-core all-electron precision. Furthermore, our work paves the way to large-scale and potentially order-N simulations within a PAW method.
Hamel, Sébastien; Casida, Mark E.; Salahub, Dennis R.
2001-05-01
The Roothaan-Hartree-Fock (HF) method has been implemented in deMon-DynaRho within the resolution-of-the-identity (RI) auxiliary-function approximation. While previous studies have focused primarily upon the effect of the RI approximation on total energies, very little information has been available regarding the effect of the RI approximation on orbital energies, even though orbital energies play a central role in many theories of ionization and excitation. We fill this gap by testing the accuracy of the RI approximation against non-RI-HF calculations using the same basis sets, for the occupied orbital energies and an equal number of unoccupied orbital energies of five small molecules, namely CO, N2, CH2O, C2H4, and pyridine (in total 102 orbitals). These molecules have well-characterized excited states and so are commonly used to test and validate molecular excitation spectra computations. Of the deMon auxiliary basis sets tested, the best results are obtained with the (44) auxiliary basis sets, yielding orbital energies to within 0.05 eV, which is adequate for analyzing typical low resolution polyatomic molecule ionization and excitation spectra. Interestingly, we find that the error in orbital energies due to the RI approximation does not seem to increase with the number of electrons. The absolute RI error in the orbital energies is also roughly related to their absolute magnitude, being larger for the core orbitals where the magnitude of orbital energy is large and smallest where the molecular orbital energy is smallest. Two further approximations were also considered, namely uniterated ("zero-order") and single-iteration ("first-order") calculations of orbital energies beginning with a local density approximation initial guess. We find that zero- and first-order orbital energies are very similar for occupied but not for unoccupied orbitals, and that the first-order orbital energies are fairly close to the corresponding fully converged values. Typical root
Fábri, Csaba; Szidarovszky, Tamás; Magyarfalvi, Gábor; Tarczay, György
2011-05-12
Scaling factors for Pulay's scaled quantum mechanical (SQM) scheme have been determined for four different widely used DFT functionals (PBE, B3LYP, B3PW91, and M06-2X) and for two basis sets (6-31++G** and aug-cc-pVTZ) by fitting computed results to 347 fundamental experimental vibrational frequencies of 33 molecules. Measurements in the gas phase and in solid argon matrices were used independently in the fitting procedure in order to provide a simple method of estimating matrix shifts. The accuracy of the new scaling factors is demonstrated on test molecules including hydrogen-bonded systems and molecules containing chlorine and sulfur atoms.
Non-Orthogonal Multiple Access for Large-Scale 5G Networks: Interference Aware Design
Ali, Konpal S.
2017-09-18
Non-orthogonal multiple access (NOMA) is promoted as a key component of 5G cellular networks. As the name implies, NOMA operation introduces intracell interference (i.e., interference arising within the cell) to the cellular operation. The intracell interference is managed by careful NOMA design (e.g., user clustering and resource allocation) along with successive interference cancellation. However, most of the proposed NOMA designs are agnostic to intercell interference (i.e., interference from outside the cell), which is a major performance limiting parameter in 5G networks. This article sheds light on the drastic negative-impact of intercell interference on the NOMA performance and advocates interference-aware NOMA design that jointly accounts for both intracell and intercell interference. To this end, a case study for fair NOMA operation is presented and intercell interference mitigation techniques for NOMA networks are discussed. This article also investigates the potential of integrating NOMA with two important 5G transmission schemes, namely, full duplex and device-to-device communication. This is important since the ambitious performance defined by the 3rd Generation Partnership Project (3GPP) for 5G is foreseen to be realized via seamless integration of several new technologies and transmission techniques.
Ellmauthaler, Andreas; Pagliari, Carla L; da Silva, Eduardo A B
2013-03-01
Multiscale transforms are among the most popular techniques in the field of pixel-level image fusion. However, the fusion performance of these methods often deteriorates for images derived from different sensor modalities. In this paper, we demonstrate that for such images, results can be improved using a novel undecimated wavelet transform (UWT)-based fusion scheme, which splits the image decomposition process into two successive filtering operations using spectral factorization of the analysis filters. The actual fusion takes place after convolution with the first filter pair. Its significantly smaller support size leads to the minimization of the unwanted spreading of coefficient values around overlapping image singularities. This usually complicates the feature selection process and may lead to the introduction of reconstruction errors in the fused image. Moreover, we will show that the nonsubsampled nature of the UWT allows the design of nonorthogonal filter banks, which are more robust to artifacts introduced during fusion, additionally improving the obtained results. The combination of these techniques leads to a fusion framework, which provides clear advantages over traditional multiscale fusion approaches, independent of the underlying fusion rule, and reduces unwanted side effects such as ringing artifacts in the fused reconstruction.
Ahmed, Qasim Zeeshan
2014-04-01
The ever growing demand of higher data rates can now be addressed by exploiting cooperative diversity. This form of diversity has become a fundamental technique for achieving spatial diversity by exploiting the presence of idle users in the network. This has led to new challenges in terms of designing new protocols and detectors for cooperative communications. Among various amplify-and-forward (AF) protocols, the half duplex non-orthogonal amplify-and-forward (NAF) protocol is superior to other AF schemes in terms of error performance and capacity. However, this superiority is achieved at the cost of higher receiver complexity. Furthermore, in order to exploit the full diversity of the system an optimal precoder is required. In this paper, an optimal joint linear transceiver is proposed for the NAF protocol. This transceiver operates on the principles of minimum bit error rate (BER), and is referred as joint bit error rate (JBER) detector. The BER performance of JBER detector is superior to all the proposed linear detectors such as channel inversion, the maximal ratio combining, the biased maximum likelihood detectors, and the minimum mean square error. The proposed transceiver also outperforms previous precoders designed for the NAF protocol. © 2002-2012 IEEE.
Energy Technology Data Exchange (ETDEWEB)
Evarestov, R A; Panin, A I; Bandura, A V; Losev, M V [Department of Quantum Chemistry, St. Petersburg State University, University Prospect 26, Stary Peterghof, St. Petersburg, 198504 (Russian Federation)], E-mail: re1973@re1973.spb.edu
2008-06-01
The results of LCAO DFT calculations of lattice parameters, cohesive energy and bulk modulus of the crystalline uranium nitrides UN, U{sub 2}N{sub 3} and UN{sub 2} are presented and discussed. The LCAO computer codes Gaussian03 and Crystal06 are applied. The calculations are made with the uranium atom relativistic effective small core potential by Stuttgart-Cologne group (60 electrons in the core). The calculations include the U atom basis set optimization. Powell, Hooke-Jeeves, conjugated gradient and Box methods are implemented in the author's optimization package, being external to the codes for molecular and periodic calculations. The basis set optimization in LCAO calculations improves the agreement of the lattice parameter and bulk modulus of UN crystal with the experimental data, the change of the cohesive energy due to the optimization is small. The mixed metallic-covalent chemical bonding is found both in LCAO calculations of UN and U{sub 2}N{sub 3} crystals; UN{sub 2} crystal has the semiconducting nature.
Goldey, Matthew; Head-Gordon, Martin
2012-12-06
Second-order Møller-Plesset perturbation theory (MP2) treats electron correlation at low computational cost, but suffers from basis set superposition error (BSSE) and fundamental inaccuracies in long-range contributions. The cost differential between complete basis set (CBS) and small basis MP2 restricts system sizes where BSSE can be removed. Range-separation of MP2 could yield more tractable and/or accurate forms for short- and long-range correlation. Retaining only short-range contributions proves to be effective for MP2 in the small aug-cc-pVDZ (aDZ) basis. Using one range-separation parameter, superior behavior is obtained versus both MP2/aDZ and MP2/CBS for inter- and intramolecular test sets. Attenuation of the long-range helps to cancel both BSSE and intrinsic MP2 errors. Direct scaling of the MP2 correlation energy proves useful as well. The resulting SMP2/aDZ, MP2(erfc, aDZ), and MP2(terfc, aDZ) methods perform far better than MP2/aDZ across systems with hydrogen-bonding, dispersion, and mixed interactions at a fraction of MP2/CBS computational cost.
Kashinski, D O; Chase, G M; Nelson, R G; Di Nallo, O E; Scales, A N; VanderLey, D L; Byrd, E F C
2017-03-23
We propose new approximate global multiplicative scaling factors for the DFT calculation of ground state harmonic vibrational frequencies using functionals from the TPSS, M06, and M11 functional families with standard correlation consistent cc-pVxZ and aug-cc-pVxZ (x = D, T, and Q), 6-311G split valence family, Sadlej and Sapporo polarized triple-ζ basis sets. Results for B3LYP, CAM-B3LYP, B3PW91, PBE, and PBE0 functionals with these basis sets are also reported. A total of 99 harmonic frequencies were calculated for 26 gas-phase organic and nonorganic molecules typically found in detonated solid propellant residue. Our proposed approximate multiplicative scaling factors are determined using a least-squares approach comparing the computed harmonic frequencies to experimental counterparts well established in the scientific literature. A comparison of our work to previously published global scaling factors is made to verify method reliability and the applicability of our molecular test set.
Zen, Andrea; Luo, Ye; Sorella, Sandro; Guidoni, Leonardo
2013-10-08
Quantum Monte Carlo methods are accurate and promising many body techniques for electronic structure calculations which, in the last years, are encountering a growing interest thanks to their favorable scaling with the system size and their efficient parallelization, particularly suited for the modern high performance computing facilities. The ansatz of the wave function and its variational flexibility are crucial points for both the accurate description of molecular properties and the capabilities of the method to tackle large systems. In this paper, we extensively analyze, using different variational ansatzes, several properties of the water molecule, namely, the total energy, the dipole and quadrupole momenta, the ionization and atomization energies, the equilibrium configuration, and the harmonic and fundamental frequencies of vibration. The investigation mainly focuses on variational Monte Carlo calculations, although several lattice regularized diffusion Monte Carlo calculations are also reported. Through a systematic study, we provide a useful guide to the choice of the wave function, the pseudopotential, and the basis set for QMC calculations. We also introduce a new method for the computation of forces with finite variance on open systems and a new strategy for the definition of the atomic orbitals involved in the Jastrow-Antisymmetrised Geminal power wave function, in order to drastically reduce the number of variational parameters. This scheme significantly improves the efficiency of QMC energy minimization in case of large basis sets.
Non-orthogonal tool/flange and robot/world calibration.
Ernst, Floris; Richter, Lars; Matthäus, Lars; Martens, Volker; Bruder, Ralf; Schlaefer, Alexander; Schweikard, Achim
2012-12-01
For many robot-assisted medical applications, it is necessary to accurately compute the relation between the robot's coordinate system and the coordinate system of a localisation or tracking device. Today, this is typically carried out using hand-eye calibration methods like those proposed by Tsai/Lenz or Daniilidis. We present a new method for simultaneous tool/flange and robot/world calibration by estimating a solution to the matrix equation AX = YB. It is computed using a least-squares approach. Because real robots and localisation are all afflicted by errors, our approach allows for non-orthogonal matrices, partially compensating for imperfect calibration of the robot or localisation device. We also introduce a new method where full robot/world and partial tool/flange calibration is possible by using localisation devices providing less than six degrees of freedom (DOFs). The methods are evaluated on simulation data and on real-world measurements from optical and magnetical tracking devices, volumetric ultrasound providing 3-DOF data, and a surface laser scanning device. We compare our methods with two classical approaches: the method by Tsai/Lenz and the method by Daniilidis. In all experiments, the new algorithms outperform the classical methods in terms of translational accuracy by up to 80% and perform similarly in terms of rotational accuracy. Additionally, the methods are shown to be stable: the number of calibration stations used has far less influence on calibration quality than for the classical methods. Our work shows that the new method can be used for estimating the relationship between the robot's and the localisation device's coordinate systems. The new method can also be used for deficient systems providing only 3-DOF data, and it can be employed in real-time scenarios because of its speed. Copyright © 2012 John Wiley & Sons, Ltd.
Maltsev, I A; Tupitsyn, I I; Shabaev, V M; Kozhedub, Y S; Plunien, G; Stoehlker, Th
2013-01-01
A new approach for solving the time-dependent two-center Dirac equation is presented. The method is based on using the finite basis set of cubic Hermite splines on a two-dimensional lattice. The Dirac equation is treated in rotating reference frame. The collision of U92+ (as a projectile) and U91+ (as a target) is considered at energy E_lab=6 MeV/u. The charge transfer probabilities are calculated for different values of the impact parameter. The obtained results are compared with the previous calculations [I. I. Tupitsyn et al., Phys. Rev. A 82, 042701 (2010)], where a method based on atomic-like Dirac-Sturm orbitals was employed. This work can provide a new tool for investigation of quantum electrodynamics effects in heavy-ion collisions near the supercritical regime.
Hellweg, Arnim; Rappoport, Dmitrij
2015-01-14
We report optimized auxiliary basis sets for use with the Karlsruhe segmented contracted basis sets including moderately diffuse basis functions (Rappoport and Furche, J. Chem. Phys., 2010, 133, 134105) in resolution-of-the-identity (RI) post-self-consistent field (post-SCF) computations for the elements H-Rn (except lanthanides). The errors of the RI approximation using optimized auxiliary basis sets are analyzed on a comprehensive test set of molecules containing the most common oxidation states of each element and do not exceed those of the corresponding unaugmented basis sets. During these studies an unsatisfying performance of the def2-SVP and def2-QZVPP auxiliary basis sets for Barium was found and improved sets are provided. We establish the versatility of the def2-SVPD, def2-TZVPPD, and def2-QZVPPD basis sets for RI-MP2 and RI-CC (coupled-cluster) energy and property calculations. The influence of diffuse basis functions on correlation energy, basis set superposition error, atomic electron affinity, dipole moments, and computational timings is evaluated at different levels of theory using benchmark sets and showcase examples.
On the Performance of Non-Orthogonal Multiple Access in 5G Systems with Randomly Deployed Users
Ding, Zhiguo; Yang, Zheng; Fan, Pingzhi; Poor, H. Vincent
2014-12-01
In this letter, the performance of non-orthogonal multiple access (NOMA) is investigated in a cellular downlink scenario with randomly deployed users. The developed analytical results show that NOMA can achieve superior performance in terms of ergodic sum rates; however, the outage performance of NOMA depends critically on the choices of the users' targeted data rates and allocated power. In particular, a wrong choice of the targeted data rates and allocated power can lead to a situation in which the user's outage probability is always one, i.e. the user's targeted quality of service will never be met.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The Unit Vector Method (UVM) is an orbit determination method extensively applied. In this paper, the UVM and classical Differential Orbit Improvement (DOI) are compared, and a fusion method is given for the orbit determination with different kind data. Based on non-orthogonal decomposition of position and velocity vectors, an approximation scheme is constructed to calculate the state transition matrix. This method simplifies the calculation of the approximate state transition matrix, analyzes the convergence mechanism of the UVM, and makes clear the defect of weight strategy in UVM. Results of orbit the determination with simulating and real data show that this method has good numerical stability and rational weight distribution.
Goerigk, Lars; Collyer, Charles A; Reimers, Jeffrey R
2014-12-18
We demonstrate the importance of properly accounting for London dispersion and basis-set-superposition error (BSSE) in quantum-chemical optimizations of protein structures, factors that are often still neglected in contemporary applications. We optimize a portion of an ensemble of conformationally flexible lysozyme structures obtained from highly accurate X-ray crystallography data that serve as a reliable benchmark. We not only analyze root-mean-square deviations from the experimental Cartesian coordinates, but also, for the first time, demonstrate how London dispersion and BSSE influence crystallographic R factors. Our conclusions parallel recent recommendations for the optimization of small gas-phase peptide structures made by some of the present authors: Hartree-Fock theory extended with Grimme's recent dispersion and BSSE corrections (HF-D3-gCP) is superior to popular density functional theory (DFT) approaches. Not only are statistical errors on average lower with HF-D3-gCP, but also the convergence behavior is much better. In particular, we show that the BP86/6-31G* approach should not be relied upon as a black-box method, despite its widespread use, as its success is based on an unpredictable cancellation of errors. Using HF-D3-gCP is technically straightforward, and we therefore encourage users of quantum-chemical methods to adopt this approach in future applications.
Energy Technology Data Exchange (ETDEWEB)
Rodriguez-Bautista, Mariano; Díaz-García, Cecilia; Navarrete-López, Alejandra M.; Vargas, Rubicelia; Garza, Jorge, E-mail: jgo@xanum.uam.mx [Departamento de Química, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Col. Vicentina, Iztapalapa C. P. 09340, México D. F., México (Mexico)
2015-07-21
In this report, we use a new basis set for Hartree-Fock calculations related to many-electron atoms confined by soft walls. One- and two-electron integrals were programmed in a code based in parallel programming techniques. The results obtained with this proposal for hydrogen and helium atoms were contrasted with other proposals to study just one and two electron confined atoms, where we have reproduced or improved the results previously reported. Usually, an atom enclosed by hard walls has been used as a model to study confinement effects on orbital energies, the main conclusion reached by this model is that orbital energies always go up when the confinement radius is reduced. However, such an observation is not necessarily valid for atoms confined by penetrable walls. The main reason behind this result is that for atoms with large polarizability, like beryllium or potassium, external orbitals are delocalized when the confinement is imposed and consequently, the internal orbitals behave as if they were in an ionized atom. Naturally, the shell structure of these atoms is modified drastically when they are confined. The delocalization was an argument proposed for atoms confined by hard walls, but it was never verified. In this work, the confinement imposed by soft walls allows to analyze the delocalization concept in many-electron atoms.
Richard, Ryan M.
2016-01-05
© 2016 American Chemical Society. In designing organic materials for electronics applications, particularly for organic photovoltaics (OPV), the ionization potential (IP) of the donor and the electron affinity (EA) of the acceptor play key roles. This makes OPV design an appealing application for computational chemistry since IPs and EAs are readily calculable from most electronic structure methods. Unfortunately reliable, high-accuracy wave function methods, such as coupled cluster theory with single, double, and perturbative triples [CCSD(T)] in the complete basis set (CBS) limit are too expensive for routine applications to this problem for any but the smallest of systems. One solution is to calibrate approximate, less computationally expensive methods against a database of high-accuracy IP/EA values; however, to our knowledge, no such database exists for systems related to OPV design. The present work is the first of a multipart study whose overarching goal is to determine which computational methods can be used to reliably compute IPs and EAs of electron acceptors. This part introduces a database of 24 known organic electron acceptors and provides high-accuracy vertical IP and EA values expected to be within ±0.03 eV of the true non-relativistic, vertical CCSD(T)/CBS limit. Convergence of IP and EA values toward the CBS limit is studied systematically for the Hartree-Fock, MP2 correlation, and beyond-MP2 coupled cluster contributions to the focal point estimates.
Peverati, Roberto; Baldridge, Kim K
2009-10-13
The implementation, optimization, and performance of DFT-D, including the effects of solvation, has been tested on applications of polar processes in solution, where dispersion and hydrogen bonding is known to be involved. Solvent effects are included using our ab initio continuum solvation strategy, COSab, a conductor-like continuum solvation model, modified for ab initio in the quantum chemistry program GAMESS. Structure and properties are investigated across various functionals to evaluate their ability to properly model dispersion and solvation effects. The commonly used S22 set with accurate interaction energies of organic complexes has been used for parametrization studies of dispersion parameters and relevant solvation parameters. Dunning's correlation consistent basis sets, cc-pVnZ (n = D, T), are used in the optimization, together with the Grimme B97-D exchange-correlation functional. Both water (ε = 78.4) and ether (ε = 4.33) environments are considered. Optimized semiempirical dispersion correction parameters and solvent extent radii are proposed for several functionals. We find that special parametrization of the semiempirical dispersion correction when used together in the DFT-D/COSab approach is not necessary. The global performance is quite acceptable in terms of chemical accuracy and suggests that this approach is a reliable as well as economical method for evaluation of solvent effects in systems with dispersive interactions. The resulting theory is applied to a group of push-pull pyrrole systems to illustrate the effects of donor/acceptor and solvation on their conformational and energetic properties.
Third-Order Incremental Dual-Basis Set Zero-Buffer Approach for Large High-Spin Open-Shell Systems.
Zhang, Jun; Dolg, Michael
2015-03-10
The third-order incremental dual-basis set zero-buffer approach (inc3-db-B0) is an efficient, accurate, and black-box quantum chemical method for obtaining correlation energies of large systems, and it has been successfully applied to many real chemical problems. In this work, we extend this approach to high-spin open-shell systems. In the open-shell approach, we will first decompose the occupied orbitals of a system into several domains by a K-means clustering algorithm. The essential part is that we preserve the active (singly occupied) orbitals in all the calculations of the domain correlation energies. The duplicated contributions of the active orbitals to the correlation energy are subtracted from the incremental expansion. All techniques of truncating the virtual space such as the B0 approximation can be applied. This open-shell inc3-db-B0 approach is combined with the CCSD and CCSD(T) methods and applied to the computations of a singlet-triplet gap and an electron detachment process. Our approach exhibits an accuracy better than 0.6 kcal/mol or 0.3 eV compared with the standard implementation, while it saves a large amount of the computational time and can be efficiently parallelized.
Rodriguez-Bautista, Mariano; Díaz-García, Cecilia; Navarrete-López, Alejandra M; Vargas, Rubicelia; Garza, Jorge
2015-07-21
In this report, we use a new basis set for Hartree-Fock calculations related to many-electron atoms confined by soft walls. One- and two-electron integrals were programmed in a code based in parallel programming techniques. The results obtained with this proposal for hydrogen and helium atoms were contrasted with other proposals to study just one and two electron confined atoms, where we have reproduced or improved the results previously reported. Usually, an atom enclosed by hard walls has been used as a model to study confinement effects on orbital energies, the main conclusion reached by this model is that orbital energies always go up when the confinement radius is reduced. However, such an observation is not necessarily valid for atoms confined by penetrable walls. The main reason behind this result is that for atoms with large polarizability, like beryllium or potassium, external orbitals are delocalized when the confinement is imposed and consequently, the internal orbitals behave as if they were in an ionized atom. Naturally, the shell structure of these atoms is modified drastically when they are confined. The delocalization was an argument proposed for atoms confined by hard walls, but it was never verified. In this work, the confinement imposed by soft walls allows to analyze the delocalization concept in many-electron atoms.
Directory of Open Access Journals (Sweden)
D. Simpson
2012-02-01
Full Text Available A new organic aerosol (OA module has been implemented into the EMEP chemical transport model. Four different volatility basis set (VBS schemes have been tested in long-term simulations for Europe, covering the six years 2002–2007. Different assumptions regarding partitioning of primary OA (POA and aging of POA and secondary OA (SOA, have been explored. Model results are compared to filter measurements, AMS-data and source-apportionment studies, as well as to other model studies. The present study indicates that many different sources contribute significantly to OA in Europe. Fossil POA and oxidised POA, biogenic and anthropogenic SOA (BSOA and ASOA, residential burning of biomass fuels and wildfire emissions may all contribute more than 10% each over substantial parts of Europe. Simple VBS based OA models can give reasonably good results for summer OA but more observational studies are needed to constrain the VBS parameterisations and to help improve emission inventories. The volatility distribution of primary emissions is an important issue for further work. This study shows smaller contributions from BSOA to OA in Europe than earlier work, but relatively greater ASOA. BVOC emissions are highly uncertain and need further validation. We can not reproduce winter levels of OA in Europe, and there are many indications that the present emission inventories substantially underestimate emissions from residential wood burning in large parts of Europe.
Rodriguez-Bautista, Mariano; Díaz-García, Cecilia; Navarrete-López, Alejandra M.; Vargas, Rubicelia; Garza, Jorge
2015-07-01
In this report, we use a new basis set for Hartree-Fock calculations related to many-electron atoms confined by soft walls. One- and two-electron integrals were programmed in a code based in parallel programming techniques. The results obtained with this proposal for hydrogen and helium atoms were contrasted with other proposals to study just one and two electron confined atoms, where we have reproduced or improved the results previously reported. Usually, an atom enclosed by hard walls has been used as a model to study confinement effects on orbital energies, the main conclusion reached by this model is that orbital energies always go up when the confinement radius is reduced. However, such an observation is not necessarily valid for atoms confined by penetrable walls. The main reason behind this result is that for atoms with large polarizability, like beryllium or potassium, external orbitals are delocalized when the confinement is imposed and consequently, the internal orbitals behave as if they were in an ionized atom. Naturally, the shell structure of these atoms is modified drastically when they are confined. The delocalization was an argument proposed for atoms confined by hard walls, but it was never verified. In this work, the confinement imposed by soft walls allows to analyze the delocalization concept in many-electron atoms.
