Systematic study on intermolecular valence-band dispersion in molecular crystalline films

International Nuclear Information System (INIS)

Yamane, Hiroyuki; Kosugi, Nobuhiro

2015-01-01

Highlights: • Intermolecular valence-band dispersion of crystalline films of phthalocyanines. • Intermolecular transfer integral versus lattice constant. • Site-specific intermolecular interaction and resultant valence-band dispersion. • Band narrowing effect induced by elevated temperature. - Abstract: Functionalities of organic semiconductors are governed not only by individual properties of constituent molecules but also by solid-state electronic states near the Fermi level such as frontier molecular orbitals, depending on weak intermolecular interactions in various conformations. The individual molecular property has been widely investigated in detail; on the other hand, the weak intermolecular interaction is difficult to investigate precisely due to the presence of the structural and thermal energy broadenings in organic solids. Here we show quite small but essential intermolecular valence band dispersions and their temperature dependence of sub-0.1-eV scale in crystalline films of metal phthalocyanines (H_2Pc, ZnPc, CoPc, MnPc, and F_1_6ZnPc) by using angle-resolved photoemission spectroscopy (ARPES) with synchrotron radiation. The observed bands show intermolecular and site dependent dispersion widths, phases, and periodicities, for different chemical substitution of terminal groups and central metals in the phthalocyanine molecule. The precise and systematic band-dispersion measurement would be a credible approach toward the comprehensive understanding of intermolecular interactions and resultant charge transport properties as well as their tuning by substituents in organic molecular systems.

Orbital momentum distribution and binding energies for the complete valence shell of molecular chlorine by electron momentum spectroscopy

International Nuclear Information System (INIS)

Frost, L.; Grisogono, A.M.; McCarthy, I.E.

1986-10-01

The complete valence shell binding energy spectrum (10-50 eV) of Cl 2 has been determined using electron momentum (binary (e,2e)) spectroscopy. The inner valence region, corresponding to 4σ u and 4σ g ionization, has been measured for the first time and shows extensive splitting of the ionization strength due to electron correlation effects. These measurements are compared with the results of many-body calculations using Green's function and CI methods employing unpolarised as well as polarised wave functions. Momentum distributions, measured in both the outer and inner valence regions, are compared with calculations using a range of unpolarised and polarised wave functions. Computed orbital density maps in momentum and position space for oriented Cl 2 molecules are discussed in comparison with the measured and calculated spherically averaged momentum distributions

Laplace-transformed multi-reference second-order perturbation theories in the atomic and active molecular orbital basis

NARCIS (Netherlands)

Helmich-Paris, B.; Knecht, Stefan

2017-01-01

In the present article, we show how to formulate the partially contracted n-electron valence second-order perturbation theory (NEVPT2) energies in the atomic and active molecular orbital basis by employing the Laplace transformation of orbital-energy denominators (OEDs). As atomic-orbital (AO) basis

Internuclear Separation Dependent Ionization of the Valence Orbitals of I2 by Strong Laser Fields

Science.gov (United States)

Chen, H.; Tagliamonti, V.; Gibson, G. N.

2012-11-01

Using a pump-dump-probe technique and Fourier-transform spectroscopy, we study the internuclear separation R dependence and relative strength of the ionization rates of the π and σ electrons of I2, whose valence orbitals are σg2πu4πg4σu0. We find that ionization of the highest occupied molecular orbital (HOMO)-2 (σg) has a strong dependence on R while the HOMO and HOMO-1 do not. Surprisingly, the ionization rate of the HOMO-2 exceeds the combined ionization rate of the less bound orbitals and this branching ratio increases with R. Since our technique produces target molecules that are highly aligned with the laser polarization, the σ orbitals will be preferentially ionized and undergo enhanced ionization at larger R compared to the π orbitals. Nevertheless, it is highly unusual that an inner orbital provides the dominant strong field ionization pathway in a small molecule.

On the basis of molecular orbitals for relativistic bound systems of many bodies

International Nuclear Information System (INIS)

Cook, A.H.

1987-09-01

The quasi-relativistic Hamiltonian for bound states of many bodies proposed in previous articles (Cook, 1986, 1987a) is shown to provide a basis for the molecular orbital scheme of constructing wavefunctions and calculating eigenenergies. (author). 5 refs

X-ray photoelectron spectra structure of actinide compounds stipulated by electrons of the inner valence molecular orbitals (IVMO)

International Nuclear Information System (INIS)

Teterin, Yu. A.; Ivanov, K. E.

1997-01-01

Development of precise X-ray photoelectron spectroscopy using X-ray radiation hν< 1.5 KeV allowed to carry out immediate investigations of fine spectra structure of both weakly bond and deep electrons. Based on the experiments and the obtained results it may be concluded: 1. Under favourable conditions the inner valence molecular orbitals (IVMO) may form in all actinide compounds. 2. The XPS spectra fine structure stipulated by IVMO electrons allows to judge upon the degree of participation of the filled AO electrons in the chemical bond, on the structure o considered atom close environment and the bond lengths in compounds. For amorphous compounds the obtaining of such data based on X-ray structure analysis is restricted. 3. The summary contribution of IVMO electrons to the absolute value of the chemical bonding is comparable with the corresponding value of OMO electrons contribution to the atomic bonding. This fact is very important and new in chemistry. (author)

In silico simulations of tunneling barrier measurements for molecular orbital-mediated junctions: A molecular orbital theory approach to scanning tunneling microscopy

Energy Technology Data Exchange (ETDEWEB)

Terryn, Raymond J.; Sriraman, Krishnan; Olson, Joel A., E-mail: jolson@fit.edu; Baum, J. Clayton, E-mail: cbaum@fit.edu [Department of Chemistry, Florida Institute of Technology, 150 West University Boulevard, Melbourne, Florida 32901 (United States); Novak, Mark J. [Department of Chemistry and Applied Biological Sciences, South Dakota School of Mines and Technology, 501 E. Saint Joseph Street, Rapid City, South Dakota 57701 (United States)

2016-09-15

A new simulator for scanning tunneling microscopy (STM) is presented based on the linear combination of atomic orbitals molecular orbital (LCAO-MO) approximation for the effective tunneling Hamiltonian, which leads to the convolution integral when applied to the tip interaction with the sample. This approach intrinsically includes the structure of the STM tip. Through this mechanical emulation and the tip-inclusive convolution model, dI/dz images for molecular orbitals (which are closely associated with apparent barrier height, ϕ{sub ap}) are reported for the first time. For molecular adsorbates whose experimental topographic images correspond well to isolated-molecule quantum chemistry calculations, the simulator makes accurate predictions, as illustrated by various cases. Distortions in these images due to the tip are shown to be in accord with those observed experimentally and predicted by other ab initio considerations of tip structure. Simulations of the tunneling current dI/dz images are in strong agreement with experiment. The theoretical framework provides a solid foundation which may be applied to LCAO cluster models of adsorbate–substrate systems, and is extendable to emulate several aspects of functional STM operation.

In silico simulations of tunneling barrier measurements for molecular orbital-mediated junctions: A molecular orbital theory approach to scanning tunneling microscopy

International Nuclear Information System (INIS)

Terryn, Raymond J.; Sriraman, Krishnan; Olson, Joel A.; Baum, J. Clayton; Novak, Mark J.

2016-01-01

A new simulator for scanning tunneling microscopy (STM) is presented based on the linear combination of atomic orbitals molecular orbital (LCAO-MO) approximation for the effective tunneling Hamiltonian, which leads to the convolution integral when applied to the tip interaction with the sample. This approach intrinsically includes the structure of the STM tip. Through this mechanical emulation and the tip-inclusive convolution model, dI/dz images for molecular orbitals (which are closely associated with apparent barrier height, ϕ_a_p) are reported for the first time. For molecular adsorbates whose experimental topographic images correspond well to isolated-molecule quantum chemistry calculations, the simulator makes accurate predictions, as illustrated by various cases. Distortions in these images due to the tip are shown to be in accord with those observed experimentally and predicted by other ab initio considerations of tip structure. Simulations of the tunneling current dI/dz images are in strong agreement with experiment. The theoretical framework provides a solid foundation which may be applied to LCAO cluster models of adsorbate–substrate systems, and is extendable to emulate several aspects of functional STM operation.

Investigation of electron momentum distributions for outer valence orbitals of trichlorofluoromethane by (e, 2e) electron momentum spectroscopy

International Nuclear Information System (INIS)

Zhou, L.X.; Shan, X.; Chen, X.J.; Yin, X.F.; Zhang, X.H.; Xu, C.K.; Wei, Z.; Xu, K.Z.

2006-01-01

The binding energy spectra and electron momentum distributions for the outer valence orbitals of trichlorofluoromethane (CFCl 3 ) have been measured by binary (e, 2e) electron momentum spectroscopy (EMS) at an impact energy of 1200 eV + binding energy. The experimental electron momentum profiles are compared with Hartree-Fock and density functional theory (DFT) calculations with different-sized basis sets. Generally, the DFT calculations employing B3LYP functional with large basis sets of AUG-cc-pVDZ and AUG-cc-pVTZ give better description of the experimental results. But for 3e orbital, all the theoretical calculations underestimate the experiment, which is probably due to the distorted-wave effect that often occurs in π*-like molecular orbital

Valence photoelectron spectrum of KBr: Effects of electron correlation

International Nuclear Information System (INIS)

Calo, A.; Huttula, M.; Patanen, M.; Aksela, H.; Aksela, S.

2008-01-01

The valence photoelectron spectrum has been measured for molecular KBr. Experimental energies of the main and satellite structures have been compared with the results of ab initio calculations based on molecular orbital theory including configuration and multiconfiguration interaction approaches. Comparison between the experimental KBr spectrum and previously reported Kr valence photoelectron spectrum has also been performed in order to find out if electron correlation is of the same importance in the valence ionized state of KBr as in the corresponding state of Kr

Pair natural orbital and canonical coupled cluster reaction enthalpies involving light to heavy alkali and alkaline earth metals: the importance of sub-valence correlation

KAUST Repository

Minenkov, Yury

2017-03-07

In this work, we tested canonical and domain based pair natural orbital coupled cluster methods (CCSD(T) and DLPNO-CCSD(T), respectively) for a set of 32 ligand exchange and association/dissociation reaction enthalpies involving ionic complexes of Li, Be, Na, Mg, Ca, Sr, Ba and Pb(ii). Two strategies were investigated: in the former, only valence electrons were included in the correlation treatment, giving rise to the computationally very efficient FC (frozen core) approach; in the latter, all non-ECP electrons were included in the correlation treatment, giving rise to the AE (all electron) approach. Apart from reactions involving Li and Be, the FC approach resulted in non-homogeneous performance. The FC approach leads to very small errors (<2 kcal mol-1) for some reactions of Na, Mg, Ca, Sr, Ba and Pb, while for a few reactions of Ca and Ba deviations up to 40 kcal mol-1 have been obtained. Large errors are both due to artificial mixing of the core (sub-valence) orbitals of metals and the valence orbitals of oxygen and halogens in the molecular orbitals treated as core, and due to neglecting core-core and core-valence correlation effects. These large errors are reduced to a few kcal mol-1 if the AE approach is used or the sub-valence orbitals of metals are included in the correlation treatment. On the technical side, the CCSD(T) and DLPNO-CCSD(T) results differ by a fraction of kcal mol-1, indicating the latter method as the perfect choice when the CPU efficiency is essential. For completely black-box applications, as requested in catalysis or thermochemical calculations, we recommend the DLPNO-CCSD(T) method with all electrons that are not covered by effective core potentials included in the correlation treatment and correlation-consistent polarized core valence basis sets of cc-pwCVQZ(-PP) quality.

Core-electron binding energies from self-consistent field molecular orbital theory using a mixture of all-electron real atoms and valence-electron model atoms

International Nuclear Information System (INIS)

Quinn, C.M.; Schwartz, M.E.

1981-01-01

The chemistry of large systems such as clusters may be readily investigated by valence-electron theories based on model potentials, but such an approach does not allow for the examination of core-electron binding energies which are commonly measured experimentally for such systems. Here we merge our previously developed Gaussian based valence-electron model potential theory with all-electron ab initio theory to allow for the calculation of core orbital binding energies when desired. For the atoms whose cores are to be examined, we use the real nuclear changes, all of the electrons, and the appropriate many-electron basis sets. For the rest of the system we use reduced nuclear charges, the Gaussian based model potentials, only the valence electrons, and appropriate valence-electron basis sets. Detailed results for neutral Al 2 are presented for the cases of all-electron, mixed real--model, and model--model SCF--MO calculations. Several different all-electron and valence electron calculations have been done to test the use of the model potential per se, as well as the effect of basis set choice. The results are in all cases in excellent agreement with one another. Based on these studies, a set of ''double-zeta'' valence and all-electron basis functions have been used for further SCF--MO studies on Al 3 , Al 4 , AlNO, and OAl 3 . For a variety of difference combinations of real and model atoms we find excellent agreement for relative total energies, orbital energies (both core and valence), and Mulliken atomic populations. Finally, direct core-hole-state ionic calculations are reported in detail for Al 2 and AlNO, and noted for Al 3 and Al 4 . Results for corresponding frozen-orbital energy differences, relaxed SCF--MO energy differences, and relaxation energies are in all cases in excellent agreement (never differing by more than 0.07 eV, usually by somewhat less). The study clearly demonstrates the accuracy of the mixed real--model theory

Superconductivity, Mott-Hubbard states, and molecular orbital order in intercalated fullerides

CERN Document Server

Iwasa, Y

2003-01-01

This article reviews the current status of chemically doped fullerene superconductors and related compounds, with particular focus on Mott-Hubbard states and the role of molecular orbital degeneracy. Alkaline-earth metal fullerides produce superconductors of several kinds, all of which have states with higher valence than (C sub 6 sub 0) sup 6 sup - , where the second lowest unoccupied molecular orbital (the LUMO + 1 state) is filled. Alkali-metal-doped fullerides, on the other hand, afford superconductors only at the stoichiometry A sub 3 C sub 6 sub 0 (A denotes alkali metal) and in basically fcc structures. The metallicity and superconductivity of A sub 3 C sub 6 sub 0 compounds are destroyed either by reduction of the crystal symmetry or by change in the valence of C sub 6 sub 0. This difference is attributed to the narrower bandwidth in the A sub 3 C sub 6 sub 0 system, causing electronic instability in Jahn-Teller insulators and Mott-Hubbard insulators. The latter metal-insulator transition is driven by...

Electron momentum distributions and binding energies for the valence orbitals of hydrogen bromide and hydrogen iodide

International Nuclear Information System (INIS)

Brion, C.E.; McCarthy, I.E.; Suzuki, I.H.; Weigold, E.; Williams, G.R.J.; Bedford, K.L.; Kunz, A.B.; Weidman, R.

1981-12-01

The electron binding energy spectra and momentum distributions have been obtained for the valence orbitals of HBr and HI using noncoplanar symmetric electron coincidence spectroscopy at 1200eV. The weakly bonding inner valence ns orbitals, which have not been previously observed, have their spectroscopic (pole) strength severely split among a number of ion states. For HBr the strength of the main inner valence (ns) transition is 0.42 0.03 whereas for HI it is 0.37 0.04, in close agreement with that observed for the valence s orbitals of the corresponding isoelectronic inert gas atoms. The spectroscopic strength for the two outermost orbitals is found to be close to unity, in agreement with many body Green's function calculations. The measured momentum distributions are compared with several spherically averaged MO momentum distributions, as well as (for HBr) with a Green's function calculation of the generalized overlap amplitude (GOA). The GOA momentum distributions are in excellent agreement with the HBr data, both in shape and relative magnitude. Not all of the MO momentum distributions are in reasonable agreement with the data. Comparison is also made with the calculated momentum distributions for Kr, Br, Xe and I

Momentum distributions and binding energies for the valence orbitals of methanol

International Nuclear Information System (INIS)

Minchinton, A.; Brion, C.E.; Weigold, E.

1981-06-01

Methanol has been studied by binary (e,2e) coincidence spectroscopy at 1200 eV using symmetric non-coplanar geometry. The binding energy spectrum has been determined in the energy range up to 46eV at azimuthal angles of 0 deg. and 7 deg. Momentum distributions measured for the valence orbitals are compared with calculations using the wave functions (essentially double-zeta quality) reported by Snyder and Basch. Agreement is generally quite good except for the outermost orbitals and the 5a' orbital which all show somewhat larger low momentum components than predicted by the calculations. This is indicative of a more spatially extended orbital than is predicted

Electron structure of molecules with very heavy atoms using effective core potentials

International Nuclear Information System (INIS)

Pitzer, K.S.

1982-01-01

Topics covered include effective potential, Hamiltonian for valence-electron motion, molecular calculations, spin-spin coupling, L-S coupling, numerical results of molecular calculations, and results of configuration-interaction Slater-orbital calculations in L-S coupling

Molecular orbitals of nucleons in nucleus-nucleus collisions

International Nuclear Information System (INIS)

Imanishi, B.; Oertzen, W. von.

1986-05-01

A formalism for the dynamical treatment of the molecular orbitals of valence nucleons in nucleus-nucleus collisions at low bombarding energy is developed with the use of the coupled-reaction-channel (CRC) method. The Coriolis coupling effects as well as the finite mass effects of the nucleon are taken into account in this model, of rotating molecular orbitals, RMO. First, the validity of the concept is examined from the view point of the multi-step processes in a standard CRC calculation for systems containing two identical [core] nuclei. The calculations show strong CRC effects particularly in the case where the mixing of different l-parity orbitals - called hybridization in atomic physics - occurs. Then, the RMO representation for active nucleons is applied to the same systems and compared to the CRC results. Its validity is investigated with respect to the radial motion (adiabaticity) and the rotation of the molecular axis (radial and rotational coupling). Characteristic molecular orbitals of covalent molecules appear as rotationally stable states (K = 1/2) with good adiabaticity. Using the RMO's we obtain a new interpretation of various scattering phenomena. Dynamically induced changes in the effective Q-values (or scaling of energies), dynamically induced moments of inertia and an dynamically induced effective (L · S) interaction are obtained as a result of the molecular orbital formation. Various experimental data on transfer and subbarrier fusion reactions are understood in terms of the RMO's and their adiabatic potentials. Landau-Zener transitions, which strongly depend on the total angular momentum of the system, definitely predict the observation of characteristic changes in the cross sections for the inelastic scattering 13 C( 12 C, 12 C) 13 C* (3.086 MeV, 1/2 + ) with the change of the bombarding energy. (author)

Localized description of valence fluctuations

International Nuclear Information System (INIS)

Alascio, B.; Allub, R.; Aligia, A.

1979-07-01

The authors set up a model for intermediate valence equivalent to the ''atomic'' limit of the Anderson Hamiltonian. Detailed analysis of this model shows that most of the essential characteristics of valence fluctuators are already present in this crudely simplified Hamiltonian. The spin-spin and the 4f charge-charge correlation functions are studied and it is shown that it is possible to define a spin fluctuation frequency ωsub(s.f.) and a charge fluctuation frequency ωsub(ch.f.).ωsub(s.f.) and ωsub(ch.f.) can differ considerably for some values of the parameters of the model. The magnetic susceptibility and the specific heat are calculated as functions of temperature and it is shown how the results simulate the behaviour found in valence fluctuators. (author)

Universality class of non-Fermi liquid behaviour in mixed valence systems

International Nuclear Information System (INIS)

Zhang Guangming; Su Zhaobin; Lu Yu

1995-11-01

A generalized Anderson single-impurity model with off-site Coulomb interactions is derived from the extended three-band Hubbard model, originally proposed to describe the physics of the copper-oxides. Using the abelian bosonization technique and canonical transformations, an effective Hamiltonian is derived in the strong coupling limit, which is essentially analogous to the Toulouse limit of the ordinary Kondo problem. In this limit, the effective Hamiltonian can be exactly solved, with a mixed valence quantum critical point separating two different Fermi liquid phases, i.e. the Kondo phase and the empty orbital phase. In the mixed valence quantum critical regime, the local moment is only partially quenched and X-ray edge singularities are generated. Around the quantum critical point, a new type of non-Fermi liquid behaviour is predicted with an extra specific heat C imp ∼ T 1/4 and a singular spin-susceptibility χ imp ∼ T -3/4 . At the same time, the effective Hamiltonian under single occupancy is transformed into a resonant-level model, from which the correct Kondo physical properties (specific heat, spin susceptibility, and an enhanced Wilson ratio) are easily rederived. Finally, a brief discussion is given to relate these theoretical results to observations in U Pd x Cu 5-x (x=1, 1.5) alloys, which show single-impurity critical behaviour consistent with our predictions. (author). 30 refs

Universality class of non-Fermi-liquid behavior in mixed-valence systems

Science.gov (United States)

Zhang, Guang-Ming; Su, Zhao-Bin; Yu, Lu

1996-01-01

A generalized Anderson single-impurity model with off-site Coulomb interactions is derived from the extended three-band Hubbard model, originally proposed to describe the physics of the copper oxides. Using the Abelian bosonization technique and canonical transformations, an effective Hamiltonian is derived in the strong-coupling limit, which is essentially analogous to the Toulouse limit of the ordinary Kondo problem. In this limit, the effective Hamiltonian can be exactly solved, with a mixed-valence quantum critical point separating two different Fermi-liquid phases, i.e., the Kondo phase and the empty orbital phase. In the mixed-valence quantum critical regime, the local moment is only partially quenched and x-ray edge singularities are generated. Around the quantum critical point, a type of non-Fermi-liquid behavior is predicted with an extra specific heat Cimp~T1/4 and a singular spin susceptibility χimp~T-3/4. At the same time, the effective Hamiltonian under single occupancy is transformed into a resonant-level model, from which the correct Kondo physical properties (specific heat, spin susceptibility, and an enhanced Wilson ratio) are easily rederived. Finally, a brief discussion is given to relate these theoretical results to observations in UPdxCu5-x (x=1,1.5) alloys, which show single-impurity critical behavior consistent with our predictions.

Analysis of spin-Hamiltonian and molecular orbital coefficients of Cu2+ doped C8H11KO8 single crystal through EPR technique

Science.gov (United States)

Juliet sheela, K.; Krishnan, S. Radha; Shanmugam, V. M.; Subramanian, P.

2018-04-01

Electron paramagnetic resonance (EPR) studies have been investigated at X-band microwave frequency on Cu2+ ion incorporated into the single crystal of potassium succinate-succinic acid (KSSA) at room temperature. The angular variation of the EPR spectra has shown two magnetically in-equivalent Cu2+ sites in the KSSA single crystal system. The spin Hamiltonian parameters g and A are determined which reveals that the site I and site II occupied in rhombic and axial local field symmetry around the impurity ion. Among the two paramagnetic impurity ions, sites one occupies at substituitional position in the place of monovalent cation (K+) in the crystal whereas the other enters in its lattice interstitially by the correlation of EPR and crystal structure data. From the calculated principle values gxx, gyy, gzz and Axx, Ayy, Azz of both the sites, the admixture coefficients and molecular orbital coefficients were evaluated which gives the information of ground state wave function and types of bonding of impurity ions with the ligands.

Destructive quantum interference in electron transport: A reconciliation of the molecular orbital and the atomic orbital perspective

Science.gov (United States)

Zhao, Xin; Geskin, Victor; Stadler, Robert

2017-03-01

Destructive quantum interference (DQI) in single molecule electronics is a purely quantum mechanical effect and is entirely defined by the inherent properties of the molecule in the junction such as its structure and symmetry. This definition of DQI by molecular properties alone suggests its relation to other more general concepts in chemistry as well as the possibility of deriving simple models for its understanding and molecular device design. Recently, two such models have gained a wide spread attention, where one was a graphical scheme based on visually inspecting the connectivity of the carbon sites in conjugated π systems in an atomic orbital (AO) basis and the other one puts the emphasis on the amplitudes and signs of the frontier molecular orbitals (MOs). There have been discussions on the range of applicability for these schemes, but ultimately conclusions from topological molecular Hamiltonians should not depend on whether they are drawn from an AO or a MO representation, as long as all the orbitals are taken into account. In this article, we clarify the relation between both models in terms of the zeroth order Green's function and compare their predictions for a variety of systems. From this comparison, we conclude that for a correct description of DQI from a MO perspective, it is necessary to include the contributions from all MOs rather than just those from the frontier orbitals. The cases where DQI effects can be successfully predicted within a frontier orbital approximation we show them to be limited to alternant even-membered hydrocarbons, as a direct consequence of the Coulson-Rushbrooke pairing theorem in quantum chemistry.

Laplace-transformed atomic orbital-based Møller–Plesset perturbation theory for relativistic two-component Hamiltonians

Energy Technology Data Exchange (ETDEWEB)

Helmich-Paris, Benjamin, E-mail: b.helmichparis@vu.nl; Visscher, Lucas, E-mail: l.visscher@vu.nl [Section of Theoretical Chemistry, VU University Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands); Repisky, Michal, E-mail: michal.repisky@uit.no [CTCC, Department of Chemistry, UIT The Arctic University of Norway, N-9037 Tromø (Norway)

2016-07-07

We present a formulation of Laplace-transformed atomic orbital-based second-order Møller–Plesset perturbation theory (MP2) energies for two-component Hamiltonians in the Kramers-restricted formalism. This low-order scaling technique can be used to enable correlated relativistic calculations for large molecular systems. We show that the working equations to compute the relativistic MP2 energy differ by merely a change of algebra (quaternion instead of real) from their non-relativistic counterparts. With a proof-of-principle implementation we study the effect of the nuclear charge on the magnitude of half-transformed integrals and show that for light elements spin-free and spin-orbit MP2 energies are almost identical. Furthermore, we investigate the effect of separation of charge distributions on the Coulomb and exchange energy contributions, which show the same long-range decay with the inter-electronic/atomic distance as for non-relativistic MP2. A linearly scaling implementation is possible if the proper distance behavior is introduced to the quaternion Schwarz-type estimates as for non-relativistic MP2.

Laplace-transformed atomic orbital-based Møller–Plesset perturbation theory for relativistic two-component Hamiltonians

International Nuclear Information System (INIS)

Helmich-Paris, Benjamin; Visscher, Lucas; Repisky, Michal

2016-01-01

We present a formulation of Laplace-transformed atomic orbital-based second-order Møller–Plesset perturbation theory (MP2) energies for two-component Hamiltonians in the Kramers-restricted formalism. This low-order scaling technique can be used to enable correlated relativistic calculations for large molecular systems. We show that the working equations to compute the relativistic MP2 energy differ by merely a change of algebra (quaternion instead of real) from their non-relativistic counterparts. With a proof-of-principle implementation we study the effect of the nuclear charge on the magnitude of half-transformed integrals and show that for light elements spin-free and spin-orbit MP2 energies are almost identical. Furthermore, we investigate the effect of separation of charge distributions on the Coulomb and exchange energy contributions, which show the same long-range decay with the inter-electronic/atomic distance as for non-relativistic MP2. A linearly scaling implementation is possible if the proper distance behavior is introduced to the quaternion Schwarz-type estimates as for non-relativistic MP2.

Long-time correlation for the chaotic orbit in the two-wave Hamiltonian

International Nuclear Information System (INIS)

Hatori, Tadatsugu; Irie, Haruyuki.

1987-03-01

The time correlation function of velocity is found to decay with the power law for the orbit governed by a Hamiltonian, H = v 2 /2-M cos x - P cos[k(x - t)]. The renormalization group technique can predict the power of decay for the correlation function defined by the ensemble average. The power spectrum becomes the 1/f-type for a special case. (author)

Atomic spectral-product representations of molecular electronic structure: metric matrices and atomic-product composition of molecular eigenfunctions.