Monari, Antonio; Bendazzoli, Gian Luigi; Evangelisti, Stefano; Angeli, Celestino; Ben Amor, Nadia; Borini, Stefano; Maynau, Daniel; Rossi, Elda
2007-03-01
The dispersion interactions of the Ne2 dimer were studied using both the long-range perturbative and supramolecular approaches: for the long-range approach, full CI or string-truncated CI methods were used, while for the supramolecular treatments, the energy curves were computed by using configuration interaction with single and double excitation (CISD), coupled cluster with single and double excitation, and coupled-cluster with single and double (and perturbative) triple excitations. From the interatomic potential-energy curves obtained by the supramolecular approach, the C6 and C8 dispersion coefficients were computed via an interpolation scheme, and they were compared with the corresponding values obtained within the long-range perturbative treatment. We found that the lack of size consistency of the CISD approach makes this method completely useless to compute dispersion coefficients even when the effect of the basis-set superposition error on the dimer curves is considered. The largest full-CI space we were able to use contains more than 1 billion symmetry-adapted Slater determinants, and it is, to our knowledge, the largest calculation of second-order properties ever done at the full-CI level so far. Finally, a new data format and libraries (Q5Cost) have been used in order to interface different codes used in the present study.
Spatio-temporal evolutions of non-orthogonal equatorial wave modes derived from observations
Barton, Cory
Equatorial waves have been studied extensively due to their importance to the tropical climate and weather systems. Historically, their activity is diagnosed mainly in the wavenumber-frequency domain. Recently, many studies have projected observational data onto parabolic cylinder functions (PCFs), which represent the meridional structure of individual wave modes, to attain time-dependent spatial wave structures. The non-orthogonality of wave modes has yet posed a problem when attempting to separate data into wave fields where the waves project onto the same structure functions. We propose the development and application of a new methodology for equatorial wave expansion of instantaneous flows using the full equatorial wave spectrum. By creating a mapping from the meridional structure function amplitudes to the equatorial wave class amplitudes, we are able to diagnose instantaneous wave fields and determine their evolution. Because all meridional modes are shared by some subset of the wave classes, we require constraints on the wave class amplitudes to yield a closed system with a unique solution for all waves' spatial structures, including IG waves. A synthetic field is analyzed using this method to determine its accuracy for data of a single vertical mode. The wave class spectra diagnosed using this method successfully match the correct dispersion curves even if the incorrect depth is chosen for the spatial decomposition. In the case of more than one depth scale, waves with varying equivalent depth may be similarly identified using the dispersion curves. The primary vertical mode is the 200 m equivalent depth mode, which is that of the peak projection response. A distinct spectral power peak along the Kelvin wave dispersion curve for this value validates our choice of equivalent depth, although the possibility of depth varying with time and height is explored. The wave class spectra diagnosed assuming this depth scale mostly match their expected dispersion curves
Tsimpidi, A. P.; Karydis, V. A.; Pandis, S. N.; Zavala, M.; Lei, W.; Molina, L. T.
2007-12-01
Anthropogenic air pollution is an increasingly serious problem for public health, agriculture, and global climate. Organic material (OM) contributes ~ 20-50% to the total fine aerosol mass at continental mid-latitudes. Although OM accounts for a large fraction of PM2.5 concentration worldwide, the contributions of primary and secondary organic aerosol have been difficult to quantify. In this study, new primary and secondary organic aerosol modules were added to PMCAMx, a three dimensional chemical transport model (Gaydos et al., 2007), for use with the SAPRC99 chemistry mechanism (Carter, 2000; ENVIRON, 2006) based on recent smog chamber studies (Robinson et al., 2007). The new modeling framework is based on the volatility basis-set approach (Lane et al., 2007): both primary and secondary organic components are assumed to be semivolatile and photochemically reactive and are distributed in logarithmically spaced volatility bins. The emission inventory, which uses as starting point the MCMA 2004 official inventory (CAM, 2006), is modified and the primary organic aerosol (POA) emissions are distributed by volatility based on dilution experiments (Robinson et al., 2007). Sensitivity tests where POA is considered as nonvolatile and POA and SOA as chemically reactive are also described. In all cases PMCAMx is applied in the Mexico City Metropolitan Area during March 2006. The modeling domain covers a 180x180x6 km region in the MCMA with 3x3 km grid resolution. The model predictions are compared with Aerodyne's Aerosol Mass Spectrometry (AMS) observations from the MILAGRO Campaign. References Robinson, A. L.; Donahue, N. M.; Shrivastava, M. K.; Weitkamp, E. A.; Sage, A. M.; Grieshop, A. P.; Lane, T. E.; Pandis, S. N.; Pierce, J. R., 2007. Rethinking organic aerosols: semivolatile emissions and photochemical aging. Science 315, 1259-1262. Gaydos, T. M.; Pinder, R. W.; Koo, B.; Fahey, K. M.; Pandis, S. N., 2007. Development and application of a three- dimensional aerosol
Goldfeld, Dahlia A; Bochevarov, Arteum D; Friesner, Richard A
2008-12-07
This paper is a logical continuation of the 22 parameter, localized orbital correction (LOC) methodology that we developed in previous papers [R. A. Friesner et al., J. Chem. Phys. 125, 124107 (2006); E. H. Knoll and R. A. Friesner, J. Phys. Chem. B 110, 18787 (2006).] This methodology allows one to redress systematic density functional theory (DFT) errors, rooted in DFT's inherent inability to accurately describe nondynamical correlation. Variants of the LOC scheme, in conjunction with B3LYP (denoted as B3LYP-LOC), were previously applied to enthalpies of formation, ionization potentials, and electron affinities and showed impressive reduction in the errors. In this paper, we demonstrate for the first time that the B3LYP-LOC scheme is robust across different basis sets [6-31G( *), 6-311++G(3df,3pd), cc-pVTZ, and aug-cc-pVTZ] and reaction types (atomization reactions and molecular reactions). For example, for a test set of 70 molecular reactions, the LOC scheme reduces their mean unsigned error from 4.7 kcal/mol [obtained with B3LYP/6-311++G(3df,3pd)] to 0.8 kcal/mol. We also verified whether the LOC methodology would be equally successful if applied to the promising M05-2X functional. We conclude that although M05-2X produces better reaction enthalpies than B3LYP, the LOC scheme does not combine nearly as successfully with M05-2X than with B3LYP. A brief analysis of another functional, M06-2X, reveals that it is more accurate than M05-2X but its combination with LOC still cannot compete in accuracy with B3LYP-LOC. Indeed, B3LYP-LOC remains the best method of computing reaction enthalpies.
Yoshida, Tatsusada; Hayashi, Takahisa; Mashima, Akira; Chuman, Hiroshi
2015-10-01
One of the most challenging problems in computer-aided drug discovery is the accurate prediction of the binding energy between a ligand and a protein. For accurate estimation of net binding energy ΔEbind in the framework of the Hartree-Fock (HF) theory, it is necessary to estimate two additional energy terms; the dispersion interaction energy (Edisp) and the basis set superposition error (BSSE). We previously reported a simple and efficient dispersion correction, Edisp, to the Hartree-Fock theory (HF-Dtq). In the present study, an approximation procedure for estimating BSSE proposed by Kruse and Grimme, a geometrical counterpoise correction (gCP), was incorporated into HF-Dtq (HF-Dtq-gCP). The relative weights of the Edisp (Dtq) and BSSE (gCP) terms were determined to reproduce ΔEbind calculated with CCSD(T)/CBS or /aug-cc-pVTZ (HF-Dtq-gCP (scaled)). The performance of HF-Dtq-gCP (scaled) was compared with that of B3LYP-D3(BJ)-bCP (dispersion corrected B3LYP with the Boys and Bernadi counterpoise correction (bCP)), by taking ΔEbind (CCSD(T)-bCP) of small non-covalent complexes as 'a golden standard'. As a critical test, HF-Dtq-gCP (scaled)/6-31G(d) and B3LYP-D3(BJ)-bCP/6-31G(d) were applied to the complex model for HIV-1 protease and its potent inhibitor, KNI-10033. The present results demonstrate that HF-Dtq-gCP (scaled) is a useful and powerful remedy for accurately and promptly predicting ΔEbind between a ligand and a protein, albeit it is a simple correction procedure.
Ramírez-Solís, A; Zicovich-Wilson, C M; Hernández-Lamoneda, R; Ochoa-Calle, A J
2017-01-25
The question of the non-magnetic (NM) vs. antiferromagnetic (AF) nature of the ε phase of solid oxygen is a matter of great interest and continuing debate. In particular, it has been proposed that the ε phase is actually composed of two phases, a low-pressure AF ε1 phase and a higher pressure NM ε0 phase [Crespo et al., Proc. Natl. Acad. Sci. U. S. A., 2014, 111, 10427]. We address this problem through periodic spin-restricted and spin-polarized Kohn-Sham density functional theory calculations at pressures from 10 to 50 GPa using calibrated GGA and hybrid exchange-correlation functionals with Gaussian atomic basis sets. The two possible configurations for the antiferromagnetic (AF1 and AF2) coupling of the 0 ≤ S ≤ 1 O2 molecules in the (O2)4 unit cell were studied. Full enthalpy-driven geometry optimizations of the (O2)4 unit cells were done to study the pressure evolution of the enthalpy difference between the non-magnetic and both antiferromagnetic structures. We also address the evolution of structural parameters and the spin-per-molecule vs. pressure. We find that the spin-less solution becomes more stable than both AF structures above 50 GPa and, crucially, the spin-less solution yields lattice parameters in much better agreement with experimental data at all pressures than the AF structures. The optimized AF2 broken-symmetry structures lead to large errors of the a and b lattice parameters when compared with experiments. The results for the NM model are in much better agreement with the experimental data than those found for both AF models and are consistent with a completely non-magnetic (O2)4 unit cell for the low-pressure regime of the ε phase.
Directory of Open Access Journals (Sweden)
A. P. Tsimpidi
2010-01-01
Full Text Available New primary and secondary organic aerosol modules have been added to PMCAMx, a three dimensional chemical transport model (CTM, for use with the SAPRC99 chemistry mechanism based on recent smog chamber studies. The new modelling framework is based on the volatility basis-set approach: both primary and secondary organic components are assumed to be semivolatile and photochemically reactive and are distributed in logarithmically spaced volatility bins. This new framework with the use of the new volatility basis parameters for low-NO_{x} and high-NO_{x} conditions tends to predict 4–6 times higher anthropogenic SOA concentrations than those predicted with the older generation of models. The resulting PMCAMx-2008 was applied in Mexico City Metropolitan Area (MCMA for approximately a week during April 2003 during a period of very low regional biomass burning impact. The emission inventory, which uses as a starting point the MCMA 2004 official inventory, is modified and the primary organic aerosol (POA emissions are distributed by volatility based on dilution experiments. The predicted organic aerosol (OA concentrations peak in the center of Mexico City, reaching values above 40 μg m^{−3}. The model predictions are compared with the results of the Positive Matrix Factorization (PMF analysis of the Aerosol Mass Spectrometry (AMS observations. The model reproduces both Hydrocarbon-like Organic Aerosol (HOA and Oxygenated Organic Aerosol (OOA concentrations and diurnal profiles. The small OA underprediction during the rush-hour periods and overprediction in the afternoon suggest potential improvements to the description of fresh primary organic emissions and the formation of the oxygenated organic aerosols, respectively, although they may also be due to errors in the simulation of dispersion and vertical mixing. However, the AMS OOA data are not specific enough to prove that the model reproduces the organic aerosol
Baranowska-Łączkowska, Angelika; Bartkowiak, Wojciech; Góra, Robert W; Pawłowski, Filip; Zaleśny, Robert
2013-04-05
Static longitudinal electric dipole (hyper)polarizabilities are calculated for six medium-sized π-conjugated organic molecules using recently developed LPol-n basis set family to assess their performance. Dunning's correlation-consistent basis sets of triple-ζ quality combined with MP2 method and supported by CCSD(T)/aug-cc-pVDZ results are used to obtain the reference values of analyzed properties. The same reference is used to analyze (hyper)polarizabilities predicted by selected exchange-correlation functionals, particularly those asymptotically corrected.
Bayesian learning of sparse multiscale image representations.
Hughes, James Michael; Rockmore, Daniel N; Wang, Yang
2013-12-01
Multiscale representations of images have become a standard tool in image analysis. Such representations offer a number of advantages over fixed-scale methods, including the potential for improved performance in denoising, compression, and the ability to represent distinct but complementary information that exists at various scales. A variety of multiresolution transforms exist, including both orthogonal decompositions such as wavelets as well as nonorthogonal, overcomplete representations. Recently, techniques for finding adaptive, sparse representations have yielded state-of-the-art results when applied to traditional image processing problems. Attempts at developing multiscale versions of these so-called dictionary learning models have yielded modest but encouraging results. However, none of these techniques has sought to combine a rigorous statistical formulation of the multiscale dictionary learning problem and the ability to share atoms across scales. We present a model for multiscale dictionary learning that overcomes some of the drawbacks of previous approaches by first decomposing an input into a pyramid of distinct frequency bands using a recursive filtering scheme, after which we perform dictionary learning and sparse coding on the individual levels of the resulting pyramid. The associated image model allows us to use a single set of adapted dictionary atoms that is shared--and learned--across all scales in the model. The underlying statistical model of our proposed method is fully Bayesian and allows for efficient inference of parameters, including the level of additive noise for denoising applications. We apply the proposed model to several common image processing problems including non-Gaussian and nonstationary denoising of real-world color images.
Quiney, HM; Glushkov, VN; Wilson, S
2002-01-01
Using basis sets of distributed s-type Gaussian functions with positions and exponents optimized so as to support Hartree-Fock total energies with an accuracy approaching the sub-muHartree level, Dirac-Hartree-Fock-Coulomb calculations are reported for the ground states of the H-2, LiH, and BH molec
Schiffler, Ralf
2014-01-01
This book is intended to serve as a textbook for a course in Representation Theory of Algebras at the beginning graduate level. The text has two parts. In Part I, the theory is studied in an elementary way using quivers and their representations. This is a very hands-on approach and requires only basic knowledge of linear algebra. The main tool for describing the representation theory of a finite-dimensional algebra is its Auslander-Reiten quiver, and the text introduces these quivers as early as possible. Part II then uses the language of algebras and modules to build on the material developed before. The equivalence of the two approaches is proved in the text. The last chapter gives a proof of Gabriel’s Theorem. The language of category theory is developed along the way as needed.
DEFF Research Database (Denmark)
Wulf-Andersen, Trine Østergaard
2012-01-01
This article is based on a Danish research project with young people in vulnerable positions. Young people are involved throughout the research process, including the interpretation of material produced through interviews, and discussions on how reflections and conclusions from the research should......, and dialogue, of situated participants. The article includes a lengthy example of a poetic representation of one participant’s story, and the author comments on the potentials of ‘doing’ poetic representations as an example of writing in ways that challenges what sometimes goes unasked in participative social...
DEFF Research Database (Denmark)
Rasmussen, Majken Kirkegaard; Petersen, Marianne Graves
2011-01-01
Stereotypic presumptions about gender affect the design process, both in relation to how users are understood and how products are designed. As a way to decrease the influence of stereotypic presumptions in design process, we propose not to disregard the aspect of gender in the design process......, as the perspective brings valuable insights on different approaches to technology, but instead to view gender through a value lens. Contributing to this perspective, we have developed Value Representations as a design-oriented instrument for staging a reflective dialogue with users. Value Representations...
A non-orthogonal SVD-based decomposition for phase invariant error-related potential estimation.
Phlypo, Ronald; Jrad, Nisrine; Rousseau, Sandra; Congedo, Marco
2011-01-01
The estimation of the Error Related Potential from a set of trials is a challenging problem. Indeed, the Error Related Potential is of low amplitude compared to the ongoing electroencephalographic activity. In addition, simple summing over the different trials is prone to errors, since the waveform does not appear at an exact latency with respect to the trigger. In this work, we propose a method to cope with the discrepancy of these latencies of the Error Related Potential waveform and offer a framework in which the estimation of the Error Related Potential waveform reduces to a simple Singular Value Decomposition of an analytic waveform representation of the observed signal. The followed approach is promising, since we are able to explain a higher portion of the variance of the observed signal with fewer components in the expansion.
DEFF Research Database (Denmark)
Petersson, Dag; Dahlgren, Anna; Vestberg, Nina Lager
to the enterprises of the medium. This is the subject of Representational Machines: How photography enlists the workings of institutional technologies in search of establishing new iconic and social spaces. Together, the contributions to this edited volume span historical epochs, social environments, technological...
Shternin, Peter S; Vasyutinskii, Oleg S
2008-05-21
We present a theoretical framework for calculating the recoil-angle dependence of the photofragment angular momentum polarization taking into account both radial and Coriolis nonadiabatic interactions in the diatomic/linear photodissociating molecules. The parity-adapted representation of the total molecular wave function has been used throughout the paper. The obtained full quantum-mechanical expressions for the photofragment state multipoles have been simplified by using the semiclassical approximation in the high-J limit and then analyzed for the cases of direct photodissociation and slow predissociation in terms of the anisotropy parameters. In both cases, each anisotropy parameter can be presented as a linear combination of the generalized dynamical functions fK(q,q',q,q') of the rank K representing contribution from different dissociation mechanisms including possible radial and Coriolis nonadiabatic transitions, coherent effects, and the rotation of the recoil axis. In the absence of the Coriolis interactions, the obtained results are equivalent to the earlier published ones. The angle-recoil dependence of the photofragment state multipoles for an arbitrary photolysis reaction is derived. As shown, the polarization of the photofragments in the photolysis of a diatomic or a polyatomic molecule can be described in terms of the anisotropy parameters irrespective of the photodissociation mechanism.
Wang, Yi-Feng; Jing, Xiu-Juan; Liu, Feng; Li, Mei-Ling; Long, Zhi-Liang; Yan, Jin H; Chen, Hua-Fu
2015-05-21
The attention system can be divided into alerting, orienting, and executive control networks. The efficiency and independence of attention networks have been widely tested with the attention network test (ANT) and its revised versions. However, many studies have failed to find effects of attention network scores (ANSs) and inter-network relationships (INRs). Moreover, the low reliability of ANSs can not meet the demands of theoretical and empirical investigations. Two methodological factors (the inter-trial influence in the event-related design and the inter-network interference in orthogonal contrast) may be responsible for the unreliability of ANT. In this study, we combined the mixed design and non-orthogonal method to explore ANSs and directional INRs. With a small number of trials, we obtained reliable and independent ANSs (split-half reliability of alerting: 0.684; orienting: 0.588; and executive control: 0.616), suggesting an individual and specific attention system. Furthermore, mutual inhibition was observed when two networks were operated simultaneously, indicating a differentiated but integrated attention system. Overall, the reliable and individual specific ANSs and mutually inhibited INRs provide novel insight into the understanding of the developmental, physiological and pathological mechanisms of attention networks, and can benefit future experimental and clinical investigations of attention using ANT.
Directory of Open Access Journals (Sweden)
Mirkov Nikola S.
2016-01-01
Full Text Available In this paper we validate an improved finite volume approximation of Reynolds Averaged Navier-Stokes equations for simulation of wind flows in body-fitted grids generated by algebraic extrusion from digital terrain elevation data, proposed in N. Mirkov et. al. J. Comput. Phys. 287, 18-45(2015, [1]. The approach is based on second-order accurate finite volume method with collocated variable arrangement and pressure-velocity coupling trough SIMPLE algorithm. The main objective is the attenuation of spurious pressure field oscillations in regions with discontinuity in grid line slopes, as encountered in grids representing highly non-uniform terrains. Moreover, the approach relaxes the need for grid generation based on elliptic PDEs or grid smoothing by applying fixed point iterations (i.e. Gauss-Seidel to initial grid node positions resulting from algebraic grid generators. Drawbacks of previous approaches which ignored treatment of finite volume grid cell cases with intersection point offset in non-orthogonality corrections are removed. Application to real-life wind farm project at Dobrič (Srvljig, Serbia is used to assess the effectiveness of the method. The results validate the view in which accurate discretization of governing equations play more important role than the choice of turbulence modelling closures. [Projekat Ministarstva nauke Republike Srbije, br. TR-33036
Dimensionality of object representations in monkey inferotemporal cortex.
Lehky, Sidney R; Kiani, Roozbeh; Esteky, Hossein; Tanaka, Keiji
2014-10-01
We have calculated the intrinsic dimensionality of visual object representations in anterior inferotemporal (AIT) cortex, based on responses of a large sample of cells stimulated with photographs of diverse objects. Because dimensionality was dependent on data set size, we determined asymptotic dimensionality as both the number of neurons and number of stimulus image approached infinity. Our final dimensionality estimate was 93 (SD: ± 11), indicating that there is basis set of approximately 100 independent features that characterize the dimensions of neural object space. We believe this is the first estimate of the dimensionality of neural visual representations based on single-cell neurophysiological data. The dimensionality of AIT object representations was much lower than the dimensionality of the stimuli. We suggest that there may be a gradual reduction in the dimensionality of object representations in neural populations going from retina to inferotemporal cortex as receptive fields become increasingly complex.
Gao, Hongwei; Wei, Xiujuan; Liu, Xuting; Yan, Tingxia
2010-03-25
Comparisons of various density functional theory (DFT) methods at different basis sets in predicting the molecular structures and (13)C NMR spectra for [Pt(en)(CBDCA-O, O')], an analogue of the antitumor drug carboplatin, are reported. DFT methods including B3LYP, B3PW91, mPW1PW91, PBE1PBE, BPV86, PBEPBE, and LSDA are examined. Different basis sets including LANL2DZ, SDD, LANL2MB, CEP-4G, CEP-31G, and CEP-121G are also considered. It is remarkable that the LSDA/SDD level is clearly superior to all of the remaining density functional methods in predicting the structure of [Pt(en)(CBDCA-O, O')]. The results also indicate that the B3LYP/SDD level is the best to predict (13)C NMR spectra for [Pt(en)(CBDCA-O, O')] among all DFT methods.
Tsuzuki, Seiji; Honda, Kazumasa; Uchimaru, Tadafumi; Mikami, Masuhiro
2006-03-01
The MP2 (the second-order Møller-Plesset calculation) and CCSD(T) (coupled cluster calculation with single and double substitutions with noniterative triple excitations) interaction energies of all-trans n-alkane dimers were calculated using Dunning's [J. Chem. Phys. 90, 1007 (1989)] correlation consistent basis sets. The estimated MP2 interaction energies of methane, ethane, and propane dimers at the basis set limit [EMP2(limit)] by the method of Helgaker et al. [J. Chem. Phys. 106, 9639 (1997)] from the MP2/aug-cc-pVXZ (X =D and T) level interaction energies are very close to those estimated from the MP2/aug-cc-pVXZ (X =T and Q) level interaction energies. The estimated EMP2(limit) values of n-butane to n-heptane dimers from the MP2/cc-pVXZ (X =D and T) level interaction energies are very close to those from the MP2/aug-cc-pVXZ (X =D and T) ones. The EMP2(limit) values estimated by Feller's [J. Chem. Phys. 96, 6104 (1992)] method from the MP2/cc-pVXZ (X =D, T, and Q) level interaction energies are close to those estimated by the method of Helgaker et al. from the MP2/cc-pVXZ (X =T and Q) ones. The estimated EMP2(limit) values by the method of Helgaker et al. using the aug-cc-pVXZ (X =D and T) are close to these values. The estimated EMP2(limit) of the methane, ethane, propane, n-butane, n-pentane, n-hexane, n-heptane, n-octane, n-nonane, and n-decane dimers by the method of Helgaker et al. are -0.48, -1.35, -2.08, -2.97, -3.92, -4.91, -5.96, -6.68, -7.75, and -8.75kcal /mol, respectively. Effects of electron correlation beyond MP2 are not large. The estimated CCSD(T) interaction energies of the methane, ethane, propane, and n-butane dimers at the basis set limit by the method of Helgaker et al. (-0.41, -1.22, -1.87, and -2.74kcal/mol, respectively) from the CCSD(T )/cc-pVXZ (X =D and T) level interaction energies are close to the EMP2(limit) obtained using the same basis sets. The estimated EMP2(limit) values of the ten dimers were fitted to the form m0+m1X (X
DEFF Research Database (Denmark)
Mullins, Michael
elements into the process of design. Through its immersive properties, virtual reality allows access to a spatial experience of a computer model very different to both screen based simulations as well as traditional forms of architectural representation. The dissertation focuses on processes of the current......Contemporary communicational and informational processes contribute to the shaping of our physical environment by having a powerful influence on the process of design. Applications of virtual reality (VR) are transforming the way architecture is conceived and produced by introducing dynamic...... by ‘professionals’ to ‘laypeople’. The thesis articulates problems in VR’s current application, specifically the CAVE and Panorama theatres, and seeks an understanding of how these problems may be addressed. The central questions that have motivated this research project are thus: What is architectural VR...
A note on the pulay force at finite temperatures
Energy Technology Data Exchange (ETDEWEB)
Niklasson, Anders M N [Los Alamos National Laboratory
2008-01-01
Pulay's original expression for the basis-set dependent adjustment term to the Hellmann-Feynman force in electronic structure theory, which occurs for nonorthogonal local basis-set representations, is based on the idempotency condition of a pure ensemble. At finite electronic temperatures with a fractional occupation of the states, the conventional expression of the Pulay force is therefore no longer valid. Here we derive a simple and computationally efficient expression for a generalized Pulay force, which is suitable for large-scale ab initio simulations at finite electronic temperatures using local nonorthogonal basis-set representations. The generalized Pulay force expression is given in terms of the temperature-dependent density matrix. For the construction of the density matrix, we propose a recursive Fermi operator expansion algorithm that automatically converges to the correct chemical potential.
Tests for Wavelets as a Basis Set
Baker, Thomas; Evenbly, Glen; White, Steven
A wavelet transformation is a special type of filter usually reserved for image processing and other applications. We develop metrics to evaluate wavelets for general problems on test one-dimensional systems. The goal is to eventually use a wavelet basis in electronic structure calculations. We compare a variety of orthogonal wavelets such as coiflets, symlets, and daubechies wavelets. We also evaluate a new type of orthogonal wavelet with dilation factor three which is both symmetric and compact in real space. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award #DE-SC008696.
Representations of coherent and squeezed states in an extended two-parameter Fock space
Institute of Scientific and Technical Information of China (English)
M. K. Tavassoly; M. H. Lake
2012-01-01
Recently an f-deformed Fock space which is spanned by ｜n〉λ was introduced.These bases are the eigenstates of a deformed non-Hermitian Hamiltonian.In this contribution,we will use rather new nonorthogonal basis vectors for the construction of coherent and squeezed states,which in special case lead to the earlier known states.For this purpose,we first generalize the previously introduced Fock space spanned by ｜n〉λ bases,to a new one,spanned by extended two-parameters bases ｜n〉λ1,λ2.These bases are now the eigenstates of a non-Hermitian Hamiltonian Hλ1,λ2 =a(+)1,λ2a +1/2,where a(+)λ1,λ2 =a(+) + λ1a + λ2 and a are,respectively,the deformed creation and ordinary bosonic annihilation operators.The bases ｜n〉λ1,λ2 are nonorthogonal (squeezed states),but normalizable.Then,we deduce the new representations of coherent and squeezed states in our two-parameter Fock space.Finally,we discuss the quantum statistical properties,as well as the non-classical properties of the obtained states numerically.
Representations of Coherent and Squeezed States in an Extended Two-parameters Fock Space
Tavassoly, M K
2012-01-01
Recently a $f$-deformed Fock space which is spanned by $|n>_{\\lambda}$ has been introduced. These bases are indeed the eigen-states of a deformed non-Hermitian Hamiltonian. In this contribution, we will use a rather new non-orthogonal basis vectors for the construction of coherent and squeezed states, which in special case lead to the earlier known states. For this purpose, we first generalize the previously introduced Fock space spanned by $|n>_{\\lambda}$ bases, to a new one, spanned by an extended two-parameters bases $|n>_{\\lambda_{1},\\lambda_{2}}$. These bases are now the eigen-states of a non-Hermitian Hamiltonian $H_{\\lambda_{1},\\lambda_{2}}=a^{\\dagger}_{\\lambda_{1},\\lambda_{2}}a+1/2$, where $a^{\\dagger}_{\\lambda_{1},\\lambda_{2}}=a^{\\dagger}+\\lambda_{1}a + \\lambda_{2}$ and $a$ are respectively, the deformed creation and ordinary bosonic annihilation operators. The bases $|n>_{\\lambda_{1},\\lambda_{2}}$ are non-orthogonal (squeezed states), but normalizable. Then, we deduce the new representations of cohe...
Sherrill, C David; Takatani, Tait; Hohenstein, Edward G
2009-09-24
Large, correlation-consistent basis sets have been used to very closely approximate the coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] complete basis set potential energy curves of several prototype nonbonded complexes, the sandwich, T-shaped, and parallel-displaced benzene dimers, the methane-benzene complex, the H2S-benzene complex, and the methane dimer. These benchmark potential energy curves are used to assess the performance of several methods for nonbonded interactions, including various spin-component-scaled second-order perturbation theory (SCS-MP2) methods, the spin-component-scaled coupled-cluster singles and doubles method (SCS-CCSD), density functional theory empirically corrected for dispersion (DFT-D), and the meta-generalized-gradient approximation functionals M05-2X and M06-2X. These approaches generally provide good results for the test set, with the SCS methods being somewhat more robust. M05-2X underbinds for the test cases considered, while the performances of DFT-D and M06-2X are similar. Density fitting, dual basis, and local correlation approximations all introduce only small errors in the interaction energies but can speed up the computations significantly, particulary when used in combination.
Gao, Wei; Feng, Huajie; Xuan, Xiaopeng; Chen, Liuping
2012-10-01
An assessment study is presented about energy decomposition analysis (EDA) in combination with DFT including revised dispersion correction (DFT-D3) with Slater-type orbital (STO) basis set. There has been little knowledge about the performance of the EDA + DFT-D3 concerning STOs. In this assessment such an approach was applied to calculate noncovalent interaction energies and their corresponding components. Complexes in S22 set were used to evaluate the performance of EDA in conjunction with four representative types of GGA-functionals of DFT-D3 (BP86-D3, BLYP-D3, PBE-D3 and SSB-D3) with three STO basis sets ranging in complexity from DZP, TZ2P to QZ4P. The results showed that the approach of EDA + BLYP-D3/TZ2P has a better performance not only in terms of calculating noncovalent interaction energy quantitatively but also in analyzing corresponding energy components qualitatively. This approach (EDA + BLYP-D3/TZ2P) was thus applied further to two representative large-system complexes including porphine dimers and fullerene aggregates to gain a better insight into binding characteristics.
On the use of the Discrete Variable Representation Basis in Nuclear Physics
Bulgac, Aurel
2013-01-01
The discrete variable representation (DVR) basis is nearly optimal for numerically representing wave functions in nuclear physics: Suitable problems enjoy exponential convergence, yet the Hamiltonian remains sparse. We show that one can often use smaller basis sets than with the traditional harmonic oscillator basis, and still benefit from the simple analytic properties of the DVR basis which requires no overlap integrals, simply permit using various Jacobi coordinates, and admit straightforward analyses of the UV and IR convergence properties.
Dattani, Nikesh S.; Sharma, Sandeep; Alavi, Ali
2016-06-01
Being the simplest uncharged homonuclear dimer after H_2 that has a stable ground state, Li_2 is one of the most important benchmark systems for theory and experiment. In 1930, Delbruck used Li_2 to test his theory of homopolar binding, and it was used again and again as a prototype to test what have now become some of the most ubiquitous concepts in molecular physics (LCAO, SCF, MO, just to name a few). Experimentally, Roscoe and Schuster studied alkali dimers back in 1874. At the dawn of quantum mechanics, the emerging types of spectroscopic analyses we now use today, were tested on Li_2 in the labs of Wurm (1928), Harvey (1929), Lewis (1931), and many others, independently. Li_2 was at the centre of the development of PFOODR in the 80s, and PAS in the 90s; and Lithium Bose-Einstein condensates were announced only 1 month after the Nobel Prize winning BEC announcement in 1995. Even now in the 2010s, numerous experimental and theoretical studies on Li have tested QED up to the 7th power of the fine structure constant. Li_2 has also been of interest to sub-atomic physicists, as it was spectroscopic measurements on ^7Li_2 that determined the spin of ^7Li to be 3/2 in 1931; and Li_2 has been proposed in 2014 as a candidate for the first ``halo nucleonic molecule". The lowest triplet state a(1^3Σ_u^+) is an excellent benchmark system for all newly emerging ab initio techniques because it has only 6e^-, its potential is only 334 cm-1 deep, it avoids harsh complications from spin-orbit coupling, and it is the deepest potential for which all predicted vibrational energy levels have been observed with 0.0001 cm-1 precision. However the current best ab initio potentials do not even yield all vibrational energy spacings correct to within 1 cm-1. This could be because the calculation was only done on a cc-pV5Z basis set, or because the QCISD(T,full) method that the authors used, only considered triple excitations while a full CI calculation should include up to hexuple
Orlando, Roberto; Lacivita, Valentina; Bast, Radovan; Ruud, Kenneth
2010-06-01
The computational scheme for the evaluation of the second-order electric susceptibility tensor in periodic systems, recently implemented in the CRYSTAL code within the coupled perturbed Hartree-Fock (HF) scheme, has been extended to local-density, gradient-corrected, and hybrid density functionals (coupled-perturbed Kohn-Sham) and applied to a set of cubic and hexagonal semiconductors. The method is based on the use of local basis sets and analytical calculation of derivatives. The high-frequency dielectric tensor (ɛ∞) and second-harmonic generation susceptibility (d) have been calculated with hybrid functionals (PBE0 and B3LYP) and the HF approximation. Results are compared with the values of ɛ∞ and d obtained from previous plane-wave local density approximation or generalized gradient approximation calculations and from experiment. The agreement is in general good, although comparison with experiment is affected by a certain degree of uncertainty implicit in the experimental techniques.
Orlando, Roberto; Lacivita, Valentina; Bast, Radovan; Ruud, Kenneth
2010-06-28
The computational scheme for the evaluation of the second-order electric susceptibility tensor in periodic systems, recently implemented in the CRYSTAL code within the coupled perturbed Hartree-Fock (HF) scheme, has been extended to local-density, gradient-corrected, and hybrid density functionals (coupled-perturbed Kohn-Sham) and applied to a set of cubic and hexagonal semiconductors. The method is based on the use of local basis sets and analytical calculation of derivatives. The high-frequency dielectric tensor (epsilon(infinity)) and second-harmonic generation susceptibility (d) have been calculated with hybrid functionals (PBE0 and B3LYP) and the HF approximation. Results are compared with the values of epsilon(infinity) and d obtained from previous plane-wave local density approximation or generalized gradient approximation calculations and from experiment. The agreement is in general good, although comparison with experiment is affected by a certain degree of uncertainty implicit in the experimental techniques.
Howard, J Coleman; Tschumper, Gregory S
2015-05-12
A series of (H2O)n clusters ranging from the dimer to the hexamer have been characterized with the CCSD(T) and the 2-body:Many-body CCSD(T):MP2 methods near the complete basis set (CBS) limit to generate benchmark-quality optimized structures and harmonic vibrational frequencies for these important systems. Quadruple-ζ correlation-consistent basis sets that augment the O atoms with diffuse functions have been employed in the analytic computation of harmonic vibrational frequencies for the global minima of the dimer, trimer, tetramer, and pentamer as well as the ring, book, cage, and prism isomers of the hexamer. Prior calibration [J. Chem. Phys. 2013, 139, 184113 and J. Chem. Theory Comput. 2014, 10, 5426] suggests that harmonic frequencies computed with this approach will lie within a few cm(-1) of the canonical CCSD(T) CBS limit. These data are used as reference values to gauge the performance of harmonic frequencies obtained with other ab initio methods (e.g., LCCSD(T) and MP2) and water potentials (e.g., TTM3-F and WHBB). This comparison reveals that it is far more challenging to converge harmonic vibrational frequencies for the bound OH stretching modes in these (H2O)n clusters to the CCSD(T) CBS limit than the free OH stretches, the n intramonomer HOH bending modes and even the 6n - 6 intermonomer modes. Deviations associated with the bound OH stretching harmonic frequencies increase rapidly with the size of the cluster for all methods and potentials examined, as do the corresponding frequency shifts relative to the monomer OH stretches.
Yildiz, F; Przybylski, M; Kirschner, J
2009-10-02
Tetragonal distortion in Fe1-xCox alloy films grown epitaxially on Rh(001) substrates results in a strong perpendicular magnetic anisotropy. Since the perpendicular magnetic anisotropy varies with the Fe1-xCox film composition, one can grow multilayer structures with ferromagnetic films sequentially showing either an in-plane (e.g., Fe) or out-of-plane (e.g., Fe0.5Co0.5) easy-magnetization axis. The Rh spacers mediate an interlayer coupling which couples the magnetizations either ferromagnetically or antiferromagnetically, depending on the spacer thickness. When the anisotropy energy is compatible to the coupling, it produces nonorthogonal magnetization configurations which vary under a small change of the external magnetic field.
Institute of Scientific and Technical Information of China (English)
虞忠衡; 彭晓琦; 郭彦伸; 宣正乾
2001-01-01
高度定域的、对称的、键轨道基组的建立是一个多步的计算程序：(1)以定域片断轨道[Фk，Фi，φj]为基，对分子作有条件的RHF运算，算得FUL和DSI°态的片断分子轨道[Ф0l，Ф0n，Ф0m]和[Фl，Фn，Фm].在基组[Фk，Фi，φj]中，Фi∈双占据和空σ片断分子轨道(FMOs)组，φi∈πFMO组，Фk∈单占据σFMO组，它们都精确地定域在各自的片断内；(2)利用Ф0l与Фl间的重叠积分值(Sll>O.5)，可以从DSI°态中，自动地选出Ns个对称的、由单占据轨道线性组合而成的分子轨道Ф0l=∑akФk(k=1，2，…，Ns).接着，用Ф0l取代FUL态中同类的、非对称轨道组Фl=∑aldФk(k=1，2，…，Ns)；(3)以上述新的轨道组[Ф0l，Фn，Фm]为基(其中，Ф0l∈DSI0态，它们离域于整个分子；双占据及空σFMO组Фn和πFMO组Фm属于FUL态)，按FUL态的条件，再次对分子作有条件的RHF运算，从中得到一组对称的、闭壳层正则FMOs，而且每一个FMO均有正确的电子占据数；(4)利用Perkin原理，将第3步所得的正则FMO组定域成一个对称的键轨道基组[Фl′，Фn′Фm′].在这个基组中，π体系Фm′与σ构架Фn′是彻底分离的，而且这两个轨道组始终精确地定域在各自的片断内.%A procedure for constructing a highly localized and symmetrical bond orbital basis set with the πsystems separated off from the σ frameworks has been developed. It is a four- step procedure: ( 1 )over the opened-shell localized fragment molecular orbital (FMO) basis set [φk, φi, φj] where φi ∈ doubly occ. And vacant σFMOs, φj ∈ πFMOs, and φk ∈ singly occ. FMOs, the conditional RHF computations provide each of the FUL and DSI° electronic states of a molecule, such as norbornadiene with a set of the closed-shell FMOs;(2) the symmetrical MOs, φ0l′= ∑ akl′ φk ( k = 1,2,…, Ns) which have delocalized over the whole molecule, in the DSI° substitutes for the
Williamson, Rodney Lowell
Total geometry optimizations are reported for Cr(CO)_6, HMn(CO)_5 , Fe(CO)_5, Ni(CO) _4, Cr(C_6H _6)_2, Fe(C_5H _5)_2, Ni(C_4 H_4)_2, Cr(NO) _4, (C_5H _5)Mn(CO)_3, and (C _6H_6)Cr(CO) _3. A variety of basis sets were examined, and, based on the results, a relatively compact and accurate basis set is proposed. Addition of electron correlation at the perfect pairing GVB level reduced the average difference in the metal-cyclopentadienyl bond length of 0.08 A. Optimization of the geometry of TiCl_4 and TiCl_3CH_3 at the self-consistent-field (SCF) level results in Ti-Cl bond lengths longer than the experimental values, even when d- and f-type polarization functions are added to the basis set. The bond lengths remain too long even as the Hartree-Fock limit is approached because the SCF level of theory over-estimates the noble-gas-like Cl cdotsCl repulsions, which hinder close Ti -Cl approach. The Ti-C-H angle of TiCl_3 CH_3 is calculated to be close to tetrahedral geometry with little flattening of the hydrogen atoms, which apparently was observed in the electron diffraction. These same calculations do predict the anomalously low methyl-rocking frequency for the titanium complex in agreement with the experimental IR. The large positive geminal hydrogen coupling constant observed in the NMR experiment is due primarily to the sigma -donor and pi-acceptor character of the TiCl_3 moiety and not to any flattening of the methyl group. The structure and bonding of (Cr(Cp)(CO) _2) _2 was examined by optimizing the geometry of the dimer, fragment moiety, and analogous stable monomers. The optimized structure of Cr(Cp)(CO)_2N has a "piano stool" geometry with a fragment moiety geometry nearly identical to the geometry of the fragment moiety in the dimer. Examination of x-ray and theoretical geometries of monomers with the fragment moiety bonded to single ligand show that the geometry of the fragment moiety is insensitive to the ligands bonded to it. Van der Waals calculations
Representation as the representation of experience
Ankersmit, FR
This essay deals, mainly, with the notion of representation. Representation is associated with texts and, as such, is contrasted to the true singular statement. It is argued that the relationship between the text and what the text represents can never be modeled on the relationship between the true
Energy Technology Data Exchange (ETDEWEB)
Morgado, Claudio A.; Jurecka, Petr; Svozil, Daniel; Hobza, Pavel; Sponer, Jiri
2009-06-09
We have carried out reference quantum-chemical calculations for about 100 geometries of the uracil dimer in stacked conformations. The calculations have been specifically aimed at geometries with unoptimized distances between the monomers including geometries with mutually tilted monomers. Such geometries are characterized by a delicate balance between local steric clashes and local unstacking and had until now not been investigated using reference quantummechanics (QM) methods. Nonparallel stacking geometries often occur in nucleic acids and are of decisive importance, for example, for local conformational variations in B-DNA. Errors in the shortrange repulsion region would have a major impact on potential energy scans which were often used in the past to investigate local geometry variations in DNA. An incorrect description of such geometries may also partially affect molecular dynamics (MD) simulations in applications when quantitative accuracy is required. The reference QM calculations have been carried out using the MP2 method extrapolated to the complete basis-set limit and corrected for higher-order electron-correlation contributions using CCSD(T) calculations with a medium-sized basis set. These reference calculations have been used as benchmark data to test the performance of the DFT-D, SCS(MI)-MP2, and DFTSAPT QM methods and of the AMBER molecular-mechanics (MM) force field. The QM methods show close to quantitative agreement with the reference data, albeit the DFT-D method tends to modestly exaggerate the repulsion of steric clashes. The force field in general also provides a good description of base stacking for the systems studied here. However, for geometries with close interatomic contacts and clashes, the repulsion effects are rather severely exaggerated. The discrepancy reported here should not affect the overall stability of MD simulations and qualitative applications of the force field. However, it may affect the description of subtle
Institute of Scientific and Technical Information of China (English)
Zhang Jin-Ping; Cheng Xin-Lu; Zhang Hong; Yang Xiang-Dong
2011-01-01
Three low-lying electronic states (X1∑+, a3∑+, and A1Ⅱ) of NO+ ion are studied using the complete active space self-consistent-field (CASSCF) method followed by highly accurate valence internally contracted multi-reference configuration interaction (MRCI) approach in combination of the correlation-consistent sextuple basis set augmented with diffuse functions, aug-cc-pV6Z. The potential energy curves (PECs) of the NO+(X1∑+, a3∑+, A1Ⅱ) are calculated. Based on the PECs, the spectroscopic parameters Re, De, ωe, ωeXe, αe, Be, and D0 are reproduced, which are in excellent agreement with the available measurements. By numerically solving the radial Schr(o)dinger equation of nuclear motion using the Numerov method, the first 20 vibrational levels, inertial rotation and centrifugal distortion constants of NO+(X1∑+, a3∑+, A1Ⅱ) ion are derived when the rotational quantum number J is equal to zero (J = 0)for the first time, which accord well with the available measurements. Finally, the analytical potential energy functions of these states are fitted, which are used to accurately derive the first 20 classical turning points when J = 0. These results are compared in detail with those of previous investigations reported in the literature.
Roper, Ian P E; Besley, Nicholas A
2016-03-21
The simulation of X-ray emission spectra of transition metal complexes with time-dependent density functional theory (TDDFT) is investigated. X-ray emission spectra can be computed within TDDFT in conjunction with the Tamm-Dancoff approximation by using a reference determinant with a vacancy in the relevant core orbital, and these calculations can be performed using the frozen orbital approximation or with the relaxation of the orbitals of the intermediate core-ionised state included. Both standard exchange-correlation functionals and functionals specifically designed for X-ray emission spectroscopy are studied, and it is shown that the computed spectral band profiles are sensitive to the exchange-correlation functional used. The computed intensities of the spectral bands can be rationalised by considering the metal p orbital character of the valence molecular orbitals. To compute X-ray emission spectra with the correct energy scale allowing a direct comparison with experiment requires the relaxation of the core-ionised state to be included and the use of specifically designed functionals with increased amounts of Hartree-Fock exchange in conjunction with high quality basis sets. A range-corrected functional with increased Hartree-Fock exchange in the short range provides transition energies close to experiment and spectral band profiles that have a similar accuracy to those from standard functionals.
Campos, Cesar T; Jorge, Francisco E; Alves, Júlia M A
2012-09-01
Recently, segmented all-electron contracted double, triple, quadruple, quintuple, and sextuple zeta valence plus polarization function (XZP, X = D, T, Q, 5, and 6) basis sets for the elements from H to Ar were constructed for use in conjunction with nonrelativistic and Douglas-Kroll-Hess Hamiltonians. In this work, in order to obtain a better description of some molecular properties, the XZP sets for the second-row elements were augmented with high-exponent d "inner polarization functions," which were optimized in the molecular environment at the second-order Møller-Plesset level. At the coupled cluster level of theory, the inclusion of tight d functions for these elements was found to be essential to improve the agreement between theoretical and experimental zero-point vibrational energies (ZPVEs) and atomization energies. For all of the molecules studied, the ZPVE errors were always smaller than 0.5 %. The atomization energies were also improved by applying corrections due to core/valence correlation and atomic spin-orbit effects. This led to estimates for the atomization energies of various compounds in the gaseous phase. The largest error (1.2 kcal mol(-1)) was found for SiH(4).
Sankaranarayanan, S
2003-01-01
In the present study, an existing two-dimensional boundary-fitted model [J. Hydraul. Eng.-ASCE 122 (9) (1996) 512] is used to study the effect of grid non-orthogonality on the solution of shallow water equations using boundary-fitted grids. The linearized two-dimensional shallow water equations are expressed in terms of the grid angle and aspect ratio. The truncation errors of the finite difference approximations used in the solution of the governing equations are shown to be dependent on the grid angle and the aspect ratio. The coefficient of the truncation error was shown to increase, with the decrease in the grid angle. The RMS errors in model predicted surface elevations and velocities for the case of seiching in a rectangular basin are found to increase gradually, as the grid resolution decreases from 174 to 80 gridpoints per wavelength or as the grid angle decreases from 90 deg. to 50 deg. and increases rather sharply for a grid angle of 30 deg. at grid resolutions less than 80 gridpoints per wavelength...
Social representations of women
Directory of Open Access Journals (Sweden)
Álvaro Estramiana, José Luis
2006-05-01
Full Text Available Social Representations is one of the most important theories in contemporary social psychology. Since the social psychologist Serge Moscovici developed his theory of social representations to explain how a scientific theory such as the psychoanalysis turns into a common sense knowledge many studies have been done by different social psychologists. The analysis of the social representations of women as represented in myths and popular beliefs is an excellent opportunity to study how this theory can be applied to this representational field. At the same time it makes possible to understand the formation of attitudes towards women
Extensions of tempered representations
Opdam, E.; Solleveld, M.
2013-01-01
Let π, π′ be irreducible tempered representations of an affine Hecke algebra H with positive parameters. We compute the higher extension groups Ext nH(π,π′) explicitly in terms of the representations of analytic R-groups corresponding to π and π′. The result has immediate applications to the computa
Multiple sparse representations classification
E. Plenge (Esben); S.K. Klein (Stefan); W.J. Niessen (Wiro); E. Meijering (Erik)
2015-01-01
textabstractSparse representations classification (SRC) is a powerful technique for pixelwise classification of images and it is increasingly being used for a wide variety of image analysis tasks. The method uses sparse representation and learned redundant dictionaries to classify image pixels. In t
Embedded Data Representations.
Willett, Wesley; Jansen, Yvonne; Dragicevic, Pierre
2017-01-01
We introduce embedded data representations, the use of visual and physical representations of data that are deeply integrated with the physical spaces, objects, and entities to which the data refers. Technologies like lightweight wireless displays, mixed reality hardware, and autonomous vehicles are making it increasingly easier to display data in-context. While researchers and artists have already begun to create embedded data representations, the benefits, trade-offs, and even the language necessary to describe and compare these approaches remain unexplored. In this paper, we formalize the notion of physical data referents - the real-world entities and spaces to which data corresponds - and examine the relationship between referents and the visual and physical representations of their data. We differentiate situated representations, which display data in proximity to data referents, and embedded representations, which display data so that it spatially coincides with data referents. Drawing on examples from visualization, ubiquitous computing, and art, we explore the role of spatial indirection, scale, and interaction for embedded representations. We also examine the tradeoffs between non-situated, situated, and embedded data displays, including both visualizations and physicalizations. Based on our observations, we identify a variety of design challenges for embedded data representation, and suggest opportunities for future research and applications.