Science.gov (United States)

Ben-Nun, M; Mills, J D; Hinde, R J; Winstead, C L; Boatz, J A; Gallup, G A; Langhoff, P W

2009-07-02

Recent progress is reported in development of ab initio computational methods for the electronic structures of molecules employing the many-electron eigenstates of constituent atoms in spectral-product forms. The approach provides a universal atomic-product description of the electronic structure of matter as an alternative to more commonly employed valence-bond- or molecular-orbital-based representations. The Hamiltonian matrix in this representation is seen to comprise a sum over atomic energies and a pairwise sum over Coulombic interaction terms that depend only on the separations of the individual atomic pairs. Overall electron antisymmetry can be enforced by unitary transformation when appropriate, rather than as a possibly encumbering or unnecessary global constraint. The matrix representative of the antisymmetrizer in the spectral-product basis, which is equivalent to the metric matrix of the corresponding explicitly antisymmetric basis, provides the required transformation to antisymmetric or linearly independent states after Hamiltonian evaluation. Particular attention is focused in the present report on properties of the metric matrix and on the atomic-product compositions of molecular eigenstates as described in the spectral-product representations. Illustrative calculations are reported for simple but prototypically important diatomic (H(2), CH) and triatomic (H(3), CH(2)) molecules employing algorithms and computer codes devised recently for this purpose. This particular implementation of the approach combines Slater-orbital-based one- and two-electron integral evaluations, valence-bond constructions of standard tableau functions and matrices, and transformations to atomic eigenstate-product representations. The calculated metric matrices and corresponding potential energy surfaces obtained in this way elucidate a number of aspects of the spectral-product development, including the nature of closure in the representation, the general redundancy or

Molecular invariants: atomic group valence

International Nuclear Information System (INIS)

Mundim, K.C.; Giambiagi, M.; Giambiagi, M.S. de.

1988-01-01

Molecular invariants may be deduced in a very compact way through Grassman algebra. In this work, a generalized valence is defined for an atomic group; it reduces to the Known expressions for the case of an atom in a molecule. It is the same of the correlations between the fluctions of the atomic charges qc and qd (C belongs to the group and D does not) around their average values. Numerical results agree with chemical expectation. (author) [pt

Hole subbands in quantum wells: exact solution for six-dimensional Luttinger–Kohn Hamiltonian

International Nuclear Information System (INIS)

Belykh, V G; Tulupenko, V N

2009-01-01

The exact solution for wavefunctions of six-dimensional Luttinger–Kohn Hamiltonian, describing the valence band of cubic semiconductors in the effective mass approximation, is derived. The problem of space quantization for a rectangular quantum well with finite depth is solved. The wavefunctions of carriers in the quantum well are built up of a complete set of exact wavefunctions for the bulk materials constituting the heterojunction. Obtained formulae for wavefunctions permit one to derive the analytical expression for a determinant, which nulls give the allowed energy values. Comparison of the energy spectra for the Si/Si 0.88 Ge 0.12 quantum well obtained in the framework of the developed technique, and using four-dimensional Luttinger–Kohn Hamiltonian allows us to trace clearly the impact of the spin–orbit interaction on the formation of the energy spectrum for the quantum well

Block correlated second order perturbation theory with a generalized valence bond reference function.

Science.gov (United States)

Xu, Enhua; Li, Shuhua

2013-11-07

The block correlated second-order perturbation theory with a generalized valence bond (GVB) reference (GVB-BCPT2) is proposed. In this approach, each geminal in the GVB reference is considered as a "multi-orbital" block (a subset of spin orbitals), and each occupied or virtual spin orbital is also taken as a single block. The zeroth-order Hamiltonian is set to be the summation of the individual Hamiltonians of all blocks (with explicit two-electron operators within each geminal) so that the GVB reference function and all excited configuration functions are its eigenfunctions. The GVB-BCPT2 energy can be directly obtained without iteration, just like the second order Mo̸ller-Plesset perturbation method (MP2), both of which are size consistent. We have applied this GVB-BCPT2 method to investigate the equilibrium distances and spectroscopic constants of 7 diatomic molecules, conformational energy differences of 8 small molecules, and bond-breaking potential energy profiles in 3 systems. GVB-BCPT2 is demonstrated to have noticeably better performance than MP2 for systems with significant multi-reference character, and provide reasonably accurate results for some systems with large active spaces, which are beyond the capability of all CASSCF-based methods.

Seniority Number in Valence Bond Theory.

Science.gov (United States)

Chen, Zhenhua; Zhou, Chen; Wu, Wei

2015-09-08

In this work, a hierarchy of valence bond (VB) methods based on the concept of seniority number, defined as the number of singly occupied orbitals in a determinant or an orbital configuration, is proposed and applied to the studies of the potential energy curves (PECs) of H8, N2, and C2 molecules. It is found that the seniority-based VB expansion converges more rapidly toward the full configuration interaction (FCI) or complete active space self-consistent field (CASSCF) limit and produces more accurate PECs with smaller nonparallelity errors than its molecular orbital (MO) theory-based analogue. Test results reveal that the nonorthogonal orbital-based VB theory provides a reverse but more efficient way to truncate the complete active Hilbert space by seniority numbers.

Homotopical Dynamics IV: Hopf invariants and hamiltonian flows

OpenAIRE

Cornea, Octavian

2001-01-01

In a non-compact context the first natural step in the search for periodic orbits of a hamiltonian flow is to detect bounded ones. In this paper we show that, in a non-compact setting, certain algebraic topological constraints imposed to a gradient flow of the hamiltonian function $f$ imply the existence of bounded orbits for the hamiltonian flow of $f$. Once the existence of bounded orbits is established, under favorable circumstances, application of the $C^{1}$-closing lemma leads to period...

Ab initio effective core potentials for molecular calculations. Potentials for K to Au including the outermost core orbitals

International Nuclear Information System (INIS)

Hay, P.J.; Wadt, W.R.

1985-01-01

Ab initio effective core potentials (ECP's) have been generated to replace the innermost core electron for third-row (K--Au), fourth-row (Rb--Ag), and fifth-row (Cs--Au) atoms. The outermost core orbitals: corresponding to the ns 2 np 6 configuration for the three rows here: are not replaced by the ECP but are treated on an equal footing with the nd, (n+1)s and (n+1)p valence orbitals. These ECP's have been derived for use in molecular calculations where these outer core orbitals need to be treated explicitly rather than to be replaced by an ECP. The ECP's for the forth and fifth rows also incorporate the mass--velocity and Darwin relativistic effects into the potentials. Analytic fits to the potentials are presented for use in multicenter integral evaluation. Gaussian orbital valence basis sets are developed for the (3s, 3p, 3d, 4s, 4p), (4s, 4p, 4d, 5s, 5p), and (5s, 5p, 5d, 6s, 6p) ortibals of the three respective rows

Investigation of the Impact of Different Terms in the Second Order Hamiltonian on Excitation Energies of Valence and Rydberg States.

Science.gov (United States)

Tajti, Attila; Szalay, Péter G

2016-11-08

Describing electronically excited states of molecules accurately poses a challenging problem for theoretical methods. Popular second order techniques like Linear Response CC2 (CC2-LR), Partitioned Equation-of-Motion MBPT(2) (P-EOM-MBPT(2)), or Equation-of-Motion CCSD(2) (EOM-CCSD(2)) often produce results that are controversial and are ill-balanced with their accuracy on valence and Rydberg type states. In this study, we connect the theory of these methods and, to investigate the origin of their different behavior, establish a series of intermediate variants. The accuracy of these on excitation energies of singlet valence and Rydberg electronic states is benchmarked on a large sample against high-accuracy Linear Response CC3 references. The results reveal the role of individual terms of the second order similarity transformed Hamiltonian, and the reason for the bad performance of CC2-LR in the description of Rydberg states. We also clarify the importance of the T̂ 1 transformation employed in the CC2 procedure, which is found to be very small for vertical excitation energies.

Error bounds for molecular Hamiltonians inverted from experimental data

International Nuclear Information System (INIS)

Geremia, J.M.; Rabitz, Herschel

2003-01-01

Inverting experimental data provides a powerful technique for obtaining information about molecular Hamiltonians. However, rigorously quantifying how laboratory error propagates through the inversion algorithm has always presented a challenge. In this paper, we develop an inversion algorithm that realistically treats experimental error. It propagates the distribution of observed laboratory measurements into a family of Hamiltonians that are statistically consistent with the distribution of the data. This algorithm is built upon the formalism of map-facilitated inversion to alleviate computational expense and permit the use of powerful nonlinear optimization algorithms. Its capabilities are demonstrated by identifying inversion families for the X 1 Σ g + and a 3 Σ u + states of Na 2 that are consistent with the laboratory data

Experimental investigation of the EPR parameters and molecular orbital bonding coefficients for VO{sup 2+} ion in NaH{sub 2}PO{sub 4}·2H{sub 2}O single crystals

Energy Technology Data Exchange (ETDEWEB)

Kalfaoğlu, Emel [Ondokuz Mayıs University, Faculty of Sciences, Department of Physics, 55139 Kurupelit-Samsun (Turkey); Karabulut, Bünyamin, E-mail: bbulut@omu.edu.tr [Ondokuz Mayıs University, Faculty of Engineering, Department of Computer Engineering, 55139 Kurupelit-Samsun (Turkey)

2016-09-15

Electron paramagnetic resonance (EPR) spectra of VO{sup 2+} ions in NaH{sub 2}PO{sub 4}·2H{sub 2}O single crystal have been studied. The spin-Hamiltonian parameters and molecular orbital bonding coefficients were calculated. The angular variation of the EPR spectra shows two different VO{sup 2+} complexes. These are located in different chemical environment and each environment contains four magnetically inequivalent VO{sup 2+} sites. The crystal field around VO{sup 2+} ion is approximately axially symmetric since a strong V=O bond distorts the crystal lattice. Spin Hamiltonian parameters and molecular orbital bonding coefficients were calculated from the EPR data and the nature of bonding in the complex was discussed together.

Valence fluctuations between two magnetic configurations

International Nuclear Information System (INIS)

Mazzaferro, J.O.

1982-01-01

The subject of this work is the study of a microscopic model which describes TmSe through its most important feature, i.e.: the valence fluctuations between two magnetic configurations. Chapter I is a general review of the most important physical properties of rare-earth systems with intermediate valence (I.V.) and a general description of experimental results and theoretical models on Tm compounds. In Chapter II the Hamiltonian model is discussed and the loss of rotational invariance is also analyzed. Chapter III is devoted to the study of non-stoichiometric Tsub(x)Se compounds. It is shown that these compounds can be considered as a mixture of TmSe (I.V. system) and Tm 3+ 0.87Se. Chapter IV is devoted to the calculation of spin-and charge susceptibilities. The results obtained permit to explain the essential features of the neutron scattering spectrum in TmSe. In Chapter V, an exactly solvable periodic Hamiltonian is presented. From the experimental results, some fundamental features are deduced to describe TmSe as an intermediate valence system whose two accessible ionic configurations are magnetic (degenerated fundamental state). (M.E.L) [es

Nucleon molecular orbitals and the transition mechanism between molecular orbitals in nucleus-nucleus collisions

International Nuclear Information System (INIS)

Imanishi, B.; Misono, S.; von Oertzen, W.; Voit, H.

1988-08-01

The molecular orbitals of the nucleon(s) in nucleus-nucleus collisions are dynamically defined as a linear combination of nucleon single-particle orbits (LCNO) in a rotating frame by using the coupled-reaction-channel (CRC) theory. Nucleon molecular orbitals and the promotions of nucleon, - especially due to the Landau-Zener radial coupling are discussed with the method above mentioned. (author)

Periodic orbits and 10 cases of unbounded dynamics for one Hamiltonian system defined by the conformally coupled field

Energy Technology Data Exchange (ETDEWEB)

Starkov, Konstantin E., E-mail: kstarkov@ipn.mx

2015-07-03

In this paper we study invariant domains with unbounded dynamics for one cosmological Hamiltonian system which is formed by the conformally coupled field; this system was introduced by Maciejewski et al. (2007). We find a few groups of conditions imposed on parameters of this system for which all trajectories are unbounded in both of time directions. Further, we present a few groups of other conditions imposed on system parameters under which we localize the invariant domain with unbounded dynamics; this domain is defined with help of bounds for values of the Hamiltonian level surface parameter. We describe one group of conditions when our system possesses two periodic orbits found explicitly. In some of rest cases we get localization bounds for compact invariant sets. - Highlights: • Equations for periodic orbits are got for many level sets. • Domains with unbounded dynamics are localized. • Localizations for compact invariant sets are obtained.

An experimental and theoretical investigation of the valence orbital momentum distributions and binding energy spectra of nitrogen

International Nuclear Information System (INIS)

Cook, J.P.D.; Pascual, R.; Weigold, E.

1989-05-01

A detailed electron momentum spectrosocpy (EMS) and a manybody theoretical study of the complete valence region of N 2 was carried out. The 1500eV EMS momentum distributions show that they provide a sensitive test for orbital wavefunctions of SCF calculations, and of correlation effects. The outermost 3σ g orbital is more sharply peaked at the origin than predicted by the orbital wavefunction. The inner valence 2σ g orbital is severely split, with spectroscopic strength ranging from 34eV to over 60eV in binding energy. The results of the present extended basis 1p Green's function calculations, as well as those of several previous manybody calculations, are only in semiquantitative agreement with this. There is a 2σ u pole at 25eV with a pole strength of approximately 0.067 in agreement with the results of manybody calculations. There is significant 2σ u and or 1π u strength and little 2σ g strength in the region 26-34eV. Poles observed at 29 and 32eV, previously attributed to the 2σ g orbital, are shown to be largely 2σ u in character. The manybody calculations predict too much 2σ g strength in the region 26-34eV. 29 refs., 1 tab., 16 figs

Physical Meaning of Virtual Kohn-Sham Orbitals and Orbital Energies: An Ideal Basis for the Description of Molecular Excitations.

Science.gov (United States)

van Meer, R; Gritsenko, O V; Baerends, E J

2014-10-14

In recent years, several benchmark studies on the performance of large sets of functionals in time-dependent density functional theory (TDDFT) calculations of excitation energies have been performed. The tested functionals do not approximate exact Kohn-Sham orbitals and orbital energies closely. We highlight the advantages of (close to) exact Kohn-Sham orbitals and orbital energies for a simple description, very often as just a single orbital-to-orbital transition, of molecular excitations. Benchmark calculations are performed for the statistical average of orbital potentials (SAOP) functional for the potential [J. Chem. Phys. 2000, 112, 1344; 2001, 114, 652], which approximates the true Kohn-Sham potential much better than LDA, GGA, mGGA, and hybrid potentials do. An accurate Kohn-Sham potential does not only perform satisfactorily for calculated vertical excitation energies of both valence and Rydberg transitions but also exhibits appealing properties of the KS orbitals including occupied orbital energies close to ionization energies, virtual-occupied orbital energy gaps very close to excitation energies, realistic shapes of virtual orbitals, leading to straightforward interpretation of most excitations as single orbital transitions. We stress that such advantages are completely lost in time-dependent Hartree-Fock and partly in hybrid approaches. Many excitations and excitation energies calculated with local density, generalized gradient, and hybrid functionals are spurious. There is, with an accurate KS, or even the LDA or GGA potentials, nothing problematic about the "band gap" in molecules: the HOMO-LUMO gap is close to the first excitation energy (the optical gap).

Numerical continuation of families of heteroclinic connections between periodic orbits in a Hamiltonian system

Science.gov (United States)

Barrabés, E.; Mondelo, J. M.; Ollé, M.

2013-10-01

This paper is devoted to the numerical computation and continuation of families of heteroclinic connections between hyperbolic periodic orbits (POs) of a Hamiltonian system. We describe a method that requires the numerical continuation of a nonlinear system that involves the initial conditions of the two POs, the linear approximations of the corresponding manifolds and a point in a given Poincaré section where the unstable and stable manifolds match. The method is applied to compute families of heteroclinic orbits between planar Lyapunov POs around the collinear equilibrium points of the restricted three-body problem in different scenarios. In one of them, for the Sun-Jupiter mass parameter, we provide energy ranges for which the transition between different resonances is possible.

Block correlated second order perturbation theory with a generalized valence bond reference function

International Nuclear Information System (INIS)

Xu, Enhua; Li, Shuhua

2013-01-01

The block correlated second-order perturbation theory with a generalized valence bond (GVB) reference (GVB-BCPT2) is proposed. In this approach, each geminal in the GVB reference is considered as a “multi-orbital” block (a subset of spin orbitals), and each occupied or virtual spin orbital is also taken as a single block. The zeroth-order Hamiltonian is set to be the summation of the individual Hamiltonians of all blocks (with explicit two-electron operators within each geminal) so that the GVB reference function and all excited configuration functions are its eigenfunctions. The GVB-BCPT2 energy can be directly obtained without iteration, just like the second order Møller–Plesset perturbation method (MP2), both of which are size consistent. We have applied this GVB-BCPT2 method to investigate the equilibrium distances and spectroscopic constants of 7 diatomic molecules, conformational energy differences of 8 small molecules, and bond-breaking potential energy profiles in 3 systems. GVB-BCPT2 is demonstrated to have noticeably better performance than MP2 for systems with significant multi-reference character, and provide reasonably accurate results for some systems with large active spaces, which are beyond the capability of all CASSCF-based methods

New Hamiltonian constraint operator for loop quantum gravity

Energy Technology Data Exchange (ETDEWEB)

Yang, Jinsong, E-mail: yangksong@gmail.com [Department of Physics, Guizhou university, Guiyang 550025 (China); Institute of Physics, Academia Sinica, Taiwan (China); Ma, Yongge, E-mail: mayg@bnu.edu.cn [Department of Physics, Beijing Normal University, Beijing 100875 (China)

2015-12-17

A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.

New Hamiltonian constraint operator for loop quantum gravity

Directory of Open Access Journals (Sweden)

Jinsong Yang

2015-12-01

Full Text Available A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.

New conception in the theory of chemical bonding; the role of core and valence atomic orbitals in formation of chemical bonds

International Nuclear Information System (INIS)

Kostikova, G.P.; Kostikov, Yu.P.; Korol'kov, D.V.

1986-01-01

An analysis of x-ray photoelectron spectra leads to a simple and consistent conception in the theory of chemical bonding, which satisfies (unlike the simple MO-LCAO theory) the virial theorem and defines the roles of the core and valence atomic orbitals in the formation of chemical bonds. Its essence is clear from the foregoing: the exothermic effects of the formation of complexes are caused by the lowering of the energies of the core levels of the central atoms with simultaneous small changes in the energies of the core levels of the ligands despite the significant destabilization of the delocalized valence MO's in comparison to the orbital energies of the corresponding free atoms. In order to confirm these ideas, they recorded the x-ray photoelectron spectra of the valence region and the inner levels of single-crystal silicon carbide, silicon, and graphite

Multiple Time-Step Dual-Hamiltonian Hybrid Molecular Dynamics - Monte Carlo Canonical Propagation Algorithm.

Science.gov (United States)

Chen, Yunjie; Kale, Seyit; Weare, Jonathan; Dinner, Aaron R; Roux, Benoît

2016-04-12

A multiple time-step integrator based on a dual Hamiltonian and a hybrid method combining molecular dynamics (MD) and Monte Carlo (MC) is proposed to sample systems in the canonical ensemble. The Dual Hamiltonian Multiple Time-Step (DHMTS) algorithm is based on two similar Hamiltonians: a computationally expensive one that serves as a reference and a computationally inexpensive one to which the workload is shifted. The central assumption is that the difference between the two Hamiltonians is slowly varying. Earlier work has shown that such dual Hamiltonian multiple time-step schemes effectively precondition nonlinear differential equations for dynamics by reformulating them into a recursive root finding problem that can be solved by propagating a correction term through an internal loop, analogous to RESPA. Of special interest in the present context, a hybrid MD-MC version of the DHMTS algorithm is introduced to enforce detailed balance via a Metropolis acceptance criterion and ensure consistency with the Boltzmann distribution. The Metropolis criterion suppresses the discretization errors normally associated with the propagation according to the computationally inexpensive Hamiltonian, treating the discretization error as an external work. Illustrative tests are carried out to demonstrate the effectiveness of the method.

Compact invariant sets of the Bianchi VIII and Bianchi IX Hamiltonian systems

International Nuclear Information System (INIS)

Starkov, Konstantin E.

2011-01-01

In this Letter we prove that all compact invariant sets of the Bianchi VIII Hamiltonian system are contained in the set described by several simple linear equalities and inequalities. Moreover, we describe invariant domains in which the phase flow of this system has no recurrence property and show that there are no periodic orbits and neither homoclinic, nor heteroclinic orbits contained in the zero level set of its Hamiltonian. Similar results are obtained for the Bianchi IX Hamiltonian system. -- Highlights: → Zero level set of Hamiltonian of Bianchi VIII/IX systems contains no periodic orbits. → Similar conditions for homoclinic/heteroclinic orbits are given. → General nonexistence conditions of compact invariant sets are got.

Compact invariant sets of the Bianchi VIII and Bianchi IX Hamiltonian systems

Energy Technology Data Exchange (ETDEWEB)

Starkov, Konstantin E., E-mail: konst@citedi.mx [CITEDI-IPN, Av. del Parque 1310, Mesa de Otay, Tijuana, BC (Mexico)

2011-08-22

In this Letter we prove that all compact invariant sets of the Bianchi VIII Hamiltonian system are contained in the set described by several simple linear equalities and inequalities. Moreover, we describe invariant domains in which the phase flow of this system has no recurrence property and show that there are no periodic orbits and neither homoclinic, nor heteroclinic orbits contained in the zero level set of its Hamiltonian. Similar results are obtained for the Bianchi IX Hamiltonian system. -- Highlights: → Zero level set of Hamiltonian of Bianchi VIII/IX systems contains no periodic orbits. → Similar conditions for homoclinic/heteroclinic orbits are given. → General nonexistence conditions of compact invariant sets are got.

An experimental and theoretical study of the valence shell photoelectron spectra of 2-chloropyridine and 3-chloropyridine

Science.gov (United States)

Holland, D. M. P.; Powis, I.; Trofimov, A. B.; Menzies, R. C.; Potts, A. W.; Karlsson, L.; Badsyuk, I. L.; Moskovskaya, T. E.; Gromov, E. V.; Schirmer, J.

2017-10-01

The valence shell photoelectron spectra of 2-chloropyridine and 3-chloropyridine have been studied both experimentally and theoretically. Synchrotron radiation has been employed to record angle resolved photoelectron spectra in the photon energy range 20-100 eV, and these have enabled anisotropy parameters and branching ratios to be derived. The experimental results have been compared with theoretical predictions obtained using the continuum multiple scattering Xα approach. This comparison shows that the anisotropy parameter associated with the nominally chlorine lone-pair orbital lying in the molecular plane is strongly affected by the atomic Cooper minimum. In contrast, the photoionization dynamics of the second lone-pair orbital, orientated perpendicular to the molecular plane, seem relatively unaffected by this atomic phenomenon. The outer valence ionization has been studied theoretically using the third-order algebraic-diagrammatic construction (ADC(3)) approximation scheme for the one-particle Green's function, the outer valence Green's function method, and the equation-of-motion (EOM) coupled cluster (CC) theory at the level of the EOM-IP-CCSD and EOM-EE-CC3 models. The convergence of the results to the complete basis set limit has been investigated. The ADC(3) method has been employed to compute the complete valence shell ionization spectra of 2-chloropyridine and 3-chloropyridine. The relaxation mechanism for ionization of the nitrogen σ-type lone-pair orbital (σN LP) has been found to be different to that for the corresponding chlorine lone-pair (σCl LP). For the σN LP orbital, π-π* excitations play the main role in the screening of the lone-pair hole. In contrast, excitations localized at the chlorine site involving the chlorine πCl LP lone-pair and the Cl 4p Rydberg orbital are the most important for the σCl LP orbital. The calculated photoelectron spectra have allowed assignments to be proposed for most of the structure observed in the

Can the second order multireference perturbation theory be considered a reliable tool to study mixed-valence compounds?

Science.gov (United States)

Pastore, Mariachiara; Helal, Wissam; Evangelisti, Stefano; Leininger, Thierry; Malrieu, Jean-Paul; Maynau, Daniel; Angeli, Celestino; Cimiraglia, Renzo

2008-05-07

In this paper, the problem of the calculation of the electronic structure of mixed-valence compounds is addressed in the frame of multireference perturbation theory (MRPT). Using a simple mixed-valence compound (the 5,5(') (4H,4H('))-spirobi[ciclopenta[c]pyrrole] 2,2('),6,6(') tetrahydro cation), and the n-electron valence state perturbation theory (NEVPT2) and CASPT2 approaches, it is shown that the ground state (GS) energy curve presents an unphysical "well" for nuclear coordinates close to the symmetric case, where a maximum is expected. For NEVPT, the correct shape of the energy curve is retrieved by applying the MPRT at the (computationally expensive) third order. This behavior is rationalized using a simple model (the ionized GS of two weakly interacting identical systems, each neutral system being described by two electrons in two orbitals), showing that the unphysical well is due to the canonical orbital energies which at the symmetric (delocalized) conformation lead to a sudden modification of the denominators in the perturbation expansion. In this model, the bias introduced in the second order correction to the energy is almost entirely removed going to the third order. With the results of the model in mind, one can predict that all MRPT methods in which the zero order Hamiltonian is based on canonical orbital energies are prone to present unreasonable energy profiles close to the symmetric situation. However, the model allows a strategy to be devised which can give a correct behavior even at the second order, by simply averaging the orbital energies of the two charge-localized electronic states. Such a strategy is adopted in a NEVPT2 scheme obtaining a good agreement with the third order results based on the canonical orbital energies. The answer to the question reported in the title (is this theoretical approach a reliable tool for a correct description of these systems?) is therefore positive, but care must be exercised, either in defining the orbital

a Moessbauer Effect and Fenske-Hall Molecular Orbital Study of the Electronic Properties of Organoiron Clusters.

Science.gov (United States)

Buhl, Margaret Linn

The electronic properties of trinuclear iron, tetranuclear iron butterfly, iron-cobalt, and iron-copper clusters have been studied experimentally at 78K by the Mossbauer effect and theoretically by Fenske-Hall molecular orbital calculations. The Mossbauer effect isomer shift is very sensitive to the differences in the iron s-electron densities in these clusters and, as expected, decreases as the sum of the iron 4s Mulliken population and the Clementi and Raimondi effective nuclear charge increases. The molecular orbital wave functions and the Mulliken atomic charges are used to calculate the electric field gradient at the metal nuclei and the iron Mossbauer effect quadrupole splittings. The valence contribution was found to be the major component of the electric field gradient in all the clusters studied. In general the calculated value of Delta E_ {Q} is larger than the observed value, as a result of neglect of the valence Sternheimer factor, R. The metal charge depends upon its electronegativity and upon the nature of its Lewis base ligands. The carbonyl ligand carbon charge becomes more positive as the metal electronegativity increases. The oxygen charge becomes more negative as the anionic cluster charge increases, and in so doing, yields the maximum anionic charge separation. The electronic properties of the terminal carbonyl ligands are similar to those of carbon monoxide, whereas the electronic properties of the bridging carbonyl ligands are similar to those of the carbonyl group found in aldehydes and ketones.

The stabilities and electron structures of Al-Mg clusters with 18 and 20 valence electrons

Science.gov (United States)

Yang, Huihui; Chen, Hongshan

2017-07-01

The spherical jellium model predicts that metal clusters having 18 and 20 valence electrons correspond to the magic numbers and will show specific stabilities. We explore in detail the geometric structures, stabilities and electronic structures of Al-Mg clusters containing 18 and 20 valence electrons by using genetic algorithm combined with density functional theories. The stabilities of the clusters are governed by the electronic configurations and Mg/Al ratios. The clusters with lower Mg/Al ratios are more stable. The molecular orbitals accord with the shell structures predicted by the jellium model but the 2S level interweaves with the 1D levels and the 2S and 1D orbitals form a subgroup. The clusters having 20 valence electrons form closed 1S21P61D102S2 shells and show enhanced stability. The Al-Mg clusters with a valence electron count of 18 do not form closed shells because one 1D orbital is unoccupied. The ionization potential and electron affinity are closely related to the electronic configurations; their values are determined by the subgroups the HOMO or LUMO belong to. Supplementary material in the form of one pdf file available from the Journal web page at http://https://doi.org/10.1140/epjd/e2017-80042-9

Effective Hamiltonian theory: recent formal results and non-nuclear applications

International Nuclear Information System (INIS)

Brandow, B.H.