Ankersmit, F.R.
2010-01-01
This essay focuses on the historical text as a whole. It does so by conceiving of the historical text as representation - in the way the we may say of a photo or a painting that it represents the person depicted on it. It is argued that representation cannot be properly understood by modelling it on
Group and representation theory
Vergados, J D
2017-01-01
This volume goes beyond the understanding of symmetries and exploits them in the study of the behavior of both classical and quantum physical systems. Thus it is important to study the symmetries described by continuous (Lie) groups of transformations. We then discuss how we get operators that form a Lie algebra. Of particular interest to physics is the representation of the elements of the algebra and the group in terms of matrices and, in particular, the irreducible representations. These representations can be identified with physical observables. This leads to the study of the classical Lie algebras, associated with unitary, unimodular, orthogonal and symplectic transformations. We also discuss some special algebras in some detail. The discussion proceeds along the lines of the Cartan-Weyl theory via the root vectors and root diagrams and, in particular, the Dynkin representation of the roots. Thus the representations are expressed in terms of weights, which are generated by the application of the elemen...
DEFF Research Database (Denmark)
Willett, Wesley; Jansen, Yvonne; Dragicevic, Pierre
2017-01-01
We introduce embedded data representations, the use of visual and physical representations of data that are deeply integrated with the physical spaces, objects, and entities to which the data refers. Technologies like lightweight wireless displays, mixed reality hardware, and autonomous vehicles...... are making it increasingly easier to display data in-context. While researchers and artists have already begun to create embedded data representations, the benefits, trade-offs, and even the language necessary to describe and compare these approaches remain unexplored. In this paper, we formalize the notion...... of physical data referents – the real-world entities and spaces to which data corresponds – and examine the relationship between referents and the visual and physical representations of their data. We differentiate situated representations, which display data in proximity to data referents, and embedded...
Nori-Shargh, Davood; Mousavi, Seiedeh Negar; Kayi, Hakan
2014-05-01
Complete basis set CBS-4, hybrid-density functional theory (hybrid-DFT: B3LYP/6-311+G**) based methods and natural bond orbital (NBO) interpretations have been used to examine the contributions of the hyperconjugative, electrostatic, and steric effects on the conformational behaviors of trans-2,3-dihalo-1,4-diselenane [halo = F (1), Cl (2), Br (3)] and trans-2,5-dihalo-1,4-diselenane [halo = F (4), Cl (5), Br (6)]. Both levels of theory showed that the axial conformation stability, compared to its corresponding equatorial conformation, decreases from compounds 1 → 3 and 4 → 6. Based on the results obtained from the NBO analysis, there are significant anomeric effects for compounds 1-6. The anomeric effect associated with the electron delocalization is in favor of the axial conformation and increases from compounds 1 → 3 and 4 → 6. On the other hand, dipole moment differences between the axial and equatorial conformations [Δ(μ(eq)-μ(ax)] decrease from compounds 1 → 3. Although Δ(μ(eq)-μ(ax)) parameter decreases from compound 1 to compound 3, the dipole moment values of the axial conformations are smaller than those of their corresponding equatorial conformations. Therefore, the anomeric effect associated with the electron delocalizations (for halogen-C-Se segments) and the electrostatic model associated with the dipole-dipole interactions fail to account for the increase of the equatorial conformations stability on going from compound 1 to compound 3. Since there is no dipole moment for the axial and equatorial conformations of compounds 4-6, consequently, the conformational preferences in compounds 1-6 is in general dictated by the steric hindrance factor associated with the 1,3-syn-axial repulsions. Importantly, the CBS-4 results show that the entropy difference (∆S) between the equatorial axial conformations increases from compounds 1 → 3 and 4 → 6. This fact can be explained by the anomeric effect associated
Solving Dirac equation using the tridiagonal matrix representation approach
Energy Technology Data Exchange (ETDEWEB)
Alhaidari, A.D. [Saudi Center for Theoretical Physics, P.O. Box 32741, Jeddah 21438 (Saudi Arabia); Bahlouli, H., E-mail: bahlouli@kfupm.edu.sa [Saudi Center for Theoretical Physics, P.O. Box 32741, Jeddah 21438 (Saudi Arabia); Physics Department, King Fahd University of Petroleum & Minerals, Dhahran 31261 (Saudi Arabia); Assi, I.A. [Physics Department, King Fahd University of Petroleum & Minerals, Dhahran 31261 (Saudi Arabia)
2016-04-22
The aim of this work is to find exact solutions of the one dimensional Dirac equation using the tridiagonal matrix representation. We write the spinor wavefunction as a bounded infinite sum in a complete basis set, which is chosen such that the matrix representation of the Dirac wave operator becomes tridiagonal and symmetric. This makes the wave equation equivalent to a symmetric three-term recursion relation for the expansion coefficients of the wavefunction. We solve the recursion relation and obtain the relativistic energy spectrum and corresponding state functions. We are honored to dedicate this work to Prof. Hashim A. Yamani on the occasion of his 70th birthday. - Highlights: • We choose L2 basis such that the Dirac wave operator is tridiagonal matrix. • We use the tridiagonal-matrix-representation approach. • The wave equation becomes a symmetric three-term recursion relation. • We solve the associated three-term recursion relation exactly. • The energy spectrum formula is obtained.
Miliordos, Evangelos; Xantheas, Sotiris S
2015-06-21
We report MP2 and Coupled Cluster Singles, Doubles, and perturbative Triples [CCSD(T)] binding energies with basis sets up to pentuple zeta quality for the (H2O)m=2-6,8 water clusters. Our best CCSD(T)/Complete Basis Set (CBS) estimates are -4.99 ± 0.04 kcal/mol (dimer), -15.8 ± 0.1 kcal/mol (trimer), -27.4 ± 0.1 kcal/mol (tetramer), -35.9 ± 0.3 kcal/mol (pentamer), -46.2 ± 0.3 kcal/mol (prism hexamer), -45.9 ± 0.3 kcal/mol (cage hexamer), -45.4 ± 0.3 kcal/mol (book hexamer), -44.3 ± 0.3 kcal/mol (ring hexamer), -73.0 ± 0.5 kcal/mol (D2d octamer), and -72.9 ± 0.5 kcal/mol (S4 octamer). We have found that the percentage of both the uncorrected (De) and basis set superposition error-corrected (De (CP)) binding energies recovered with respect to the CBS limit falls into a narrow range on either sides of the CBS limit for each basis set for all clusters. In addition, this range decreases upon increasing the basis set. Relatively accurate estimates (within set) or the "12, 12" (for the AVTZ, AVQZ, and AV5Z sets) mixing ratio between De and De (CP). These mixing rations are determined via a least-mean-squares approach from a dataset that encompasses clusters of various sizes. Based on those findings, we propose an accurate and efficient computational protocol that can be presently used to estimate accurate binding energies of water clusters containing up to 30 molecules (for CCSD(T)) and up to 100 molecules (for MP2).
Analytic derivatives for the Cholesky representation of the two-electron integrals.
Aquilante, Francesco; Lindh, Roland; Pedersen, Thomas Bondo
2008-07-21
We propose a formalism for calculating analytic derivatives of the electronic energy with respect to nuclear coordinates using Cholesky decomposition of the two-electron integrals. The formalism is derived by exploiting the equivalence of Cholesky decomposition and density fitting when a suitable auxiliary basis set is used for expanding atomic orbital product densities in the latter. An implementation of gradients at the nonhybrid density functional theory level is presented, and sample calculations demonstrate that the errors in equilibrium geometries due to the Cholesky representation of the integrals can be controlled by adjusting the decomposition threshold.
Hyperfinite Representation of Distributions
Indian Academy of Sciences (India)
J Sousa Pinto; R F Hoskins
2000-11-01
Hyperfinite representation of distributions is studied following the method introduced by Kinoshita [2, 3], although we use a different approach much in the vein of [4]. Products and Fourier transforms of representatives of distributions are also analysed.
Income, Ideology, and Representation
Directory of Open Access Journals (Sweden)
Chris Tausanovitch
2016-11-01
Full Text Available Do legislators represent the rich better than they represent the poor? Recent work provides mixed support for this proposition. I test the hypothesis of differential representation using a data set on the political preferences of 318,537 individuals. Evidence of differential representation in the House of Representatives is weak. Support for differential representation is stronger in the Senate. In recent years, representation has occurred primarily through the selection of a legislator from the appropriate party. Although the preferences of higher-income constituents account for more of the variation in legislator voting behavior, higher-income constituents also account for much more of the variation in district preferences. In light of the low level of overall responsiveness, differential responsiveness appears small.
Ordering ambiguity versus representation
Energy Technology Data Exchange (ETDEWEB)
Souza de Dutra, A [Abdus Salam ICTP, Strada Costiera 11, 34014 Trieste (Italy); UNESP-Campus de Guaratingueta-DFQ , Av. Dr. Ariberto Pereira da Cunha, 333, C.P. 205, 12516-410 Guaratingueta SP (Brazil)
2006-01-06
In this work we show that the ordering ambiguity on quantization depends on the representation choice. This property is then used to solve unambiguously some particular systems. Finally, we speculate on the consequences for more involved cases.
MORPHOLOGICAL REPRESENTATION AND SEMANTIC ...
African Journals Online (AJOL)
The morphological representation assigned to a complex word must provide the formal structure .... This brings us to the cases where, on Williams's (1981a:258) analysis, the compositional notion ...... Die en moda Ii tei t . Kaaps tad: Ba 1 kema.
Function, anticipation, representation
Bickhard, Mark. H.
2001-06-01
Function emerges in certain kinds of far-from-equilibrium systems. One important kind of function is that of interactive anticipation, an adaptedness to temporal complexity. Interactive anticipation is the locus of the emergence of normative representational content, and, thus, of representation in general: interactive anticipation is the naturalistic core of the evolution of cognition. Higher forms of such anticipation are involved in the subsequent macro-evolutionary sequence of learning, emotions, and reflexive consciousness.
Representation Elements of Spatial Thinking
Fiantika, F. R.
2017-04-01
This paper aims to add a reference in revealing spatial thinking. There several definitions of spatial thinking but it is not easy to defining it. We can start to discuss the concept, its basic a forming representation. Initially, the five sense catch the natural phenomenon and forward it to memory for processing. Abstraction plays a role in processing information into a concept. There are two types of representation, namely internal representation and external representation. The internal representation is also known as mental representation; this representation is in the human mind. The external representation may include images, auditory and kinesthetic which can be used to describe, explain and communicate the structure, operation, the function of the object as well as relationships. There are two main elements, representations properties and object relationships. These elements play a role in forming a representation.
Representation, interaction, and intersubjectivity.
Alterman, Richard
2007-09-10
What the participants share, their common "sense" of the world, creates a foundation, a framing, an orientation that enables human actors to see and act in coordination with one another. For recurrent activities, the methods the participants use to understand each other as they act change, making the intersubjective space in which actors operate richer and easier to produce. This article works through some of the issues that emerge from a close examination of intersubjectivity as it is managed through representation and interaction. The data that are presented document, in detail, a sequence of related interactions, within and across episodes of cooperation, where continuity and change can be observed. The emergence of conversational structure and coordinating representations are significant milestones in the long-term development of a representational practice that support the runtime co-construction of intersubjective space. Conversational structures emerge interactively to mediate recurrent points of coordination in the domain activity, and only secondarily the conversation itself. Coordinating representations change the representational practice of the participants by making it easier to manage their "shared view" of the collective work, enabling the participants to make progress, expand the field of the common activity, while exhibiting more control of if and when explicit grounding occurs.
Representation Discovery using Harmonic Analysis
Mahadevan, Sridhar
2008-01-01
Representations are at the heart of artificial intelligence (AI). This book is devoted to the problem of representation discovery: how can an intelligent system construct representations from its experience? Representation discovery re-parameterizes the state space - prior to the application of information retrieval, machine learning, or optimization techniques - facilitating later inference processes by constructing new task-specific bases adapted to the state space geometry. This book presents a general approach to representation discovery using the framework of harmonic analysis, in particu
Towards Multimodal Content Representation
Bunt, Harry
2009-01-01
Multimodal interfaces, combining the use of speech, graphics, gestures, and facial expressions in input and output, promise to provide new possibilities to deal with information in more effective and efficient ways, supporting for instance: - the understanding of possibly imprecise, partial or ambiguous multimodal input; - the generation of coordinated, cohesive, and coherent multimodal presentations; - the management of multimodal interaction (e.g., task completion, adapting the interface, error prevention) by representing and exploiting models of the user, the domain, the task, the interactive context, and the media (e.g. text, audio, video). The present document is intended to support the discussion on multimodal content representation, its possible objectives and basic constraints, and how the definition of a generic representation framework for multimodal content representation may be approached. It takes into account the results of the Dagstuhl workshop, in particular those of the informal working group...
Post-representational cartography
Directory of Open Access Journals (Sweden)
Rob Kitchin
2010-03-01
Full Text Available Over the past decade there has been a move amongst critical cartographers to rethink maps from a post-representational perspective – that is, a vantage point that does not privilege representational modes of thinking (wherein maps are assumed to be mirrors of the world and automatically presumes the ontological security of a map as a map, but rather rethinks and destabilises such notions. This new theorisation extends beyond the earlier critiques of Brian Harley (1989 that argued maps were social constructions. For Harley a map still conveyed the truth of a landscape, albeit its message was bound within the ideological frame of its creator. He thus advocated a strategy of identifying the politics of representation within maps in order to circumnavigate them (to reveal the truth lurking underneath, with the ontology of cartographic practice remaining unquestioned.
Learning network representations
Moyano, Luis G.
2017-02-01
In this review I present several representation learning methods, and discuss the latest advancements with emphasis in applications to network science. Representation learning is a set of techniques that has the goal of efficiently mapping data structures into convenient latent spaces. Either for dimensionality reduction or for gaining semantic content, this type of feature embeddings has demonstrated to be useful, for example, for node classification or link prediction tasks, among many other relevant applications to networks. I provide a description of the state-of-the-art of network representation learning as well as a detailed account of the connections with other fields of study such as continuous word embeddings and deep learning architectures. Finally, I provide a broad view of several applications of these techniques to networks in various domains.
Mobilities and Representations
DEFF Research Database (Denmark)
Thelle, Mikkel
2016-01-01
, literature, and film. Moreover, we hope the authors of future reviews will reflect on the ways they approached those representations. Such commentaries would provide valuable methodological insights, and we hope to begin that effort with this interview. We have asked four prominent mobility scholars...... to consider how they and their peers are currently confronting representations of mobility. This is particularly timely given the growing academic focus on practices, material mediation, and nonrepresentational theories, as well as on bodily reactions, emotions, and feelings that, according to those theories...
Additive and polynomial representations
Krantz, David H; Suppes, Patrick
1971-01-01
Additive and Polynomial Representations deals with major representation theorems in which the qualitative structure is reflected as some polynomial function of one or more numerical functions defined on the basic entities. Examples are additive expressions of a single measure (such as the probability of disjoint events being the sum of their probabilities), and additive expressions of two measures (such as the logarithm of momentum being the sum of log mass and log velocity terms). The book describes the three basic procedures of fundamental measurement as the mathematical pivot, as the utiliz
Non-Orthogonal Iris Segmentation
2005-05-09
Gonzalez , Rafael C., R. E. Woods, and Steven L. Eddins. Digital Image Processing using MATLAB. Upper Saddle River, New Jersey: Prentice Hall, 2004... images . Over the last ten years, algorithms used to digitize and process biometric signals have been enhanced to increase both accuracy over repeated...Steven L. Eddins. “ Digital Image Processing using MATLAB.” Prentice Hall, Upper Saddle River, NJ. 20044. [15] A. J. Bron, R. C. Tripathi, and B. J
Moment graphs and representations
DEFF Research Database (Denmark)
Jantzen, Jens Carsten
2012-01-01
Moment graphs and sheaves on moment graphs are basically combinatorial objects that have be used to describe equivariant intersectiion cohomology. In these lectures we are going to show that they can be used to provide a direct link from this cohomology to the representation theory of simple Lie...
Compact Information Representations
2016-08-02
network traffic, information retrieval, and databases are faced with very large, inherently high-dimensional, or naturally streaming datasets. This...proposal aims at developing mathematically rigorous and general- purpose statistical methods based on stable random projections, to achieve compact...detections (e.g., DDoS attacks), machine learning, databases , and search. Fundamentally, compact data representations are highly beneficial because they
Representation and human reasoning
ter Meulen, Alice G.B.
2003-01-01
Interpretation and reasoning are two sides of sharing information. Representations of the context and common ground must capture the rich content of what has been said, by linking to situations in the world as well as to what has been said before, common sense and to the presuppositions and entailme
Moment graphs and representations
DEFF Research Database (Denmark)
Jantzen, Jens Carsten
2012-01-01
Moment graphs and sheaves on moment graphs are basically combinatorial objects that have be used to describe equivariant intersectiion cohomology. In these lectures we are going to show that they can be used to provide a direct link from this cohomology to the representation theory of simple Lie...... algebras and of simple algebraic groups. The first section contains some background on equivariant cohomology....
DEFF Research Database (Denmark)
Loddegaard, Anne
2009-01-01
out of place in a novel belonging to the serious combat literature of the Catholic Revival, and the direct representation of the supernatural is also surprising because previous Catholic Revival novelists, such as Léon Bloy and Karl-Joris Huysmans, maintain a realistic, non-magical world and deal...
DEFF Research Database (Denmark)
Loddegaard, Anne
2012-01-01
out of place in a novel belonging to the serious combat literature of the Catholic Revival, and the direct representation of the supernatural is also surprising because previous Catholic Revival novelists, such as Léon Bloy and Karl-Joris Huysmans, maintain a realistic, non-magical world and deal...
Women and political representation.
Rathod, P B
1999-01-01
A remarkable progress in women's participation in politics throughout the world was witnessed in the final decade of the 20th century. According to the Inter-Parliamentary Union report, there were only eight countries with no women in their legislatures in 1998. The number of women ministers at the cabinet level worldwide doubled in a decade, and the number of countries without any women ministers dropped from 93 to 48 during 1987-96. However, this progress is far from satisfactory. Political representation of women, minorities, and other social groups is still inadequate. This may be due to a complex combination of socioeconomic, cultural, and institutional factors. The view that women's political participation increases with social and economic development is supported by data from the Nordic countries, where there are higher proportions of women legislators than in less developed countries. While better levels of socioeconomic development, having a women-friendly political culture, and higher literacy are considered favorable factors for women's increased political representation, adopting one of the proportional representation systems (such as a party-list system, a single transferable vote system, or a mixed proportional system with multi-member constituencies) is the single factor most responsible for the higher representation of women.
Sociocognitive Perspectives on Representation.
Jacob, Elin K.; Shaw, Debora
1998-01-01
Discusses research dealing with the cognitive aspects of formal systems of knowledge representation. Highlights include the origins and theoretical foundations of the cognitive viewpoint; cognition and information science; cognitivism, mentalism, and subjective individualism; categorization; mental models; and sociocognitive approaches to indexing…
Between Representation and Eternity
DEFF Research Database (Denmark)
Atzbach, Rainer
2016-01-01
. At death, an indi- vidual’s corpse and burial primarily reflect the social act of representation during the funeral. The position of the arms, which have incorrectly been used as a chronological tool in Scandinavia, may indicate an evolution from a more collective act of prayer up to the eleventh century...
Sociocognitive Perspectives on Representation.
Jacob, Elin K.; Shaw, Debora
1998-01-01
Discusses research dealing with the cognitive aspects of formal systems of knowledge representation. Highlights include the origins and theoretical foundations of the cognitive viewpoint; cognition and information science; cognitivism, mentalism, and subjective individualism; categorization; mental models; and sociocognitive approaches to indexing…
Spectral representation of fingerprints
Xu, Haiyun; Bazen, Asker M.; Veldhuis, Raymond N.J.; Kevenaar, Tom A.M.; Akkermans, Anton H.M.
2007-01-01
Most fingerprint recognition systems are based on the use of a minutiae set, which is an unordered collection of minutiae locations and directions suffering from various deformations such as translation, rotation and scaling. The spectral minutiae representation introduced in this paper is a novel m
Representations of the occupation number matrix on the LDA/GGA+U method
Energy Technology Data Exchange (ETDEWEB)
Tablero, C [Instituto de EnergIa Solar, Universidad Politecnica de Madrid, Ciudad Universitaria s/n, E-28040 Madrid (Spain)
2008-08-13
An analysis of the general representation of the occupation number matrix on density functional theory in conjunction with the generalized Hubbard model is presented. A central fact that will be addressed is that the total charge density cannot be broken down into simple atomic contributions. This fact means that the orbital occupations are not well defined. Different representations of the occupation number matrix, both that it conserves and that it does not conserve the number of electrons of the system, are compared. A localized basis set is used, which is suitable for large-scale electronic structure calculations based on the density functional theory. This methodology is applied to typical and well-analysed transition-metal oxide bulk systems and to Cr-doped zinc chalogenides and chalcopyrites. The bandgap, magnetic moment and detailed electronic structures are investigated and discussed with the different choices of the occupation number matrix. The results are in good agreement with previous theoretical and experimental studies.
Realizations of the Canonical Representation
Indian Academy of Sciences (India)
M K Vemuri
2008-02-01
A characterisation of the maximal abelian subalgebras of the bounded operators on Hilbert space that are normalised by the canonical representation of the Heisenberg group is given. This is used to classify the perfect realizations of the canonical representation.
Standard model of knowledge representation
Yin, Wensheng
2016-09-01
Knowledge representation is the core of artificial intelligence research. Knowledge representation methods include predicate logic, semantic network, computer programming language, database, mathematical model, graphics language, natural language, etc. To establish the intrinsic link between various knowledge representation methods, a unified knowledge representation model is necessary. According to ontology, system theory, and control theory, a standard model of knowledge representation that reflects the change of the objective world is proposed. The model is composed of input, processing, and output. This knowledge representation method is not a contradiction to the traditional knowledge representation method. It can express knowledge in terms of multivariate and multidimensional. It can also express process knowledge, and at the same time, it has a strong ability to solve problems. In addition, the standard model of knowledge representation provides a way to solve problems of non-precision and inconsistent knowledge.
Harmonic Analysis and Group Representation
Figa-Talamanca, Alessandro
2011-01-01
This title includes: Lectures - A. Auslander, R. Tolimeri - Nilpotent groups and abelian varieties, M Cowling - Unitary and uniformly bounded representations of some simple Lie groups, M. Duflo - Construction de representations unitaires d'un groupe de Lie, R. Howe - On a notion of rank for unitary representations of the classical groups, V.S. Varadarajan - Eigenfunction expansions of semisimple Lie groups, and R. Zimmer - Ergodic theory, group representations and rigidity; and, Seminars - A. Koranyi - Some applications of Gelfand pairs in classical analysis.
DEFF Research Database (Denmark)
Sannino, Francesco
2010-01-01
We uncover novel solutions of the 't Hooft anomaly matching conditions for scalarless gauge theories with matter transforming according to higher dimensional representations of the underlying gauge group. We argue that, if the duals exist, they are gauge theories with fermions transforming...... according to the defining representation of the dual gauge group. The resulting conformal windows match the one stemming from the all-orders beta function results when taking the anomalous dimension of the fermion mass to be unity which are also very close to the ones obtained using the Schwinger......-Dyson approximation. We use the solutions to gain useful insight on the conformal window of the associated electric theory. A consistent picture emerges corroborating previous results obtained via different analytic methods and in agreement with first principle lattice explorations....
Constructing visual representations
DEFF Research Database (Denmark)
Huron, Samuel; Jansen, Yvonne; Carpendale, Sheelagh
2014-01-01
The accessibility of infovis authoring tools to a wide audience has been identified as a major research challenge. A key task in the authoring process is the development of visual mappings. While the infovis community has long been deeply interested in finding effective visual mappings......, comparatively little attention has been placed on how people construct visual mappings. In this paper, we present the results of a study designed to shed light on how people transform data into visual representations. We asked people to create, update and explain their own information visualizations using only...... tangible building blocks. We learned that all participants, most of whom had little experience in visualization authoring, were readily able to create and talk about their own visualizations. Based on our observations, we discuss participants’ actions during the development of their visual representations...
MENTAL STATE REPRESENTATION: SPATIOTEMPORAL CHARACTERISTICS
Directory of Open Access Journals (Sweden)
Alexander Oktyabrinovich Prokhorov
2014-01-01
Full Text Available Since the time of statement of the problem of states in psychology, the study of “sensuous” tissue – the mental state representation-takes a fundamental meaning. The problem is concluded in the following questions: “How is mental state represented in the consciousness of an individual?”, “What is the specificity of the mental state representation as distinguished from the subject-matter representation?”, “What are the mechanisms of the mental state representation occurrence and the peculiarities of its dynamics? The study of the mental state representation will allow to explain its specificity and difference from the figurative representation, the peculiarities of state explication as a representation in the consciousness and its relation with other elements of consciousness, will allow to show the regularities of the mental state representation development and its dynamics, factors, which influence the specificity of its occurrence, the regulatory role of the state representation in the vital function. From these perspectives, the article presents the results of the study of spatiotemporal characteristics of the mental state representation; reveals the peculiar features of the spatiotemporal organization of mental state representations: Relieves, specificity, magnitude, variability of indicators, changes of structural characteristics in time spans; considers the age-specific peculiar features of the spatiotemporal organization of mental state representations in terms of organization, stability, coherence and differentiated nature of spatiotemporal structures with the representatives of certain age groups.