1981-01-01

Effective Hamiltonian theory is discussed from the points of view of the unitary transformation method and degenerate perturbation theory. It is shown that the two approaches are identical term by term. The main features of a formulation of the coupled-cluster method for open-shell systems are outlined. Finally, recent applications of the many-body linked-cluster form of degenerate perturbation theory are described: the derivation of effective spin Hamiltonians in magnetic insulator systems, the derivation and calculation ab initio of effective π-electron Hamiltonians for planar conjugated hydrocarbon molecules, and understanding the so-called valence fluctuation phenomenon exhibited by certain rare earth compounds

Atomic contributions to the valence band photoelectron spectra of metal-free, iron and manganese phthalocyanines

Energy Technology Data Exchange (ETDEWEB)

Bidermane, I., E-mail: ieva.bidermane@physics.uu.se [Department of Physics and Astronomy, Uppsala University, Box-516, 75120 Uppsala (Sweden); Institut des Nanosciences de Paris, UPMC Univ. Paris 06, CNRS UMR 7588, F-75005 Paris (France); Brumboiu, I.E. [Department of Physics and Astronomy, Uppsala University, Box-516, 75120 Uppsala (Sweden); Totani, R. [Department of Physical and Chemical Sciences, University of L’Aquila, Via Vetoio, Coppito, I-67010 L’Aquila (Italy); Grazioli, C. [CNR-IOM, Laboratorio TASC, ss. 14 km. 163.5, Basovizza, 34149 Trieste (Italy); Departement of Chemical and Pharmaceutical Sciences, University of Trieste (Italy); Shariati-Nilsson, M.N.; Herper, H.C.; Eriksson, O.; Sanyal, B. [Department of Physics and Astronomy, Uppsala University, Box-516, 75120 Uppsala (Sweden); Ressel, B. [University of Nova Gorica, Vipavska Cesta 11c, 5270 Ajdovščina (Slovenia); Simone, M. de [CNR-IOM, Laboratorio TASC, ss. 14 km. 163.5, Basovizza, 34149 Trieste (Italy); Lozzi, L. [Department of Physical and Chemical Sciences, University of L’Aquila, Via Vetoio, Coppito, I-67010 L’Aquila (Italy); Brena, B.; Puglia, C. [Department of Physics and Astronomy, Uppsala University, Box-516, 75120 Uppsala (Sweden)

2015-11-15

Highlights: • In detail comparison between the valence band structure of H{sub 2}Pc, FePc and MnPc. • Comparison between the gas phase samples and thin evaporated films on Au (1 1 1). • Detailed analysis of the atomic orbital contributions to the valence band features. • DFT/HSE06 study of the valence band electronic structure of H{sub 2}Pc, FePc and MnPc. - Abstract: The present work reports a photoelectron spectroscopy study of the low-energy region of the valence band of metal-free phthalocyanine (H{sub 2}Pc) compared with those of iron phthalocyanine (FePc) and manganese phthalocyanine (MnPc). We have analysed in detail the atomic orbital composition of the valence band both experimentally, by making use of the variation in photoionization cross-sections with photon energy, and theoretically, by means of density functional theory. The atomic character of the Highest Occupied Molecular Orbital (HOMO), reflected on the outermost valence band binding energy region, is different for MnPc as compared to the other two molecules. The peaks related to the C 2p contributions, result in the HOMO for H{sub 2}Pc and FePc and in the HOMO-1 for MnPc as described by the theoretical predictions, in very good agreement with the experimental results. The DFT simulations, discerning the atomic contribution to the density of states, indicate how the central metal atom interacts with the C and N atoms of the molecule, giving rise to different partial and total density of states for these three Pc molecules.

Treating sub-valence correlation effects in domain based pair natural orbital coupled cluster calculations: an out-of-the-box approach

KAUST Repository

Bistoni, Giovanni

2017-06-12

The validity of the main approximations used in canonical and domain based pair natural orbital coupled cluster methods (CCSD(T) and DLPNO-CCSD(T), respectively) in standard chemical applications is discussed. In particular, we investigate the dependence of the results on the number of electrons included in the correlation treatment in frozen-core (FC) calculations and on the main threshold governing the accuracy of DLPNO all-electron (AE) calculations. Initially, scalar relativistic orbital energies for the ground state of the atoms from Li to Rn in the periodic table are calculated. An energy criterion is applied for determining the orbitals that can be excluded from the correlation treatment in FC coupled cluster calculations without significant loss of accuracy. The heterolytic dissociation energy (HDE) of a series of metal compounds (LiF, NaF, AlF3, CaF2, CuF, GaF3, YF3, AgF, InF3, HfF4 and AuF) is calculated at the canonical CCSD(T) level, and the dependence of the results on the number of correlated electrons is investigated. Although for many of the studied reactions sub-valence correlation effects contribute significantly to the HDE, the use of an energy criterion permits a conservative definition of the size of the core, allowing FC calculations to be performed in a black-box fashion while retaining chemical accuracy. A comparison of the CCSD and the DLPNO-CCSD methods in describing the core-core, core-valence and valence-valence components of the correlation energy is given. It is found that more conservative thresholds must be used for electron pairs containing at least one core electron in order to achieve high accuracy in AE DLPNO-CCSD calculations relative to FC calculations. With the new settings, the DLPNO-CCSD method reproduces canonical CCSD results in both AE and FC calculations with the same accuracy.

Treating sub-valence correlation effects in domain based pair natural orbital coupled cluster calculations: an out-of-the-box approach

KAUST Repository

Bistoni, Giovanni; Riplinger, Christoph; Minenkov, Yury; Cavallo, Luigi; Auer, Alexander A.; Neese, Frank

2017-01-01

The validity of the main approximations used in canonical and domain based pair natural orbital coupled cluster methods (CCSD(T) and DLPNO-CCSD(T), respectively) in standard chemical applications is discussed. In particular, we investigate the dependence of the results on the number of electrons included in the correlation treatment in frozen-core (FC) calculations and on the main threshold governing the accuracy of DLPNO all-electron (AE) calculations. Initially, scalar relativistic orbital energies for the ground state of the atoms from Li to Rn in the periodic table are calculated. An energy criterion is applied for determining the orbitals that can be excluded from the correlation treatment in FC coupled cluster calculations without significant loss of accuracy. The heterolytic dissociation energy (HDE) of a series of metal compounds (LiF, NaF, AlF3, CaF2, CuF, GaF3, YF3, AgF, InF3, HfF4 and AuF) is calculated at the canonical CCSD(T) level, and the dependence of the results on the number of correlated electrons is investigated. Although for many of the studied reactions sub-valence correlation effects contribute significantly to the HDE, the use of an energy criterion permits a conservative definition of the size of the core, allowing FC calculations to be performed in a black-box fashion while retaining chemical accuracy. A comparison of the CCSD and the DLPNO-CCSD methods in describing the core-core, core-valence and valence-valence components of the correlation energy is given. It is found that more conservative thresholds must be used for electron pairs containing at least one core electron in order to achieve high accuracy in AE DLPNO-CCSD calculations relative to FC calculations. With the new settings, the DLPNO-CCSD method reproduces canonical CCSD results in both AE and FC calculations with the same accuracy.

MgH Rydberg series: Transition energies from electron propagator theory and oscillator strengths from the molecular quantum defect orbital method

Science.gov (United States)

Corzo, H. H.; Velasco, A. M.; Lavín, C.; Ortiz, J. V.

2018-02-01

Vertical excitation energies belonging to several Rydberg series of MgH have been inferred from 3+ electron-propagator calculations of the electron affinities of MgH+ and are in close agreement with experiment. Many electronically excited states with n > 3 are reported for the first time and new insight is given on the assignment of several Rydberg series. Valence and Rydberg excited states of MgH are distinguished respectively by high and low pole strengths corresponding to Dyson orbitals of electron attachment to the cation. By applying the Molecular Quantum Defect Orbital method, oscillator strengths for electronic transitions involving Rydberg states also have been determined.

Molecular orbitals for properties and spectroscopies

Energy Technology Data Exchange (ETDEWEB)

Robert, Vincent [Laboratoire de Chimie Quantique, Institut de Chimie, Université de Strasbourg, 1 rue Blaise Pascal 67000 Strasbourg-France (France); Domingo, Alex [Quantum Chemistry and Physical Chemistry Celestijnenlaan 200f, 3001 Heverlee - Belgium (Belgium); Braunstein, Pierre; Danopoulos, Andreas; Monakhov, Kirill [Laboratoire de Chimie de Coordination, Institut de Chimie, Université de Strasbourg, 4 rue Blaise Pascal 67081 Strasbourg-France (France)

2015-12-31

The description and clarification of spectroscopies and properties goes through ab initio calculations. Wave function based calculations (CASSCF/CASPT2) are particularly appealing since they offer spectroscopic accuracy and means of interpretation. we performed such calculations to elucidate the origin of unusual structural changes and intramolecular electron transfer phenomenon. Based on optimized molecular orbitals and a reading of the multireference wave function, it is suggested that intimate interactions are likely to considerably modify the standard pictures. A so-called PIMA (polarization-induced metalâĹŠarene) interaction similar to the more familiar anion-π interaction is responsible for a significant deviation from sp{sup 3} geometry and an energetic stabilization of 50 kJ/mol in Cr(II) benzyl organometallic complexes. In a similar fashion, it is proposed that the energetic profile of the IVCT (inter valence charge transfer) exhibits strong similarities to the Marcus’ theory, suggesting a response behaviour of the ensemble of electrons as electron transfer occurs in Fe{sup 2+}/Fe{sup 3+} bimetallic compound. The electronic reorganization induced by the IVCT process accounts for 11.8 eV, a very large effect that reduces the transfer energy down to 0.89 eV, in very good agreement with experiments.

Effect of three-body transformed Hamiltonian (H3) using full ...

Indian Academy of Sciences (India)

Home; Journals; Pramana – Journal of Physics; Volume 90; Issue 3 ... Research Article Volume 90 Issue 3 March 2018 Article ID 36 ... Valence universal multireference coupled cluster (VUMRCC) method via eigenvalue independent partitioning has been applied to estimate the effect of three-body transformed Hamiltonian ...

Magnetic-field-induced valence transition in rare-earth systems

Indian Academy of Sciences (India)

In the present work we investigate the scaling behavior observed experimentally based on an electronic model which has not yet been attempted. 2. The model and approximation. The Hamiltonian of the periodic Anderson model (PAM) with Falicov–Kimball term used to describe both continuous and discontinuous valence ...

The 4-particle hydrogen-anti-hydrogen system revisited. Twofold molecular Hamiltonian symmetry and natural atom anti-hydrogen

International Nuclear Information System (INIS)

Van Hooydonk, G.

2005-01-01

The historical importance of the original quantum mechanical bond theory proposed by Heitler and London in 1927 as well as its pitfalls are reviewed. Modern ab initio treatments of H-H-bar systems are inconsistent with the logic behind algebraic Hamiltonians H ± = H 0 ± ΔH for charge-symmetrical and charge-asymmetrical 4 unit charge systems like H 2 and HH-bar. Their eigenvalues are exactly those of 1927 Heitler-London (HL) theory. Since these 2 Hamiltonians are mutually exclusive, only the attractive one can apply for stable natural molecular H 2 . A wrong choice leads to problems with anti-atom H-bar. In line with earlier results on band and line spectra, we now prove that HL chose the wrong Hamiltonian for H 2 . Their theory explains the stability of attractive system H 2 with a repulsive Hamiltonian H 0 + ΔH instead of with the attractive one H 0 - ΔH, representative for charge-asymmetrical system HH-bar. A new second order symmetry effect is detected in this attractive Hamiltonian, which leads to a 3-dimensional structure for the 4-particle system. Repulsive HL Hamiltonian H + applies at long range but at the critical distance, attractive charge-inverted Hamiltonian H - takes over and leads to bond H 2 but in reality, HH-bar, for which we give an analytical proof. This analysis confirms and generalizes an earlier critique of the wrong long range behavior of HL-theory by Bingel, Preuss and Schmidtke and by Herring. Another wrong asymptote choice in the past also applies for atomic anti-hydrogen H-bar, which has hidden the Mexican hat potential for natural hydrogen. This generic solution removes most problems, physicists and chemists experience with atomic H-bar and molecular HH-bar, including the problem with antimatter in the Universe. (author)

Electronic structure studies of La2CuO4

International Nuclear Information System (INIS)

Wachs, A.L.; Turchi, P.E.A.; Jean, Y.C.

1988-01-01

We report results of positron-electron momentum-distribution measurements of single-crystal La 2 CuO 4 using two-dimensional angular correlation of positron-annihilation-radiation techniques. The data contain two components: a large (∼85%), isotropic corelike electron contribution and a remaining, anisotropic valence-electron contribution modeled using a linear combination of atomic orbitals--molecular orbital method and a localized ion scheme, within the independent-particle model approximation. This work suggests a ligand-field Hamiltonian to be justified for describing the electronic properties of perovskite materials

Electronic structure studies of La2CuO4

Science.gov (United States)

Wachs, A. L.; Turchi, P. E. A.; Jean, Y. C.; Wetzler, K. H.; Howell, R. H.; Fluss, M. J.; Harshman, D. R.; Remeika, J. P.; Cooper, A. S.; Fleming, R. M.

1988-07-01

We report results of positron-electron momentum-distribution measurements of single-crystal La2CuO4 using two-dimensional angular correlation of positron-annihilation-radiation techniques. The data contain two components: a large (~85%), isotropic corelike electron contribution and a remaining, anisotropic valence-electron contribution modeled using a linear combination of atomic orbitals-molecular orbital method and a localized ion scheme, within the independent-particle model approximation. This work suggests a ligand-field Hamiltonian to be justified for describing the electronic properties of perovskite materials.

Effective hamiltonian within the microscopic unitary nuclear model

International Nuclear Information System (INIS)

Avramenko, V.I.; Blokhin, A.L.

1989-01-01

Within the microscopic version of the unitary collective model with the horizontal mixing the effective Hamiltonian for 18 O and 18 Ne nuclei is constructed. The algebraic structure of the Hamiltonian is compared to the familiar phenomenological ones with the SU(3)-mixing terms which describe the coupled rotational and vibrational spectra. The Hamiltonian, including central nuclear and Coulomb interaction, is diagonalized on the basis of three SU(3) irreducible representations with two orbital symmetries. 32 refs.; 2 figs.; 4 tabs

New classes of nonlinear vector coherent states of generalized spin-orbit Hamiltonians

International Nuclear Information System (INIS)

Geloun, Joseph Ben; Norbert Hounkonnou, Mahouton

2009-01-01

This paper deals with an extension of our previous work (Ben Geloun and Hounkonnou 2007 J. Phys. A: Math. Theor. 40 F817) by considering an alternative construction of canonical and deformed vector coherent states (VCSs) of the Gazeau-Klauder type associated with generalized spin-orbit Hamiltonians. We define an annihilation operator which takes into account the finite-dimensional space of states induced by the k-photon transition processes of the two-level atom interacting with the single-mode radiation field. The class of nonlinear VCSs (NVCSs) corresponding to the action of the annihilation operator is deduced and expressed in terms of generalized displacement operators. Various NVCSs including their 'dual' counterparts are also discussed. Also, by using the Hilbert space structure, a new family of NVCSs parametrized by unit vectors of the S 3 sphere has been identified without making use of the annihilation operator.

Nuclear properties with realistic Hamiltonians through spectral distribution theory

International Nuclear Information System (INIS)

Vary, J.P.; Belehrad, R.; Dalton, B.J.

1979-01-01

Motivated by the need of non-perturbative methods for utilizing realistic nuclear Hamiltonians H, the authors use spectral distribution theory, based on calculated moments of H, to obtain specific bulk and valence properties of finite nuclei. The primary emphasis here is to present results for the binding energies of nuclei obtained with and without an assumed core. (Auth.)

The rotational barrier in ethane: a molecular orbital study.

Science.gov (United States)

Quijano-Quiñones, Ramiro F; Quesadas-Rojas, Mariana; Cuevas, Gabriel; Mena-Rejón, Gonzalo J

2012-04-20

The energy change on each Occupied Molecular Orbital as a function of rotation about the C-C bond in ethane was studied using the B3LYP, mPWB95 functional and MP2 methods with different basis sets. Also, the effect of the ZPE on rotational barrier was analyzed. We have found that σ and π energies contribution stabilize a staggered conformation. The σ(s) molecular orbital stabilizes the staggered conformation while the stabilizes the eclipsed conformation and destabilize the staggered conformation. The π(z) and molecular orbitals stabilize both the eclipsed and staggered conformations, which are destabilized by the π(v) and molecular orbitals. The results show that the method of calculation has the effect of changing the behavior of the energy change in each Occupied Molecular Orbital energy as a function of the angle of rotation about the C-C bond in ethane. Finally, we found that if the molecular orbital energy contribution is deleted from the rotational energy, an inversion in conformational preference occurs.

The Rotational Barrier in Ethane: A Molecular Orbital Study

Directory of Open Access Journals (Sweden)

Gonzalo J. Mena-Rejón

2012-04-01

Full Text Available The energy change on each Occupied Molecular Orbital as a function of rotation about the C-C bond in ethane was studied using the B3LYP, mPWB95 functional and MP2 methods with different basis sets. Also, the effect of the ZPE on rotational barrier was analyzed. We have found that σ and π energies contribution stabilize a staggered conformation. The σ_s molecular orbital stabilizes the staggered conformation while the  stabilizes the eclipsed conformation and destabilize the staggered conformation. The π_z and  molecular orbitals stabilize both the eclipsed and staggered conformations, which are destabilized by the π_v and  molecular orbitals. The results show that the method of calculation has the effect of changing the behavior of the energy change in each Occupied Molecular Orbital energy as a function of the angle of rotation about the C–C bond in ethane. Finally, we found that if the molecular orbital energy contribution is deleted from the rotational energy, an inversion in conformational preference occurs.

Equilibrium Solutions of the Logarithmic Hamiltonian Leapfrog for the N-body Problem

Science.gov (United States)

Minesaki, Yukitaka

2018-04-01

We prove that a second-order logarithmic Hamiltonian leapfrog for the classical general N-body problem (CGNBP) designed by Mikkola and Tanikawa and some higher-order logarithmic Hamiltonian methods based on symmetric multicompositions of the logarithmic algorithm exactly reproduce the orbits of elliptic relative equilibrium solutions in the original CGNBP. These methods are explicit symplectic methods. Before this proof, only some implicit discrete-time CGNBPs proposed by Minesaki had been analytically shown to trace the orbits of elliptic relative equilibrium solutions. The proof is therefore the first existence proof for explicit symplectic methods. Such logarithmic Hamiltonian methods with a variable time step can also precisely retain periodic orbits in the classical general three-body problem, which generic numerical methods with a constant time step cannot do.

16O + 16O molecular structures of superdeformed states in S isotopes

Science.gov (United States)

Taniguchi, Y.

2017-06-01

Structures of excited states in S isotopes are investigated by using the antisymmetrized molecular dynamics and generator coordinate method (GCM). The GCM basis wave functions are calculated via energy variation with a constraint on the quadrupole deformation parameter β. By applying the GCM after parity and angular momentum projections, the coexistence of positive- and negative-parity superdeformed (SD) bands are predicted in 33-36S except for negative-parity states in 36S. The SD bands have structures of 16O + 16O + valence neutron(s) in molecular orbitals around the two 16O cores in a cluster picture. The configurations of the valence neutron(s) in the SD states are δ and/or π molecular orbitals.

Charge transfer interaction using quasiatomic minimal-basis orbitals in the effective fragment potential method

International Nuclear Information System (INIS)

Xu, Peng; Gordon, Mark S.

2013-01-01

The charge transfer (CT) interaction, the most time-consuming term in the general effective fragment potential method, is made much more computationally efficient. This is accomplished by the projection of the quasiatomic minimal-basis-set orbitals (QUAMBOs) as the atomic basis onto the self-consistent field virtual molecular orbital (MO) space to select a subspace of the full virtual space called the valence virtual space. The diagonalization of the Fock matrix in terms of QUAMBOs recovers the canonical occupied orbitals and, more importantly, gives rise to the valence virtual orbitals (VVOs). The CT energies obtained using VVOs are generally as accurate as those obtained with the full virtual space canonical MOs because the QUAMBOs span the valence part of the virtual space, which can generally be regarded as “chemically important.” The number of QUAMBOs is the same as the number of minimal-basis MOs of a molecule. Therefore, the number of VVOs is significantly smaller than the number of canonical virtual MOs, especially for large atomic basis sets. This leads to a dramatic decrease in the computational cost

Next generation of the self-consistent and environment-dependent Hamiltonian: Applications to various boron allotropes from zero- to three-dimensional structures

Energy Technology Data Exchange (ETDEWEB)

Tandy, P.; Yu, Ming; Leahy, C.; Jayanthi, C. S.; Wu, S. Y. [Department of Physics and Astronomy, University of Louisville, Louisville, Kentucky 40292 (United States)

2015-03-28

An upgrade of the previous self-consistent and environment-dependent linear combination of atomic orbitals Hamiltonian (referred as SCED-LCAO) has been developed. This improved version of the semi-empirical SCED-LCAO Hamiltonian, in addition to the inclusion of self-consistent determination of charge redistribution, multi-center interactions, and modeling of electron-electron correlation, has taken into account the effect excited on the orbitals due to the atomic aggregation. This important upgrade has been subjected to a stringent test, the construction of the SCED-LCAO Hamiltonian for boron. It was shown that the Hamiltonian for boron has successfully characterized the electron deficiency of boron and captured the complex chemical bonding in various boron allotropes, including the planar and quasi-planar, the convex, the ring, the icosahedral, and the fullerene-like clusters, the two-dimensional monolayer sheets, and the bulk alpha boron, demonstrating its transferability, robustness, reliability, and predictive power. The molecular dynamics simulation scheme based on the Hamiltonian has been applied to explore the existence and the energetics of ∼230 compact boron clusters B{sub N} with N in the range from ∼100 to 768, including the random, the rhombohedral, and the spherical icosahedral structures. It was found that, energetically, clusters containing whole icosahedral B{sub 12} units are more stable for boron clusters of larger size (N > 200). The ease with which the simulations both at 0 K and finite temperatures were completed is a demonstration of the efficiency of the SCED-LCAO Hamiltonian.

Valence electronic structure of the indene molecule: Experiment vs. GW calculations

Energy Technology Data Exchange (ETDEWEB)

Umari, P.; Stenuit, G. [CNR-IOM DEMOCRITOS Theory Elettra Group, Basovizza, Trieste (Italy); Castellarin-Cudia, C.; Feyer, V.; Di Santo, G.; Goldoni, A. [Sincrotrone Trieste S.C.p.A., Basovizza, Trieste (Italy); Borghetti, P.; Sangaletti, L. [Dipartimento di Matematica e Fisica, Universita Cattolica del Sacro Cuore, Brescia (Italy)

2011-04-15

We investigate the valence electronic properties in the gas phase of the indene molecule, which is one of the simplest polycyclic aromatic hydrocarbons, with photoemission spectroscopy using synchrotron light and through first-principles calculations using a many-body perturbation theory GW approach. We found an excellent agreement between theory and experiment. This allows us to assign to the peaks appearing in the photoemission spectrum the calculated molecular orbitals. (Copyright copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Derivation of Hamiltonians for accelerators

Energy Technology Data Exchange (ETDEWEB)

Symon, K.R.

1997-09-12

In this report various forms of the Hamiltonian for particle motion in an accelerator will be derived. Except where noted, the treatment will apply generally to linear and circular accelerators, storage rings, and beamlines. The generic term accelerator will be used to refer to any of these devices. The author will use the usual accelerator coordinate system, which will be introduced first, along with a list of handy formulas. He then starts from the general Hamiltonian for a particle in an electromagnetic field, using the accelerator coordinate system, with time t as independent variable. He switches to a form more convenient for most purposes using the distance s along the reference orbit as independent variable. In section 2, formulas will be derived for the vector potentials that describe the various lattice components. In sections 3, 4, and 5, special forms of the Hamiltonian will be derived for transverse horizontal and vertical motion, for longitudinal motion, and for synchrobetatron coupling of horizontal and longitudinal motions. Hamiltonians will be expanded to fourth order in the variables.

Investigation of the molecular conformations of ethanol using electron momentum spectroscopy

International Nuclear Information System (INIS)

Ning, C G; Luo, Z H; Huang, Y R; Liu, K; Zhang, S F; Deng, J K; Hajgato, B; Morini, F; Deleuze, M S

2008-01-01

The valence electronic structure and momentum-space electron density distributions of ethanol have been investigated with our newly constructed high-resolution electron momentum spectrometer. The measurements are compared to thermally averaged simulations based on Kohn-Sham (B3LYP) orbital densities as well as one-particle Green's function calculations of ionization spectra and Dyson orbital densities, assuming Boltzmann's statistical distribution of the molecular structure over the two energy minima defining the anti and gauche conformers. One-electron ionization energies and momentum distributions in the outer-valence region were found to be highly dependent upon the molecular conformation. Calculated momentum distributions indeed very sensitively reflect the distortions and topological changes that molecular orbitals undergo due to the internal rotation of the hydroxyl group, and thereby exhibit variations which can be traced experimentally. The B3LYP model Kohn-Sham orbital densities are overall in good agreement with the experimental distributions, and closely resemble benchmark ADC(3) Dyson orbital densities. Both approaches fail to quantitatively reproduce the experimental momentum distributions characterizing the highest occupied molecular orbital. Since electron momentum spectroscopy measurements at various electron impact energies indicate that the plane wave impulse approximation is valid, this discrepancy between theory and experiment is tentatively ascribed to thermal disorder, i.e. large-amplitude and thermally induced dynamical distortions of the molecular structure in the gas phase

Alternative Hamiltonian for molecular dynamics simulations in the grand canonical ensemble

International Nuclear Information System (INIS)

Lo, C.; Palmer, B.

1995-01-01

An alternative to the Hamiltonian of Cagin and Pettitt for performing molecular dynamics simulations in the grand canonical ensemble is presented and used as the basis for a new algorithm. The algorithm is tested on the ideal gas and the truncated and shifted Lennard-Jones fluid. Simulations are used to calculate the vapor--liquid coexistence points for the Lennard-Jones system and are found to be in agreement with previous calculations using Gibbs ensemble calculations and with the Nicolas equation of state. Simulations are also performed on the Lennard-Jones solid

Taking account of valence and core electronic wavefunction orthogonality in the semiempirical molecular orbital calculations

International Nuclear Information System (INIS)

Ginejtite, V.L.; Balyavichyus, L.Z.

1979-01-01

Some shortcomings of the semiempirical method CNDO/1 (complete naglect of differential overlap) taking into account wave function orthogonalities of outer valence electrons to inner shells are being explained. To avoid these shortcomings the introduction of pseudopotential is recommended. Addition of the potential excludes overestimation of attraction among chemically unbounded atoms, corrects underestimation of the single, double and triple S-S coupling, gives reasons for some suppositions of the semiempirical methods, gives a truthful distribution of the electronic levels

Existence of 121 limit cycles in a perturbed planar polynomial Hamiltonian vector field of degree 11

International Nuclear Information System (INIS)

Wang, S.; Yu, P.