Comprehension and Representation in Translation
Institute of Scientific and Technical Information of China (English)
徐玉萍
2010-01-01
Transhfion is the faithful rcpresentation in one language of the thought, content, feeling and style written in another language. It involves two processes: comprehension and representation. Correct comprehension is the base for adequate representation. Criteria for good representation lies in two points: the version should be faithful to the original, and the version should be as intelligible as possible.
Learning Multisensory Representations
2016-05-23
AFRL-AFOSR-VA-TR-2016-0183 Learning Multisensory Representations Robert Jacobs UNIVERSITY OF ROCHESTER Final Report 05/23/2016 DISTRIBUTION A...DD-MM-YYYY) 16-05-2016 2. REPORT TYPE Final Performance Report 3. DATES COVERED (From - To) 01-09-2012 - 29-02-2016 4. TITLE AND SUBTITLE Learning ...perception; visual perception; haptic perception; auditory perception; perceptual learning ; perceptual decision making 16. SECURITY CLASSIFICATION OF
DEFF Research Database (Denmark)
Jensen, Ole B.
2016-01-01
Dette kapitel gennemgår den såkaldte ”Non-Representational Theory” (NRT), der primært er kendt fra den Angelsaksiske humangeografi, og som særligt er blevet fremført af den engelske geograf Nigel Thrift siden midten af 2000 årtiet. Da positionen ikke kan siges at være specielt homogen vil kapitlet...
The field representation language.
Tsafnat, Guy
2008-02-01
The complexity of quantitative biomedical models, and the rate at which they are published, is increasing to a point where managing the information has become all but impossible without automation. International efforts are underway to standardise representation languages for a number of mathematical entities that represent a wide variety of physiological systems. This paper presents the Field Representation Language (FRL), a portable representation of values that change over space and/or time. FRL is an extensible mark-up language (XML) derivative with support for large numeric data sets in Hierarchical Data Format version 5 (HDF5). Components of FRL can be reused through unified resource identifiers (URI) that point to external resources such as custom basis functions, boundary geometries and numerical data. To demonstrate the use of FRL as an interchange we present three models that study hyperthermia cancer treatment: a fractal model of liver tumour microvasculature; a probabilistic model simulating the deposition of magnetic microspheres throughout it; and a finite element model of hyperthermic treatment. The microsphere distribution field was used to compute the heat generation rate field around the tumour. We used FRL to convey results from the microsphere simulation to the treatment model. FRL facilitated the conversion of the coordinate systems and approximated the integral over regions of the microsphere deposition field.
Translation between representation languages
Vanbaalen, Jeffrey
1994-01-01
A capability for translating between representation languages is critical for effective knowledge base reuse. A translation technology for knowledge representation languages based on the use of an interlingua for communicating knowledge is described. The interlingua-based translation process consists of three major steps: translation from the source language into a subset of the interlingua, translation between subsets of the interlingua, and translation from a subset of the interlingua into the target language. The first translation step into the interlingua can typically be specified in the form of a grammar that describes how each top-level form in the source language translates into the interlingua. In cases where the source language does not have a declarative semantics, such a grammar is also a specification of a declarative semantics for the language. A methodology for building translators that is currently under development is described. A 'translator shell' based on this methodology is also under development. The shell has been used to build translators for multiple representation languages and those translators have successfully translated nontrivial knowledge bases.
[Time perceptions and representations].
Tordjman, S
2015-09-01
Representations of time and time measurements depend on subjective constructs that vary according to changes in our concepts, beliefs, societal needs and technical advances. Similarly, the past, the future and the present are subjective representations that depend on each individual's psychic time and biological time. Therefore, there is no single, one-size-fits-all time for everyone, but rather a different, subjective time for each individual. We need to acknowledge the existence of different inter-individual times but also intra-individual times, to which different functions and different rhythms are attached, depending on the system of reference. However, the construction of these time perceptions and representations is influenced by objective factors (physiological, physical and cognitive) related to neuroscience which will be presented and discussed in this article. Thus, studying representation and perception of time lies at the crossroads between neuroscience, human sciences and philosophy. Furthermore, it is possible to identify several constants among the many and various representations of time and their corresponding measures, regardless of the system of time reference. These include the notion of movements repeated in a stable rhythmic pattern involving the recurrence of the same interval of time, which enables us to define units of time of equal and invariable duration. This rhythmicity is also found at a physiological level and contributes through circadian rhythms, in particular the melatonin rhythm, to the existence of a biological time. Alterations of temporality in mental disorders will be also discussed in this article illustrated by certain developmental disorders such as autism spectrum disorders. In particular, the hypothesis will be developed that children with autism would need to create discontinuity out of continuity through stereotyped behaviors and/or interests. This discontinuity repeated at regular intervals could have been
Pioneers of representation theory
Curtis, Charles W
1999-01-01
The year 1897 was marked by two important mathematical events: the publication of the first paper on representations of finite groups by Ferdinand Georg Frobenius (1849-1917) and the appearance of the first treatise in English on the theory of finite groups by William Burnside (1852-1927). Burnside soon developed his own approach to representations of finite groups. In the next few years, working independently, Frobenius and Burnside explored the new subject and its applications to finite group theory. They were soon joined in this enterprise by Issai Schur (1875-1941) and some years later, by Richard Brauer (1901-1977). These mathematicians' pioneering research is the subject of this book. It presents an account of the early history of representation theory through an analysis of the published work of the principals and others with whom the principals' work was interwoven. Also included are biographical sketches and enough mathematics to enable readers to follow the development of the subject. An introductor...
Covariant representations of subproduct systems
Viselter, Ami
2010-01-01
A celebrated theorem of Pimsner states that a covariant representation $T$ of a $C^*$-correspondence $E$ extends to a $C^*$-representation of the Toeplitz algebra of $E$ if and only if $T$ is isometric. This paper is mainly concerned with finding conditions for a covariant representation of a \\emph{subproduct system} to extend to a $C^*$-representation of the Toeplitz algebra. This framework is much more general than the former. We are able to find sufficient conditions, and show that in important special cases, they are also necessary. Further results include the universality of the tensor algebra, dilations of completely contractive covariant representations, Wold decompositions and von Neumann inequalities.
Categorification and higher representation theory
Beliakova, Anna
2017-01-01
The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorified representation theory, or higher representation theory, aims to understand a new level of structure present in representation theory. Rather than studying actions of algebras on vector spaces where algebra elements act by linear endomorphisms of the vector space, higher representation theory describes the structure present when algebras act on categories, with algebra elements acting by functors. The new level of structure in higher representation theory arises by studying the natural transformations between functors. This enhanced perspective brings into play a powerful new set of tools that deepens our understanding of traditional representation theory. This volume exhibits some of the current trends in higher representation theory and the diverse te...
Institute of Scientific and Technical Information of China (English)
孙伟; 尹华磊; 孙祥祥; 陈腾云
2016-01-01
非正交编码协议和诱骗态方法可以有效地抵御光子数分离攻击。由于相干叠加态中单光子成分高达90%，常作为单光子量子比特的替代出现，用于量子信息过程处理和计算。本文结合非正交编码协议和诱骗态方法提出一种新的量子密钥分发方案，光源采用相干叠加态，推导了单光子的密钥生成速率、计数率下限和误码率的上限，利用Matlab 模拟了无限多诱骗态情况下和有限多诱骗态情况下密钥生成速率和传输距离的关系，得出该方案可以提升密钥生成速率并且提高安全传输距离，验证了该方案可以进一步提高量子密钥分发系统的性能。%Nonorthogonal coded agreements and decoy state method can effectively protect the photon number against split-ting attack. Owing to the fact that the component of single-photon in the coherent-state superposition (CSS) is as high as 90%, CSS has recently emerged as an alternative to single-photon qubits for quantum information processing and metrology. The approximate CSS of small amplitudes is generated by the subtraction of photons from a squeezed vacuum state, and the approximate CSS of large amplitude is generated from Fock state by using a single homodyne detection. Here, we combine both of the methods and propose a new protocol by using the CSS as a light source. We derive the secure key generation rate, the lower bound of count rate and upper bound of error rate of single-photon. We simulate the curves relationship between secure key generation rate and safety transmission distance in the case of an infinite number of decoy states by using matlab. The parameters are given according to the Gobby-Yuan-Shields (GYS) experiment. We infer that the safety transmission distance achieves 147.4 km and the secure key generation rate is much higher than those of other schemes. We also simulate the relationship between key generation rate and safety transmission distance in
Representations of commonsense knowledge
Davis, Ernest
1990-01-01
Representations of Commonsense Knowledge provides a rich language for expressing commonsense knowledge and inference techniques for carrying out commonsense knowledge. This book provides a survey of the research on commonsense knowledge.Organized into 10 chapters, this book begins with an overview of the basic ideas on artificial intelligence commonsense reasoning. This text then examines the structure of logic, which is roughly analogous to that of a programming language. Other chapters describe how rules of universal validity can be applied to facts known with absolute certainty to deduce ot
Residual Representations of Spacetime
Saller, H
2001-01-01
Spacetime is modelled by binary relations - by the classes of the automorphisms $\\GL(\\C^2)$ of a complex 2-dimensional vector space with respect to the definite unitary subgroup $\\U(2)$. In extension of Feynman propagators for particle quantum fields representing only the tangent spacetime structure, global spacetime representations are given, formulated as residues using energy-momentum distributions with the invariants as singularities. The associatated quantum fields are characterized by two invariant masses - for time and position - supplementing the one mass for the definite unitary particle sector with another mass for the indefinite unitary interaction sector without asymptotic particle interpretation.
Boot, Inge; Pecher, Diane
2011-01-01
In the present study we investigated whether the mental representation of the concept categories is represented by the container image schema (Lakoff & Johnson, 1980). In two experiments participants decided whether two pictures were from the same category (animal or vehicle). Pictures were presented inside or outside a frame that should activate the container schema. We found that performance to pictures was influenced by the frame in congruence with the metaphorical mapping (same category—inside bounded region; different category—not in same bounded region). These results show that the concept categories is metaphorically represented by containers.
Social Representations of Intelligence
Directory of Open Access Journals (Sweden)
Elena Zubieta
2016-02-01
Full Text Available The article stresses the relationship between Explicit and Implicit theories of Intelligence. Following the line of common sense epistemology and the theory of Social Representations, a study was carried out in order to analyze naive’s explanations about Intelligence Definitions. Based on Mugny & Carugati (1989 research, a self-administered questionnaire was designed and filled in by 286 subjects. Results are congruent with the main hyphotesis postulated: A general overlap between explicit and implicit theories showed up. According to the results Intelligence appears as both, a social attribute related to social adaptation and as a concept defined in relation with contextual variables similar to expert’s current discourses. Nevertheless, conceptions based on “gifted ideology” still are present stressing the main axes of Intelligence debate: biological and sociological determinism. In the same sense, unfamiliarity and social identity are reaffirmed as organizing principles of social representation. The distance with the object -measured as the belief in intelligence differences as a solve/non solve problem- and the level of implication with the topic -teachers/no teachers- appear as discriminating elements at the moment of supporting specific dimensions.
Knowledge representation with SOA
Directory of Open Access Journals (Sweden)
Daniela Gotseva
2013-01-01
Full Text Available This paper addresses the problem of supporting the software development process through the artificial intelligence. The expert systems could advise the Domain Engineer in programming without the detailed experience in programming languages. He will use and integrate, with the help of deductive database and domain knowledge, the previously developed software components to new complex functionalities. The objective of this document is to provide the knowledge representation about atomic Web Services which will be registered as the facts in the deductive database. The author proposes to use the decision rules in decision tables for representing the service model which consists of semantic specification, interface description, service quality (QoS, non-functional properties. Also the use of Domain Specific Languages (DSL for modeling Domain Engineers re-quests to the expert system will be considered within this document. As the illustrative use case for described knowledge representation the author proposes the domain of SOA-based geographic information systems (GIS which represent a new branch of information and communication technologies.
A Complete Basis Set Model Chemistry for Excited States
2007-11-02
6-311G(2d,d,p) ZPE & Thermal: B3LYP/6-311G(2d,d,p) SCF: UHF/6-311+G(3d2f,2df,2p) CBS( extrap ) - MP2: UHF/6-311+G(3d2f,2df,2p) MP3, MP4(SDQ...0.0000956 0.0000245 Before Extrap 0.0030328 0.0005829 0.0001180 "Approved for public release; distribution unlimited" 22 MP2 CBS Limit The αα second- order
Nuclear second analytical derivative calculations using auxiliary basis set expansions
Deglmann, Peter; May, Klaus; Furche, Filipp; Ahlrichs, Reinhart
2004-01-01
We present an efficient implementation of second order analytical derivatives (force constants) within density functional theory which applies to non-hybrid functionals. The dominant step in force constant treatments concerns the solution of the coupled perturbed Kohn-Sham equations (CPKS). We employ an auxiliary basis expansion, the RI- J technique (resolution of the identity for the interelectronic Couomb energy J), to accelerate the solution of the CPKS equations. This results in pronounced reductions of computational work and implies insignificant losses in accuracy as is shown by extensive tests. A force constant calculation of cyanocobalamin is reported as a demonstrative application.
CLOPW: a mixed basis set full potential electronic structure method
Bekker, Hermie Gerhard
1997-01-01
This thesis is about the development of the full potental CLOPW package for electronic structure calculations. Chapter 1 provides the necessary background in the theory of solid state physics. It gives a short overview of the effective one particle model as commonly used in solid state physics. It a
Integral geometry and representation theory
Gel'fand, I M; Vilenkin, N Ya
1966-01-01
Generalized Functions, Volume 5: Integral Geometry and Representation Theory is devoted to the theory of representations, focusing on the group of two-dimensional complex matrices of determinant one.This book emphasizes that the theory of representations is a good example of the use of algebraic and geometric methods in functional analysis, in which transformations are performed not on the points of a space, but on the functions defined on it. The topics discussed include Radon transform on a real affine space, integral transforms in the complex domain, and representations of the group of comp
Intentionality, Representation, and Anticipation
De Preester, Helena
2002-09-01
Both Brentano and Merleau-Ponty have developed an account of intentionality, which nevertheless differ profoundly in the following respect. According to Brentano, intentionality mainly is a matter of mental presentations. This marks the beginning of phenomenology's difficult relation with the nature of the intentional reference. Merleau-Ponty, on the other hand, has situated intentionality on the level of the body, a turn which has important implications for the nature of intentionality. Intentionality no longer is primarily based on having (re)presentations, but is rooted in the dynamics of the living body. To contrast those approaches enables us to make clear in what way intentionality is studied nowadays. On the one hand, intentionality is conceived of as a matter of formal-syntactical causality in cognitive science, and in particular in classical-computational theory. On the other hand, a interactivist approach offers a more Merleau-Ponty-like point of view, in which autonomy, embodiment and interaction are stressed.
Going beyond representational anthropology
DEFF Research Database (Denmark)
Winther, Ida Wentzel
an education. There is a close connection between: 1) The dream and the desire for education; 2) Mobility (away from the family, home and friends in a very young age for getting an education; 3) Transforming a new and unknown site and space into a known place, where one can make one-self at home ('home one......Going beyond representational anthropology: Re-presenting bodily, emotional and virtual practices in everyday life. Separated youngsters and families in Greenland Greenland is a huge island, with a total of four high-schools. Many youngsters (age 16-18) move far away from home in order to get...... transformation work into the young people and their families. In this presentation I want to screen two sequences from the film, in order to show and clarify how mobility and transformation are made and dealt with both from the youngsters’ and their parents’ perspectives, but in asynchronous loups. I want...
Linear recursive distributed representations.
Voegtlin, Thomas; Dominey, Peter F
2005-09-01
Connectionist networks have been criticized for their inability to represent complex structures with systematicity. That is, while they can be trained to represent and manipulate complex objects made of several constituents, they generally fail to generalize to novel combinations of the same constituents. This paper presents a modification of Pollack's Recursive Auto-Associative Memory (RAAM), that addresses this criticism. The network uses linear units and is trained with Oja's rule, in which it generalizes PCA to tree-structured data. Learned representations may be linearly combined, in order to represent new complex structures. This results in unprecedented generalization capabilities. Capacity is orders of magnitude higher than that of a RAAM trained with back-propagation. Moreover, regularities of the training set are preserved in the new formed objects. The formation of new structures displays developmental effects similar to those observed in children when learning to generalize about the argument structure of verbs.
Computer aided surface representation
Energy Technology Data Exchange (ETDEWEB)
Barnhill, R.E.
1990-02-19
The central research problem of this project is the effective representation, computation, and display of surfaces interpolating to information in three or more dimensions. If the given information is located on another surface, then the problem is to construct a surface defined on a surface''. Sometimes properties of an already defined surface are desired, which is geometry processing''. Visualization of multivariate surfaces is possible by means of contouring higher dimensional surfaces. These problems and more are discussed below. The broad sweep from constructive mathematics through computational algorithms to computer graphics illustrations is utilized in this research. The breadth and depth of this research activity makes this research project unique.
Preschool Children's Participation in Representational and Non-Representational Activities
Braswell, Gregory S.
2017-01-01
The present study examined representational and non-representational activities in which children in a Head Start classroom participated. This was an investigation from the perspective of cultural-historical activity theory of how components (e.g. artifacts and division of labour) of classroom activities vary across and within types of activities.…
Parrish, Robert M; Hohenstein, Edward G; Martínez, Todd J; Sherrill, C David
2013-05-21
We investigate the application of molecular quadratures obtained from either standard Becke-type grids or discrete variable representation (DVR) techniques to the recently developed least-squares tensor hypercontraction (LS-THC) representation of the electron repulsion integral (ERI) tensor. LS-THC uses least-squares fitting to renormalize a two-sided pseudospectral decomposition of the ERI, over a physical-space quadrature grid. While this procedure is technically applicable with any choice of grid, the best efficiency is obtained when the quadrature is tuned to accurately reproduce the overlap metric for quadratic products of the primary orbital basis. Properly selected Becke DFT grids can roughly attain this property. Additionally, we provide algorithms for adopting the DVR techniques of the dynamics community to produce two different classes of grids which approximately attain this property. The simplest algorithm is radial discrete variable representation (R-DVR), which diagonalizes the finite auxiliary-basis representation of the radial coordinate for each atom, and then combines Lebedev-Laikov spherical quadratures and Becke atomic partitioning to produce the full molecular quadrature grid. The other algorithm is full discrete variable representation (F-DVR), which uses approximate simultaneous diagonalization of the finite auxiliary-basis representation of the full position operator to produce non-direct-product quadrature grids. The qualitative features of all three grid classes are discussed, and then the relative efficiencies of these grids are compared in the context of LS-THC-DF-MP2. Coarse Becke grids are found to give essentially the same accuracy and efficiency as R-DVR grids; however, the latter are built from explicit knowledge of the basis set and may guide future development of atom-centered grids. F-DVR is found to provide reasonable accuracy with markedly fewer points than either Becke or R-DVR schemes.
Congruence properties of induced representations
DEFF Research Database (Denmark)
Mayer, Dieter; Momeni, Arash; Venkov, Alexei
In this paper we study representations of the projective modular group induced from the Hecke congruence group of level 4 with Selberg's character. We show that the well known congruence properties of Selberg's character are equivalent to the congruence properties of the induced representations. ...
Representation of Fuzzy Symmetric Relations
1986-03-19
Std Z39-18 REPRESENTATION OF FUZZY SYMMETRIC RELATIONS L. Valverde Dept. de Matematiques i Estadistica Universitat Politecnica de Catalunya Avda...REPRESENTATION OF FUZZY SYMMETRIC RELATIONS L. "Valverde* Dept. de Matematiques i Estadistica Universitat Politecnica de Catalunya Avda. Diagonal, 649
Scientific Representation and Science Learning
Matta, Corrado
2014-01-01
In this article I examine three examples of philosophical theories of scientific representation with the aim of assessing which of these is a good candidate for a philosophical theory of scientific representation in science learning. The three candidate theories are Giere's intentional approach, Suárez's inferential approach and Lynch and…
Adjoint Functors and Representation Dimensions
Institute of Scientific and Technical Information of China (English)
Chang Chang XI
2006-01-01
We study the global dimensions of the coherent functors over two categories that are linked by a pair of adjoint functors. This idea is then exploited to compare the representation dimensions of two algebras. In particular, we show that if an Artin algebra is switched from the other, then they have the same representation dimension.
$\\alpha$-Representation for QCD
Tuan, Richard Hong
1998-01-01
An $\\alpha$-parameter representation is derived for gauge field theories.It involves, relative to a scalar field theory, only constants and derivatives with respect to the $\\alpha$-parameters. Simple rules are given to obtain the $\\alpha$-representation for a Feynman graph with an arbitrary number of loops in gauge theories in the Feynman gauge.
International agreements on commercial representation
Slanař, Jan
2014-01-01
The purpose of the thesis is to describe the possibilities for fixing the position of a company in the market through contracts for commercial representation with a focus to finding legal and economic impact on the company that contracted for exclusive representation.
Scientific Representation and Science Learning
Matta, Corrado
2014-01-01
In this article I examine three examples of philosophical theories of scientific representation with the aim of assessing which of these is a good candidate for a philosophical theory of scientific representation in science learning. The three candidate theories are Giere's intentional approach, Suárez's inferential approach and Lynch and…
Teachers’ representations of school indiscipline
Directory of Open Access Journals (Sweden)
Joe Garcia
2015-11-01
Full Text Available In this article we analyze a set of teachers’ representations of school indiscipline and its implications for pedagogical practices, particularly related to the resolution of problems in the classroom. Initially we explore three teachers’ representations on the genesis of school indiscipline. The first representation attributes prominence to the student as the singular subject in the production of indiscipline and who will be the center of the pedagogical intervention. The second representation attributes the genesis of the indiscipline to the context of the relations among the subjects in the classroom. The third representation suggests that the indiscipline would be something socially constructed in the schools, where it is intrinsically related to its nature and social function, and is an intrinsic part of its institutional culture. This third representation is distant of the previous ones, and provides an understanding of the indiscipline as a cultural message. In the second part of this article we analyze a set of implications of the teachers’ representations in relation to their pedagogical practices. At the ending of the text, we present some notes that put in evidence some issues that seems to be at the center in the study of the representations regarding to school indiscipline, in relation to the roles teachers are supposed to taken in contexts of indiscipline.
Revealing children's implicit spelling representations.
Critten, Sarah; Pine, Karen J; Messer, David J
2013-06-01
Conceptualizing the underlying representations and cognitive mechanisms of children's spelling development is a key challenge for literacy researchers. Using the Representational Redescription model (Karmiloff-Smith), Critten, Pine and Steffler (2007) demonstrated that the acquisition of phonological and morphological knowledge may be underpinned by increasingly explicit levels of spelling representation. However, their proposal that implicit representations may underlie early 'visually based' spelling remains unresolved. Children (N = 101, aged 4-6 years) were given a recognition task (Critten et al., 2007) and a novel production task, both involving verbal justifications of why spellings are correct/incorrect, strategy use and word pattern similarity. Results for both tasks supported an implicit level of spelling characterized by the ability to correctly recognize/produce words but the inability to explain operational strategies or generalize knowledge. Explicit levels and multiple representations were also in evidence across the two tasks. Implications for cognitive mechanisms underlying spelling development are discussed.
Fuzzy Morphological Polynomial Image Representation
Directory of Open Access Journals (Sweden)
Chin-Pan Huang
2010-01-01
Full Text Available A novel signal representation using fuzzy mathematical morphology is developed. We take advantage of the optimum fuzzy fitting and the efficient implementation of morphological operators to extract geometric information from signals. The new representation provides results analogous to those given by the polynomial transform. Geometrical decomposition of a signal is achieved by windowing and applying sequentially fuzzy morphological opening with structuring functions. The resulting representation is made to resemble an orthogonal expansion by constraining the results of opening to equate adapted structuring functions. Properties of the geometric decomposition are considered and used to calculate the adaptation parameters. Our procedure provides an efficient and flexible representation which can be efficiently implemented in parallel. The application of the representation is illustrated in data compression and fractal dimension estimation temporal signals and images.