2006-01-01

In this article, a systematic procedure has been explored to studying general Z q -equivariant planar polynomial Hamiltonian vector fields for the maximal number of closed orbits and the maximal number of limit cycles after perturbation. Following the procedure by taking special consideration of Z 12 -equivariant vector fields of degree 11, the maximal of 99 closed orbits are obtained under a well-defined coefficient group. Consequently, perturbation parameter control in limit cycle computation leads to the existence of 121 limit cycles in the perturbed Hamiltonian vector field, which gives rise to the lower bound of Hilbert number of 11th-order systems as H(11) ≥ 11 2 . Two conjectures are proposed regarding the maximal number of closed orbits for equivariant polynomial Hamiltonian vector fields and the maximal number of limit cycles bifurcated from the well defined Hamiltonian vector fields after perturbation

Hamiltonian reduction and supersymmetric mechanics with Dirac monopole

International Nuclear Information System (INIS)

Bellucci, Stefano; Nersessian, Armen; Yeranyan, Armen

2006-01-01

We apply the technique of Hamiltonian reduction for the construction of three-dimensional N=4 supersymmetric mechanics specified by the presence of a Dirac monopole. For this purpose we take the conventional N=4 supersymmetric mechanics on the four-dimensional conformally-flat spaces and perform its Hamiltonian reduction to three-dimensional system. We formulate the final system in the canonical coordinates, and present, in these terms, the explicit expressions of the Hamiltonian and supercharges. We show that, besides a magnetic monopole field, the resulting system is specified by the presence of a spin-orbit coupling term. A comparision with previous work is also carried out

Periodic orbits of the hydrogen molecular ion and their quantization

International Nuclear Information System (INIS)

Duan, Y.; Yuan, J.; Bao, C.

1995-01-01

In a classical study of the hydrogen molecular ion beyond the Born-Oppenheimer approximation (BOA), we have found that segments of trajectories resemble that of the Born-Oppenheimer approximation periodic orbits. The importance of this fact to the classical understanding of chemical bonding leads us to a systematic study of the periodic orbits of the planar hydrogen molecular ion within the BOA. Besides introducing a classification scheme for periodic orbits, we discuss the convergence properties of families of periodic orbits and their bifurcation patterns according to their types. Semiclassical calculations of the density of states based on these periodic orbits yield results in agreement with the exact quantum eigenvalues of the hydrogen molecular ion system

Photoion mass spectroscopy and valence photoionization of hypoxanthine, xanthine and caffeine

Energy Technology Data Exchange (ETDEWEB)

Feyer, Vitaliy, E-mail: vitaliy.feyer@elettra.trieste.it [Sincrotrone Trieste, in Area Science Park, I-34012 Basovizza (Trieste) (Italy); Plekan, Oksana [Sincrotrone Trieste, in Area Science Park, I-34012 Basovizza (Trieste) (Italy)] [Institute of Electron Physics, 21 Universitetska St., 88017 Uzhgorod (Ukraine); Richter, Robert [Sincrotrone Trieste, in Area Science Park, I-34012 Basovizza (Trieste) (Italy); Coreno, Marcello [CNR-IMIP, Area della Ricerca di Roma 1, CP10, I-00016 Monterotondo Scalo (Italy)] [CNR-Laboratorio Nazionale TASC-INFM, I-34012 Basovizza (Trieste) (Italy); Prince, Kevin C. [Sincrotrone Trieste, in Area Science Park, I-34012 Basovizza (Trieste) (Italy)] [CNR-Laboratorio Nazionale TASC-INFM, I-34012 Basovizza (Trieste) (Italy)

2009-03-30

Photoionization mass spectra of hypoxanthine, xanthine and caffeine were measured using the photoelectron-photoion coincidence technique and noble gas resonance radiation at energies from 8.4 to 21.2 eV for ionization. The fragmentation patterns for these compounds show that hydrogen cyanide is the main neutral loss species at higher photon energies, while photoionization below 16.67 eV led predominantly to the parent ion. The valence photoelectron spectra of this family of molecules were measured over an extended energy range, including the inner C, N and O 2s valence orbitals. The observed ion fragments were related to ionization of the valence orbitals.

A study of the valence shell photoelectron and photoabsorption spectra of CF3SF5

International Nuclear Information System (INIS)

Holland, D M P; Shaw, D A; Walker, I C; McEwen, I J; Apra, E; Guest, M F

2005-01-01

The outer valence shell photoelectron spectrum of CF 3 SF 5 has been studied experimentally and theoretically. Synchrotron radiation has been used to record angle-resolved outer valence shell photoelectron spectra of CF 3 SF 5 in the photon energy range 18-60 eV. These spectra have allowed photoelectron asymmetry parameters and branching ratios to be derived. The Outer Valence Green's Function approach has been employed to calculate the molecular orbital configuration and associated binding energies. A charge distribution analysis has also been obtained. Assignments have been proposed for the peaks observed in the photoelectron spectrum. The absolute photoabsorption cross section of CF 3 SF 5 has been measured from threshold to 40 eV, and strongly resembles that of SF 6 . Assignments, involving intravalence transitions, have been proposed for some of the principal features appearing in the photoabsorption spectrum of CF 3 SF 5

Entanglement of the valence-bond-solid state on an arbitrary graph

International Nuclear Information System (INIS)

Xu Ying; Korepin, Vladimir E

2008-01-01

The Affleck-Kennedy-Lieb-Tasaki (AKLT) spin interacting model can be defined on an arbitrary graph. We explain the construction of the AKLT Hamiltonian. Given certain conditions, the ground state is unique and known as the valence-bond-solid (VBS) state. It can be used in measurement-based quantum computation as a resource state instead of the cluster state. We study the VBS ground state on an arbitrary connected graph. The graph is cut into two disconnected parts: the block and the environment. We study the entanglement between these two parts and prove that many eigenvalues of the density matrix of the block are zero. We describe a subspace of eigenvectors of the density matrix corresponding to non-zero eigenvalues. The subspace is the degenerate ground states of some Hamiltonian which we call the block Hamiltonian

BOA valence bonding with f-character in highly coordinated actinides

International Nuclear Information System (INIS)

Carter, F.L.

1979-01-01

The addition of f character to bidirectional orbitals enhances their flexibility significantly. The resultant Cf and Gf orbitals are applied to some common high coordinations of the actinides. The valence bond approach implies d and f orbital radial splitting into bonding hybrids and either contracted localized or extended supra-valent d and f orbitals

Understanding valence-shell electron-pair repulsion (VSEPR) theory using origami molecular models

International Nuclear Information System (INIS)

Saraswati, Teguh Endah; Saputro, Sulistyo; Ramli, Murni; Praseptiangga, Danar; Khasanah, Nurul; Marwati, Sri

2017-01-01

Valence-shell electron-pair repulsion (VSEPR) theory is conventionally used to predict molecular geometry. However, it is difficult to explore the full implications of this theory by simply drawing chemical structures. Here, we introduce origami modelling as a more accessible approach for exploration of the VSEPR theory. Our technique is simple, readily accessible and inexpensive compared with other sophisticated methods such as computer simulation or commercial three-dimensional modelling kits. This method can be implemented in chemistry education at both the high school and university levels. We discuss the example of a simple molecular structure prediction for ammonia (NH 3 ). Using the origami model, both molecular shape and the scientific justification can be visualized easily. This ‘hands-on’ approach to building molecules will help promote understanding of VSEPR theory. (paper)

Understanding valence-shell electron-pair repulsion (VSEPR) theory using origami molecular models

Science.gov (United States)

Endah Saraswati, Teguh; Saputro, Sulistyo; Ramli, Murni; Praseptiangga, Danar; Khasanah, Nurul; Marwati, Sri

2017-01-01

Valence-shell electron-pair repulsion (VSEPR) theory is conventionally used to predict molecular geometry. However, it is difficult to explore the full implications of this theory by simply drawing chemical structures. Here, we introduce origami modelling as a more accessible approach for exploration of the VSEPR theory. Our technique is simple, readily accessible and inexpensive compared with other sophisticated methods such as computer simulation or commercial three-dimensional modelling kits. This method can be implemented in chemistry education at both the high school and university levels. We discuss the example of a simple molecular structure prediction for ammonia (NH3). Using the origami model, both molecular shape and the scientific justification can be visualized easily. This ‘hands-on’ approach to building molecules will help promote understanding of VSEPR theory.

Linearly scaling and almost Hamiltonian dielectric continuum molecular dynamics simulations through fast multipole expansions

Energy Technology Data Exchange (ETDEWEB)

Lorenzen, Konstantin; Mathias, Gerald; Tavan, Paul, E-mail: tavan@physik.uni-muenchen.de [Lehrstuhl für BioMolekulare Optik, Ludig–Maximilians Universität München, Oettingenstr. 67, 80538 München (Germany)

2015-11-14

Hamiltonian Dielectric Solvent (HADES) is a recent method [S. Bauer et al., J. Chem. Phys. 140, 104103 (2014)] which enables atomistic Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric solvent continua. Such simulations become rapidly impractical for large proteins, because the computational effort of HADES scales quadratically with the number N of atoms. If one tries to achieve linear scaling by applying a fast multipole method (FMM) to the computation of the HADES electrostatics, the Hamiltonian character (conservation of total energy, linear, and angular momenta) may get lost. Here, we show that the Hamiltonian character of HADES can be almost completely preserved, if the structure-adapted fast multipole method (SAMM) as recently redesigned by Lorenzen et al. [J. Chem. Theory Comput. 10, 3244-3259 (2014)] is suitably extended and is chosen as the FMM module. By this extension, the HADES/SAMM forces become exact gradients of the HADES/SAMM energy. Their translational and rotational invariance then guarantees (within the limits of numerical accuracy) the exact conservation of the linear and angular momenta. Also, the total energy is essentially conserved—up to residual algorithmic noise, which is caused by the periodically repeated SAMM interaction list updates. These updates entail very small temporal discontinuities of the force description, because the employed SAMM approximations represent deliberately balanced compromises between accuracy and efficiency. The energy-gradient corrected version of SAMM can also be applied, of course, to MD simulations of all-atom solvent-solute systems enclosed by periodic boundary conditions. However, as we demonstrate in passing, this choice does not offer any serious advantages.

Hamiltonian flow over saddles for exploring molecular phase space structures

Science.gov (United States)

Farantos, Stavros C.

2018-03-01

Despite using potential energy surfaces, multivariable functions on molecular configuration space, to comprehend chemical dynamics for decades, the real happenings in molecules occur in phase space, in which the states of a classical dynamical system are completely determined by the coordinates and their conjugate momenta. Theoretical and numerical results are presented, employing alanine dipeptide as a model system, to support the view that geometrical structures in phase space dictate the dynamics of molecules, the fingerprints of which are traced by following the Hamiltonian flow above saddles. By properly selecting initial conditions in alanine dipeptide, we have found internally free rotor trajectories the existence of which can only be justified in a phase space perspective. This article is part of the theme issue `Modern theoretical chemistry'.

Mimicking the action of folding chaperones by Hamiltonian replica-exchange molecular dynamics simulations : Application in the refinement of de novo models

NARCIS (Netherlands)

Fan, Hao; Periole, Xavier; Mark, Alan E.

The efficiency of using a variant of Hamiltonian replica-exchange molecular dynamics (Chaperone H-replica-exchange molecular dynamics [CH-REMD]) for the refinement of protein structural models generated de novo is investigated. In CH-REMD, the interaction between the protein and its environment,

Model Hamiltonian Calculations of the Nonlinear Polarizabilities of Conjugated Molecules.

Science.gov (United States)

Risser, Steven Michael

This dissertation advances the theoretical knowledge of the nonlinear polarizabilities of conjugated molecules. The unifying feature of these molecules is an extended delocalized pi electron structure. The pi electrons dominate the electronic properties of the molecules, allowing prediction of molecular properties based on the treatment of just the pi electrons. Two separate pi electron Hamiltonians are used in the research. The principal Hamiltonian used is the non-interacting single-particle Huckel Hamiltonian, which replaces the Coulomb interaction among the pi electrons with a mean field interaction. The simplification allows for exact solution of the Hamiltonian for large molecules. The second Hamiltonian used for this research is the interacting multi-particle Pariser-Parr-Pople (PPP) Hamiltonian, which retains explicit Coulomb interactions. This limits exact solutions to molecules containing at most eight electrons. The molecular properties being investigated are the linear polarizability, and the second and third order hyperpolarizabilities. The hyperpolarizabilities determine the nonlinear optical response of materials. These molecular parameters are determined by two independent approaches. The results from the Huckel Hamiltonian are obtained through first, second and third order perturbation theory. The results from the PPP Hamiltonian are obtained by including the applied field directly in the Hamiltonian and determining the ground state energy at a series of field strengths. By fitting the energy to a polynomial in field strength, the polarizability and hyperpolarizabilities are determined. The Huckel Hamiltonian is used to calculate the third order hyperpolarizability of polyenes. These calculations were the first to show the average hyperpolarizability of the polyenes to be positive, and also to show the saturation of the hyperpolarizability. Comparison of these Huckel results to those from the PPP Hamiltonian shows the lack of explicit Coulomb

Hamiltonian formalisms and symmetries of the Pais–Uhlenbeck oscillator

Directory of Open Access Journals (Sweden)

Krzysztof Andrzejewski

2014-12-01

Full Text Available The study of the symmetry of Pais–Uhlenbeck oscillator initiated in Andrzejewski et al. (2014 [24] is continued with special emphasis put on the Hamiltonian formalism. The symmetry generators within the original Pais and Uhlenbeck Hamiltonian approach as well as the canonical transformation to the Ostrogradski Hamiltonian framework are derived. The resulting algebra of generators appears to be the central extension of the one obtained on the Lagrangian level; in particular, in the case of odd frequencies one obtains the centrally extended l-conformal Newton–Hooke algebra. In this important case the canonical transformation to an alternative Hamiltonian formalism (related to the free higher derivatives theory is constructed. It is shown that all generators can be expressed in terms of the ones for the free theory and the result agrees with that obtained by the orbit method.

Ab initio molecular-orbital study on electron correlation effects in CuO6 clusters relating to high-Tc superconductivity

International Nuclear Information System (INIS)

Yamamoto, S.; Yamaguchi, K.; Nasu, K.

1990-01-01

Ab initio molecular-orbital calculations for CuO 6 clusters have been performed to elucidate the electronic structures of undoped and doped copper oxides, which are of current interest in relation to high-T c superconductivity. The electron correlation effects for these species are thoroughly investigated by the full-valence configuration-interaction method and the complete-active-space self-consistent-field method. The electron correlation effect is relatively simple for the A g state (σ hole), whereas pair excitations and spin-flip excitations give sizable contributions to the configuration-interaction wave function for the B state (in-plane π hole). Implications of these results are discussed in relation to the mechanisms of the high-T c superconductivity

Computing pKa Values with a Mixing Hamiltonian Quantum Mechanical/Molecular Mechanical Approach.

Science.gov (United States)

Liu, Yang; Fan, Xiaoli; Jin, Yingdi; Hu, Xiangqian; Hu, Hao

2013-09-10

Accurate computation of the pKa value of a compound in solution is important but challenging. Here, a new mixing quantum mechanical/molecular mechanical (QM/MM) Hamiltonian method is developed to simulate the free-energy change associated with the protonation/deprotonation processes in solution. The mixing Hamiltonian method is designed for efficient quantum mechanical free-energy simulations by alchemically varying the nuclear potential, i.e., the nuclear charge of the transforming nucleus. In pKa calculation, the charge on the proton is varied in fraction between 0 and 1, corresponding to the fully deprotonated and protonated states, respectively. Inspired by the mixing potential QM/MM free energy simulation method developed previously [H. Hu and W. T. Yang, J. Chem. Phys. 2005, 123, 041102], this method succeeds many advantages of a large class of λ-coupled free-energy simulation methods and the linear combination of atomic potential approach. Theory and technique details of this method, along with the calculation results of the pKa of methanol and methanethiol molecules in aqueous solution, are reported. The results show satisfactory agreement with the experimental data.

An approach for obtaining integrable Hamiltonians from Poisson-commuting polynomial families

Science.gov (United States)

Leyvraz, F.

2017-07-01

We discuss a general approach permitting the identification of a broad class of sets of Poisson-commuting Hamiltonians, which are integrable in the sense of Liouville. It is shown that all such Hamiltonians can be solved explicitly by a separation of variables ansatz. The method leads in particular to a proof that the so-called "goldfish" Hamiltonian is maximally superintegrable and leads to an elementary identification of a full set of integrals of motion. The Hamiltonians in involution with the "goldfish" Hamiltonian are also explicitly integrated. New integrable Hamiltonians are identified, among which some have the property of being isochronous, that is, all their orbits have the same period. Finally, a peculiar structure is identified in the Poisson brackets between the elementary symmetric functions and the set of Hamiltonians commuting with the "goldfish" Hamiltonian: these can be expressed as products between elementary symmetric functions and Hamiltonians. The structure displays an invariance property with respect to one element and has both a symmetry and a closure property. The meaning of this structure is not altogether clear to the author, but it turns out to be a powerful tool.

Intermediate L-K molecular-orbital radiation from heavy ion collisions

International Nuclear Information System (INIS)

Heinig, K.H.; Jaeger, H.U.; Richter, H.; Woittennek, H.

1976-01-01

The structure of X-ray continua observed recently in violent collisions between mean-mass atoms can be explained by a superposition of K molecular orbital (KMO) radiation and an intermediate L-K molecular orbital (ILKMO) radiation of high intensity which is due to 2psigma vacancies. (Auth.)

Intermediate L-K molecular orbital radiation from heavy ion collisions

International Nuclear Information System (INIS)

Heinig, K.H.; Jaeger, H.U.; Richter, H.; Woittennek, H.

1975-09-01

The structure of x-ray continua observed recently in violent collisions between intermediate mass atoms can be explained by a superposition of K molecular orbital (KMO) radiation and of an intermediate L-K molecular orbital (ILKMO) radiation of high intensity which is due to 2psigma vacancies. (author)

Analytical and molecular dynamical investigations of the influence of molecular vibrations upon the (e,2e) electron momentum distributions of furan

International Nuclear Information System (INIS)

Morini, F; Deleuze, M S; Watanabe, N; Takahashi, M

2015-01-01

The role of molecular vibrations has been theoretically investigated in the electronic ground state on the (e, 2e) valence orbital momentum profiles of furan by means of two complementary approaches. The first one relies upon the principles of Born-Oppenheimer Molecular Dynamics (BOMD), whereas the second one, referred as Harmonic Analytical Quantum Mechanical (HAQM) approach, includes on quantum-mechanical (paper)

Spectroscopic determination of valence band parameters in InP

International Nuclear Information System (INIS)

Lewis, R.A.; Lough, B.C.C.

2003-01-01

Full text: The general form of the Hamiltonian for an electron or hole in a semiconductor has been given by Luttinger. The valence band is characterised by three parameters - γ 1 , γ 2 , γ 3 -now commonly known as the Luttinger parameters. Despite many investigations there is still considerable uncertainty regarding the Luttinger parameters of InP. The situation has been reviewed by Hackenberg et al. These authors themselves sought to determine the Luttinger parameters by hot-electron luminescence and discovered that many Luttinger parameter triplets were consistent with their data. We employ a spectroscopic approach to estimating valence-band parameters in InP. Calculations have been made for both the unperturbed energy levels and the energy levels in a magnetic field of acceptor impurities in semiconductors characterised by different Luttinger parameters. We compare our recent experimental data for the transitions associated with the Zn acceptor impurity in InP in magnetic fields up to 30 T to determine the most appropriate set of valence-band parameters for InP

A combined reaction class approach with integrated molecular orbital+molecular orbital (IMOMO) methodology: A practical tool for kinetic modeling

International Nuclear Information System (INIS)

Truong, Thanh N.; Maity, Dilip K.; Truong, Thanh-Thai T.

2000-01-01

We present a new practical computational methodology for predicting thermal rate constants of reactions involving large molecules or a large number of elementary reactions in the same class. This methodology combines the integrated molecular orbital+molecular orbital (IMOMO) approach with our recently proposed reaction class models for tunneling. With the new methodology, we show that it is possible to significantly reduce the computational cost by several orders of magnitude while compromising the accuracy in the predicted rate constants by less than 40% over a wide range of temperatures. Another important result is that the computational cost increases only slightly as the system size increases. (c) 2000 American Institute of Physics

Lie algebraic approach to valence bond theory of π-electron systems: a preliminary study of excited states

Science.gov (United States)

Paldus, J.; Li, X.

1992-10-01

Following a brief outline of various developments and exploitations of the unitary group approach (UGA), and its extension referred to as Clifford algebra UGA (CAUGA), in molecular electronic structure calculations, we present a summary of a recently introduced implementation of CAUGA for the valence bond (VB) method based on the Pariser-Parr-Pople (PPP)-type Hamiltonian. The existing applications of this PPP-VB approach have been limited to groundstates of various π-electron systems or, at any rate, to the lowest states of a given multiplicity. In this paper the method is applied to the low-lying excited states of several archetypal models, namely cyclobutadiene and benzene, representing antiaromatic and aromatic systems, hexatriene, representing linear polyenic systems and, finally, naphthalene, representing polyacenes.

Pair natural orbital and canonical coupled cluster reaction enthalpies involving light to heavy alkali and alkaline earth metals: the importance of sub-valence correlation.

Science.gov (United States)

Minenkov, Yury; Bistoni, Giovanni; Riplinger, Christoph; Auer, Alexander A; Neese, Frank; Cavallo, Luigi

2017-04-05

In this work, we tested canonical and domain based pair natural orbital coupled cluster methods (CCSD(T) and DLPNO-CCSD(T), respectively) for a set of 32 ligand exchange and association/dissociation reaction enthalpies involving ionic complexes of Li, Be, Na, Mg, Ca, Sr, Ba and Pb(ii). Two strategies were investigated: in the former, only valence electrons were included in the correlation treatment, giving rise to the computationally very efficient FC (frozen core) approach; in the latter, all non-ECP electrons were included in the correlation treatment, giving rise to the AE (all electron) approach. Apart from reactions involving Li and Be, the FC approach resulted in non-homogeneous performance. The FC approach leads to very small errors (correlation effects. These large errors are reduced to a few kcal mol -1 if the AE approach is used or the sub-valence orbitals of metals are included in the correlation treatment. On the technical side, the CCSD(T) and DLPNO-CCSD(T) results differ by a fraction of kcal mol -1 , indicating the latter method as the perfect choice when the CPU efficiency is essential. For completely black-box applications, as requested in catalysis or thermochemical calculations, we recommend the DLPNO-CCSD(T) method with all electrons that are not covered by effective core potentials included in the correlation treatment and correlation-consistent polarized core valence basis sets of cc-pwCVQZ(-PP) quality.

Seniority and orbital symmetry as tools for establishing a full configuration interaction hierarchy.

Science.gov (United States)

Bytautas, Laimutis; Henderson, Thomas M; Jiménez-Hoyos, Carlos A; Ellis, Jason K; Scuseria, Gustavo E

2011-07-28

We explore the concept of seniority number (defined as the number of unpaired electrons in a determinant) when applied to the problem of electron correlation in atomic and molecular systems. Although seniority is a good quantum number only for certain model Hamiltonians (such as the pairing Hamiltonian), we show that it provides a useful partitioning of the electronic full configuration interaction (FCI) wave function into rapidly convergent Hilbert subspaces whose weight diminishes as its seniority number increases. The primary focus of this study is the adequate description of static correlation effects. The examples considered are the ground states of the helium, beryllium, and neon atoms, the symmetric dissociation of the N(2) and CO(2) molecules, as well as the symmetric dissociation of an H(8) hydrogen chain. It is found that the symmetry constraints that are normally placed on the spatial orbitals greatly affect the convergence rate of the FCI expansion. The energy relevance of the seniority zero sector (determinants with all paired electrons) increases dramatically if orbitals of broken spatial symmetry (as those commonly used for Hubbard Hamiltonian studies) are allowed in the wave function construction. © 2011 American Institute of Physics

Relative Stabilities and Reactivities of Isolated Versus Conjugated Alkenes: Reconciliation Via a Molecular Orbital Approach

Science.gov (United States)

Sotiriou-Leventis, Chariklia; Hanna, Samir B.; Leventis, Nicholas

1996-04-01

The well-accepted practice of generating a pair of molecular orbitals, one of lower energy and another of higher energy than the original pair of overlapping atomic orbitals, and the concept of a particle in a one-dimensional box are implemented in a simplified, nonmathematical method that explains the relative stabilities and reactivities of alkenes with conjugated versus isolated double bonds. In this method, Huckel-type MO's of higher polyenes are constructed by energy rules of linear combination of atomic orbitals. One additional rule is obeyed: bonding molecular orbitals overlap only with bonding molecular orbitals, and antibonding molecular orbitals overlap only with antibonding molecular orbitals.

Stable Molecular Diodes Based on π-π Interactions of the Molecular Frontier Orbitals with Graphene Electrodes.

Science.gov (United States)

Song, Peng; Guerin, Sarah; Tan, Sherman Jun Rong; Annadata, Harshini Venkata; Yu, Xiaojiang; Scully, Micheál; Han, Ying Mei; Roemer, Max; Loh, Kian Ping; Thompson, Damien; Nijhuis, Christian A

2018-03-01

In molecular electronics, it is important to control the strength of the molecule-electrode interaction to balance the trade-off between electronic coupling strength and broadening of the molecular frontier orbitals: too strong coupling results in severe broadening of the molecular orbitals while the molecular orbitals cannot follow the changes in the Fermi levels under applied bias when the coupling is too weak. Here, a platform based on graphene bottom electrodes to which molecules can bind via π-π interactions is reported. These interactions are strong enough to induce electronic function (rectification) while minimizing broadening of the molecular frontier orbitals. Molecular tunnel junctions are fabricated based on self-assembled monolayers (SAMs) of Fc(CH 2 ) 11 X (Fc = ferrocenyl, X = NH 2 , Br, or H) on graphene bottom electrodes contacted to eutectic alloy of gallium and indium top electrodes. The Fc units interact more strongly with graphene than the X units resulting in SAMs with the Fc at the bottom of the SAM. The molecular diodes perform well with rectification ratios of 30-40, and they are stable against bias stressing under ambient conditions. Thus, tunnel junctions based on graphene with π-π molecule-electrode coupling are promising platforms to fabricate stable and well-performing molecular diodes. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Transient dynamics of a quantum-dot: From Kondo regime to mixed valence and to empty orbital regimes

Science.gov (United States)

Cheng, YongXi; Li, ZhenHua; Wei, JianHua; Nie, YiHang; Yan, YiJing

2018-04-01

Based on the hierarchical equations of motion approach, we study the time-dependent transport properties of a strongly correlated quantum dot system in the Kondo regime (KR), mixed valence regime (MVR), and empty orbital regime (EOR). We find that the transient current in KR shows the strongest nonlinear response and the most distinct oscillation behaviors. Both behaviors become weaker in MVR and diminish in EOR. To understand the physical insight, we examine also the corresponding dot occupancies and the spectral functions, with their dependence on the Coulomb interaction, temperature, and applied step bias voltage. The above nonlinear and oscillation behaviors could be understood as the interplay between dynamical Kondo resonance and single electron resonant-tunneling.

Density functional theory, comparative vibrational spectroscopic studies, highest occupied molecular orbital and lowest unoccupied molecular orbital analysis of Linezolid

Science.gov (United States)

Rajalakshmi, K.; Gunasekaran, S.; Kumaresan, S.