Archival Representation in the Digital Age
Zhang, Jane
2012-01-01
This study analyzes the representation systems of three digitized archival collections using the traditional archival representation framework of provenance, order, and content. The results of the study reveal a prominent role of provenance representation, a compromised role of order representation, and an active role of content representation in…
Archival Representation in the Digital Age
Zhang, Jane
2012-01-01
This study analyzes the representation systems of three digitized archival collections using the traditional archival representation framework of provenance, order, and content. The results of the study reveal a prominent role of provenance representation, a compromised role of order representation, and an active role of content representation in…
Islam and Media Representations
Directory of Open Access Journals (Sweden)
Mohamed Bensalah
2006-04-01
Full Text Available For the author of this article, the media’s treatment of Islam has raised numerous polymorphous questions and debates. Reactivated by the great scares of current events, the issue, though an ancient one, calls many things into question. By way of introduction, the author tries to analyse the complex processes of elaboration and perception of the representations that have prevailed during the past century. In referring to the semantic decoding of the abundant colonial literature and iconography, the author strives to translate the extreme xenophobic tensions and the identity crystallisations associated with the current media orchestration of Islam, both in theWest and the East. He then evokes the excesses of the media that are found at the origin of many amalgams wisely maintained between Islam, Islamism and Islamic terrorism, underscoring their duplicity and their willingness to put themselves, consciously, in service to deceivers and directors of awareness, who are very active at the heart of the politico-media sphere. After levelling a severe accusation against the harmful drifts of the media, especially in times of crisis and war, the author concludes by asserting that these tools of communication, once they are freed of their masks and invective apparatuses, can be re-appropriated by new words and bya true communication between peoples and cultures.
Irreducible representations of Birman-Wenzl algebras
Institute of Scientific and Technical Information of China (English)
潘峰
1995-01-01
Irreducible representations of Birman-Wenzl algebras are constructed by using the induced representation and the linear equation method. Self-adjoint representations of Birman-Wenzl algebras Cf (r, q) with f≤4 are presented.
From Local to Global Additive Representation
Wakker, P.P.; Chateauneuf, A.
1993-01-01
This paper studies continuous additive representations of transitive preferences on connected subdomains of product sets. Contrary to what has sometimes been thought, local additive representability does not imply global additive representability. It is shown that the result can nevertheless be
From local to global additive representation
A. Chateauneuf (Alain); P.P. Wakker (Peter)
1993-01-01
textabstractThis paper studies continuous additive representations of transitive preferences on connected subdomains of product sets. Contrary to what has sometimes been thought, local additive representability does not imply global additive representability. It is shown that the result can
Functional Representations for Fock Superalgebras
Kupsch, J; Kupsch, Joachim; Smolyanov, Oleg G.
1997-01-01
The Fock space of bosons and fermions and its underlying superalgebra are represented by algebras of functions on a superspace. We define Gaussian integration on infinite dimensional superspaces, and construct superanalogs of the classical function spaces with a reproducing kernel -- including the Bargmann-Fock representation -- and of the Wiener-Segal representation. The latter representation requires the investigation of Wick ordering on Z2-graded algebras. As application we derive a Mehler formula for the Ornstein-Uhlenbeck semigroup on the Fock space.
Multi-parameter Burau representations
Mohammad N. Abdulrahim; Madline Al- Tahan; Samer S. Habre
2013-01-01
We consider the multi-parameter representation of Artin's braid group introduced by D. D. Long and J. P. Tian, namely $\\alpha: B_{n}\\rightarrow GL_{m}(C)$, where $m=n!n$ . First, we show that there exists a complex specialization of the multi-parameter representation that does not arise from any Hecke algebra. Second, we find conditions under which the images of the generators of the braid group on three strings under the multi-parameter representation are unitary relative to a nonsingular he...
Thinking together with material representations
DEFF Research Database (Denmark)
Stege Bjørndahl, Johanne; Fusaroli, Riccardo; Østergaard, Svend
2014-01-01
How do material representations such as models, diagrams and drawings come to shape and aid collective, epistemic processes? This study investigated how groups of participants spontaneously recruited material objects (in this case LEGO blocks) to support collective creative processes in the context......, the material representations were experimented on and physical attributes were explored resulting in discoveries of new meaning potentials and creative solutions. We discuss these different ways in which material representations do their work in collective reasoning processes in relation to ideas about top...
Computer aided surface representation
Energy Technology Data Exchange (ETDEWEB)
Barnhill, R.E.
1989-02-09
The central research problem of this project is the effective representation and display of surfaces, interpolating to given information, in three or more dimensions. In a typical problem, we wish to create a surface from some discrete information. If this information is itself on another surface, the problem is to determine a surface defined on a surface,'' which is discussed below. Often, properties of an already constructed surface are desired: such geometry processing'' is described below. The Summary of Proposed Research from our original proposal describes the aims of this research project. This Summary and the Table of Contents from the original proposal are enclosed as an Appendix to this Progress Report. The broad sweep from constructive mathematics through algorithms and computer graphics displays is utilized in the research. The wide range of activity, directed in both theory and applications, makes this project unique. Last month in the first Ardent Titan delivered in the State of Arizona came to our group, funded by the DOE and Arizona State University. Although the Titan is a commercial product, its newness requires our close collaboration with Ardent to maximize results. During the past year, four faculty members and several graduate research assistants have worked on this DOE project. The gaining of new professionals is an important aspect of this project. A listing of the students and their topics is given in the Appendix. The most significant publication during the past year is the book, Curves and Surfaces for Computer Aided Geometric Design, by Dr. Gerald Farin. This 300 page volume helps fill a considerable gap in the subject and includes many new results on Bernstein-Bezier curves and surfaces.
Representation of identities and the politics of representation in cognition
Directory of Open Access Journals (Sweden)
Kanavillil Rajagopalan
2001-02-01
Full Text Available
In this paper, I make a plea for viewing representation as first and foremost a political matter. I argue that by so doing we may avoid the many of pitfalls of contemporary theories of cognition as they attempt to tackle the issue of representation. Most of these problems have to do with the fact that representation is treated exclusively as a mimetic or theatrical question. The fact of the matter is however that representation also has a political dimension. Indeed it has always had this political dimension which, counterintuitive though it may seem at first glimpse, manifests itself even in very the attempt to aestheticise the whole issue of representation (as in some versions of postmodernism or to deny its role altogether as a tertium quid between the external world and the cognising mind (as in contemporary neo-pragmatism. I also contend that, by recognising the political nature of representation, we also pave the way for endorsing the thesis that the mind is a social construct, thereby taking some steam out of the thesis of "mind-brain identity" (so-called "identity theory of mind".
(Self)-representations on youtube
DEFF Research Database (Denmark)
Simonsen, Thomas Mosebo
This paper examines forms of self-representation on YouTube with specific focus on Vlogs (Video blogs). The analytical scope of the paper is on how User-generated Content on YouTube initiates a certain kind of audiovisual representation and a particular interpretation of reality that can...... be distinguished within Vlogs. This will be analysed through selected case studies taken from a representative sample of empirically based observations of YouTube videos. The analysis includes a focus on how certain forms of representation can be identified as representations of the self (Turkle 1995, Scannell...... 1996, Walker 2005) and further how these forms must be comprehended within a context of technological constrains, institutional structures and social as well as economical practices on YouTube (Burgess and Green 2009, Van Dijck 2009). It is argued that these different contexts play a vital part...
Computer representation of molecular surfaces
Energy Technology Data Exchange (ETDEWEB)
Max, N.L.
1981-07-06
This review article surveys recent work on computer representation of molecular surfaces. Several different algorithms are discussed for producing vector or raster drawings of space-filling models formed as the union of spheres. Other smoother surfaces are also considered.
Semantic Knowledge Representation (SKR) API
U.S. Department of Health & Human Services — The SKR Project was initiated at NLM in order to develop programs to provide usable semantic representation of biomedical free text by building on resources...
Integral representation of Skorokhod reflection
Anantharam, Venkat
2010-01-01
We show that a certain integral representation of the one-sided Skorokhod reflection of a continuous bounded variation function characterizes the reflection in that it possesses a unique maximal solution which solves the Skorokhod reflection problem.
Probability representation of classical states
Man'ko, OV; Man'ko, [No Value; Pilyavets, OV
2005-01-01
Probability representation of classical states described by symplectic tomograms is discussed. Tomographic symbols of classical observables which are functions on phase-space are studied. Explicit form of kernel of commutative star-product of the tomographic symbols is obtained.
Number line representations of fractions
Behr, Merlyn J.; Bright, George W.; Wachsmuth, Ipke; Wagner, Sigrid
1982-01-01
The study explored students' interpretations of representations of fractions on number lines and the effect of instruction on those interpretations. Subjects were five fourth-graders, and instruction was a four-day unit on the use of number lines. A 16-item, multiple-choice pre- and posttest was used along with videotaped interviews. Performance improved except when students had to associate a reduced fraction symbol with an equivalent, unreduced fraction representation on a number line. The ...
The Fifth Mode of Representation
DEFF Research Database (Denmark)
Behrendt, Poul; Krogh Hansen, Per
2011-01-01
“The fifth mode of representation: Ambiguous voices in unreliable third person narration”. Sammen med Poul Behrendt. In Per Krogh Hansen, Stefan Iversen, Henrik Skov Nielsen og Rolf Reitan (red.): Strange Voices. Walter de Gruyter, Berlin & New York......“The fifth mode of representation: Ambiguous voices in unreliable third person narration”. Sammen med Poul Behrendt. In Per Krogh Hansen, Stefan Iversen, Henrik Skov Nielsen og Rolf Reitan (red.): Strange Voices. Walter de Gruyter, Berlin & New York...
Generalized S-matrix in Mixed Representations
Ishikawa, K; Ishikawa, Kenzo; Shimomura, Takashi
2006-01-01
A generalized scattering amplitude where momenta of incoming-particles and outgoing-particles as well as positions of incoming-particles and outgoing-particles are specified is formulated. Idealistic beams and idealistic measuring instruments where momenta and positions satisfy minimum uncertainty are studied with a use of minimum wave packets, coherent states. In the present work, we show general features of the generalized scattering amplitudes based on ${\\phi}^4$ theory. We give a proof of completeness of many body states, asymptotic behaviors in the large distance region, and factorization of the amplitudes. Despite of the non-orthogonal properties of wave packets, we found that the probability interpretation is verified. A differential probability depends upon the wave packet size but a total probability that is integrated in the final states is independent from the size of final state wave packet and becomes universal. Few body amplitudes are studied as examples.
32 CFR 724.215 - Military representation.
2010-07-01
... 32 National Defense 5 2010-07-01 2010-07-01 false Military representation. 724.215 Section 724.215... BOARD Authority/Policy for Departmental Discharge Review § 724.215 Military representation. Military... consult legal counsel before undertaking such representation. Such representation may be prohibited by 18...
Representations Of The Super-virasoro Algebra fock Representations
Polychronidis, V J
1999-01-01
In this dissertation the complete classification of the Super- Virasoro modules M (h, c) of the Neveu-Schwarz and Ramond algebras is constructed. A family of representations F p, po of the Neveu- Schwarz and Ramond algebras, which generalize the Fock representations of the Virasoro algebra, is constructed. The Felder's construction of Fock space resolutions for the Virasoro minimal models is generalized in the Super-Virasoro minimal models case. In particular, a two-sided resolution of the irreducible Super-Verma module L( h, c) of the Neveu- Schwarz algebra is provided. --- 8 --- AN
On Representation in Information Theory
Directory of Open Access Journals (Sweden)
Joseph E. Brenner
2011-09-01
Full Text Available Semiotics is widely applied in theories of information. Following the original triadic characterization of reality by Peirce, the linguistic processes involved in information—production, transmission, reception, and understanding—would all appear to be interpretable in terms of signs and their relations to their objects. Perhaps the most important of these relations is that of the representation-one, entity, standing for or representing some other. For example, an index—one of the three major kinds of signs—is said to represent something by being directly related to its object. My position, however, is that the concept of symbolic representations having such roles in information, as intermediaries, is fraught with the same difficulties as in representational theories of mind. I have proposed an extension of logic to complex real phenomena, including mind and information (Logic in Reality; LIR, most recently at the 4th International Conference on the Foundations of Information Science (Beijing, August, 2010. LIR provides explanations for the evolution of complex processes, including information, that do not require any entities other than the processes themselves. In this paper, I discuss the limitations of the standard relation of representation. I argue that more realistic pictures of informational systems can be provided by reference to information as an energetic process, following the categorial ontology of LIR. This approach enables naïve, anti-realist conceptions of anti-representationalism to be avoided, and enables an approach to both information and meaning in the same novel logical framework.
Srivastava, Saurabh; Sathyamurthy, N
2012-12-01
The spin forbidden transition a(1)Δ → X(3)Σ(-) in CH(-) has been studied using the Breit-Pauli Hamiltonian for a large number of geometries. This transition acquires intensity through spin-orbit coupling with singlet and triplet Π states. The transition moment matrix including more than one singlet and triplet Π states was calculated at the multi-reference configuration interaction/aug-cc-pV6Z level of theory. The computed radiative lifetime of 5.63 s is in good agreement with the experimental (5.9 s) and other theoretical (6.14 s) results. Transition moment values of the spin allowed A(3)Π → X(3)Σ(-) transition have also been calculated at the same level of theory. Calculations show that the corresponding radiative lifetime is considerably low, 2.4 × 10(-7) s. Complete basis set extrapolated potential energy curves for the ground state of CH and the ground state and six low lying excited states (a(1)Δ, b(1)Σ(+), two (3)Π, and two (1)Π) of CH(-) are reported. These curves are then used to calculate the vibrational bound states for CH and CH(-). The computed electron affinity of CH supports the electron affinity bounds reported by Okumura et al. [J. Chem. Phys. 85, 1971 (1986)].
Digital models for architectonical representation
Directory of Open Access Journals (Sweden)
Stefano Brusaporci
2011-12-01
Full Text Available Digital instruments and technologies enrich architectonical representation and communication opportunities. Computer graphics is organized according the two phases of visualization and construction, that is modeling and rendering, structuring dichotomy of software technologies. Visualization modalities give different kinds of representations of the same 3D model and instruments produce a separation between drawing and image’s creation. Reverse modeling can be related to a synthesis process, ‘direct modeling’ follows an analytic procedure. The difference between interactive and not interactive applications is connected to the possibilities offered by informatics instruments, and relates to modeling and rendering. At the same time the word ‘model’ describes different phenomenon (i.e. files: mathematical model of the building and of the scene; raster representation and post-processing model. All these correlated different models constitute the architectonical interpretative model, that is a simulation of reality made by the model for improving the knowledge.
Executive control influences linguistic representations.
Lev-Ari, Shiri; Keysar, Boaz
2014-02-01
Although it is known that words acquire their meanings partly from the contexts in which they are used, we proposed that the way in which words are processed can also influence their representation. We further propose that individual differences in the way that words are processed can consequently lead to individual differences in the way that they are represented. Specifically, we showed that executive control influences linguistic representations by influencing the coactivation of competing and reinforcing terms. Consequently, people with poorer executive control perceive the meanings of homonymous terms as being more similar to one another, and those of polysemous terms as being less similar to one another, than do people with better executive control. We also showed that bilinguals with poorer executive control experience greater cross-linguistic interference than do bilinguals with better executive control. These results have implications for theories of linguistic representation and language organization.
Concepts, ontologies, and knowledge representation
Jakus, Grega; Omerovic, Sanida; Tomažic, Sašo
2013-01-01
Recording knowledge in a common framework that would make it possible to seamlessly share global knowledge remains an important challenge for researchers. This brief examines several ideas about the representation of knowledge addressing this challenge. A widespread general agreement is followed that states uniform knowledge representation should be achievable by using ontologies populated with concepts. A separate chapter is dedicated to each of the three introduced topics, following a uniform outline: definition, organization, and use. This brief is intended for those who want to get to know
Rotation-independent representations for haptic movements
Shioiri, Satoshi; Yamazaki, Takanori; Matsumiya, Kazumichi; Kuriki, Ichiro
2013-01-01
The existence of a common mechanism for visual and haptic representations has been reported in object perception. In contrast, representations of movements might be more specific to modalities. Referring to the vertical axis is natural for visual representations whereas a fixed reference axis might be inappropriate for haptic movements and thus also inappropriate for its representations in the brain. The present study found that visual and haptic movement representations are processed independently. A psychophysical experiment examining mental rotation revealed the well-known effect of rotation angle for visual representations whereas no such effect was found for haptic representations. We also found no interference between processes for visual and haptic movements in an experiment where different stimuli were presented simultaneously through visual and haptic modalities. These results strongly suggest that (1) there are separate representations of visual and haptic movements, and (2) the haptic process has a rotation-independent representation. PMID:24005481
Quantum mechanics using Fradkin's representation
Shajesh, K V; Milton, Kimball A.
2005-01-01
Fradkin's representation is a general method of attacking problems in quantum field theory, having as its basis the functional approach of Schwinger. As a pedagogical illustration of that method, we explicitly formulate it for quantum mechanics (field theory in one dimension) and apply it to the solution of Schrodinger's equation for the quantum harmonic oscillator.
Adaptive representations for reinforcement learning
Whiteson, S.
2010-01-01
This book presents new algorithms for reinforcement learning, a form of machine learning in which an autonomous agent seeks a control policy for a sequential decision task. Since current methods typically rely on manually designed solution representations, agents that automatically adapt their own r
Acquired Equivalence Changes Stimulus Representations
Meeter, M.; Shohamy, D.; Myers, C. E.
2009-01-01
Acquired equivalence is a paradigm in which generalization is increased between two superficially dissimilar stimuli (or antecedents) that have previously been associated with similar outcomes (or consequents). Several possible mechanisms have been proposed, including changes in stimulus representations, either in the form of added associations or…
Octonionic matrix representation and electromagnetism
Energy Technology Data Exchange (ETDEWEB)
Chanyal, B. C. [Kumaun University, S. S. J. Campus, Almora (India)
2014-12-15
Keeping in mind the important role of octonion algebra, we have obtained the electromagnetic field equations of dyons with an octonionic 8 x 8 matrix representation. In this paper, we consider the eight - dimensional octonionic space as a combination of two (external and internal) four-dimensional spaces for the existence of magnetic monopoles (dyons) in a higher-dimensional formalism. As such, we describe the octonion wave equations in terms of eight components from the 8 x 8 matrix representation. The octonion forms of the generalized potential, fields and current source of dyons in terms of 8 x 8 matrix are discussed in a consistent manner. Thus, we have obtained the generalized Dirac-Maxwell equations of dyons from an 8x8 matrix representation of the octonion wave equations in a compact and consistent manner. The generalized Dirac-Maxwell equations are fully symmetric Maxwell equations and allow for the possibility of magnetic charges and currents, analogous to electric charges and currents. Accordingly, we have obtained the octonionic Dirac wave equations in an external field from the matrix representation of the octonion-valued potentials of dyons.
Minimal Surfaces for Hitchin Representations
DEFF Research Database (Denmark)
Li, Qiongling; Dai, Song
2016-01-01
Given a reductive representation $\\rho: \\pi_1(S)\\rightarrow G$, there exists a $\\rho$-equivariant harmonic map $f$ from the universal cover of a fixed Riemann surface $\\Sigma$ to the symmetric space $G/K$ associated to $G$. If the Hopf differential of $f$ vanishes, the harmonic map is then minimal...
Reusable Lexical Representations for Idioms
Odijk, J.E.J.M.
2004-01-01
In this paper I introduce (1) a technically simple and highly theory-independent way for lexically representing flexible idiomatic expressions, and (2) a procedure to incorporate these lexical representations in a wide variety of NLP systems. The method is based on Structural EQuivalence Classes
Empirical studies on word representations
Suster, Simon
2016-01-01
One of the most fundamental tasks in natural language processing is representing words with mathematical objects (such as vectors). The word representations, which are most often estimated from data, allow capturing the meaning of words. They enable comparing words according to their semantic simila
Reusable Lexical Representations for Idioms
Odijk, J.E.J.M.
2004-01-01
In this paper I introduce (1) a technically simple and highly theory-independent way for lexically representing flexible idiomatic expressions, and (2) a procedure to incorporate these lexical representations in a wide variety of NLP systems. The method is based on Structural EQuivalence Classes for
Correct Representation of Conformational Equilibria.
Fulop, F.; And Others
1983-01-01
In representing conformational equilibria of compounds having only one chiral center, erroneous formulas showing different antipodes on the two sides of the equilibrium are rare. In contrast, with compounds having two or more chiral centers especially with saturated heterocycles, this erroneous representation occurs frequently in the chemical…
Spectral representation of Gaussian semimartingales
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas
2009-01-01
The aim of the present paper is to characterize the spectral representation of Gaussian semimartingales. That is, we provide necessary and sufficient conditions on the kernel K for X t =∫ K t (s) dN s to be a semimartingale. Here, N denotes an independently scattered Gaussian random measure...
Representational Momentum in Older Adults
Piotrowski, Andrea S.; Jakobson, Lorna S.
2011-01-01
Humans have a tendency to perceive motion even in static images that simply "imply" movement. This tendency is so strong that our memory for actions depicted in static images is distorted in the direction of implied motion--a phenomenon known as representational momentum (RM). In the present study, we created an RM display depicting a pattern of…
Digital Image Representation and Access.
Mostafa, Javed
1994-01-01
Reviews the literature relating to the development and application of modern imaging technology between 1987 and 1993. Highlights include image representation, including image data, compression, and image formats; and image access, including indexing and modeling, user interface design, and distributed access. (143 references) (LRW)
Measurable representation of biconjugate integrands
Directory of Open Access Journals (Sweden)
Ottavio Caligaris
1986-11-01
Full Text Available We find here a representation of convex regularization of a non convex proper function and of a non convex proper normal integrand by means of a suitable multifunction which reveals to be very useful in existence theorems for non convex problems of calculus of variations.
Mental Representations of Social Status
Chiao, Joan Y.; Bordeaux, Andrew R.; Ambady, Nalni
2004-01-01
How do people think about social status? We investigated the nature of social status and number representations using a semantic distance latency test. In Study 1, 21 college students compared words connoting different social status as well as numbers, which served as a control task. Participants were faster at comparing occupations and numbers…
Multipolar representation of protein structure
Directory of Open Access Journals (Sweden)
Bourne Philip E
2006-05-01
Full Text Available Abstract Background That the structure determines the function of proteins is a central paradigm in biology. However, protein functions are more directly related to cooperative effects at the residue and multi-residue scales. As such, current representations based on atomic coordinates can be considered inadequate. Bridging the gap between atomic-level structure and overall protein-level functionality requires parameterizations of the protein structure (and other physicochemical properties in a quasi-continuous range, from a simple collection of unrelated amino acids coordinates to the highly synergistic organization of the whole protein entity, from a microscopic view in which each atom is completely resolved to a "macroscopic" description such as the one encoded in the three-dimensional protein shape. Results Here we propose such a parameterization and study its relationship to the standard Euclidian description based on amino acid representative coordinates. The representation uses multipoles associated with residue Cα coordinates as shape descriptors. We demonstrate that the multipoles can be used for the quantitative description of the protein shape and for the comparison of protein structures at various levels of detail. Specifically, we construct a (dissimilarity measure in multipolar configuration space, and show how such a function can be used for the comparison of a pair of proteins. We then test the parameterization on a benchmark set of the protein kinase-like superfamily. We prove that, when the biologically relevant portions of the proteins are retained, it can robustly discriminate between the various families in the set in a way not possible through sequence or conventional structural representations alone. We then compare our representation with the Cartesian coordinate description and show that, as expected, the correlation with that representation increases as the level of detail, measured by the highest rank of multipoles
The extended loop representation of quantum gravity
Di Bartolo, C; Griego, J R
1995-01-01
A new representation of Quantum Gravity is developed. This formulation is based on an extension of the group of loops. The enlarged group, that we call the Extended Loop Group, behaves locally as an infinite dimensional Lie group. Quantum Gravity can be realized on the state space of extended loop dependent wavefunctions. The extended representation generalizes the loop representation and contains this representation as a particular case. The resulting diffeomorphism and hamiltonian constraints take a very simple form and allow to apply functional methods and simplify the loop calculus. In particular we show that the constraints are linear in the momenta. The nondegenerate solutions known in the loop representation are also solutions of the constraints in the new representation. The practical calculation advantages allows to find a new solution to the Wheeler-DeWitt equation. Moreover, the extended representation puts in a precise framework some of the regularization problems of the loop representation. We sh...
FILMIC REPRESENTATION IN POSTCOLONIAL DISCOURSE: A ...
African Journals Online (AJOL)
implicated in the public debate about representation. Representations come in .... A mapping of the dominant discourse, a reading and expressing of its .... This relationship, not only boosted Europe and developed. America, also, Africa was ...
Representation learning for cross-modality classification
G. van Tulder (Gijs); M. de Bruijne (Marleen)
2017-01-01
textabstractDifferences in scanning parameters or modalities can complicate image analysis based on supervised classification. This paper presents two representation learning approaches, based on autoencoders, that address this problem by learning representations that are similar across domains. Bot
The communicative constitution of representation and exclusion
Wessel, van M.G.J.