2015-06-01

The Fourier transform infrared spectra and Fourier transform Raman spectra of Linezolid have been recorded in the regions 4,000-400 and 4,000-100 cm-1, respectively. Utilizing the observed Fourier transform infrared spectra and Fourier transform Raman spectra data, a complete vibrational assignment and analysis of the fundamental modes of the compound have been carried out. The optimum molecular geometry, harmonic vibrational frequencies, infrared intensities and Raman scattering activities, have been calculated by density functional theory with 6-31G(d,p), 6-311G(d,p) and M06-2X/6-31G(d,p) levels. The difference between the observed and scaled wavenumber values of most of the fundamentals is very small. A detailed interpretation of the infrared and Raman spectra of Linezolid is reported. Mulliken's net charges have also been calculated. Ultraviolet-visible spectrum of the title molecule has also been calculated using time-dependent density functional method. Besides, molecular electrostatic potential, highest occupied molecular orbital and lowest unoccupied molecular orbital analysis and several thermodynamic properties have been performed by the density functional theoretical method.

Theoretical studies of spin-Hamiltonian parameters of Mo{sup 5+} ion doped in K{sub 2}SnCl{sub 6} crystal

Energy Technology Data Exchange (ETDEWEB)

Fang, Wang, E-mail: mailfangwang@163.com; Yang, Da-Xiao; Chen, Heng-Jie; Tang, Hai-Yan

2013-11-15

The spin-Hamiltonian (SH) parameters (g factors g{sub //}, g{sub ⊥} and hyperfine structure constants A{sub //}, A{sub ⊥} ) of K{sub 2}SnCl{sub 6}: Mo{sup 5+} (4d{sup 1}) crystal are theoretically studied by the use of two microscopic spin-Hamiltonian (SH) methods, the high-order perturbation theory method (PTM) and the complete diagonalization (of energy matrix) method (CDM) within the molecular orbital (MO) scheme. The contributions arising both from the crystal field and charge transfer excitations are taken into account. The investigations show that the charge transfer mechanism plays a decisive role in the understanding of the spin-Hamiltonian (SH) parameters for 4d{sup 1} ions in crystals with the strong coordinate covalence, especially for g{sub //}>g{sub ⊥} which cannot be explained in the frame work of traditional crystal field approximation (CFA). The local defect structure around Mo{sup 5+} impurity ion center is determined to be D{sub 4} {sub h} point group symmetry.

Tunneling anisotropic magnetoresistance via molecular π orbitals of Pb dimers

Science.gov (United States)

Schöneberg, Johannes; Ferriani, Paolo; Heinze, Stefan; Weismann, Alexander; Berndt, Richard

2018-01-01

Pb dimers on a ferromagnetic surface are shown to exhibit large tunneling anisotropic magnetoresistance (TAMR) due to molecular π orbitals. Dimers oriented differently with respect to the magnetization directions of a ferromagnetic Fe double layer on W(110) were made with a scanning tunneling microscope. Depending on the dimer orientations, TAMR is absent or as large as 20% at the Fermi level. General arguments and first-principles calculations show that mixing of molecular orbitals due to spin-orbit coupling, which leads to TAMR, is maximal when the magnetization is oriented parallel to the dimer axis.

Molecular orbital calculations using chemical graph theory

CERN Document Server

Dias, Jerry Ray

1993-01-01

Professor John D. Roberts published a highly readable book on Molecular Orbital Calculations directed toward chemists in 1962. That timely book is the model for this book. The audience this book is directed toward are senior undergraduate and beginning graduate students as well as practicing bench chemists who have a desire to develop conceptual tools for understanding chemical phenomena. Although, ab initio and more advanced semi-empirical MO methods are regarded as being more reliable than HMO in an absolute sense, there is good evidence that HMO provides reliable relative answers particularly when comparing related molecular species. Thus, HMO can be used to rationalize electronic structure in 1t-systems, aromaticity, and the shape use HMO to gain insight of simple molecular orbitals. Experimentalists still into subtle electronic interactions for interpretation of UV and photoelectron spectra. Herein, it will be shown that one can use graph theory to streamline their HMO computational efforts and to arrive...

Orbital tomography: Molecular band maps, momentum maps and the imaging of real space orbitals of adsorbed molecules

Energy Technology Data Exchange (ETDEWEB)

Offenbacher, Hannes; Lüftner, Daniel; Ules, Thomas; Reinisch, Eva Maria; Koller, Georg, E-mail: georg.koller@uni-graz.at; Puschnig, Peter; Ramsey, Michael G., E-mail: michael.ramsey@uni-graz.at

2015-10-01

Highlights: • Orbital tomography within the plane wave final state approximation. • One electron orbital predictions versus angle resolved photoemission experiment. • Geometric and electronic structure of organic thin films elucidated by ARUPS. • Influence of molecular conformation and orientation on ARUPS. • Retrieval of sexiphenyl and pentacene orbitals in real space. - Abstract: The frontier orbitals of molecules are the prime determinants of their chemical, optical and electronic properties. Arguably, the most direct method of addressing the (filled) frontier orbitals is ultra-violet photoemission spectroscopy (UPS). Although UPS is a mature technique from the early 1970s on, the angular distribution of the photoemitted electrons was thought to be too complex to be analysed quantitatively. Recently angle resolved UPS (ARUPS) work on conjugated molecules both, in ordered thick films and chemisorbed monolayers, has shown that the angular (momentum) distribution of the photocurrent from orbital emissions can be simply understood. The approach, based on the assumption of a plane wave final state is becoming known as orbital tomography. Here we will demonstrate, with selected examples of pentacene (5A) and sexiphenyl (6P), the potential of orbital tomography. First it will be shown how the full angular distribution of the photocurrent (momentum map) from a specific orbital is related to the real space orbital by a Fourier transform. Examples of the reconstruction of 5A orbitals will be given and the procedure for recovering the lost phase information will be outlined. We then move to examples of sexiphenyl where we interrogate the original band maps of thick sexiphenyl in the light of our understanding of orbital tomography that has developed since then. With comparison to theoretical simulations of the molecular band maps, the molecular conformation and orientation will be concluded. New results for the sexiphenyl monolayer on Al(1 1 0) will then be

Valence electronic properties of porphyrin derivatives.

Science.gov (United States)

Stenuit, G; Castellarin-Cudia, C; Plekan, O; Feyer, V; Prince, K C; Goldoni, A; Umari, P

2010-09-28

We present a combined experimental and theoretical investigation of the valence electronic structure of porphyrin-derived molecules. The valence photoemission spectra of the free-base tetraphenylporphyrin and of the octaethylporphyrin molecule were measured using synchrotron radiation and compared with theoretical spectra calculated using the GW method and the density-functional method within the generalized gradient approximation. Only the GW results could reproduce the experimental data. We found that the contribution to the orbital energies due to electronic correlations has the same linear behavior in both molecules, with larger deviations in the vicinity of the HOMO level. This shows the importance of adequate treatment of electronic correlations in these organic systems.

Experimental study of the rearrangements of valence protons and neutrons amongst single-particle orbits during double-β decay in 100Mo

Science.gov (United States)

Freeman, S. J.; Sharp, D. K.; McAllister, S. A.; Kay, B. P.; Deibel, C. M.; Faestermann, T.; Hertenberger, R.; Mitchell, A. J.; Schiffer, J. P.; Szwec, S. V.; Thomas, J. S.; Wirth, H.-F.

2017-11-01

The rearrangements of protons and neutrons amongst the valence single-particle orbitals during double-β decay of 100Mo have been determined by measuring cross sections in (d ,p ), (p ,d ), (3He,α ), and (3He,d ) reactions on Mo,10098 and Ru,102100 targets. The deduced nucleon occupancies reveal significant discrepancies when compared with theoretical calculations; the same calculations have previously been used to determine the nuclear matrix element associated with the decay probability of double-β decay of the 100Mo system.

Recursive tridiagonalization of infinite dimensional Hamiltonians

International Nuclear Information System (INIS)

Haydock, R.; Oregon Univ., Eugene, OR

1989-01-01

Infinite dimensional, computable, sparse Hamiltonians can be numerically tridiagonalized to finite precision using a three term recursion. Only the finite number of components whose relative magnitude is greater than the desired precision are stored at any stage in the computation. Thus the particular components stored change as the calculation progresses. This technique avoids errors due to truncation of the orbital set, and makes terminators unnecessary in the recursion method. (orig.)

Symplectic topology of integrable Hamiltonian systems

International Nuclear Information System (INIS)

Nguyen Tien Zung.

1993-08-01

We study the topology of integrable Hamiltonian systems, giving the main attention to the affine structure of their orbit spaces. In particular, we develop some aspects of Fomenko's theory about topological classification of integrable non-degenerate systems, and consider some relations between such systems and ''pure'' contact and symplectic geometry. We give a notion of integrable surgery and use it to obtain some interesting symplectic structures. (author). Refs, 10 figs

Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics

Science.gov (United States)

Tao, Xuecheng; Shushkov, Philip; Miller, Thomas F.

2018-03-01

We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on the implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. We present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.

Complex molecular orbital method: open-shell theory

International Nuclear Information System (INIS)

Hendekovic, J.

1976-01-01

A singe-determinant open-shell formalism for complex molecular orbitals is developed. An iterative algorithm for solving the resulting secular equations is constructed. It is based on a sequence of similarity transformations and matrix triangularizations

Useful forms of the Hamiltonian for ion-optical systems

International Nuclear Information System (INIS)

Davies, W.G.

1991-04-01

The symbiosis of differential algebra and the Lie-algebraic formulation of optics provides a set of very powerful tools for analyzing and understanding the orbit dynamics of complex accelerators up to very high orders. In order to use these tools effectively it is usually necessary to express the Hamiltonian in the appropriate coordinate system. In this report, the relativistic Hamiltonian is derived in curvilinear (the fundamental coordinate system for ion-optics), Cartesian and polar coordinates, in forms suitable for solving problems in ion optics and accelerator physics both with and without the help of differential algebra

Calculations on thirteen Λ–S states of PO radical: Electronic structure, spectroscopy and spin–orbit coupling

International Nuclear Information System (INIS)

Liu, Hui; Shi, Deheng; Sun, Jinfeng; Zhu, Zunlue

2013-01-01

This paper presents the potential energy curves (PECs) of X 2 Π, B 2 Σ + , B′ 2 Π, C 2 Σ − , C′ 2 Δ, 3 2 Π, a 4 Π, b 4 Σ − , 1 4 Δ, 2 4 Δ, 1 4 Σ + , 1 6 Σ + and 1 6 Π Λ–S states and the PECs of 16 Ω states generated from the eight bound Λ–S states of PO radical. All the PECs are calculated by the CASSCF method, which is followed by the internally contracted MRCI approach with the Davidson modification. The spin–orbit coupling is included by the state interaction approach with the Breit–Pauli Hamiltonian. The convergent behavior is observed and discussed with respect to the correlation-consistent basis set and level of theory. The effect on the energy splitting by core-electron correlations is studied. To improve the quality of PECs, core-valence correlation corrections are included by a cc-pCVTZ basis set. Scalar relativistic correction calculations are made by the third-order Douglas–Kroll Hamiltonian approximation at the level of a cc-pV5Z basis set. All the PECs are extrapolated to the complete basis set limit. With these PECs, the spectroscopic parameters of 10 Λ–S and 16 Ω bound states are evaluated. The vibrational manifolds of the first 16 vibrational states are evaluated for each Λ–S and Ω state of non-rotation radical. With the PECs obtained by the MRCI+Q/CV+DK+56+SO calculations, the SO coupling splitting energy of X 2 Π Λ–S state is determined as 225.18 cm −1 , which agrees well with the measurements of 224.17 cm −1 . Moreover, other spectroscopic parameters and molecular constants calculated here are also in excellent agreement with the available measurements. It shows that the spectroscopic parameters and molecular constants reported here can be expected to be reliable predicted ones. -- Highlights: ► Convergent behavior is observed with respect to the basis set and level of theory. ► Effect on the PECs by core-valence correlation and relativistic corrections is included. ► PECs are extrapolated

Exchange Coupling Interactions from the Density Matrix Renormalization Group and N-Electron Valence Perturbation Theory: Application to a Biomimetic Mixed-Valence Manganese Complex.

Science.gov (United States)

Roemelt, Michael; Krewald, Vera; Pantazis, Dimitrios A

2018-01-09

The accurate description of magnetic level energetics in oligonuclear exchange-coupled transition-metal complexes remains a formidable challenge for quantum chemistry. The density matrix renormalization group (DMRG) brings such systems for the first time easily within reach of multireference wave function methods by enabling the use of unprecedentedly large active spaces. But does this guarantee systematic improvement in predictive ability and, if so, under which conditions? We identify operational parameters in the use of DMRG using as a test system an experimentally characterized mixed-valence bis-μ-oxo/μ-acetato Mn(III,IV) dimer, a model for the oxygen-evolving complex of photosystem II. A complete active space of all metal 3d and bridge 2p orbitals proved to be the smallest meaningful starting point; this is readily accessible with DMRG and greatly improves on the unrealistic metal-only configuration interaction or complete active space self-consistent field (CASSCF) values. Orbital optimization is critical for stabilizing the antiferromagnetic state, while a state-averaged approach over all spin states involved is required to avoid artificial deviations from isotropic behavior that are associated with state-specific calculations. Selective inclusion of localized orbital subspaces enables probing the relative contributions of different ligands and distinct superexchange pathways. Overall, however, full-valence DMRG-CASSCF calculations fall short of providing a quantitative description of the exchange coupling owing to insufficient recovery of dynamic correlation. Quantitatively accurate results can be achieved through a DMRG implementation of second order N-electron valence perturbation theory (NEVPT2) in conjunction with a full-valence metal and ligand active space. Perspectives for future applications of DMRG-CASSCF/NEVPT2 to exchange coupling in oligonuclear clusters are discussed.

Adaptive frozen orbital treatment for the fragment molecular orbital method combined with density-functional tight-binding

Science.gov (United States)

Nishimoto, Yoshio; Fedorov, Dmitri G.

2018-02-01

The exactly analytic gradient is derived and implemented for the fragment molecular orbital (FMO) method combined with density-functional tight-binding (DFTB) using adaptive frozen orbitals. The response contributions which arise from freezing detached molecular orbitals on the border between fragments are computed by solving Z-vector equations. The accuracy of the energy, its gradient, and optimized structures is verified on a set of representative inorganic materials and polypeptides. FMO-DFTB is applied to optimize the structure of a silicon nano-wire, and the results are compared to those of density functional theory and experiment. FMO accelerates the DFTB calculation of a boron nitride nano-ring with 7872 atoms by a factor of 406. Molecular dynamics simulations using FMO-DFTB applied to a 10.7 μm chain of boron nitride nano-rings, consisting of about 1.2 × 106 atoms, reveal the rippling and twisting of nano-rings at room temperature.

Normal form for mirror machine Hamiltonians

International Nuclear Information System (INIS)

Dragt, A.J.; Finn, J.M.

1979-01-01

A systematic algorithm is developed for performing canonical transformations on Hamiltonians which govern particle motion in magnetic mirror machines. These transformations are performed in such a way that the new Hamiltonian has a particularly simple normal form. From this form it is possible to compute analytic expressions for gyro and bounce frequencies. In addition, it is possible to obtain arbitrarily high order terms in the adiabatic magnetic moment expansion. The algorithm makes use of Lie series, is an extension of Birkhoff's normal form method, and has been explicitly implemented by a digital computer programmed to perform the required algebraic manipulations. Application is made to particle motion in a magnetic dipole field and to a simple mirror system. Bounce frequencies and locations of periodic orbits are obtained and compared with numerical computations. Both mirror systems are shown to be insoluble, i.e., trajectories are not confined to analytic hypersurfaces, there is no analytic third integral of motion, and the adiabatic magnetic moment expansion is divergent. It is expected also that the normal form procedure will prove useful in the study of island structure and separatrices associated with periodic orbits, and should facilitate studies of breakdown of adiabaticity and the onset of ''stochastic'' behavior

Calculation of fluctuations and photoemission properties in a tetrahedral-cluster model for an intermediate-valence system

International Nuclear Information System (INIS)

Reich, A.; Falicov, L.M.

1986-01-01

An exact solution of a four-site tetrahedral-crystal model, the smallest face-centered-cubic crystal, is presented in the case of an intermediate-valence system. The model consists of the following: (a) one extended orbital and one localized orbital per atom, (b) an interatomic transfer term between extended orbitals, (c) an interatomic hybridization between the localized and extended orbitals, (d) strong intra-atomic Coulomb repulsion between opposite-spin localized states, and (e) intermediate-strength intra-atomic Coulomb repulsion between the localized and extended states. These competing effects are examined as they manifest themselves in the intermediate-valence, photoemission, inverse-photoemission, and thermodynamic properties

Analytic solutions of QCD motivated Hamiltonians at low energy

International Nuclear Information System (INIS)

Yepez, T.; Amor, A.; Hess, P.O.; Szczepaniak, A.; Civitarese, O.

2011-01-01

A model Hamiltonian, motivated by QCD, is investigated in order to study only the quark sector, then only the gluon sector and finally both together. Restricting to the pure quark sector and setting the mass of the quarks to zero, we find analytic solutions, involving two to three orbitals. Allowing the mass of the quarks to be different to zero, we find semi-analytic solutions involving an arbitrary number of orbitals. Afterwards, we indicate on how to incorporate gluons. (author)

Hamilton-Jacobi theorems for regular reducible Hamiltonian systems on a cotangent bundle

Science.gov (United States)

Wang, Hong

2017-09-01

In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system and regular reduced Hamiltonian systems are given. At first, an important lemma is proved, and it is a modification for the corresponding result of Abraham and Marsden (1978), such that we can prove two types of geometric Hamilton-Jacobi theorem for a Hamiltonian system on the cotangent bundle of a configuration manifold, by using the symplectic form and dynamical vector field. Then these results are generalized to the regular reducible Hamiltonian system with symmetry and momentum map, by using the reduced symplectic form and the reduced dynamical vector field. The Hamilton-Jacobi theorems are proved and two types of Hamilton-Jacobi equations, for the regular point reduced Hamiltonian system and the regular orbit reduced Hamiltonian system, are obtained. As an application of the theoretical results, the regular point reducible Hamiltonian system on a Lie group is considered, and two types of Lie-Poisson Hamilton-Jacobi equation for the regular point reduced system are given. In particular, the Type I and Type II of Lie-Poisson Hamilton-Jacobi equations for the regular point reduced rigid body and heavy top systems are shown, respectively.

Molecular Orbital Principles of Oxygen-Redox Battery Electrodes.

Science.gov (United States)

Okubo, Masashi; Yamada, Atsuo

2017-10-25

Lithium-ion batteries are key energy-storage devices for a sustainable society. The most widely used positive electrode materials are LiMO 2 (M: transition metal), in which a redox reaction of M occurs in association with Li + (de)intercalation. Recent developments of Li-excess transition-metal oxides, which deliver a large capacity of more than 200 mAh/g using an extra redox reaction of oxygen, introduce new possibilities for designing higher energy density lithium-ion batteries. For better engineering using this fascinating new chemistry, it is necessary to achieve a full understanding of the reaction mechanism by gaining knowledge on the chemical state of oxygen. In this review, a summary of the recent advances in oxygen-redox battery electrodes is provided, followed by a systematic demonstration of the overall electronic structures based on molecular orbitals with a focus on the local coordination environment around oxygen. We show that a π-type molecular orbital plays an important role in stabilizing the oxidized oxygen that emerges upon the charging process. Molecular orbital principles are convenient for an atomic-level understanding of how reversible oxygen-redox reactions occur in bulk, providing a solid foundation toward improved oxygen-redox positive electrode materials for high energy-density batteries.

Orbitals, correlation, valencies in high-Tc superconductors

International Nuclear Information System (INIS)

Khomskii, D.I.

1990-09-01

The survey is given of certain properties of high-Tc superconductors connected with the details of their electronic structure such as the kind of orbitals involved and the degree of correlation. Special attention is paid to the properties of cuprates at high doping level. The problem whether there exists a ''Mott transition'' at high electron or a hole concentration is discussed. We also discuss physical factors (d-p Coulomb interaction, orbital mixing) leading to the partial occupation of copper d x 2 -orbital. In particular we show that in localized picture (x 2 -y 2 ) and z 2 -levels in La 2-x Sr x CuO 4 may cross at x approx. 0.4 which may be responsible for a marked change of many properties at this doping. The possible role of x 2 -electrons in pairing is discussed in connection with some recent experiments. (author). 28 refs, 6 figs, 1 tab

Manipulating localized molecular orbitals by single-atom contacts.

Science.gov (United States)

Wang, Weihua; Shi, Xingqiang; Lin, Chensheng; Zhang, Rui Qin; Minot, Christian; Van Hove, Michel A; Hong, Yuning; Tang, Ben Zhong; Lin, Nian

2010-09-17

We have fabricated atom-molecule contacts by attachment of single Cu atoms to terpyridine side groups of bis-terpyridine tetra-phenyl ethylene molecules on a Cu(111) surface. By means of scanning tunneling microscopy, spectroscopy, and density functional calculations, we have found that, due to the localization characteristics of molecular orbitals, the Cu-atom contact modifies the state localized at the terpyridine side group which is in contact with the Cu atom but does not affect the states localized at other parts of the molecule. These results illustrate the contact effects at individual orbitals and offer possibilities to manipulate orbital alignments within molecules.

On the physical interpretation of the nuclear molecular orbital energy.

Science.gov (United States)

Charry, Jorge; Pedraza-González, Laura; Reyes, Andrés

2017-06-07

Recently, several groups have extended and implemented molecular orbital (MO) schemes to simultaneously obtain wave functions for electrons and selected nuclei. Many of these schemes employ an extended Hartree-Fock approach as a first step to find approximate electron-nuclear wave functions and energies. Numerous studies conducted with these extended MO methodologies have explored various effects of quantum nuclei on physical and chemical properties. However, to the best of our knowledge no physical interpretation has been assigned to the nuclear molecular orbital energy (NMOE) resulting after solving extended Hartree-Fock equations. This study confirms that the NMOE is directly related to the molecular electrostatic potential at the position of the nucleus.

Valence-to-core-detected X-ray absorption spectroscopy

DEFF Research Database (Denmark)

Hall, Eleanor R.; Pollock, Christopher J.; Bendix, Jesper

2014-01-01

X-ray absorption spectroscopy (XAS) can provide detailed insight into the electronic and geometric structures of transition-metal active sites in metalloproteins and chemical catalysts. However, standard XAS spectra inherently represent an average contribution from the entire coordination...... environment with limited ligand selectivity. To address this limitation, we have investigated the enhancement of XAS features using valence-to-core (VtC)-detected XAS, whereby XAS spectra are measured by monitoring fluorescence from valence-to-core X-ray emission (VtC XES) events. VtC emission corresponds...... to transitions from filled ligand orbitals to the metal 1s core hole, with distinct energetic shifts for ligands of differing ionization potentials. VtC-detected XAS data were obtained from multiple valence emission features for a series of well-characterized Mn model compounds; taken together, these data...

Quantum electrodynamic corrections for the valence shell in heavy many-electron atoms

International Nuclear Information System (INIS)

Thierfelder, C.; Schwerdtfeger, P.

2010-01-01

We present quantum electrodynamic (QED) calculations within the picture of bound-state QED for the frequency-dependent Breit interaction between electrons, the vacuum polarization, and the electron self-energy correction starting from the Dirac-Coulomb Hamiltonian for the ionization potentials of the group 1, 2, 11, 12, 13, and 18 elements of the periodic table, and down to the superheavy elements up to nuclear charge Z=120. The results for the s-block elements are in very good agreement with earlier studies by Labzowsky et al. [Phys. Rev. A 59, 2707 (1999)]. We discuss the influence of the variational versus perturbative treatment of the Breit interaction for valence-space ionization potentials. We argue that the lowest-order QED contributions become as important as the Breit interaction for ionization potentials out of the valence s shell.

Multi-reference approach to the calculation of photoelectron spectra including spin-orbit coupling

Energy Technology Data Exchange (ETDEWEB)

Grell, Gilbert; Bokarev, Sergey I., E-mail: sergey.bokarev@uni-rostock.de; Kühn, Oliver [Institut für Physik, Universität Rostock, D-18051 Rostock (Germany); Winter, Bernd; Seidel, Robert [Helmholtz-Zentrum Berlin für Materialien und Energie, Methods for Material Development, Albert-Einstein-Strasse 15, D-12489 Berlin (Germany); Aziz, Emad F. [Helmholtz-Zentrum Berlin für Materialien und Energie, Methods for Material Development, Albert-Einstein-Strasse 15, D-12489 Berlin (Germany); Department of Physics, Freie Universität Berlin, Arnimalle 14, D-14159 Berlin (Germany); Aziz, Saadullah G. [Chemistry Department, Faculty of Science, King Abdulaziz University, 21589 Jeddah (Saudi Arabia)

2015-08-21

X-ray photoelectron spectra provide a wealth of information on the electronic structure. The extraction of molecular details requires adequate theoretical methods, which in case of transition metal complexes has to account for effects due to the multi-configurational and spin-mixed nature of the many-electron wave function. Here, the restricted active space self-consistent field method including spin-orbit coupling is used to cope with this challenge and to calculate valence- and core-level photoelectron spectra. The intensities are estimated within the frameworks of the Dyson orbital formalism and the sudden approximation. Thereby, we utilize an efficient computational algorithm that is based on a biorthonormal basis transformation. The approach is applied to the valence photoionization of the gas phase water molecule and to the core ionization spectrum of the [Fe(H{sub 2}O){sub 6}]{sup 2+} complex. The results show good agreement with the experimental data obtained in this work, whereas the sudden approximation demonstrates distinct deviations from experiments.

Molecular integrals for slater type orbitals using coulomb sturmians

DEFF Research Database (Denmark)

Avery, James Emil; Avery, John Scales

2014-01-01

The use of Slater type orbitals in molecular calculations is hindered by the slowness of integral evaluation. In the present paper, we introduce a method for overcoming this problem by expanding STO's in terms of Coulomb Sturmians, for which the problem of evaluating molecular integrals rapidly has...

QED effects on individual atomic orbital energies

Science.gov (United States)

Kozioł, Karol; Aucar, Gustavo A.

2018-04-01

Several issues, concerning QED corrections, that are important in precise atomic calculations are presented. The leading QED corrections, self-energy and vacuum polarization, to the orbital energy for selected atoms with 30 ≤ Z ≤ 118 have been calculated. The sum of QED and Breit contributions to the orbital energy is analyzed. It has been found that for ns subshells the Breit and QED contributions are of comparative size, but for np and nd subshells the Breit contribution takes a major part of the QED+Breit sum. It has also, been found that the Breit to leading QED contributions ratio for ns subshells is almost independent of Z. The Z-dependence of QED and Breit+QED contributions per subshell is shown. The fitting coefficients may be used to estimate QED effects on inner molecular orbitals. We present results of our calculations for QED contributions to orbital energy of valence ns-subshell for group 1 and 11 atoms and discuss about the reliability of these numbers by comparing them with experimental first ionization potential data.

On the effects of the two-body non-fine-structure operators of the Breit-Pauli Hamiltonian

International Nuclear Information System (INIS)

Badnell, N.R.

1997-01-01

We have incorporated the two-body non-fine-structure operators of the Breit-Pauli Hamiltonian, namely contact spin-spin, two-body Darwin and orbit-orbit, into the program AUTOSTRUCTURE. Illustrative results are presented, including some for reactions involving the process of autoionization. (author)

Anisotropic optical absorption induced by Rashba spin-orbit coupling in monolayer phosphorene

Science.gov (United States)

Li, Yuan; Li, Xin; Wan, Qi; Bai, R.; Wen, Z. C.

2018-04-01

We obtain the effective Hamiltonian of the phosphorene including the effect of Rashba spin-orbit coupling in the frame work of the low-energy theory. The spin-splitting energy bands show an anisotropy feature for the wave vectors along kx and ky directions, where kx orients to ΓX direction in the k space. We numerically study the optical absorption of the electrons for different wave vectors with Rashba spin-orbit coupling. We find that the spin-flip transition from the valence band to the conduction band induced by the circular polarized light closes to zero with increasing the x-component wave vector when ky equals to zero, while it can be significantly increased to a large value when ky gets a small value. When the wave vector varies along the ky direction, the spin-flip transition can also increase to a large value, however, which shows an anisotropy feature for the optical absorption. Especially, the spin-conserved transitions keep unchanged and have similar varying trends for different wave vectors. This phenomenon provides a novel route for the manipulation of the spin-dependent property of the fermions in the monolayer phosphorene.

Deep impurity levels in n-type copper oxides

International Nuclear Information System (INIS)

Ovchinnikov, S.G.

1994-01-01

The density of Nd 2-x Ce x CuO 4 monoparticle states was calculated by the method of precise diagonalization of multielectron hamiltonian of 6-zone model for CuO cluster. Emergence of a deep impurity state of a symmetry in the middle of dielectric slit, which is a mixture of d z 2-states of copper and a 1 -molecular orbital of oxygen, is shown. Fluctuation of parameters of p-d jump and energies of charge transfer provide additional fine impurity levels near the bottom of conductivity zone and ceiling of valency zone. 30 refs., 4 figs

Valence and inner-valence shell dissociative photoionization of CO in the 26-33 eV range. II. Molecular-frame and recoil-frame photoelectron angular distributions

DEFF Research Database (Denmark)

Lebech, M.; Houver, J.C.; Raseev, G.

2012-01-01

Experimental and theoretical results for molecular-frame photoemission are presented for inner-valence shell photoionization of the CO molecule induced by linearly and circularly polarized light. The experimental recoil frame photoelectron angular distributions (RFPADs) obtained from dissociative...... photoionization measurements where the velocities of the ionic fragment and photoelectron were detected in coincidence, are compared to RFPADs computed using the multichannel Schwinger configuration interaction method. The formalism for including a finite lifetime of the predissociative ion state is presented...... for the case of general elliptically polarized light, to obtain the RFPAD rather than the molecular frame photoelectron angular distribution (MFPAD), which would be obtained with the assumption of instantaneous dissociation. We have considered photoionization of CO for the photon energies of 26.0 eV, 29.5 e...

Assessing the Bonding Properties of Individual Molecular Orbitals

OpenAIRE

Robinson, PJ; Alexandrova, AN

2015-01-01

© 2015 American Chemical Society. Molecular orbitals (MOs), while one of the most widely used representations of the electronic structure of a system, are often too complex to intuit properties. Aside from the simplest of cases, it is not necessarily possible to visually tell which orbitals are bonding or antibonding along particular directions, especially in cases of highly delocalized and nontrivial bonding like metal clusters or solids. We propose a method for easily assessing and comparin...

Computing magnetic anisotropy constants of single molecule magnets

Indian Academy of Sciences (India)

We present here a theoretical approach to compute the molecular magnetic anisotropy parameters, and for single molecule magnets in any given spin eigenstate of exchange spin Hamiltonian. We first describe a hybrid constant -valence bond (VB) technique of solving spin Hamiltonians employing full spatial ...

BEC-BCS crossover in a (p+ip)-wave pairing Hamiltonian coupled to bosonic molecular pairs

International Nuclear Information System (INIS)

Dunning, Clare; Isaac, Phillip S.; Links, Jon; Zhao, Shao-You

2011-01-01

We analyse a (p+ip)-wave pairing BCS Hamiltonian, coupled to a single bosonic degree of freedom representing a molecular condensate, and investigate the nature of the BEC-BCS crossover for this system. For a suitable restriction on the coupling parameters, we show that the model is integrable and we derive the exact solution by the algebraic Bethe ansatz. In this manner we also obtain explicit formulae for correlation functions and compute these for several cases. We find that the crossover between the BEC state and the strong pairing p+ip phase is smooth for this model, with no intermediate quantum phase transition.

Molecular orbital (SCF-Xα-SW) theory of metal-metal charge transfer processes in minerals - II. Application to Fe2+ --> Ti4+ charge transfer transitions in oxides and silicates

Science.gov (United States)

Sherman, David M.

1987-01-01

A molecular orbital description, based on Xα-Scattered wave calculations on a (FeTiO10)14− cluster, is given for Fe2+ → Ti4+ charge transfer transitions in minerals. The calculated energy for the lowest Fe2+ → Ti4+ metal-metal charge transfer transition is 18040 cm−1 in reasonable agreement with energies observed in the optical spectra of Fe-Ti oxides and silicates. As in the case of Fe2+ → Fe3+ charge transfer in mixed-valence iron oxides and silicates, Fe2+ → Ti4+ charge transfer is associated with Fe-Ti bonding across shared polyhedral edges. Such bonding results from the overlap of the Fe(t 2g ) and Ti(t 2g ) 3d orbitals.

Theoretical study of molecular vibrations in electron momentum spectroscopy experiments on furan: An analytical versus a molecular dynamical approach

International Nuclear Information System (INIS)

Morini, Filippo; Deleuze, Michael S.; Watanabe, Noboru; Takahashi, Masahiko

2015-01-01

The influence of thermally induced nuclear dynamics (molecular vibrations) in the initial electronic ground state on the valence orbital momentum profiles of furan has been theoretically investigated using two different approaches. The first of these approaches employs the principles of Born-Oppenheimer molecular dynamics, whereas the so-called harmonic analytical quantum mechanical approach resorts to an analytical decomposition of contributions arising from quantized harmonic vibrational eigenstates. In spite of their intrinsic differences, the two approaches enable consistent insights into the electron momentum distributions inferred from new measurements employing electron momentum spectroscopy and an electron impact energy of 1.2 keV. Both approaches point out in particular an appreciable influence of a few specific molecular vibrations of A 1 symmetry on the 9a 1 momentum profile, which can be unravelled from considerations on the symmetry characteristics of orbitals and their energy spacing

Modeling Optical Spectra of Large Organic Systems Using Real-Time Propagation of Semiempirical Effective Hamiltonians.

Science.gov (United States)

Ghosh, Soumen; Andersen, Amity; Gagliardi, Laura; Cramer, Christopher J; Govind, Niranjan

2017-09-12

We present an implementation of a time-dependent semiempirical method (INDO/S) in NWChem using real-time (RT) propagation to address, in principle, the entire spectrum of valence electronic excitations. Adopting this model, we study the UV/vis spectra of medium-sized systems such as P3B2 and f-coronene, and in addition much larger systems such as ubiquitin in the gas phase and the betanin chromophore in the presence of two explicit solvents (water and methanol). RT-INDO/S provides qualitatively and often quantitatively accurate results when compared with RT- TDDFT or experimental spectra. Even though we only consider the INDO/S Hamiltonian in this work, our implementation provides a framework for performing electron dynamics in large systems using semiempirical Hartree-Fock Hamiltonians in general.

A comprehensive analysis of molecule-intrinsic quasi-atomic, bonding, and correlating orbitals. I. Hartree-Fock wave functions

International Nuclear Information System (INIS)

West, Aaron C.; Schmidt, Michael W.; Gordon, Mark S.; Ruedenberg, Klaus

2013-01-01

Through a basis-set-independent web of localizing orbital-transformations, the electronic wave function of a molecule is expressed in terms of a set of orbitals that reveal the atomic structure and the bonding pattern of a molecule. The analysis is based on resolving the valence orbital space in terms of an internal space, which has minimal basis set dimensions, and an external space. In the internal space, oriented quasi-atomic orbitals and split-localized molecular orbitals are determined by new, fast localization methods. The density matrix between the oriented quasi-atomic orbitals as well as the locations of the split-localized orbitals exhibit atomic populations and inter-atomic bonding patterns. A correlation-adapted quasi-atomic basis is determined in the external orbital space. The general formulations are specified in detail for Hartree-Fock wave functions. Applications to specific molecules exemplify the general scheme

Action-minimizing methods in Hamiltonian dynamics

CERN Document Server

Sorrentino, Alfonso

2015-01-01

John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical mechanics. His novel approach-known as Aubry-Mather theory-singles out the existence of special orbits and invariant measures of the system, which possess a very rich dynamical and geometric structure. In particular, the associated invariant sets play a leading role in determining the global dynamics of the system. This book provides a comprehensive introduction to Mather's theory, and can serve as a

Ground state and elementary excitations of a model valence-fluctuation system

International Nuclear Information System (INIS)

Brandow, B.H.

1979-01-01

The nature of the valence fluctuation problem is described, and motivations are given for an Anderson-lattice model Hamiltonian. A simple trial wave function is posed for the ground state, and the variational problem is solved. This demonstrates clearly that there is no Kondo-like divergence; the present concentrated Kondo problem is thus more simple mathematically than the sngle-impurity problem. Elementary excitations are studies by the Green's function techniques of Zubarev and Hubbard. Quenching of local moments and a large specific heat are found at low temperatures. The quasi-particle spectrum exhibits a gap, but epsilon/sub F/ does not lie in this gap. The insulation-like feature of SmB 6 , SmS, and TmSe at very low temperatures is explained in terms of a strongly reduced mobility for states near the gap, and reasons are given why this feature is not observed in other valence-fluctuation compounds. 73 references

Valence band structure of binary chalcogenide vitreous semiconductors by high-resolution XPS

International Nuclear Information System (INIS)

Kozyukhin, S.; Golovchak, R.; Kovalskiy, A.; Shpotyuk, O.; Jain, H.

2011-01-01

High-resolution X-ray photoelectron spectroscopy (XPS) is used to study regularities in the formation of valence band electronic structure in binary As x Se 100−x , As x S 100−x , Ge x Se 100−x and Ge x S 100−x chalcogenide vitreous semiconductors. It is shown that the highest occupied energetic states in the valence band of these materials are formed by lone pair electrons of chalcogen atoms, which play dominant role in the formation of valence band electronic structure of chalcogen-rich glasses. A well-expressed contribution from chalcogen bonding p electrons and more deep s orbitals are also recorded in the experimental valence band XPS spectra. Compositional dependences of the observed bands are qualitatively analyzed from structural and compositional points of view.

Valence band structure of binary chalcogenide vitreous semiconductors by high-resolution XPS

Energy Technology Data Exchange (ETDEWEB)

Kozyukhin, S., E-mail: sergkoz@igic.ras.ru [Russian Academy of Science, Institute of General and Inorganic Chemistry (Russian Federation); Golovchak, R. [Lviv Scientific Research Institute of Materials of SRC ' Carat' (Ukraine); Kovalskiy, A. [Lehigh University, Department of Materials Science and Engineering (United States); Shpotyuk, O. [Lviv Scientific Research Institute of Materials of SRC ' Carat' (Ukraine); Jain, H. [Lehigh University, Department of Materials Science and Engineering (United States)

2011-04-15

High-resolution X-ray photoelectron spectroscopy (XPS) is used to study regularities in the formation of valence band electronic structure in binary As{sub x}Se{sub 100-x}, As{sub x}S{sub 100-x}, Ge{sub x}Se{sub 100-x} and Ge{sub x}S{sub 100-x} chalcogenide vitreous semiconductors. It is shown that the highest occupied energetic states in the valence band of these materials are formed by lone pair electrons of chalcogen atoms, which play dominant role in the formation of valence band electronic structure of chalcogen-rich glasses. A well-expressed contribution from chalcogen bonding p electrons and more deep s orbitals are also recorded in the experimental valence band XPS spectra. Compositional dependences of the observed bands are qualitatively analyzed from structural and compositional points of view.

Effect of Molecular Guest Binding on the d-d Transitions of Ni2+ of CPO-27-Ni: A Combined UV-Vis, Resonant-Valence-to-Core X-ray Emission Spectroscopy, and Theoretical Study.

Science.gov (United States)

Gallo, Erik; Gorelov, Evgeny; Guda, Alexander A; Bugaev, Aram L; Bonino, Francesca; Borfecchia, Elisa; Ricchiardi, Gabriele; Gianolio, Diego; Chavan, Sachin; Lamberti, Carlo

2017-12-04

We used Ni K-edge resonant-valence-to-core X-ray emission spectroscopy (RVtC-XES, also referred to as direct RIXS), an element-selective bulk-sensitive synchrotron-based technique, to investigate the electronic structure of the CPO-27-Ni metal-organic framework (MOF) upon molecular adsorption of significant molecular probes: H 2 O, CO, H 2 S, and NO. We compare RVtC-XES with UV-vis spectroscopy, and we show that the element selectivity of RVtC-XES is of strategic significance to observe the full set of d-d excitations in Ni 2+ , which are partially overshadowed by the low-energy π-π* transitions of the Ni ligands in standard diffuse-reflectance UV-vis experiments. Our combined RVtC-XES/UV-vis approach provides access to the whole set of d-d excitations, allowing us a complete discussion of the changes undergone by the electronic configuration of the Ni 2+ sites hosted within the MOF upon molecular adsorption. The experimental data have been interpreted by multiplet ligand-field theory calculations based on Wannier orbitals. This study represents a step further in understanding the ability of the CPO-27-Ni MOFs in molecular sorption and separation applications.

Valence configurations in 214Rn

International Nuclear Information System (INIS)

Dracoulis, G.D.; Byrne, A.P.; Stuchbery, A.E.; Bark, R.A.; Poletti, A.R.

1987-01-01

Excited states of 214 Rn, up to spins of ≅ 24 ℎ have been studied using γ-ray and electron spectroscopy following the 208 Pb( 9 Be,3n) 214 Rn reaction. The level scheme (which differs substantially from earlier work) is compared with the results of a semi-empirical shell model calculation. The availability of high-spin orbitals for the four valence protons and two valence neutrons, and the effect of the attractive proton-neutron interaction, leads to the prediction of high-spin states at an unusually low excitation energy. Experimentally, the high level density leads to difficulties in the level scheme assignments at high spin. Nevertheless, configuration assignments, supported by transition strengths deduced from the measured lifetimes (in the nanosecond region) are suggested for the main yrast states. The decay properties also suggest that configuration mixing is important. The possibility of a gradual transition to octupole deformation, implied by the decay properties of the 11 - and 10 + yrast states is also discussed. (orig.)

Micro-Valences: Affective valence in neutral everyday objects

Directory of Open Access Journals (Sweden)

Sophie eLebrecht

2012-04-01

Full Text Available Affective valence influences both our cognition and our perception of the world. Indeed, the speed and quality with which we recognize objects in a visual scene can vary dramatically depending on its affective content. However, affective processing of visual objects has been typically studied using only stimuli with strong affective valences (e.g., guns or roses. Here we explore whether affective valence must be strong or obvious to exert an effect on our perception. We conclude that the majority of objects carry some affective valence (micro-valences and, thus, nominally neutral objects are not really neutral. Functionally, the perception of valence in everyday objects facilitates perceptually-driven choice behavior, decision-making, and affective responses.

Time-resolved imaging of purely valence-electron dynamics during a chemical reaction

DEFF Research Database (Denmark)

Hockett, Paul; Bisgaard, Christer Z.; Clarkin, Owen J.

2011-01-01

Chemical reactions are manifestations of the dynamics of molecular valence electrons and their couplings to atomic motions. Emerging methods in attosecond science can probe purely electronic dynamics in atomic and molecular systems(1-6). By contrast, time-resolved structural-dynamics methods...... such as electron(7-10) or X-ray diffraction(11) and X-ray absorption(12) yield complementary information about the atomic motions. Time-resolved methods that are directly sensitive to both valence-electron dynamics and atomic motions include photoelectron spectroscopy(13-15) and high-harmonic generation(16......,17): in both cases, this sensitivity derives from the ionization-matrix element(18,19). Here we demonstrate a time-resolved molecular-frame photoelectron-angular-distribution (TRMFPAD) method for imaging the purely valence-electron dynamics during a chemical reaction. Specifically, the TRMFPADs measured during...

Equation of state of dense plasmas: Orbital-free molecular dynamics as the limit of quantum molecular dynamics for high-Z elements

Energy Technology Data Exchange (ETDEWEB)

Danel, J.-F.; Blottiau, P.; Kazandjian, L.; Piron, R.; Torrent, M. [CEA, DAM, DIF, 91297 Arpajon (France)

2014-10-15

The applicability of quantum molecular dynamics to the calculation of the equation of state of a dense plasma is limited at high temperature by computational cost. Orbital-free molecular dynamics, based on a semiclassical approximation and possibly on a gradient correction, is a simulation method available at high temperature. For a high-Z element such as lutetium, we examine how orbital-free molecular dynamics applied to the equation of state of a dense plasma can be regarded as the limit of quantum molecular dynamics at high temperature. For the normal mass density and twice the normal mass density, we show that the pressures calculated with the quantum approach converge monotonically towards those calculated with the orbital-free approach; we observe a faster convergence when the orbital-free approach includes the gradient correction. We propose a method to obtain an equation of state reproducing quantum molecular dynamics results up to high temperatures where this approach cannot be directly implemented. With the results already obtained for low-Z plasmas, the present study opens the way for reproducing the quantum molecular dynamics pressure for all elements up to high temperatures.

Spectral properties of minimal-basis-set orbitals: Implications for molecular electronic continuum states

Science.gov (United States)

Langhoff, P. W.; Winstead, C. L.

Early studies of the electronically excited states of molecules by John A. Pople and coworkers employing ab initio single-excitation configuration interaction (SECI) calculations helped to simulate related applications of these methods to the partial-channel photoionization cross sections of polyatomic molecules. The Gaussian representations of molecular orbitals adopted by Pople and coworkers can describe SECI continuum states when sufficiently large basis sets are employed. Minimal-basis virtual Fock orbitals stabilized in the continuous portions of such SECI spectra are generally associated with strong photoionization resonances. The spectral attributes of these resonance orbitals are illustrated here by revisiting previously reported experimental and theoretical studies of molecular formaldehyde (H2CO) in combination with recently calculated continuum orbital amplitudes.

Inclusion of orbital relaxation and correlation through the unitary group adapted open shell coupled cluster theory using non-relativistic and scalar relativistic Hamiltonians to study the core ionization potential of molecules containing light to medium-heavy elements

Science.gov (United States)

Sen, Sangita; Shee, Avijit; Mukherjee, Debashis

2018-02-01

The orbital relaxation attendant on ionization is particularly important for the core electron ionization potential (core IP) of molecules. The Unitary Group Adapted State Universal Coupled Cluster (UGA-SUMRCC) theory, recently formulated and implemented by Sen et al. [J. Chem. Phys. 137, 074104 (2012)], is very effective in capturing orbital relaxation accompanying ionization or excitation of both the core and the valence electrons [S. Sen et al., Mol. Phys. 111, 2625 (2013); A. Shee et al., J. Chem. Theory Comput. 9, 2573 (2013)] while preserving the spin-symmetry of the target states and using the neutral closed-shell spatial orbitals of the ground state. Our Ansatz invokes a normal-ordered exponential representation of spin-free cluster-operators. The orbital relaxation induced by a specific set of cluster operators in our Ansatz is good enough to eliminate the need for different sets of orbitals for the ground and the core-ionized states. We call the single configuration state function (CSF) limit of this theory the Unitary Group Adapted Open-Shell Coupled Cluster (UGA-OSCC) theory. The aim of this paper is to comprehensively explore the efficacy of our Ansatz to describe orbital relaxation, using both theoretical analysis and numerical performance. Whenever warranted, we also make appropriate comparisons with other coupled-cluster theories. A physically motivated truncation of the chains of spin-free T-operators is also made possible by the normal-ordering, and the operational resemblance to single reference coupled-cluster theory allows easy implementation. Our test case is the prediction of the 1s core IP of molecules containing a single light- to medium-heavy nucleus and thus, in addition to demonstrating the orbital relaxation, we have addressed the scalar relativistic effects on the accuracy of the IPs by using a hierarchy of spin-free Hamiltonians in conjunction with our theory. Additionally, the contribution of the spin-free component of the two

Inclusion of orbital relaxation and correlation through the unitary group adapted open shell coupled cluster theory using non-relativistic and scalar relativistic Hamiltonians to study the core ionization potential of molecules containing light to medium-heavy elements.

Science.gov (United States)

Sen, Sangita; Shee, Avijit; Mukherjee, Debashis

2018-02-07

The orbital relaxation attendant on ionization is particularly important for the core electron ionization potential (core IP) of molecules. The Unitary Group Adapted State Universal Coupled Cluster (UGA-SUMRCC) theory, recently formulated and implemented by Sen et al. [J. Chem. Phys. 137, 074104 (2012)], is very effective in capturing orbital relaxation accompanying ionization or excitation of both the core and the valence electrons [S. Sen et al., Mol. Phys. 111, 2625 (2013); A. Shee et al., J. Chem. Theory Comput. 9, 2573 (2013)] while preserving the spin-symmetry of the target states and using the neutral closed-shell spatial orbitals of the ground state. Our Ansatz invokes a normal-ordered exponential representation of spin-free cluster-operators. The orbital relaxation induced by a specific set of cluster operators in our Ansatz is good enough to eliminate the need for different sets of orbitals for the ground and the core-ionized states. We call the single configuration state function (CSF) limit of this theory the Unitary Group Adapted Open-Shell Coupled Cluster (UGA-OSCC) theory. The aim of this paper is to comprehensively explore the efficacy of our Ansatz to describe orbital relaxation, using both theoretical analysis and numerical performance. Whenever warranted, we also make appropriate comparisons with other coupled-cluster theories. A physically motivated truncation of the chains of spin-free T-operators is also made possible by the normal-ordering, and the operational resemblance to single reference coupled-cluster theory allows easy implementation. Our test case is the prediction of the 1s core IP of molecules containing a single light- to medium-heavy nucleus and thus, in addition to demonstrating the orbital relaxation, we have addressed the scalar relativistic effects on the accuracy of the IPs by using a hierarchy of spin-free Hamiltonians in conjunction with our theory. Additionally, the contribution of the spin-free component of the two

Theoretical calculations of spin-Hamiltonian parameters for the rhombic-like Mo5+ centers in KTiOPO4 crystal

International Nuclear Information System (INIS)

Yang, Mei; Wen-Chen, Zheng; Hong-Gang, Liu

2013-01-01

The spin-Hamiltonian parameters (g factors g i and hyperfine structure constants A i , were i=x, y and z) for Mo 5+ ion occupying the Ti(1) site with approximately rhombic symmetry in KTiOPO 4 crystal are calculated from the high-order perturbation formulas based on the two-mechanism model. In the model, not only the contribution due to the conventional crystal-field (CF) mechanism, but also those due to the charge-transfer (CT) mechanism are included. The six calculated spin-Hamiltonian parameters with four adjustable parameters are in reasonable agreement with the experimental values. The calculations show that for more accurate calculations of spin-Hamiltonian parameters of the high valence d n ions (e.g., Mo 5+ considered here) in crystals, the contribution from CT mechanism, which is ignored in the conventional crystal field theory, should be taken into account. The reasonable crystal field energy levels of Mo 5+ in KTiOPO 4 are also predicted from calculations

Anderson Hamiltonian description of the experimental electronic structure and magnetic interactions of copper oxide superconductors

International Nuclear Information System (INIS)

Shen, Z.; Allen, J.W.; Yeh, J.J.

1987-01-01

We describe valence-band and core-level photoemission data for copper oxide superconductors using the Anderson Hamiltonian applied to an impurity-cluster configuration-interaction model. We obtain experimental values of the parameters of the model the copper X oxygen charge transfer energy Δ∼0.4 eV, the d-d Coulomb interaction U∼6 eV, and the ligand-d hybridization T∼2.4 eV. Using these parameters, we evaluate the linear Cu-O-Cu superexchange interaction J and find it is dominated by the charge-transfer fluctuations. The magnitude obtained for J is much larger than typical Neel temperatures of these materials, and is somewhat larger than that estimated from applying the resonating-valence-bond picture to La 2 CuO 4 . We point out that for Δ >Δ, the charge-transfer degrees of freedom, and the lattice aspects of the Anderson lattice Hamiltonian, should not be neglected in constructing models for the high-T/sub c/ superconductivity. We also emphasize our resonant-photoemission result that the very small density of states at or near the Fermi level in all these materials has a substantial contribution from Cu 3d states, suggesting their importance for the superconductivity. We report other details of the resonant-photoemission data involving La and Ba states in the materials containing these elements

Non-Fermi Liquid Behavior in the Single-Impurity Mixed Valence Problem

Science.gov (United States)

Zhang, Guang-Ming; Su, Zhao-Bin; Yu, Lu

An effective Hamiltonian of the Anderson single-impurity model with finite-range Coulomb interactions is derived near a particular limit, which is analogous to the Toulouse limit of the ordinary Kondo problem, and the physical properties around the mixed valence quantum critical point are calculated. At this quantum critical point, the local moment is only partially quenched and X-ray edge singularities are exhibited. Around this point, a new type of non-Fermi liquid behavior is predicted with an extra specific heat Cimp ~ T1/4 + AT ln T and spin-susceptibility χimp ~T-3/4 + B ln T.

Theoretical study of the electronic structure of different states of the KRb+ molecular ion

International Nuclear Information System (INIS)

Korek, M.; Younis, G.

2000-01-01

Full text.The molecular activities in ultra-cold alkali atom trapping stimulate theoretical developments to compute relevant adiabatic potential curves, especially in the framework of the pseudopotential methods. For these methods the molecular ion KRb+ is treated as system with one active electron moving in a field of two ionic cores, where core valence electron interactions are presented by an effective potential. Potential energies have been calculated over a wide range of internuclear distance (5.0-60a o ) for the lowest states of symmetry 2 Σ, 2 Π, 2 Δ and Ω for the molecular ion KRb+. To avoid an over estimation of the dissociation energy the perturbative treatment is replaced by an l-dependent core-polarization potential of the Foucrault et al. For the one valence electron of the two considered atoms, we recalculated the polarization potential cut-off parameters r k l , and r R b l by taking l=0,1,2 and r i 2 =r i 3 . Molecular orbital for the molecular ion KRb+ were derived from Self Consistent Field calculations (SCF), and full valence Configuration Interaction (IC) calculations were performed. Extensive tables of energy values versus internuclear distance are displayed and molecular spectroscopic constants have been derived, for the first time, for the bound states with regular shape

Molecular models of zinc phthalocyanines: semi-empirical molecular orbital computations and physicochemical properties studied by molecular mechanics simulations

International Nuclear Information System (INIS)

Gantchev, Tsvetan G.; van Lier, Johan E.; Hunting, Darel J.

2005-01-01

To build 3D-molecular models of Zinc-phthalocyanines (ZnPc) and to study their diverse chemical and photosensitization properties, we performed quantum mechanical molecular orbital (MO) semi-empirical (AM1) computations of the ground, excited singlet and triplet states as well as free radical (ionic) species. RHF and UHF (open shell) geometry optimizations led to near-perfect symmetrical ZnPc. Predicted ionization potentials (IP), electron affinities (EA) and lowest electronic transitions of ZnPc are in good agreement with the published experimental and theoretical data. The computation-derived D 4h /D 2h -symmetry 3D-structures of ground and excited states and free radicals of ZnPc, together with the frontier orbital energies and Mulliken electron population analysis enabled us to build robust molecular models. These models were used to predict important chemical-reactivity entities such as global electronegativity (χ), hardness (η) and local softness based on Fukui-functions analysis. Examples of molecular mechanics (MM) applications of the 3D-molecular models are presented as approaches to evaluate solvation free energy (ΔG 0 ) solv and to estimate ground- and excited- state oxidation/reduction potentials as well as intermolecular interactions and stability of ground and excited state dimers (exciplexes) and radical ion-pairs

Vortices in spin-orbit-coupled Bose-Einstein condensates

International Nuclear Information System (INIS)

Radic, J.; Sedrakyan, T. A.; Galitski, V.; Spielman, I. B.