2014-01-01
In the light of current debate on representation, specifically engaging with literature showing how representation is communicatively constituted, this paper empirically shows how exclusion also can be seen as communicatively constituted. The interpretive approach toward communication employed in th
Multiple Interactive Representations for Fractions Learning
Feenstra, Laurens; Aleven, Vincent; Rummel, Nikol; Taatgen, Niels; Aleven,; Kay, J; Mostow, J
2010-01-01
Multiple External Representations (MERs) have been used successfully in instructional activities, including fractions However, students often have difficulties making the connections between the MERs spontaneously We argue that interactive fraction representations may help students in discovering re
The communicative constitution of representation and exclusion
Wessel, van M.G.J.
2014-01-01
In the light of current debate on representation, specifically engaging with literature showing how representation is communicatively constituted, this paper empirically shows how exclusion also can be seen as communicatively constituted. The interpretive approach toward communication employed in th
Some Representations of Unified Voigt Functions
Institute of Scientific and Technical Information of China (English)
M. KAMARUJJAMA; Dinesh SINGH
2005-01-01
The authors derive a set of unified representations of the Voigt functions in terms of familiar special functions of Mathematical Physics. Some deductions from these representations are also considered.
A geometric representation for the Proca model
Camacaro, J; Leal, L C; Camacaro, Jaime; Gaitan, Rolando; Leal, Lorenzo
1996-01-01
The Proca model is quantized in an open-path dependent representation that generalizes the Loop Representation of gauge theories. The starting point is a gauge invariant Lagrangian that reduces to the Proca Lagrangian when certain gauge is selected.
Attitudes, social representations and social attitudes
Farr, Robert, M.
1994-01-01
This paper plays the role of the devil's advocate in relation to Colin Fraser's paper "attitudes, social representations and widespread beliefs". It argues for the alternative perspective which Colin identifies that social representations and social attitudes are epistemologically incompatible theories.
Kernel representations for behaviors over finite rings
Kuijper, M.; Pinto, R.; Polderman, J.W.; Yamamoto, Y.
2006-01-01
In this paper we consider dynamical systems finite rings. The rings that we study are the integers modulo a power of a given prime. We study the theory of representations for such systems, in particular kernel representations.
Issack, Bilkiss B; Roy, Pierre-Nicholas
2005-08-22
An approach for the inclusion of geometric constraints in semiclassical initial value representation calculations is introduced. An important aspect of the approach is that Cartesian coordinates are used throughout. We devised an algorithm for the constrained sampling of initial conditions through the use of multivariate Gaussian distribution based on a projected Hessian. We also propose an approach for the constrained evaluation of the so-called Herman-Kluk prefactor in its exact log-derivative form. Sample calculations are performed for free and constrained rare-gas trimers. The results show that the proposed approach provides an accurate evaluation of the reduction in zero-point energy. Exact basis set calculations are used to assess the accuracy of the semiclassical results. Since Cartesian coordinates are used, the approach is general and applicable to a variety of molecular and atomic systems.
Transfinite tree quivers and their representations
Enochs, E; Özdemir, S
2012-01-01
The idea of "vertex at the infinity" naturally appears when studying indecomposable injective representations of tree quivers. In this paper we formalize this behavior and find the structure of all the indecomposable injective representations of a tree quiver of size an arbitrary cardinal $\\kappa$. As a consequence the structure of injective representations of noetherian $\\kappa$-trees is completely determined. In the second part we will consider the problem whether arbitrary trees are source injective representation quivers or not.
Paired structures in knowledge representation
DEFF Research Database (Denmark)
Montero, J.; Bustince, H.; Franco de los Ríos, Camilo;
2016-01-01
In this position paper we propose a consistent and unifying view to all those basic knowledge representation models that are based on the existence of two somehow opposite fuzzy concepts. A number of these basic models can be found in fuzzy logic and multi-valued logic literature. Here it is clai......In this position paper we propose a consistent and unifying view to all those basic knowledge representation models that are based on the existence of two somehow opposite fuzzy concepts. A number of these basic models can be found in fuzzy logic and multi-valued logic literature. Here...... of paired structures, generated from two paired concepts together with their associated neutrality, all of them to be modeled as fuzzy sets. In this way, paired structures can be viewed as a standard basic model from which different models arise. This unifying view should therefore allow a deeper analysis...
Representation theory of finite monoids
Steinberg, Benjamin
2016-01-01
This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully worked examples and exercises provide the bells and whistles for graduate accessibility, bringing a broad range of advanced readers to the forefront of research in the area. Highlights of the text include applications to probability theory, symbolic dynamics, and automata theory. Comfort with module theory, a familiarity with ordinary group representation theory, and the basics of Wedderburn theory, are prerequisites for advanced graduate level study. Researchers in algebra, algebraic combinatorics, automata theory, and probability theory, will find this text enriching with its thorough presentation of applications of the theory to these fields. Prior knowledge of semigroup theory is not expected for the diverse readership that may benefit from this exposition. The approach taken in this book is highly module-theoretic and follows the modern flavor of the theory of finite dimensional ...
Berry phase in Heisenberg representation
Andreev, V. A.; Klimov, Andrei B.; Lerner, Peter B.
1994-01-01
We define the Berry phase for the Heisenberg operators. This definition is motivated by the calculation of the phase shifts by different techniques. These techniques are: the solution of the Heisenberg equations of motion, the solution of the Schrodinger equation in coherent-state representation, and the direct computation of the evolution operator. Our definition of the Berry phase in the Heisenberg representation is consistent with the underlying supersymmetry of the model in the following sense. The structural blocks of the Hamiltonians of supersymmetrical quantum mechanics ('superpairs') are connected by transformations which conserve the similarity in structure of the energy levels of superpairs. These transformations include transformation of phase of the creation-annihilation operators, which are generated by adiabatic cyclic evolution of the parameters of the system.
Representations of mad cow disease.
Washer, Peter
2006-01-01
This paper examines the reporting of the story of Bovine Spongiform Encephalopathy (BSE) and its human derivative variant Creutzfeld-Jacob Disease (vCJD) in the British newspapers. Three 'snapshots' of newspaper coverage are sampled and analysed between the period 1986 and 1996 focusing on how representations of the disease evolved over the 10-year period. Social representations theory is used to elucidate how this new disease threat was conceptualised in the newspaper reporting and how it was explained to the UK public. This paper examines who or what was said to be at risk from the new disease, and whether some individuals or groups held to blame for the diseases' putative origins, the appearance of vCJD in human beings, and its spread.
Time representations in social science.
Schulz, Yvan
2012-12-01
Time has long been a major topic of study in social science, as in other sciences or in philosophy. Social scientists have tended to focus on collective representations of time, and on the ways in which these representations shape our everyday experiences. This contribution addresses work from such disciplines as anthropology, sociology and history. It focuses on several of the main theories that have preoccupied specialists in social science, such as the alleged "acceleration" of life and overgrowth of the present in contemporary Western societies, or the distinction between so-called linear and circular conceptions of time. The presentation of these theories is accompanied by some of the critiques they have provoked, in order to enable the reader to form her or his own opinion of them.
Time representations in social science
Schulz, Yvan
2012-01-01
Time has long been a major topic of study in social science, as in other sciences or in philosophy. Social scientists have tended to focus on collective representations of time, and on the ways in which these representations shape our everyday experiences. This contribution addresses work from such disciplines as anthropology, sociology and history. It focuses on several of the main theories that have preoccupied specialists in social science, such as the alleged “acceleration” of life and overgrowth of the present in contemporary Western societies, or the distinction between so-called linear and circular conceptions of time. The presentation of these theories is accompanied by some of the critiques they have provoked, in order to enable the reader to form her or his own opinion of them. PMID:23393420
Sparse representation of astronomical images.
Rebollo-Neira, Laura; Bowley, James
2013-04-01
Sparse representation of astronomical images is discussed. It is shown that a significant gain in sparsity is achieved when particular mixed dictionaries are used for approximating these types of images with greedy selection strategies. Experiments are conducted to confirm (i) the effectiveness at producing sparse representations and (ii) competitiveness, with respect to the time required to process large images. The latter is a consequence of the suitability of the proposed dictionaries for approximating images in partitions of small blocks. This feature makes it possible to apply the effective greedy selection technique called orthogonal matching pursuit, up to some block size. For blocks exceeding that size, a refinement of the original matching pursuit approach is considered. The resulting method is termed "self-projected matching pursuit," because it is shown to be effective for implementing, via matching pursuit itself, the optional backprojection intermediate steps in that approach.
Phases of stable representations of quivers
Engenhorst, Magnus
2015-01-01
We consider stable representations of non-Dynkin quivers with respect to a central charge. On one condition the existence of a stable representation with self-extensions implies the existence of infinitely many stables without self-extensions. In this case the phases of the stable representations approach one or two limit points. In particular, the phases are not dense in two arcs.
On Nambu-Lie 3-algebra representations
Sochichiu, Corneliu
2008-01-01
We propose a recipe to construct matrix representations of Nambu--Lie 3-algebras in terms of irreducible representations of underlying Lie algebra. The case of Euclidean four-dimensional 3-algebra is considered in details. We find that representations of this 3-algebra are not possible in terms of only Hermitian matrices in spite of its Euclidean nature.
37 CFR 350.2 - Representation.
2010-07-01
... 37 Patents, Trademarks, and Copyrights 1 2010-07-01 2010-07-01 false Representation. 350.2 Section... ROYALTY JUDGES RULES AND PROCEDURES GENERAL ADMINISTRATIVE PROVISIONS § 350.2 Representation. Individual... representation that the attorney is a member of the bar, in one or more states, in good standing. ...
24 CFR 180.305 - Representation.
2010-04-01
... 24 Housing and Urban Development 1 2010-04-01 2010-04-01 false Representation. 180.305 Section 180... Representation. (a) HUD is represented by the General Counsel. (b) Any party may appear on his/her/its own behalf... State. The attorney's representation that he/she is in good standing before any of these courts is...
2010-01-01
... 4 Accounts 1 2010-01-01 2010-01-01 false Representation. 28.25 Section 28.25 Accounts GOVERNMENT... Parties, Practitioners and Witnesses § 28.25 Representation. (a) All parties to a petition may be..., in the petition or responsive pleading. Any subsequent changes in representation shall also be in...
75 FR 32273 - Representation Election Procedure
2010-06-08
... 29 CFR Parts 1202 and 1206 RIN 3140-ZA00 Representation Election Procedure AGENCY: National Mediation... delaying the effective date of its rule regarding representation election procedures from June 10, 2010 to... Representation Election Procedure Rule have been made. The NMB will notify participants if there are any further...
33 CFR 20.301 - Representation.
2010-07-01
... 33 Navigation and Navigable Waters 1 2010-07-01 2010-07-01 false Representation. 20.301 Section 20... Motions § 20.301 Representation. (a) A party may appear— (1) Without counsel; (2) With an attorney; or (3... United States. A personal representation of membership is sufficient proof, unless the ALJ orders more...
29 CFR 4003.6 - Representation.
2010-07-01
... 29 Labor 9 2010-07-01 2010-07-01 false Representation. 4003.6 Section 4003.6 Labor Regulations... OF AGENCY DECISIONS General Provisions § 4003.6 Representation. A person may file any document or... of attorney, signed by the person making the designation, which authorizes the representation and...
7 CFR 917.15 - Representation area.
2010-01-01
... 7 Agriculture 8 2010-01-01 2010-01-01 false Representation area. 917.15 Section 917.15 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing Agreements... CALIFORNIA Order Regulating Handling Definitions § 917.15 Representation area. Representation area means any...
76 FR 37291 - Representation Case Procedures
2011-06-27
... BOARD 29 CFR Parts 101, 102, 103 RIN 3142-AAO8 Representation Case Procedures AGENCY: National Labor... amendments to the Board's rules governing representation case procedures, published at 76 FR 15307 (June 22, 2011) and make other proposals for improving representation case procedures. DATES: The meeting will be...
27 CFR 71.30 - Personal representation.
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 2 2010-04-01 2010-04-01 false Personal representation. 71.30 Section 71.30 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU... General Representation at Hearings § 71.30 Personal representation. Any individual or member of a...
46 CFR 401.615 - Representation.
2010-10-01
... 46 Shipping 8 2010-10-01 2010-10-01 false Representation. 401.615 Section 401.615 Shipping COAST... Representation. (a) The U.S. Registered Pilot, designated “respondent” in a suspension or revocation hearing or... a representation that under the provisions of this subpart and applicable law he is authorized and...
48 CFR 2009.570-4 - Representation.
2010-10-01
... 48 Federal Acquisition Regulations System 6 2010-10-01 2010-10-01 true Representation. 2009.570-4... ACQUISITION PLANNING CONTRACTOR QUALIFICATIONS Organizational Conflicts of Interest 2009.570-4 Representation... interest representation provision at 2052.209-71 must be included in solicitations and contracts resulting...
29 CFR 18.34 - Representation.
2010-07-01
... 29 Labor 1 2010-07-01 2010-07-01 true Representation. 18.34 Section 18.34 Labor Office of the... ADMINISTRATIVE LAW JUDGES General § 18.34 Representation. (a) Appearances. Any party shall have the right to... own representation that he or she is in good standing before any of such courts shall be sufficient...
2010-07-01
... 28 Judicial Administration 1 2010-07-01 2010-07-01 false Representation. 4.9 Section 4.9 Judicial... OF 1974 § 4.9 Representation. The applicant may be represented before the Commission by any person... constitute a representation to the Commission that under the provisions of this part and applicable law he is...
12 CFR 704.14 - Representation.
2010-01-01
... 12 Banks and Banking 6 2010-01-01 2010-01-01 false Representation. 704.14 Section 704.14 Banks and Banking NATIONAL CREDIT UNION ADMINISTRATION REGULATIONS AFFECTING CREDIT UNIONS CORPORATE CREDIT UNIONS § 704.14 Representation. (a) Board representation. The board will be determined as stipulated in its...
45 CFR 1613.4 - Authorized representation.
2010-10-01
... 45 Public Welfare 4 2010-10-01 2010-10-01 false Authorized representation. 1613.4 Section 1613.4... ON LEGAL ASSISTANCE WITH RESPECT TO CRIMINAL PROCEEDINGS § 1613.4 Authorized representation. Legal... professional responsibility requires representation in a criminal proceeding arising out of a transaction with...
Imitation and the Dialectic of Representation.
Zelazo, Philip David; Lourenco, Stella Felix
2003-01-01
Describes a theory of the understanding and use of representations, drawing heavily on Paul Ricoeur's and James Mark Baldwin's theories. Presents this theory as construing representation as intrinsically mimetic, characterizing the development of representational understanding as internalization, and emphasizing the importance of self-reflection…
Temporal Representation in Semantic Graphs
Energy Technology Data Exchange (ETDEWEB)
Levandoski, J J; Abdulla, G M
2007-08-07
A wide range of knowledge discovery and analysis applications, ranging from business to biological, make use of semantic graphs when modeling relationships and concepts. Most of the semantic graphs used in these applications are assumed to be static pieces of information, meaning temporal evolution of concepts and relationships are not taken into account. Guided by the need for more advanced semantic graph queries involving temporal concepts, this paper surveys the existing work involving temporal representations in semantic graphs.
Receptive fields and visual representations
Watson, Andrew B.
1989-01-01
Efficient representation of images for human use requires an understanding of how the brain processes and represents visual information. Spatial imagery is represented in the brain in the receptive fields of visual neurons. Models of these neurons lead to models of image fidelity, and to digital implementations of these neural codes. This approach will be illustrated by two example codes. The advantages and difficulties of this approach will be discussed.
Computing Visible-Surface Representations,
1985-03-01
Terzopoulos N00014-75-C-0643 9. PERFORMING ORGANIZATION NAME AMC ADDRESS 10. PROGRAM ELEMENT. PROJECT, TASK Artificial Inteligence Laboratory AREA A...Massachusetts Institute of lechnolog,. Support lbr the laboratory’s Artificial Intelligence research is provided in part by the Advanced Rtccarcl Proj...dynamically maintaining visible surface representations. Whether the intention is to model human vision or to design competent artificial vision systems
SAR Image Complex Pixel Representations
Energy Technology Data Exchange (ETDEWEB)
Doerry, Armin W. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-03-01
Complex pixel values for Synthetic Aperture Radar (SAR) images of uniform distributed clutter can be represented as either real/imaginary (also known as I/Q) values, or as Magnitude/Phase values. Generally, these component values are integers with limited number of bits. For clutter energy well below full-scale, Magnitude/Phase offers lower quantization noise than I/Q representation. Further improvement can be had with companding of the Magnitude value.
Representability of Hom Implies Flatness
Indian Academy of Sciences (India)
Nitin Nitsure
2004-02-01
Let be a projective scheme over a noetherian base scheme , and let $\\mathcal{F}$ be a coherent sheaf on . For any coherent sheaf $\\mathcal{E}$ on , consider the set-valued contravariant functor $\\hom_{(\\mathcal{E},\\mathcal{F})}$ on -schemes, defined by $\\hom_{(\\mathcal{E},\\mathcal{F})}(T)=\\mathrm{Hom}(\\mathcal{E}_T,\\mathcal{F}_T)$ where $\\mathcal{E}_T$ and $\\mathcal{F}_T$ are the pull-backs of $\\mathcal{E}$ and $\\mathcal{F}$ to $X_T=X×_s T$. A basic result of Grothendieck ([EGA], III 7.7.9) says that if $\\mathcal{F}$ is flat over then $\\hom_{(\\mathcal{E},\\mathcal{F})}$ is representable for all $\\mathcal{E}$. We prove the converse of the above, in fact, we show that if is a relatively ample line bundle on over such that the functor $\\hom_{(L^{-n},\\mathcal{F})}$ is representable for infinitely many positive integers , then $\\mathcal{F}$ is flat over . As a corollary, taking $X=S$, it follows that if $\\mathcal{F}$ is a coherent sheaf on then the functor $T\\mapsto H^0(T,\\mathcal{F}_T)$ on the category of -schemes is representable if and only if $\\mathcal{F}$ is locally free on . This answers a question posed by Angelo Vistoli. The techniques we use involve the proof of flattening stratification, together with the methods used in proving the author's earlier result (see [N1]) that the automorphism group functor of a coherent sheaf on is representable if and only if the sheaf is locally free.
Approximate Representations and Approximate Homomorphisms
Moore, Cristopher
2010-01-01
Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups: functions f:G -> U_d such that Pr[f(xy) = f(x) f(y)] is large, or more generally Exp_{x,y} ||f(xy) - f(x)f(y)||^2$ is small, where x and y are uniformly random elements of the group G and U_d denotes the unitary group of degree d. We bound these quantities in terms of the ratio d / d_min where d_min is the dimension of the smallest nontrivial representation of G. As an application, we bound the extent to which a function f : G -> H can be an approximate homomorphism where H is another finite group. We show that if H's representations are significantly smaller than G's, no such f can be much more homomorphic than a random function. We interpret these results as showing that if G is quasirandom, that is, if d_min is large, then G cannot be embedded in a small number of dimensi...
Neural Representations of Physics Concepts.
Mason, Robert A; Just, Marcel Adam
2016-06-01
We used functional MRI (fMRI) to assess neural representations of physics concepts (momentum, energy, etc.) in juniors, seniors, and graduate students majoring in physics or engineering. Our goal was to identify the underlying neural dimensions of these representations. Using factor analysis to reduce the number of dimensions of activation, we obtained four physics-related factors that were mapped to sets of voxels. The four factors were interpretable as causal motion visualization, periodicity, algebraic form, and energy flow. The individual concepts were identifiable from their fMRI signatures with a mean rank accuracy of .75 using a machine-learning (multivoxel) classifier. Furthermore, there was commonality in participants' neural representation of physics; a classifier trained on data from all but one participant identified the concepts in the left-out participant (mean accuracy = .71 across all nine participant samples). The findings indicate that abstract scientific concepts acquired in an educational setting evoke activation patterns that are identifiable and common, indicating that science education builds abstract knowledge using inherent, repurposed brain systems.
On Performance Skill Representation Framework
Furukawa, Koichi; Shimizu, Satoshi; Yoshinaga, Saori
In this paper, we propose a framework for representing performance skill. Firstly, we notice the importance of performance skill representation. We introduce five different representation targets: performance tasks, performance rules, pre-shaping actions, dynamic integrity constraints, and performance states. Performance task description consists of a sequence of performance tasks and expressions. It acts as a goal description in planning. Performance rules describe model performance methods for given tasks including how to shape body parts and how to use various muscles. Pre-shaping action rules are similar to performance rules. Its role is to pre-shape in between consecutive tasks to prepare for the next task. Dynamic integrity constraints specify constraints to be satisfied during performance. They provide such general rules as prohibiting simultaneous strong activations of agonist and antagonist. Performance states are for describing real performance done by players including professionals and amateurs. The aim of the framework is to provide a uniform scheme for representing model performance methods given performance score such as music score. The representation framework will define targets of inducing formal skill rules as well as describing performance states automatically from biomechanical performance data. It also is related to a fundamental research issue of attributes finding/selection in discovering useful rules for skillful performance. We conclude our paper by stating future research direction.
Eisenstein series and automorphic representations
Fleig, Philipp; Kleinschmidt, Axel; Persson, Daniel
2015-01-01
We provide an introduction to the theory of Eisenstein series and automorphic forms on real simple Lie groups G, emphasising the role of representation theory. It is useful to take a slightly wider view and define all objects over the (rational) adeles A, thereby also paving the way for connections to number theory, representation theory and the Langlands program. Most of the results we present are already scattered throughout the mathematics literature but our exposition collects them together and is driven by examples. Many interesting aspects of these functions are hidden in their Fourier coefficients with respect to unipotent subgroups and a large part of our focus is to explain and derive general theorems on these Fourier expansions. Specifically, we give complete proofs of Langlands' constant term formula for Eisenstein series on adelic groups G(A) as well as the Casselman--Shalika formula for the p-adic spherical Whittaker vector associated to unramified automorphic representations of G(Q_p). Somewhat ...
Symbol Systems and Pictorial Representations
Diederich, Joachim; Wright, Susan
All problem-solvers are subject to the same ultimate constraints -- limitations on space, time, and materials (Minsky, 1985). He introduces two principles: (1) Economics: Every intelligence must develop symbol-systems for representing objects, causes and goals, and (2) Sparseness: Every evolving intelligence will eventually encounter certain very special ideas -- e.g., about arithmetic, causal reasoning, and economics -- because these particular ideas are very much simpler than other ideas with similar uses. An extra-terrestrial intelligence (ETI) would have developed symbol systems to express these ideas and would have the capacity of multi-modal processing. Vakoch (1998) states that ...``ETI may rely significantly on other sensory modalities (than vision). Particularly useful representations would be ones that may be intelligible through more than one sensory modality. For instance, the information used to create a three-dimensional representation of an object might be intelligible to ETI heavily reliant on either visual or tactile sensory processes.'' The cross-modal representations Vakoch (1998) describes and the symbol systems Minsky (1985) proposes are called ``metaphors'' when combined. Metaphors allow for highly efficient communication. Metaphors are compact, condensed ways of expressing an idea: words, sounds, gestures or images are used in novel ways to refer to something they do not literally denote. Due to the importance of Minsky's ``economics'' principle, it is therefore possible that a message heavily relies on metaphors.
Coxian Representations of Generalized Erlang Distributions
Institute of Scientific and Technical Information of China (English)
Qi-ming He; Han-qin Zhang
2009-01-01
This paper studies Coxian representations of generalized Erlang distributions. A nonlinear program is derived for computing the parameters of minimal Coxian representations of generalized Erlang distributions.The nonlinear program is also used to characterize the triangular order and the admissible region of generalized Erlang distributions. It is shown that the admissible region associated with a triangular order may not be convex. For generalized Erlang distributions of ME-order 3, a minimal Coxian representation is found explicitly.In addition, an algorithm is developed for computing a special type of ordered Coxian representations - the bivariate Coxian representation - for generalized Erlang distributions.
Octree Representation and Its Applications in CAD
Institute of Scientific and Technical Information of China (English)
唐泽圣
1992-01-01
In this paper,a survey of octree representation and its applications in CAD is presented.The octree representation may be categorized as pure octree representation and polytree(or extended octree),and the latter is actually a boundary representation decomposed by octree.Linear octree which is a variant of regular octree representation has the advantage of saving memory space.The mapping between Cartesian coordinates and node addresses in linear octree is discussed.Then,algorithms for converting a boundary representation of 3D object into an octree are investiged and major approaches for transforming an octree encoded object are presented.After that,some of the applications of octree representation in CAD are listed,in particular,the applications in solid modeling,in accelerating ray tracing and in generating meshes for FEM.