2011-01-01

Realistic methods to create vortices in spin-orbit-coupled Bose-Einstein condensates are discussed. It is shown that, contrary to common intuition, rotation of the trap containing a spin-orbit condensate does not lead to an equilibrium state with static vortex structures but gives rise instead to nonequilibrium behavior described by an intrinsically time-dependent Hamiltonian. We propose here the following alternative methods to induce thermodynamically stable static vortex configurations: (i) to rotate both the lasers and the anisotropic trap and (ii) to impose a synthetic Abelian field on top of synthetic spin-orbit interactions. Effective Hamiltonians for spin-orbit condensates under such perturbations are derived for most currently known realistic laser schemes that induce synthetic spin-orbit couplings. The Gross-Pitaevskii equation is solved for several experimentally relevant regimes. The new interesting effects include spatial separation of left- and right-moving spin-orbit condensates, the appearance of unusual vortex arrangements, and parity effects in vortex nucleation where the topological excitations are predicted to appear in pairs. All these phenomena are shown to be highly nonuniversal and depend strongly on a specific laser scheme and system parameters.

Field theoretic approach to dynamical orbital localization in ab initio molecular dynamics

International Nuclear Information System (INIS)

Thomas, Jordan W.; Iftimie, Radu; Tuckerman, Mark E.

2004-01-01

Techniques from gauge-field theory are employed to derive an alternative formulation of the Car-Parrinello ab initio molecular-dynamics method that allows maximally localized Wannier orbitals to be generated dynamically as the calculation proceeds. In particular, the Car-Parrinello Lagrangian is mapped onto an SU(n) non-Abelian gauge-field theory and the fictitious kinetic energy in the Car-Parrinello Lagrangian is modified to yield a fully gauge-invariant form. The Dirac gauge-fixing method is then employed to derive a set of equations of motion that automatically maintain orbital locality by restricting the orbitals to remain in the 'Wannier gauge'. An approximate algorithm for integrating the equations of motion that is stable and maintains orbital locality is then developed based on the exact equations of motion. It is shown in a realistic application (64 water molecules plus one hydrogen-chloride molecule in a periodic box) that orbital locality can be maintained with only a modest increase in CPU time. The ability to keep orbitals localized in an ab initio molecular-dynamics calculation is a crucial ingredient in the development of emerging linear scaling approaches

Levels of valence

Directory of Open Access Journals (Sweden)

Vera eShuman

2013-05-01

Full Text Available The distinction between the positive and the negative is fundamental in our emotional life. In appraisal theories, in particular in the component process model of emotion (Scherer, 1984, 2010, qualitatively different types of valence are proposed based on appraisals of (unpleasantness, goal obstructiveness/conduciveness, low or high power, self- (incongruence, and moral badness/goodness. This multifaceted conceptualization of valence is highly compatible with the frequent observation of mixed feelings in real life. However, it seems to contradict the one-dimensional conceptualization of valence often encountered in psychological theories, and the notion of valence as a common currency used to explain choice behavior. Here, we propose a framework to integrate the seemingly disparate conceptualizations of multifaceted valence and one-dimensional valence by suggesting that valence should be conceived at different levels, micro and macro. Micro-valences correspond to qualitatively different types of evaluations, potentially resulting in mixed feelings, whereas one-dimensional macro-valence corresponds to an integrative common currency to compare alternatives for choices. We propose that conceptualizing levels of valence may focus research attention on the mechanisms that relate valence at one level (micro to valence at another level (macro, leading to new hypotheses and addressing various concerns that have been raised about the valence concept, such as the valence-emotion relation.

Redesign of the DFT/MRCI Hamiltonian

Energy Technology Data Exchange (ETDEWEB)

Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M., E-mail: Christel.Marian@hhu.de [Institute of Theoretical and Computational Chemistry, Heinrich-Heine-University Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf (Germany)

2016-01-21

The combined density functional theory and multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] is a well-established semi-empirical quantum chemical method for efficiently computing excited-state properties of organic molecules. As it turns out, the method fails to treat bi-chromophores owing to the strong dependence of the parameters on the excitation class. In this work, we present an alternative form of correcting the matrix elements of a MRCI Hamiltonian which is built from a Kohn-Sham set of orbitals. It is based on the idea of constructing individual energy shifts for each of the state functions of a configuration. The new parameterization is spin-invariant and incorporates less empirism compared to the original formulation. By utilizing damping techniques together with an algorithm of selecting important configurations for treating static electron correlation, the high computational efficiency has been preserved. The robustness of the original and redesigned Hamiltonians has been tested on experimentally known vertical excitation energies of organic molecules yielding similar statistics for the two parameterizations. Besides that, our new formulation is free from artificially low-lying doubly excited states, producing qualitatively correct and consistent results for excimers. The way of modifying matrix elements of the MRCI Hamiltonian presented here shall be considered as default choice when investigating photophysical processes of bi-chromophoric systems such as singlet fission or triplet-triplet upconversion.

Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity

Science.gov (United States)

Bridges, Thomas J.; Reich, Sebastian

2001-06-01

The symplectic numerical integration of finite-dimensional Hamiltonian systems is a well established subject and has led to a deeper understanding of existing methods as well as to the development of new very efficient and accurate schemes, e.g., for rigid body, constrained, and molecular dynamics. The numerical integration of infinite-dimensional Hamiltonian systems or Hamiltonian PDEs is much less explored. In this Letter, we suggest a new theoretical framework for generalizing symplectic numerical integrators for ODEs to Hamiltonian PDEs in R2: time plus one space dimension. The central idea is that symplecticity for Hamiltonian PDEs is directional: the symplectic structure of the PDE is decomposed into distinct components representing space and time independently. In this setting PDE integrators can be constructed by concatenating uni-directional ODE symplectic integrators. This suggests a natural definition of multi-symplectic integrator as a discretization that conserves a discrete version of the conservation of symplecticity for Hamiltonian PDEs. We show that this approach leads to a general framework for geometric numerical schemes for Hamiltonian PDEs, which have remarkable energy and momentum conservation properties. Generalizations, including development of higher-order methods, application to the Euler equations in fluid mechanics, application to perturbed systems, and extension to more than one space dimension are also discussed.

Levels of Valence

Science.gov (United States)

Shuman, Vera; Sander, David; Scherer, Klaus R.

2013-01-01

The distinction between the positive and the negative is fundamental in our emotional life. In appraisal theories, in particular in the component process model of emotion (Scherer, 1984, 2010), qualitatively different types of valence are proposed based on appraisals of (un)pleasantness, goal obstructiveness/conduciveness, low or high power, self-(in)congruence, and moral badness/goodness. This multifaceted conceptualization of valence is highly compatible with the frequent observation of mixed feelings in real life. However, it seems to contradict the one-dimensional conceptualization of valence often encountered in psychological theories, and the notion of valence as a common currency used to explain choice behavior. Here, we propose a framework to integrate the seemingly disparate conceptualizations of multifaceted valence and one-dimensional valence by suggesting that valence should be conceived at different levels, micro and macro. Micro-valences correspond to qualitatively different types of evaluations, potentially resulting in mixed feelings, whereas one-dimensional macro-valence corresponds to an integrative “common currency” to compare alternatives for choices. We propose that conceptualizing levels of valence may focus research attention on the mechanisms that relate valence at one level (micro) to valence at another level (macro), leading to new hypotheses, and addressing various concerns that have been raised about the valence concept, such as the valence-emotion relation. PMID:23717292

Bonding character and s-p hybridization of orbitals of hydride molecules according to photoelectron spectroscopy data

International Nuclear Information System (INIS)

Vovna, V.I.

1988-01-01

In consideration of the electron structure of the molecules in terms of canonical many-centered orbitals by s-p hybridization we mean mixture of the ns and np orbitals of an atom into one molecular orbital. The PE spectra of the valence levels of the molecules give direct information on the influence of s-p hybridization on the bonding character and energies of the levels [1, 3]. In this article we discuss the influence of hybridization on the bonding character of the MO of the isoelectronic series A 7 H - A 6 H 2 - A 5 H 2 - A 4 H 4 according to the results of PE spectroscopy. To simplify the discussion we adopt the approximation of Kupmans theorem IP i = -var epsilon i

Lying about the valence of affective pictures: an fMRI study.

Directory of Open Access Journals (Sweden)

Tatia M C Lee

Full Text Available The neural correlates of lying about affective information were studied using a functional magnetic resonance imaging (fMRI methodology. Specifically, 13 healthy right-handed Chinese men were instructed to lie about the valence, positive or negative, of pictures selected from the International Affective Picture System (IAPS while their brain activity was scanned by a 3T Philip Achieva scanner. The key finding is that the neural activity associated with deception is valence-related. Comparing to telling the truth, deception about the valence of the affectively positive pictures was associated with activity in the inferior frontal, cingulate, inferior parietal, precuneus, and middle temporal regions. Lying about the valence of the affectively negative pictures, on the other hand, was associated with activity in the orbital and medial frontal regions. While a clear valence-related effect on deception was observed, common neural regions were also recruited for the process of deception about the valence of the affective pictures. These regions included the lateral prefrontal and inferior parietal regions. Activity in these regions has been widely reported in fMRI studies on deception using affectively-neutral stimuli. The findings of this study reveal the effect of valence on the neural activity associated with deception. Furthermore, the data also help to illustrate the complexity of the neural mechanisms underlying deception.

Bond-Valence Constraints on Liquid Water Structure

International Nuclear Information System (INIS)

Bickmore, Barry R.; Rosso, Kevin M.; Brown, I. David; Kerisit, Sebastien N.

2009-01-01

The recent controversy about the structure of liquid water pits a new model involving water molecules in relatively stable rings-and-chains structures against the standard model that posits water molecules in distorted tetrahedral coordination. Molecular dynamics (MD) simulations 'both classical and ab initio' almost uniformly support the standard model, but since none of them can yet reproduce all the anomalous properties of water, they leave room for doubt. We argue that it is possible to evaluate these simulations by testing them against their adherence to the bond-valence model, a well known, and quantitatively accurate, empirical summary of the behavior of atoms in the bonded networks of inorganic solids. Here we use the results of ab initio molecular dynamics simulations of ice, water, and several solvated aqueous species to show that the valence sum rule (the first axiom of the bond-valence model,) is followed in both solid and liquid bond networks. We then test MD simulations of water, employing several popular potential models, against this criterion and the experimental O-O radial distribution function. It appears that most of those tested cannot satisfy both criteria well, except TIP4P and TIP5P. If the valence sum rule really can be applied to simulated liquid structures, then it follows that the bonding behaviors of atoms in liquids are in some ways identical to those in solids. We support this interpretation by showing that the simulations produce O-H-O geometries completely consistent with the range of geometries available in solids, and the distributions of instantaneous valence sums reaching the atoms in both the ice and liquid water simulations are essentially identical. Taken together, this is powerful evidence in favor of the standard distorted tetrahedral model of liquid water structure

Photo-electron spectroscopy study of energy levels in conjugated oligomers

NARCIS (Netherlands)

Veenstra, SC; Heeres, A; Stalmach, U; Wildeman, J; Hadziioannou, G; Sawatzky, GA; Jonkman, HT; Moss, SC

2002-01-01

We report on the valence orbital structure of poly(para-phenylenevinylene) (PPV)-like oligomers. We studied these molecules as isolated oligomers in the gas phase, as well as in thin films deposited on metal substrates. We use a simple model based on a previously reported Hamiltonian that accurately

Molecular orbital study of the chemisorption of carbon monoxide on a tungsten (100) surface

International Nuclear Information System (INIS)

Lee, T.H.; Rabalais, J.W.

1978-01-01

The adsorption energies of carbon monoxide chemisorbed at various sites on a tungsten (100) surface have been calculated by extended Hueckel molecular orbital theory (EHMO). The concept of a 'surface molecule' in which CO is bonded to an array of tungsten atoms Wsub(n) has been employed. Dissociative adsorption in which C occupies a four-fold, five-coordination site and O occupies either a four- or two-fold site has been found to be the most stable form for CO on a W surface. Stable one-fold and two-fold sites of molecularly adsorbed CO have also been found in which the CO group is normal to the surface plane and the C atom is nearest the surface. Adsorption energies and molecular orbitals for the stable molecularly and dissociatively adsorbed CO sites are compared with the experimental data on various types of adsorbed CO, i.e. virgin-, α-, and β-CO. Models are suggested for each of these adsorption types. The strongest bonding interactions occur between the CO 5sigma orbital and the totally symmetric 5d and 6s orbitals of the Wsub(n) cluster. Possible mechanisms for conversion of molecularly adsorbed CO to dissociatively adsorbed CO are proposed and the corresponding activation energies are estimated. (Auth.)

On the lunar node resonance of the orbital plane evolution of the Earth's satellite orbits

Science.gov (United States)

Zhu, Ting-Lei

2018-06-01

This paper aims to investigate the effects of lunar node resonance on the circular medium Earth orbits (MEO). The dynamical model is established in classical Hamiltonian systems with the application of Lie transform to remove the non-resonant terms. Resonant condition, stability and phase structures are studied. The lunar node resonance occurs when the secular changing rates of the orbital node (with respect to the equator) and the lunar node (with respect to the ecliptic) form a simple integer ratio. The resonant conditions are satisfied for both inclined and equatorial orbits. The orbital plane would have long period (with typical timescales of several centuries) fluctuation due to the resonance.

Adiabatic Hamiltonian deformation, linear response theory, and nonequilibrium molecular dynamics

International Nuclear Information System (INIS)

Hoover, W.G.

1980-01-01

Although Hamiltonians of various kinds have previously been used to derive Green-Kubo relations for the transport coefficients, the particular choice described is uniquely related to thermodynamics. This nonequilibrium Hamiltonian formulation of fluid flow provides pedagogically simple routes to nonequilibrium fluxes and distribution functions, to theoretical understanding of long-time effects, and to new numerical methods for simulating systems far from equilibrium. The same methods are now being applied to solid-phase problems. At the relatively high frequencies used in the viscous fluid calculations described, solids typically behave elastically. Lower frequencies lead to the formation of dislocations and other defects, making it possible to study plastic flow. A property of the nonequilibrium equations of motion which might be profitably explored is their effective irreversibility. Because only a few particles are necessary to generate irreversible behavior, simulations using adiabatic deformations of the kind described here could perhaps elucidate the instability in the equations of motion responsible for irreversibility

Bulk and interface quantum states of electrons in multi-layer heterostructures with topological materials

Science.gov (United States)

Nikolic, Aleksandar; Zhang, Kexin; Barnes, C. H. W.

2018-06-01

In this article we describe the bulk and interface quantum states of electrons in multi-layer heterostructures in one dimension, consisting of topological insulators (TIs) and topologically trivial materials. We use and extend an effective four-band continuum Hamiltonian by introducing position dependence to the eight material parameters of the Hamiltonian. We are able to demonstrate complete conduction-valence band mixing in the interface states. We find evidence for topological features of bulk states of multi-layer TI heterostructures, as well as demonstrating both complete and incomplete conduction-valence band inversion at different bulk state energies. We show that the linear k z terms in the low-energy Hamiltonian, arising from overlap of p z orbitals between different atomic layers in the case of chalcogenides, control the amount of tunneling from TIs to trivial insulators. Finally, we show that the same linear k z terms in the low-energy Hamiltonian affect the material’s ability to form the localised interface state, and we demonstrate that due to this effect the spin and probability density localisation in a thin film of Sb2Te3 is incomplete. We show that changing the parameter that controls the magnitude of the overlap of p z orbitals affects the transport characteristics of the topologically conducting states, with incomplete topological state localisation resulting in increased backscattering.

Spin-orbit-induced spin splittings in polar transition metal dichalcogenide monolayers

KAUST Repository

Cheng, Yingchun

2013-06-01

The Rashba effect in quasi two-dimensional materials, such as noble metal surfaces and semiconductor heterostructures, has been investigated extensively, while interest in real two-dimensional systems has just emerged with the discovery of graphene. We present ab initio electronic structure, phonon, and molecular-dynamics calculations to study the structural stability and spin-orbit-induced spin splitting in the transition metal dichalcogenide monolayers MXY (M = Mo, W and X, Y = S, Se, Te). In contrast to the non-polar systems with X = Y, in the polar systems with X ≠ Y the Rashba splitting at the Γ-point for the uppermost valence band is caused by the broken mirror symmetry. An enhancement of the splitting can be achieved by increasing the spin-orbit coupling and/or the potential gradient. © Copyright EPLA, 2013.

Contact Hamiltonian mechanics

Energy Technology Data Exchange (ETDEWEB)

Bravetti, Alessandro, E-mail: alessandro.bravetti@iimas.unam.mx [Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Cruz, Hans, E-mail: hans@ciencias.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Tapias, Diego, E-mail: diego.tapias@nucleares.unam.mx [Facultad de Ciencias, Universidad Nacional Autónoma de México, A.P. 70543, México, DF 04510 (Mexico)

2017-01-15

In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we review in detail the major features of standard symplectic Hamiltonian dynamics and show that all of them can be generalized to the contact case.

Periodic orbits and non-integrability of Henon-Heiles systems

International Nuclear Information System (INIS)

Llibre, Jaume; Jimenez-Lara, Lidia

2011-01-01

We apply the averaging theory of second order to study the periodic orbits for a generalized Henon-Heiles system with two parameters, which contains the classical Henon-Heiles system. Two main results are shown. The first result provides sufficient conditions on the two parameters of these generalized systems, which guarantee that at any positive energy level, the Hamiltonian system has periodic orbits. These periodic orbits form in the whole phase space a continuous family of periodic orbits parameterized by the energy. The second result shows that for the non-integrable Henon-Heiles systems in the sense of Liouville-Arnol'd, which have the periodic orbits analytically found with averaging theory, cannot exist any second first integral of class C 1 . In particular, for any second first integral of class C 1 , we prove that the classical Henon-Heiles system and many generalizations of it are not integrable in the sense of Liouville-Arnol'd. Moreover, the tools we use for studying the periodic orbits and the non-Liouville-Arnol'd integrability can be applied to Hamiltonian systems with an arbitrary number of degrees of freedom.

SparseMaps—A systematic infrastructure for reduced-scaling electronic structure methods. III. Linear-scaling multireference domain-based pair natural orbital N-electron valence perturbation theory

Energy Technology Data Exchange (ETDEWEB)

Guo, Yang; Sivalingam, Kantharuban; Neese, Frank, E-mail: Frank.Neese@cec.mpg.de [Max Planck Institut für Chemische Energiekonversion, Stiftstr. 34-36, D-45470 Mülheim an der Ruhr (Germany); Valeev, Edward F. [Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24014 (United States)

2016-03-07

Multi-reference (MR) electronic structure methods, such as MR configuration interaction or MR perturbation theory, can provide reliable energies and properties for many molecular phenomena like bond breaking, excited states, transition states or magnetic properties of transition metal complexes and clusters. However, owing to their inherent complexity, most MR methods are still too computationally expensive for large systems. Therefore the development of more computationally attractive MR approaches is necessary to enable routine application for large-scale chemical systems. Among the state-of-the-art MR methods, second-order N-electron valence state perturbation theory (NEVPT2) is an efficient, size-consistent, and intruder-state-free method. However, there are still two important bottlenecks in practical applications of NEVPT2 to large systems: (a) the high computational cost of NEVPT2 for large molecules, even with moderate active spaces and (b) the prohibitive cost for treating large active spaces. In this work, we address problem (a) by developing a linear scaling “partially contracted” NEVPT2 method. This development uses the idea of domain-based local pair natural orbitals (DLPNOs) to form a highly efficient algorithm. As shown previously in the framework of single-reference methods, the DLPNO concept leads to an enormous reduction in computational effort while at the same time providing high accuracy (approaching 99.9% of the correlation energy), robustness, and black-box character. In the DLPNO approach, the virtual space is spanned by pair natural orbitals that are expanded in terms of projected atomic orbitals in large orbital domains, while the inactive space is spanned by localized orbitals. The active orbitals are left untouched. Our implementation features a highly efficient “electron pair prescreening” that skips the negligible inactive pairs. The surviving pairs are treated using the partially contracted NEVPT2 formalism. A detailed

Finite-temperature orbital-free DFT molecular dynamics: Coupling PROFESS and QUANTUM ESPRESSO

Science.gov (United States)

Karasiev, Valentin V.; Sjostrom, Travis; Trickey, S. B.

2014-12-01

Implementation of orbital-free free-energy functionals in the PROFESS code and the coupling of PROFESS with the QUANTUM ESPRESSO code are described. The combination enables orbital-free DFT to drive ab initio molecular dynamics simulations on the same footing (algorithms, thermostats, convergence parameters, etc.) as for Kohn-Sham (KS) DFT. All the non-interacting free-energy functionals implemented are single-point: the local density approximation (LDA; also known as finite-T Thomas-Fermi, ftTF), the second-order gradient approximation (SGA or finite-T gradient-corrected TF), and our recently introduced finite-T generalized gradient approximations (ftGGA). Elimination of the KS orbital bottleneck via orbital-free methodology enables high-T simulations on ordinary computers, whereas those simulations would be costly or even prohibitively time-consuming for KS molecular dynamics (MD) on very high-performance computer systems. Example MD simulations on H over a temperature range 2000 K ≤ T ≤4,000,000 K are reported, with timings on small clusters (16-128 cores) and even laptops. With respect to KS-driven calculations, the orbital-free calculations are between a few times through a few hundreds of times faster.

A partial Hamiltonian approach for current value Hamiltonian systems

Science.gov (United States)

Naz, R.; Mahomed, F. M.; Chaudhry, Azam

2014-10-01

We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many state and costate variables of the current value Hamiltonian. However, we apply the method to models with one control, one state and one costate variable to illustrate its effectiveness. The current value Hamiltonian systems arise in economic growth theory and other economic models. We explain our approach with the help of a simple illustrative example and then apply it to two widely used economic growth models: the Ramsey model with a constant relative risk aversion (CRRA) utility function and Cobb Douglas technology and a one-sector AK model of endogenous growth are considered. We show that our newly developed systematic approach can be used to deduce results given in the literature and also to find new solutions.

Emulating Molecular Orbitals and Electronic Dynamics with Ultracold Atoms

Directory of Open Access Journals (Sweden)

Dirk-Sören Lühmann

2015-08-01

Full Text Available In recent years, ultracold atoms in optical lattices have proven their great value as quantum simulators for studying strongly correlated phases and complex phenomena in solid-state systems. Here, we reveal their potential as quantum simulators for molecular physics and propose a technique to image the three-dimensional molecular orbitals with high resolution. The outstanding tunability of ultracold atoms in terms of potential and interaction offer fully adjustable model systems for gaining deep insight into the electronic structure of molecules. We study the orbitals of an artificial benzene molecule and discuss the effect of tunable interactions in its conjugated π electron system with special regard to localization and spin order. The dynamical time scales of ultracold atom simulators are on the order of milliseconds, which allows for the time-resolved monitoring of a broad range of dynamical processes. As an example, we compute the hole dynamics in the conjugated π system of the artificial benzene molecule.

A UniChem and electron momentum spectroscopy investigations into the valence electronic structure of trans 1,3 butadiene

Energy Technology Data Exchange (ETDEWEB)

Michalewicz, M.T. [CSIRO, Supercomputing Support Group, Carlton, VIC (Australia). Division of Information Technology; Winkler, D.A. [Commonwealth Scientific and Industrial Research Organisation (CSIRO), Clayton, VIC (Australia). Div. of Chemical Physics; Brunger, M.J.; McCarthy, L.E. [Flinders Univ. of South Australia, Bedford Park, SA (Australia). School of Physical Sciences; Von Niessen, W. [Flinders Univ. of South Australia, Bedford Park, SA (Australia). School of Physical Sciences

1996-09-01

The experimental (e,2e) coincidence spectroscopy, known as electron momentum spectroscopy (EMS) was applied to the trans 1,3 butadiene (C{sub 4}H{sub 6}) molecule with detailed binding energy spectra and orbital momentum distributions (MDs) being measured. A small selection of this data is presented. The usage of UniChem computational chemistry codes for the Flinders-developed AMOLD program allows to calculate theoretical MDs for each orbital, to help elucidate the valence electronic structure of butadiene. The results of the many-body Green`s function calculation is also presented, to the ADC(3) level, for the binding energies and spectroscopic factors of the respective orbitals of C{sub 4}H{sub 6}. A critical comparison between the experimental and theoretical MDs allows to determine the optimum wavefunction from the basis sets studied. The determination of the wavefunction then allows to make further use of the UniChem package to derive butadiene`s chemically interesting molecular properties. A summary of these results and comparison of them with the previous results of other workers is presented. 23 refs., 2 tabs., 2 figs.

A UniChem and electron momentum spectroscopy investigations into the valence electronic structure of trans 1,3 butadiene

International Nuclear Information System (INIS)

Michalewicz, M.T.; Winkler, D.A.; Brunger, M.J.; McCarthy, L.E.; Von Niessen, W.

1996-09-01

The experimental (e,2e) coincidence spectroscopy, known as electron momentum spectroscopy (EMS) was applied to the trans 1,3 butadiene (C 4 H 6 ) molecule with detailed binding energy spectra and orbital momentum distributions (MDs) being measured. A small selection of this data is presented. The usage of UniChem computational chemistry codes for the Flinders-developed AMOLD program allows to calculate theoretical MDs for each orbital, to help elucidate the valence electronic structure of butadiene. The results of the many-body Green's function calculation is also presented, to the ADC(3) level, for the binding energies and spectroscopic factors of the respective orbitals of C 4 H 6 . A critical comparison between the experimental and theoretical MDs allows to determine the optimum wavefunction from the basis sets studied. The determination of the wavefunction then allows to make further use of the UniChem package to derive butadiene's chemically interesting molecular properties. A summary of these results and comparison of them with the previous results of other workers is presented. 23 refs., 2 tabs., 2 figs

Gaussian basis sets for use in correlated molecular calculations. XI. Pseudopotential-based and all-electron relativistic basis sets for alkali metal (K-Fr) and alkaline earth (Ca-Ra) elements

Science.gov (United States)

Hill, J. Grant; Peterson, Kirk A.

2017-12-01

New correlation consistent basis sets based on pseudopotential (PP) Hamiltonians have been developed from double- to quintuple-zeta quality for the late alkali (K-Fr) and alkaline earth (Ca-Ra) metals. These are accompanied by new all-electron basis sets of double- to quadruple-zeta quality that have been contracted for use with both Douglas-Kroll-Hess (DKH) and eXact 2-Component (X2C) scalar relativistic Hamiltonians. Sets for valence correlation (ms), cc-pVnZ-PP and cc-pVnZ-(DK,DK3/X2C), in addition to outer-core correlation [valence + (m-1)sp], cc-p(w)CVnZ-PP and cc-pwCVnZ-(DK,DK3/X2C), are reported. The -PP sets have been developed for use with small-core PPs [I. S. Lim et al., J. Chem. Phys. 122, 104103 (2005) and I. S. Lim et al., J. Chem. Phys. 124, 034107 (2006)], while the all-electron sets utilized second-order DKH Hamiltonians for 4s and 5s elements and third-order DKH for 6s and 7s. The accuracy of the basis sets is assessed through benchmark calculations at the coupled-cluster level of theory for both atomic and molecular properties. Not surprisingly, it is found that outer-core correlation is vital for accurate calculation of the thermodynamic and spectroscopic properties of diatomic molecules containing these elements.

Gaussian basis sets for use in correlated molecular calculations. XI. Pseudopotential-based and all-electron relativistic basis sets for alkali metal (K-Fr) and alkaline earth (Ca-Ra) elements.