Unitary Representations of Gauge Groups
Huerfano, Ruth Stella
I generalize to the case of gauge groups over non-trivial principal bundles representations that I. M. Gelfand, M. I. Graev and A. M. Versik constructed for current groups. The gauge group of the principal G-bundle P over M, (G a Lie group with an euclidean structure, M a compact, connected and oriented manifold), as the smooth sections of the associated group bundle is presented and studied in chapter I. Chapter II describes the symmetric algebra associated to a Hilbert space, its Hilbert structure, a convenient exponential and a total set that later play a key role in the construction of the representation. Chapter III is concerned with the calculus needed to make the space of Lie algebra valued 1-forms a Gaussian L^2-space. This is accomplished by studying general projective systems of finitely measurable spaces and the corresponding systems of sigma -additive measures, all of these leading to the description of a promeasure, a concept modeled after Bourbaki and classical measure theory. In the case of a locally convex vector space E, the corresponding Fourier transform, family of characters and the existence of a promeasure for every quadratic form on E^' are established, so the Gaussian L^2-space associated to a real Hilbert space is constructed. Chapter III finishes by exhibiting the explicit Hilbert space isomorphism between the Gaussian L ^2-space associated to a real Hilbert space and the complexification of its symmetric algebra. In chapter IV taking as a Hilbert space H the L^2-space of the Lie algebra valued 1-forms on P, the gauge group acts on the motion group of H defining in an straight forward fashion the representation desired.
Efficient Type Representation in TAL
Chen, Juan
2009-01-01
Certifying compilers generate proofs for low-level code that guarantee safety properties of the code. Type information is an essential part of safety proofs. But the size of type information remains a concern for certifying compilers in practice. This paper demonstrates type representation techniques in a large-scale compiler that achieves both concise type information and efficient type checking. In our 200,000-line certifying compiler, the size of type information is about 36% of the size of pure code and data for our benchmarks, the best result to the best of our knowledge. The type checking time is about 2% of the compilation time.
Knowledge Representation in Travelling Texts
DEFF Research Database (Denmark)
Mousten, Birthe; Locmele, Gunta
2014-01-01
and the purpose of the text in a new context as well as on predefined parameters for text travel. For texts used in marketing and in technology, the question is whether culture-bound knowledge representation should be domesticated or kept as foreign elements, or should be mirrored or moulded—or should not travel...... at all! When should semantic and pragmatic elements in a text be replaced and by which other elements? The empirical basis of our work is marketing and technical texts in English, which travel into the Latvian and Danish markets, respectively....
Cognitive representation of negative numbers.
Fischer, Martin H
2003-05-01
To understand negative numbers, must we refer to positive number representations (the phylogenetic hypothesis), or do we acquire a negative mental number line (the ontogenetic hypothesis)? In the experiment reported here, participants made lateralized button responses to indicate the larger of two digits from the range -9 to 9. Digit pairs were displayed spatially congruent or incongruent with either a phylogenetic or an ontogenetic mental number line. The pattern of decision latencies suggests that negative numbers become associated with left space, thus supporting the ontogenetic view.
Multimedia ontology representation and applications
Chaudhury, Santanu; Ghosh, Hiranmay
2015-01-01
The result of more than 15 years of collective research, Multimedia Ontology: Representation and Applications provides a theoretical foundation for understanding the nature of media data and the principles involved in its interpretation. The book presents a unified approach to recent advances in multimedia and explains how a multimedia ontology can fill the semantic gap between concepts and the media world. It relays real-life examples of implementations in different domains to illustrate how this gap can be filled.The book contains information that helps with building semantic, content-based
QED in the worldline representation
Schubert, Christian
2007-06-01
Simultaneously with inventing the modern relativistic formalism of quantum electrodynamics, Feynman presented also a first-quantized representation of QED in terms of worldline path integrals. Although this alternative formulation has been studied over the years by many authors, only during the last fifteen years it has acquired some popularity as a computational tool. I will shortly review here three very different techniques which have been developed during the last few years for the evaluation of worldline path integrals, namely (i) the "string-inspired formalism", based on the use of worldline Green functions, (ii) the numerical "worldline Monte Carlo formalism", and (iii) the semiclassical "worldline instanton" approach.
Superalgebraic representation of Dirac matrices
Monakhov, V. V.
2016-01-01
We consider a Clifford extension of the Grassmann algebra in which operators are constructed from products of Grassmann variables and derivatives with respect to them. We show that this algebra contains a subalgebra isomorphic to a matrix algebra and that it additionally contains operators of a generalized matrix algebra that mix states with different numbers of Grassmann variables. We show that these operators are extensions of spin-tensors to the case of superspace. We construct a representation of Dirac matrices in the form of operators of a generalized matrix algebra.
Nonorthogonal Decoy-State Quantum Key Distribution
Institute of Scientific and Technical Information of China (English)
LI Jing-Bo; FANG Xi-Ming
2006-01-01
@@ In practical quantum key distribution (QKD), weak coherent states as the photon source have a limit in the secure key rate and transmission distance because of the existence of multi-photon pulses and heavy loss in transmission line.
Quiver representations and quiver varieties
Jr, Alexander Kirillov
2016-01-01
This book is an introduction to the theory of quiver representations and quiver varieties, starting with basic definitions and ending with Nakajima's work on quiver varieties and the geometric realization of Kac-Moody Lie algebras. The first part of the book is devoted to the classical theory of quivers of finite type. Here the exposition is mostly self-contained and all important proofs are presented in detail. The second part contains the more recent topics of quiver theory that are related to quivers of infinite type: Coxeter functor, tame and wild quivers, McKay correspondence, and representations of Euclidean quivers. In the third part, topics related to geometric aspects of quiver theory are discussed, such as quiver varieties, Hilbert schemes, and the geometric realization of Kac-Moody algebras. Here some of the more technical proofs are omitted; instead only the statements and some ideas of the proofs are given, and the reader is referred to original papers for details. The exposition in the book requ...
Representation theory a first course
Fulton, William
1991-01-01
The primary goal of these lectures is to introduce a beginner to the finite dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book. Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians. This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways. It is for ...
Representation and Perspective in Science
Directory of Open Access Journals (Sweden)
Bas C. van Fraassen
2007-12-01
Full Text Available The world science describes tends to have a very strange look. We can’t see atoms or force fields, nor are they imaginable within visualizable categories, so neither can we even imagine what the world must be like according to recent physical theories. That tension, between what science depicts as reality and how things appear to us, though it is more striking now, has been with us since modern science began. It can be addressed, and perhaps alleviated by inquiring into how science represents nature. In general, representation is selective, the selection is of what is relevant to the purpose at hand, and success may even require distortion. From this point of view, the constraint on science, that it must ‘save the phenomena’, takes on a new form. The question to be faced is how the perspectival character of the appearances (that is, contents of measurement outcomes can be related to the hidden structure that the sciences postulate. In the competing interpretations of quantum mechanics we can see how certain traditional ideals and constraints are left behind. Specifically, Carlo Rovelli’s Relational Quantum Mechanics offers a probative example of the freedom of scientific representation.
Energy Technology Data Exchange (ETDEWEB)
Sokolov, Alexander Yu., E-mail: asokolov@uga.edu; Schaefer, Henry F. [Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602 (United States); Kutzelnigg, Werner [Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum (Germany)
2014-08-21
A new approach to density cumulant functional theory is developed that derives density cumulant N-representability conditions from an approximate Fock space unitary transformation. We present explicit equations for the third- and fourth-order two-particle cumulant N-representability, as well as the second-order contributions that depend on the connected three-particle density cumulant. These conditions are used to formulate the ODC-13 method and the non-iterative (λ{sub 3}) correction that employ an incomplete description of the fourth-order two-particle cumulant N-representability and the second-order three-particle correlation effects, respectively. We perform an analysis of the ODC-13 N-representability description for the dissociation of H{sub 2} and apply the ODC-13 method and the (λ{sub 3}) correction to diatomic molecules with multiple bond character and the symmetry-breaking tetraoxygen cation (O{sub 4}{sup +}). For the O{sub 4}{sup +} molecule, the vibrational frequencies of the ODC-13(λ{sub 3}) method do not exhibit spatial symmetry breaking and are in a good agreement with the recent infrared photodissociation experiment. We report the O{sub 4}{sup +} equilibrium structure, harmonic frequencies, and dissociation energy computed using ODC-13(λ{sub 3}) with a diffuse, core-correlated aug-cc-pCVTZ basis set.
Generative Representations for Automated Design of Robots
Homby, Gregory S.; Lipson, Hod; Pollack, Jordan B.
2007-01-01
A method of automated design of complex, modular robots involves an evolutionary process in which generative representations of designs are used. The term generative representations as used here signifies, loosely, representations that consist of or include algorithms, computer programs, and the like, wherein encoded designs can reuse elements of their encoding and thereby evolve toward greater complexity. Automated design of robots through synthetic evolutionary processes has already been demonstrated, but it is not clear whether genetically inspired search algorithms can yield designs that are sufficiently complex for practical engineering. The ultimate success of such algorithms as tools for automation of design depends on the scaling properties of representations of designs. A nongenerative representation (one in which each element of the encoded design is used at most once in translating to the design) scales linearly with the number of elements. Search algorithms that use nongenerative representations quickly become intractable (search times vary approximately exponentially with numbers of design elements), and thus are not amenable to scaling to complex designs. Generative representations are compact representations and were devised as means to circumvent the above-mentioned fundamental restriction on scalability. In the present method, a robot is defined by a compact programmatic form (its generative representation) and the evolutionary variation takes place on this form. The evolutionary process is an iterative one, wherein each cycle consists of the following steps: 1. Generative representations are generated in an evolutionary subprocess. 2. Each generative representation is a program that, when compiled, produces an assembly procedure. 3. In a computational simulation, a constructor executes an assembly procedure to generate a robot. 4. A physical-simulation program tests the performance of a simulated constructed robot, evaluating the performance
Representation and Re-Presentation in Litigation Science
Jasanoff, Sheila
2008-01-01
Federal appellate courts have devised several criteria to help judges distinguish between reliable and unreliable scientific evidence. The best known are the U.S. Supreme Court’s criteria offered in 1993 in Daubert v. Merrell Dow Pharmaceuticals, Inc. This article focuses on another criterion, offered by the Ninth Circuit Court of Appeals, that instructs judges to assign lower credibility to “litigation science” than to science generated before litigation. In this article I argue that the criterion-based approach to judicial screening of scientific evidence is deeply flawed. That approach buys into the faulty premise that there are external criteria, lying outside the legal process, by which judges can distinguish between good and bad science. It erroneously assumes that judges can ascertain the appropriate criteria and objectively apply them to challenged evidence before litigation unfolds, and before methodological disputes are sorted out during that process. Judicial screening does not take into account the dynamics of litigation itself, including gaming by the parties and framing by judges, as constitutive factors in the production and representation of knowledge. What is admitted through judicial screening, in other words, is not precisely what a jury would see anyway. Courts are sites of repeated re-representations of scientific knowledge. In sum, the screening approach fails to take account of the wealth of existing scholarship on the production and validation of scientific facts. An unreflective application of that approach thus puts courts at risk of relying upon a “junk science” of the nature of scientific knowledge. PMID:18197311
Advanced Geometric Modeler with Hybrid Representation
Institute of Scientific and Technical Information of China (English)
杨长贵; 陈玉健; 等
1996-01-01
An advanced geometric modeler GEMS4.0 has been developed,in which feature representation is used at the highest level abstraction of a product model.Boundary representation is used at the bottom level,while CSG model is adopted at the median level.A BRep data structure capable of modeling non-manifold is adopted.UNRBS representation is used for all curved surfaces,Quadric surfaces have dual representations consisting of their geometric data such as radius,center point,and center axis.Boundary representation of free form surfaces is easily built by sweeping and skinning method with NURBS geometry.Set operations on curved solids with boundary representation are performed by an evaluation process consisting of four steps.A file exchange facility is provided for the conversion between product data described by STEP and product information generated by GEMS4.0.
Full quivers of representations of algebras
Belov-Kanel, Alexei; Vishne, Uzi
2011-01-01
We introduce the notion of the full quiver of a representation of an algebra, which is a cover of the (classical) quiver, but which captures properties of the representation itself. Gluing of vertices and of arrows enables one to study subtle combinatorial aspects of algebras which are lost in the classical quiver. Full quivers of representations apply especially well to \\Zcd\\ algebras, which have properties very like those of finite dimensional algebras over fields. By choosing the representation appropriately, one can restrict the gluing to two main types: {\\it Frobenius} (along the diagonal) and, more generally {\\it proportional} Frobenius gluing (above the diagonal), and our main result is that any representable algebra has a faithful representation described completely by such a full quiver. Further reductions are considered, which bear on the polynomial identities.
Transforming Graph Representations for Statistical Relational Learning
Rossi, Ryan A; Aha, David W; Neville, Jennifer
2012-01-01
Relational data representations have become an increasingly important topic due to the recent proliferation of network datasets (e.g., social, biological, information networks) and a corresponding increase in the application of statistical relational learning (SRL) algorithms to these domains. In this article, we examine a range of representation issues for graph-based relational data. Since the choice of relational data representation for the nodes, links, and features can dramatically affect the capabilities of SRL algorithms, we survey approaches and opportunities for relational representation transformation designed to improve the performance of these algorithms. This leads us to introduce an intuitive taxonomy for data representation transformations in relational domains that incorporates link transformation and node transformation as symmetric representation tasks. In particular, the transformation tasks for both nodes and links include (i) predicting their existence, (ii) predicting their label or type...
Representations and inequalities for generalized hypergeometric functions
Karp, Dmitrii
2014-01-01
We find an integral representation for the generalized hypergeometric function unifying known representations via generalized Stieltjes, Laplace and cosine Fourier transforms. Using positivity conditions for the weight in this representation we establish various new facts regarding generalized hypergeometric functions, including complete monotonicity, log-convexity in upper parameters, monotonicity of ratios and new proofs of Luke's bounds. Besides, we derive two-sided inequalities for the Be...
Ambiguous representations as fuzzy relations between sets
Nykyforchyn, Oleh; 10.1016/j.fss.2011.02.007
2011-01-01
Crisp and $L$-fuzzy ambiguous representations of closed subsets of one space by closed subsets of another space are introduced. It is shown that, for each pair of compact Hausdorff spaces, the set of (crisp or $L$-fuzzy) ambiguous representations is a lattice and a compact Hausdorff Lawson upper semilattice. The categories of ambiguous and $L$-ambiguous representations are defined and investigated.
Social representation of the kinesiotherapist profession
Beatrice ABALAŞE
2017-01-01
The scientific approach is focused on identifying the social representation of the profession of physical therapist referring to mental images of social reality to a group consensus meeting. The goal of research identifies social representation of the profession of physical therapist, on the premise that students of the Faculty of Physical Education and Sport have made a social representation of the profession of physical therapist in accordance with the description of the occupation of CO...
Braid group representation on quantum computation
Energy Technology Data Exchange (ETDEWEB)
Aziz, Ryan Kasyfil, E-mail: kasyfilryan@gmail.com [Department of Computational Sciences, Bandung Institute of Technology (Indonesia); Muchtadi-Alamsyah, Intan, E-mail: ntan@math.itb.ac.id [Algebra Research Group, Bandung Institute of Technology (Indonesia)
2015-09-30
There are many studies about topological representation of quantum computation recently. One of diagram representation of quantum computation is by using ZX-Calculus. In this paper we will make a diagrammatical scheme of Dense Coding. We also proved that ZX-Calculus diagram of maximally entangle state satisfies Yang-Baxter Equation and therefore, we can construct a Braid Group representation of set of maximally entangle state.
Integrality of representations of finite groups
Hofmann, Tommy
2016-01-01
Since the early days of representation theory of finite groups in the 19th century, it was known that complex linear representations of finite groups live over number fields, that is, over finite extensions of the field of rational numbers. While the related question of integrality of representations was answered negatively by the work of Cliff, Ritter and Weiss as well as by Serre and Feit, it was not known how to decide integrality of a given representation. In this thesis we show tha...
On minimal integer representations of weighted games
Freixas, Josep
2011-01-01
We study minimum integer representations for the weights of weighted games, which is linked with some solution concepts in game theory. Closing some gaps in the existing literature we prove that each weighted game with two types of voters admits a unique minimum integer presentation and give examples for more than two types of voters without a minimum integer representation. We characterize the possible weights in minimum integer representations and give examples for at least four types of voters without minimum integer representations preserving types.
Minimal Model Semantics for Sorted Constraint Representation
Institute of Scientific and Technical Information of China (English)
廖乐健; 史忠植
1995-01-01
Sorted constraint representation is a very useful representation in AI which combines class hierarchies and constraint networks.For such sorted constraint representation,a problem is how to generalize the idea of default inheritance to constraint network,where the attributes in a class or between different classes interact with each other via the network.To give a formal account for the defeasible reasoning in such representation,a general sorted constraint logic is proposed,and a minimal-model semantics for the logic is presented.
SVPWM of dual three-phase motor based on non-orthogonal coordinate%非正交坐标系下双三相感应电机SVPWM控制策略
Institute of Scientific and Technical Information of China (English)
李洪亮; 姜建国
2014-01-01
To address the traditional space vector pulse width modulation algorithm of dual three-phase motor which contains a large number of trigonometric functions and finding roots of computing, and the motor stator current contains a large number of harmonic components,combined with dual three-phase mo-tor vector classification, a dual three-phase induction motor space vector pulse width modulation algorithm was proposed in non-orthogonal coordinate system of 120 ° . The maximum and minimum values of given three-phase voltage signals were determined. There is no need to calculate the sector and the role of the fundamental voltage vector time,and it can directly obtain switching time with each phase by summarizing the law. The simulation and experimental results show that compared with conventional dual three-phase SVPWM algorithm, the novel dual three-phase induction motor SVPWM algorithm effectively inhibits the motor stator current harmonics, while greatly reducing the execution time of the algorithm. Stator current harmonic suppression improves motor control performances, and shorten the execution time of the algo-rithm which saves processor resources.%针对传统双三相电机空间矢量脉冲宽度调制( space vector pulse width modulation,SVPWM)算法中含有大量的三角函数和求根运算,且电机定子电流谐波含量大的问题。结合双三相电机的矢量分类技术,在120°的非正交坐标系下提出了一种双三相感应电机的空间矢量脉冲宽度调制算法。判断三相给定电压信号的最大值和最小值,通过总结规律,可直接求得各相开关的切换时刻,无须进行扇区和基本电压矢量作用时间的计算。对仿真和实验结果的分析表明,与传统双三相SVPWM算法相比,所提出的双三相感应电机SVPWM算法可以有效抑制电机定子电流谐波的同时,大大缩短算法执行时间。定子电流谐波的抑制可提高电机控制性能,算法执行时间的缩短将为处理器节约资源。
Institute of Scientific and Technical Information of China (English)
丁纺纺; 彭雄奇
2011-01-01
A non-orthogonal constitutive model, previously developed by the authors to characterize the anisotropic material behavior of woven composite fabrics under large deformation, which results from the angle change between warp and weft yarns, was validated by a hemispherical stamping simulation of a square plain woven composite fabric at room temperature. As a comparison, the forming is simulated by using a corresponding orthotropic constitutive model. The simulation results show that the non-orthogonal constitutive model brings out almost the same boundary profile as that in the experiment and shear angles are in the experimental standard deviation range. While quite large discrepancy is found in the case with orthogonal constitutive model. The proposed non-orthogonal model is better than the orthogonal model in characterizing the anisotropic material behavior of woven composites under large shear deformation.%为了描述复合材料用机织物在大变形下由于经纱和纬纱之间角度变化所引起的非线性各向异性材料行为,前期工作中建立了一个非正交本构模型.利用半球形冲头对复合材料用平纹机织物进行冲压模拟,并将非正交本构模型和正交本构模型的模拟结果与实验结果进行对比,对非正交本构模型进行验证,以充分说明该模型的有效性和正确性.结果表明:采用非正交本构模型模拟的复合材料用平纹机织物变形后的边界轮廓与实验结果基本一致,并且剪切角都在实验结果的误差范围内;而采用正交本构模型,复合材料用机织物变形后的边界轮廓和剪切角与实验结果相差较大.研究表明,与正交本构模型相比非正交本构模型能更好地描述复合材料用机织物在大变形下的材料属性.
Wavelet Representation of Contour Sets
Energy Technology Data Exchange (ETDEWEB)
Bertram, M; Laney, D E; Duchaineau, M A; Hansen, C D; Hamann, B; Joy, K I
2001-07-19
We present a new wavelet compression and multiresolution modeling approach for sets of contours (level sets). In contrast to previous wavelet schemes, our algorithm creates a parametrization of a scalar field induced by its contoum and compactly stores this parametrization rather than function values sampled on a regular grid. Our representation is based on hierarchical polygon meshes with subdivision connectivity whose vertices are transformed into wavelet coefficients. From this sparse set of coefficients, every set of contours can be efficiently reconstructed at multiple levels of resolution. When applying lossy compression, introducing high quantization errors, our method preserves contour topology, in contrast to compression methods applied to the corresponding field function. We provide numerical results for scalar fields defined on planar domains. Our approach generalizes to volumetric domains, time-varying contours, and level sets of vector fields.
Knowledge Representation in Travelling Texts
DEFF Research Database (Denmark)
Mousten, Birthe; Locmele, Gunta
2014-01-01
Today, information travels fast. Texts travel, too. In a corporate context, the question is how to manage which knowledge elements should travel to a new language area or market and in which form? The decision to let knowledge elements travel or not travel highly depends on the limitation...... and the purpose of the text in a new context as well as on predefined parameters for text travel. For texts used in marketing and in technology, the question is whether culture-bound knowledge representation should be domesticated or kept as foreign elements, or should be mirrored or moulded—or should not travel...... at all! When should semantic and pragmatic elements in a text be replaced and by which other elements? The empirical basis of our work is marketing and technical texts in English, which travel into the Latvian and Danish markets, respectively....
[Pneumonia and its social representations].
Hamui-Sutton, Alicia; Nellen-Hummel, Haiko; Fernández-Ortega, Miguel Angel; Halabe-Cherem, José
2009-01-01
To correlate the sociostructural variables with the knowledge about pneumonia and to explore the social representations about the etiology, prevention, development and treatment in poor communities. A survey in 848 adults from seven Rural Health Centers affiliated to IMSS-Oportunidades Program in four States, was carried out. One-third of the sample did not understand the term pneumonia; 35 % of the patients with risk factors did not know its etiology; 43 % did not know about associated complications but 85 % considered that it causes death. The use of antibiotics was recognized as a therapeutic measure by 78 % and 20 % did not know how to prevent pneumonia. The findings showed a positive attitude to immunization but inadequate information about respiratory diseases. In neighborhoods with insufficient public services (purified water, electricity and paved roads) the ignorance about pneumonia tended to increase.
Style representation in design grammars
DEFF Research Database (Denmark)
Ahmad, Sumbul; Chase, Scott Curland
2012-01-01
The concept of style is relevant for both the analysis and synthesis of designs. New styles are often formed by the adaptation of previous ones based on changes in design criteria and context. A formal characterization of style is given by shape grammars, which describe the compositional rules...... underlying a set of designs. Stylistic change can be modelled by grammar transformations, which allow the transformation of the structure and vocabulary of a grammar that is used to describe a particular style. In order for grammars to be useful beyond a single application, they should have the capability...... to be transformed according to changing design style needs. Issues of formalizing stylistic change necessitate a lucid and formal definition of style in the design language generated by a grammar. Furthermore, a significant aspect of the definition of style is the representation of aesthetic qualities attributed...
Sparse Representations of Hyperspectral Images
Swanson, Robin J.
2015-11-23
Hyperspectral image data has long been an important tool for many areas of sci- ence. The addition of spectral data yields significant improvements in areas such as object and image classification, chemical and mineral composition detection, and astronomy. Traditional capture methods for hyperspectral data often require each wavelength to be captured individually, or by sacrificing spatial resolution. Recently there have been significant improvements in snapshot hyperspectral captures using, in particular, compressed sensing methods. As we move to a compressed sensing image formation model the need for strong image priors to shape our reconstruction, as well as sparse basis become more important. Here we compare several several methods for representing hyperspectral images including learned three dimensional dictionaries, sparse convolutional coding, and decomposable nonlocal tensor dictionaries. Addi- tionally, we further explore their parameter space to identify which parameters provide the most faithful and sparse representations.
Furman, Wyndol; Collibee, Charlene
2016-12-28
This study examined how representations of parent-child relationships, friendships, and past romantic relationships are related to subsequent romantic representations. Two-hundred 10th graders (100 female; Mage = 15.87 years) from diverse neighborhoods in a Western U.S. city were administered questionnaires and were interviewed to assess avoidant and anxious representations of their relationships with parents, friends, and romantic partners. Participants then completed similar questionnaires and interviews about their romantic representations six more times over the next 7.5 years. Growth curve analyses revealed that representations of relationships with parents, friends, and romantic partners each uniquely predicted subsequent romantic representations across development. Consistent with attachment and behavioral systems theory, representations of romantic relationships are revised by representations and experiences in other relationships.