Science.gov (United States)

Hill, J Grant; Peterson, Kirk A

2017-12-28

New correlation consistent basis sets based on pseudopotential (PP) Hamiltonians have been developed from double- to quintuple-zeta quality for the late alkali (K-Fr) and alkaline earth (Ca-Ra) metals. These are accompanied by new all-electron basis sets of double- to quadruple-zeta quality that have been contracted for use with both Douglas-Kroll-Hess (DKH) and eXact 2-Component (X2C) scalar relativistic Hamiltonians. Sets for valence correlation (ms), cc-pVnZ-PP and cc-pVnZ-(DK,DK3/X2C), in addition to outer-core correlation [valence + (m-1)sp], cc-p(w)CVnZ-PP and cc-pwCVnZ-(DK,DK3/X2C), are reported. The -PP sets have been developed for use with small-core PPs [I. S. Lim et al., J. Chem. Phys. 122, 104103 (2005) and I. S. Lim et al., J. Chem. Phys. 124, 034107 (2006)], while the all-electron sets utilized second-order DKH Hamiltonians for 4s and 5s elements and third-order DKH for 6s and 7s. The accuracy of the basis sets is assessed through benchmark calculations at the coupled-cluster level of theory for both atomic and molecular properties. Not surprisingly, it is found that outer-core correlation is vital for accurate calculation of the thermodynamic and spectroscopic properties of diatomic molecules containing these elements.

Construction of Vibronic Diabatic Hamiltonian for Excited-State Electron and Energy Transfer Processes.

Science.gov (United States)

Xie, Yu; Jiang, Shengshi; Zheng, Jie; Lan, Zhenggang

2017-12-21

Photoinduced excited-state electron and energy transfer processes are crucial in biological photoharvesting systems and organic photovoltaic devices. We discuss the construction of a diabatic vibronic Hamiltonian for the proper treatment of these processes involving the projection approach acting on both electronic wave functions and vibrational modes. In the electronic part, the wave function projection approach is used to construct the diabatic Hamiltonian in which both local excited states and charge-transfer states are included on the same footing. For the vibrational degrees of freedom, the vibronic couplings in the diabatic Hamiltonian are obtained in the basis of the pseudonormal modes localized on each monomer site by applying delocalized-to-localized mode projection. This systematic approach allows us to construct the vibronic diabatic Hamiltonian in molecular aggregates.

Generalized molecular orbital theory: a limited multiconfiguration self-consistent-field-theory

International Nuclear Information System (INIS)

Hall, M.B.

1981-01-01

The generalized molecular orbital (GMO) approach is a limited type of multiconfiguration self-consistent-field (MCSCF) calculation which divides the orbitals of a closed shell molecule into four shells: doubly occupied, strongly occupied, weakly occupied, and unoccupied. The orbitals within each shell have the same occupation number and are associated with the same Fock operator. Thus, the orbital optimization is ideally suited to solution via a coupling operator. The determination of the orbitals is followed by a configuration interaction (CI) calculation within the strongly and weakly occupied shells. Results for BH 3 show a striking similarity between the GMO's and the natural orbitals (NO's) from an all singles and doubles CI calculation. Although the GMO approach would not be accurate for an entire potential surface, results for spectroscopic constants of N 2 show that it is suitable near the equilibrium geometry. This paper describes the use of the GMO technique to determine the primary orbital space, but a potentially important application may be in the determination of a secondary orbital space following a more accurate MCSCF determination of the primary space

Valence bond solids for SU(n) spin chains: Exact models, spinon confinement, and the Haldane gap

International Nuclear Information System (INIS)

Greiter, Martin; Rachel, Stephan

2007-01-01

To begin with, we introduce several exact models for SU(3) spin chains: First is a translationally invariant parent Hamiltonian involving four-site interactions for the trimer chain, with a threefold degenerate ground state. We provide numerical evidence that the elementary excitations of this model transform under representation 3 of SU(3) if the original spins of the model transform under representation 3. Second is a family of parent Hamiltonians for valence bond solids of SU(3) chains with spin representations 6, 10, and 8 on each lattice site. We argue that of these three models, only the latter two exhibit spinon confinement and, hence, a Haldane gap in the excitation spectrum. We generalize some of our models to SU(n). Finally, we use the emerging rules for the construction of valence bond solid states to argue that models of antiferromagnetic chains of SU(n) spins, in general, possess a Haldane gap if the spins transform under a representation corresponding to a Young tableau consisting of a number of boxes λ which is divisible by n. If λ and n have no common divisor, the spin chain will support deconfined spinons and not exhibit a Haldane gap. If λ and n have a common divisor different from n, it will depend on the specifics of the model including the range of the interaction

Vibrational analysis of HOCl up to 98% of the dissociation energy with a Fermi resonance Hamiltonian

International Nuclear Information System (INIS)

Jost, R.; Joyeux, M.; Skokov, S.; Bowman, J.

1999-01-01

We have analyzed the vibrational energies and wave functions of HOCl obtained from previous ab initio calculations [J. Chem. Phys. 109, 2662 (1998); 109, 10273 (1998)]. Up to approximately 13 and h;000 cm -1 , the normal modes are nearly decoupled, so that the analysis is straightforward with a Dunham model. In contrast, above 13 and h;000 cm -1 the Dunham model is no longer valid for the levels with no quanta in the OH stretch (v 1 =0). In addition to v 1 , these levels can only be assigned a so-called polyad quantum number P=2v 2 +v 3 , where 2 and 3 denote, respectively, the bending and OCl stretching normal modes. In contrast, the levels with v 1 ≥2 remain assignable with three v i quantum numbers up to the dissociation (D 0 =19 and h;290 and h;cm -1 ). The interaction between the bending and the OCl stretch (ω 2 congruent 2ω 3 ) is well described with a simple, fitted Fermi resonance Hamiltonian. The energies and wave functions of this model Hamiltonian are compared with those obtained from ab initio calculations, which in turn enables the assignment of many additional ab initio vibrational levels. Globally, among the 809 bound levels calculated below dissociation, 790 have been assigned, the lowest unassigned level, No. 736, being located at 18 and h;885 cm -1 above the (0,0,0) ground level, that is, at about 98% of D 0 . In addition, 84 resonances located above D 0 have also been assigned. Our best Fermi resonance Hamiltonian has 29 parameters fitted with 725 ab initio levels, the rms deviation being of 5.3 cm -1 . This set of 725 fitted levels includes the full set of levels up to No. 702 at 18 and h;650 cm -1 . The ab initio levels, which are assigned but not included in the fit, are reasonably predicted by the model Hamiltonian, but with a typical error of the order of 20 cm -1 . The classical analysis of the periodic orbits of this Hamiltonian shows that two bifurcations occur at 13 and h;135 and 14 and h;059 cm -1 for levels with v 1 =0. Above each

Orbital free molecular dynamics; Approche sans orbitale des plasmas denses

Energy Technology Data Exchange (ETDEWEB)

Lambert, F

2007-08-15

The microscopic properties of hot and dense plasmas stay a field essentially studied thanks to classical theories like the One Component Plasma, models which rely on free parameters, particularly ionization. In order to investigate these systems, we have used, in this PhD work, a semi-classical model, without free parameters, that is based on coupling consistently classical molecular dynamics for the nuclei and orbital free density functional theory for the electrons. The electronic fluid is represented by a free energy entirely determined by the local density. This approximation was validated by a comparison with an ab initio technique, quantum molecular dynamics. This one is identical to the previous except for the description of the free energy that depends on a quantum-independent-particle model. Orbital free molecular dynamics was then used to compute equation of state of boron and iron plasmas in the hot and dense regime. Furthermore, comparisons with classical theories were performed on structural and dynamical properties. Finally, equation of state and transport coefficients mixing laws were studied by direct simulation of a plasma composed of deuterium and copper. (author)

Renormalization of Hamiltonians

International Nuclear Information System (INIS)

Glazek, S.D.; Wilson, K.G.

1993-01-01

This paper presents a new renormalization procedure for Hamiltonians such as those of light-front field theory. The bare Hamiltonian with an arbitrarily large, but finite cutoff, is transformed by a specially chosen similarity transformation. The similarity transformation has two desirable features. First, the transformed Hamiltonian is band diagonal: in particular, all matrix elements vanish which would otherwise have caused transitions with big energy jumps, such as from a state of bounded energy to a state with an energy of the order of the cutoff. At the same time, neither the similarity transformation nor the transformed Hamiltonian, computed in perturbation theory, contain vanishing or near-vanishing energy denominators. Instead, energy differences in denominators can be replaced by energy sums for purposes of order of magnitude estimates needed to determine cutoff dependences. These two properties make it possible to determine relatively easily the list of counterterms needed to obtain finite low energy results (such as for eigenvalues). A simple model Hamiltonian is discussed to illustrate the method

Discontinuous approximate molecular electronic wave-functions

International Nuclear Information System (INIS)

Stuebing, E.W.; Weare, J.H.; Parr, R.G.

1977-01-01

Following Kohn, Schlosser and Marcus and Weare and Parr an energy functional is defined for a molecular problem which is stationary in the neighborhood of the exact solution and permits the use of trial functions that are discontinuous. The functional differs from the functional of the standard Rayleigh--Ritz method in the replacement of the usual kinetic energy operators circumflex T(μ) with operators circumflex T'(μ) = circumflex T(μ) + circumflex I(μ) generates contributions from surfaces of nonsmooth behavior. If one uses the nabla PSI . nabla PSI way of writing the usual kinetic energy contributions, one must add surface integrals of the product of the average of nabla PSI and the change of PSI across surfaces of discontinuity. Various calculations are carried out for the hydrogen molecule-ion and the hydrogen molecule. It is shown that ab initio calculations on molecules can be carried out quite generally with a basis of atomic orbitals exactly obeying the zero-differential overlap (ZDO) condition, and a firm basis is thereby provided for theories of molecular electronic structure invoking the ZDO aoproximation. It is demonstrated that a valence bond theory employing orbitals exactly obeying ZDO can provide an adequate account of chemical bonding, and several suggestions are made regarding molecular orbital methods

Synthesis of a Neutral Mixed-Valence Diferrocenyl Carborane for Molecular Quantum-Dot Cellular Automata Applications.

Science.gov (United States)

Christie, John A; Forrest, Ryan P; Corcelli, Steven A; Wasio, Natalie A; Quardokus, Rebecca C; Brown, Ryan; Kandel, S Alex; Lu, Yuhui; Lent, Craig S; Henderson, Kenneth W

2015-12-14

The preparation of 7-Fc(+) -8-Fc-7,8-nido-[C2 B9 H10 ](-) (Fc(+) FcC2 B9 (-) ) demonstrates the successful incorporation of a carborane cage as an internal counteranion bridging between ferrocene and ferrocenium units. This neutral mixed-valence Fe(II) /Fe(III) complex overcomes the proximal electronic bias imposed by external counterions, a practical limitation in the use of molecular switches. A combination of UV/Vis-NIR spectroscopic and TD-DFT computational studies indicate that electron transfer within Fc(+) FcC2 B9 (-) is achieved through a bridge-mediated mechanism. This electronic framework therefore provides the possibility of an all-neutral null state, a key requirement for the implementation of quantum-dot cellular automata (QCA) molecular computing. The adhesion, ordering, and characterization of Fc(+) FcC2 B9 (-) on Au(111) has been observed by scanning tunneling microscopy. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Hamiltonian Algorithm Sound Synthesis

OpenAIRE

大矢, 健一

2013-01-01

Hamiltonian Algorithm (HA) is an algorithm for searching solutions is optimization problems. This paper introduces a sound synthesis technique using Hamiltonian Algorithm and shows a simple example. "Hamiltonian Algorithm Sound Synthesis" uses phase transition effect in HA. Because of this transition effect, totally new waveforms are produced.

Transport from chaotic orbits in the geomagnetic tail

International Nuclear Information System (INIS)

Horton, W.; Tajima, T.

1991-01-01

The rapid change in direction and magnitude of the magnetic field vector in crossing the quasineutral sheet in the geomagnetic tail leads to deterministic Hamiltonian chaos. The finite correlation times in the single particle orbits due to the continuum of orbital frequencies leads to well-defined collisionless transport coefficients. The transport coefficients are derived for plasma trapped in the quasineutral sheet

Understanding molecular structure from molecular mechanics.

Science.gov (United States)

Allinger, Norman L

2011-04-01

Molecular mechanics gives us a well known model of molecular structure. It is less widely recognized that valence bond theory gives us structures which offer a direct interpretation of molecular mechanics formulations and parameters. The electronic effects well-known in physical organic chemistry can be directly interpreted in terms of valence bond structures, and hence quantitatively calculated and understood. The basic theory is outlined in this paper, and examples of the effects, and their interpretation in illustrative examples is presented.

Valence Band Structure of InAs1-xBix and InSb1-xBix Alloy Semiconductors Calculated Using Valence Band Anticrossing Model

Directory of Open Access Journals (Sweden)

D. P. Samajdar

2014-01-01

Full Text Available The valence band anticrossing model has been used to calculate the heavy/light hole and spin-orbit split-off energies in InAs1-xBix and InSb1-xBix alloy systems. It is found that both the heavy/light hole, and spin-orbit split E+ levels move upwards in energy with an increase in Bi content in the alloy, whereas the split E− energy for the holes shows a reverse trend. The model is also used to calculate the reduction of band gap energy with an increase in Bi mole fraction. The calculated values of band gap variation agree well with the available experimental data.

Identity of the SU(3) model phenomenological hamiltonian and the hamiltonian of nonaxial rotator

International Nuclear Information System (INIS)

Filippov, G.F.; Avramenko, V.I.; Sokolov, A.M.

1984-01-01

Interpretation of nonspheric atomic nuclei spectra on the basis of phenomenological hamiltonians of SU(3) model showed satisfactory agreement of simulation calculations with experimental data. Meanwhile physical sense of phenomenological hamiltonians was not yet discussed. It is shown that phenomenological hamiltonians of SU(3) model are reduced to hamiltonian of nonaxial rotator but with additional items of the third and fourth powers angular momentum operator of rotator

Toward a W4-F12 approach: Can explicitly correlated and orbital-based ab initio CCSD(T) limits be reconciled?

Energy Technology Data Exchange (ETDEWEB)

Sylvetsky, Nitai, E-mail: gershom@weizmann.ac.il; Martin, Jan M. L., E-mail: gershom@weizmann.ac.il [Department of Organic Chemistry, Weizmann Institute of Science, 76100 Rehovot (Israel); Peterson, Kirk A., E-mail: kipeters@wsu.edu [Department of Chemistry, Washington State University, Pullman, Washington 99164-4630 (United States); Karton, Amir, E-mail: amir.karton@uwa.edu.au [School of Chemistry and Biochemistry, The University of Western Australia, Perth, WA 6009 (Australia)

2016-06-07

In the context of high-accuracy computational thermochemistry, the valence coupled cluster with all singles and doubles (CCSD) correlation component of molecular atomization energies presents the most severe basis set convergence problem, followed by the (T) component. In the present paper, we make a detailed comparison, for an expanded version of the W4-11 thermochemistry benchmark, between, on the one hand, orbital-based CCSD/AV{5,6}Z + d and CCSD/ACV{5,6}Z extrapolation, and on the other hand CCSD-F12b calculations with cc-pVQZ-F12 and cc-pV5Z-F12 basis sets. This latter basis set, now available for H–He, B–Ne, and Al–Ar, is shown to be very close to the basis set limit. Apparent differences (which can reach 0.35 kcal/mol for systems like CCl{sub 4}) between orbital-based and CCSD-F12b basis set limits disappear if basis sets with additional radial flexibility, such as ACV{5,6}Z, are used for the orbital calculation. Counterpoise calculations reveal that, while total atomization energies with V5Z-F12 basis sets are nearly free of BSSE, orbital calculations have significant BSSE even with AV(6 + d)Z basis sets, leading to non-negligible differences between raw and counterpoise-corrected extrapolated limits. This latter problem is greatly reduced by switching to ACV{5,6}Z core-valence basis sets, or simply adding an additional zeta to just the valence orbitals. Previous reports that all-electron approaches like HEAT (high-accuracy extrapolated ab-initio thermochemistry) lead to different CCSD(T) limits than “valence limit + CV correction” approaches like Feller-Peterson-Dixon and Weizmann-4 (W4) theory can be rationalized in terms of the greater radial flexibility of core-valence basis sets. For (T) corrections, conventional CCSD(T)/AV{Q,5}Z + d calculations are found to be superior to scaled or extrapolated CCSD(T)-F12b calculations of similar cost. For a W4-F12 protocol, we recommend obtaining the Hartree-Fock and valence CCSD components from CCSD-F12b

A brief introduction to molecular orbital theory of simple polyatomic molecules for undergraduate chemistry students

Directory of Open Access Journals (Sweden)

Ione M. Baibich

2012-01-01

Full Text Available A simple, four-step method for better introducing undergraduate students to the fundamentals of molecular orbital (MO theory of the polyatomic molecules H2O, NH3, BH3 and SiH4 using group theory is reported. These molecules serve to illustrate the concept of ligand group orbitals (LGOs and subsequent construction of MO energy diagrams on the basis of molecular symmetry requirements.

Micro-Valences: Affective valence in neutral everyday objects

OpenAIRE

Sophie eLebrecht; Moshe eBar; Lisa F Barrett; Michael J Tarr

2012-01-01

Affective valence influences both our cognition and our perception of the world. Indeed, the speed and quality with which we recognize objects in a visual scene can vary dramatically depending on its affective content. However, affective processing of visual objects has been typically studied using only stimuli with strong affective valences (e.g., guns or roses). Here we explore whether affective valence must be strong or obvious to exert an effect on our perception. We conclude that the maj...

[OsF6]x−: Molecular Models for Spin-Orbit Entangled Phenomena

DEFF Research Database (Denmark)

Pedersen, Kasper Steen; Woodruff, Daniel N.; Singh, Saurabh Kumar

2017-01-01

Heavy 5d elements, like osmium, feature strong spin-orbit interactions which are at the origin of exotic physical behaviors. Revealing the full potential of, for example, novel osmium oxide materials (“osmates”) is however contingent upon a detailed understanding of the local single-ion propertie...... state was elucidated; mirroring the osmium electronic structure in osmates. The realization of such molecular model systems provides a unique chemical playground to engineer materials exhibiting spin-orbit entangled phenomena....

Binding energies of sd-shell nuclei with a realistic effective Hamiltonian

International Nuclear Information System (INIS)

Dalton, B.J.; Vary, J.P.; Baldridge, W.J.

1977-01-01

The nuclear shell model with a second-order effective Hamiltonian derived within Brueckner theory from the free nucleon-nucleon interaction is shown to yield accurate binding energies of nuclei with 16 < A < 40. This agreement is obtained by choosing the spectrum of low-lying unoccupied orbitals in a justified manner and, when necessary, by employing a statistical method to approximate the lowest eigenvalue of very large shell-model diagonalizations

Unbounded dynamics and compact invariant sets of one Hamiltonian system defined by the minimally coupled field

Energy Technology Data Exchange (ETDEWEB)

Starkov, Konstantin E., E-mail: kstarkov@ipn.mx

2015-06-12

In this paper we study some features of global dynamics for one Hamiltonian system arisen in cosmology which is formed by the minimally coupled field; this system was introduced by Maciejewski et al. in 2007. We establish that under some simple conditions imposed on parameters of this system all trajectories are unbounded in both of time directions. Further, we present other conditions for system parameters under which we localize the domain with unbounded dynamics; this domain is defined with help of bounds for values of the Hamiltonian level surface parameter. We describe the case when our system possesses periodic orbits which are found explicitly. In the rest of the cases we get some localization bounds for compact invariant sets. - Highlights: • Domain with unbounded dynamics is localized. • Equations for periodic orbits are given in one level set. • Localizations for compact invariant sets are got.

Spin-splitting calculation for zincblende semiconductors using an atomic bond-orbital model

International Nuclear Information System (INIS)

Kao, Hsiu-Fen; Lo, Ikai; Chiang, Jih-Chen; Wang, Wan-Tsang; Hsu, Yu-Chi; Wu, Chieh-Lung; Gau, Ming-Hong; Chen, Chun-Nan; Ren, Chung-Yuan; Lee, Meng-En

2012-01-01

We develop a 16-band atomic bond-orbital model (16ABOM) to compute the spin splitting induced by bulk inversion asymmetry in zincblende materials. This model is derived from the linear combination of atomic-orbital (LCAO) scheme such that the characteristics of the real atomic orbitals can be preserved to calculate the spin splitting. The Hamiltonian of 16ABOM is based on a similarity transformation performed on the nearest-neighbor LCAO Hamiltonian with a second-order Taylor expansion over k-vector at the Γ point. The spin-splitting energies in bulk zincblende semiconductors, GaAs and InSb, are calculated, and the results agree with the LCAO and first-principles calculations. However, we find that the spin-orbit coupling between bonding and antibonding p-like states, evaluated by the 16ABOM, dominates the spin splitting of the lowest conduction bands in the zincblende materials.

Tuning the effective spin-orbit coupling in molecular semiconductors

KAUST Repository

Schott, Sam

2017-05-11

The control of spins and spin to charge conversion in organics requires understanding the molecular spin-orbit coupling (SOC), and a means to tune its strength. However, quantifying SOC strengths indirectly through spin relaxation effects has proven difficult due to competing relaxation mechanisms. Here we present a systematic study of the g-tensor shift in molecular semiconductors and link it directly to the SOC strength in a series of high-mobility molecular semiconductors with strong potential for future devices. The results demonstrate a rich variability of the molecular g-shifts with the effective SOC, depending on subtle aspects of molecular composition and structure. We correlate the above g-shifts to spin-lattice relaxation times over four orders of magnitude, from 200 to 0.15 μs, for isolated molecules in solution and relate our findings for isolated molecules in solution to the spin relaxation mechanisms that are likely to be relevant in solid state systems.

Tuning the effective spin-orbit coupling in molecular semiconductors

KAUST Repository

Schott, Sam; McNellis, Erik R.; Nielsen, Christian B.; Chen, Hung-Yang; Watanabe, Shun; Tanaka, Hisaaki; McCulloch, Iain; Takimiya, Kazuo; Sinova, Jairo; Sirringhaus, Henning

2017-01-01

The control of spins and spin to charge conversion in organics requires understanding the molecular spin-orbit coupling (SOC), and a means to tune its strength. However, quantifying SOC strengths indirectly through spin relaxation effects has proven difficult due to competing relaxation mechanisms. Here we present a systematic study of the g-tensor shift in molecular semiconductors and link it directly to the SOC strength in a series of high-mobility molecular semiconductors with strong potential for future devices. The results demonstrate a rich variability of the molecular g-shifts with the effective SOC, depending on subtle aspects of molecular composition and structure. We correlate the above g-shifts to spin-lattice relaxation times over four orders of magnitude, from 200 to 0.15 μs, for isolated molecules in solution and relate our findings for isolated molecules in solution to the spin relaxation mechanisms that are likely to be relevant in solid state systems.

A study of the valence shell electronic states of s-triazine by photoabsorption spectroscopy and ab initio calculations

Energy Technology Data Exchange (ETDEWEB)

Holland, D.M.P., E-mail: david.holland@stfc.ac.uk [Daresbury Laboratory, Daresbury, Warrington, Cheshire WA4 4AD (United Kingdom); Shaw, D.A. [Daresbury Laboratory, Daresbury, Warrington, Cheshire WA4 4AD (United Kingdom); Stener, M.; Decleva, P. [Dipartimento di Scienze Chimiche e Farmaceutiche, Università degli Studi di Trieste, Via L. Giorgieri, I-34127 Trieste (Italy); Consorzio Interuniversitario Nazionale per la Scienze e Tecnologia dei Materiali, INSTM, Unità di Trieste (Italy); CNR-IOM, Trieste (Italy); Coriani, S. [Dipartimento di Scienze Chimiche e Farmaceutiche, Università degli Studi di Trieste, Via L. Giorgieri, I-34127 Trieste (Italy); Consorzio Interuniversitario Nazionale per la Scienze e Tecnologia dei Materiali, INSTM, Unità di Trieste (Italy); Aarhus Institute of Advanced Studies, Aarhus University, 8000 Aarhus C (Denmark)

2016-09-30

Highlights: • The valence shell photoabsorption spectrum of s-triazine has been measured. • Electronic structure calculated with TDDFT and coupled cluster approaches. • Assignments proposed for Rydberg and valence states. • Mixing between Rydberg and valence states important. - Abstract: The absolute photoabsorption cross section of s-triazine has been measured between 4 and 40 eV, and is dominated by bands associated with valence states. Structure due to Rydberg excitations is both weak and irregular. Jahn-Teller interactions affect the vibronic structure observed in the Rydberg absorption bands due to excitation from the 1e″ or 6e′ orbitals. The interpretation of the experimental spectrum has been guided by transition energies and oscillator strengths, for Rydberg and valence states, calculated with the time-dependent version of density functional theory and with the coupled cluster linear response approach. The theoretical studies indicate that Rydberg/Rydberg and Rydberg/valence mixing is important.

A theoretical and (e,2e) experimental investigation into the complete valence electronic structure of (1.1.1) propellane

Energy Technology Data Exchange (ETDEWEB)

Adcock, W.; Clark, C.I. [Flinders Univ. of South Australia, Bedford Park, SA (Australia); Brunger, M.J.; McCarthy, I.E. [Flinders Univ. of South Australia, Bedford Park, SA (Australia). School of Physical Sciences; Michalewicz, M.T. [CSIRO, Carlton, VIC (Australia). Division of Information Technology; Von Niessen, W. [Technische Univ., Braunschweig (Germany). Institute fur Physikalische and Theoretische Chemie; Weigold, E. [Australian National Univ., Canberra, ACT (Australia). Inst. of Advanced Studies; Winkler, D.A. [Commonwealth Scientific and Industrial Research Organisation (CSIRO), Clayton, VIC (Australia). Div. of Chemical Physics

1996-08-01

The first comprehensive electronic structural study of the complete valence shell of [1.1.1] propellane is reported. Binding energy spectra were measured in the energy regime 3.5-46.5 eV over a range of different target electron momentum so that individual orbital momentum profiles could also be determined. These binding energy spectra were collected using an energy dispersive multichannel electron momentum spectrometer at a total energy of 1000 eV, with a coincidence energy resolution of 1.38 eV and a momentum resolution of about 0.1 a.u. The experimental orbital electron momentum profiles are compared with those calculated in the plane wave impulse approximation (PWIA) using both a triple zeta plus polarisation level SCF wavefunction and a further 13 basis sets as calculated using Density Functional Theory (DFT). A critical comparison between the experimental an theoretical momentum distributions (MDs) allows to determine the optimum wavefunction for [1.1.1]propellane. In general, the level of agreement between the experimental and theoretical MDs for the optimum wavefunction for all of the respective valence orbitals was very good. The determination of this wavefunction then allowed to derive the chemically interesting molecular properties of [1.1.1]propellane. These include infrared spectra, bond lengths, bond orders, electron densities and many others. A summary of these results and a comparison of them with the previous results of other workers is presented with the level of agreement typically being good. In particular, the existence of the C1-C3 bridging bond with a bond order of 0.70 was confirmed. 59 refs., 4 tabs., 11 figs.

Fulde-Ferrell-Like Molecular States in Spin-Orbit Coupled Ultracold Fermi Gases

Science.gov (United States)

Ye, Chong; Fu, Li-Bin

2017-08-01

We study the molecular state in three-component Fermi gases with a single impurity of 6 Li immersing in a no-interacting Fermi sea of 40 K in the presence of an equal weight combination of Rashba-type and Dresselhaus-type spin-orbit coupling. In the region where the Fermi sea has two disjointed Fermi surfaces, we find that there are two Fulde-Ferrell-like molecular states with dominating contributions from the lower helicity branch. Decreasing the scattering length or the spin-orbit coupled Fermi energy, we find the Fulde-Ferrell-like molecular state with small center-of-mass momentum is always energy favored and the other one will suddenly disappear. Supported by the National Basic Research Program of China (973 Program) under Grant Nos. 2013CBA01502, 2013CB834100, and the National Natural Science Foundation of China under Grant Nos. 11374040, 11475027, 11575027, 11274051, and 11075020

Electronic structure and molecular orbital study of hole-transport material triphenylamine derivatives

International Nuclear Information System (INIS)

Wang, B.-C.; Liao, H.-R.; Chang, J.-C.; Chen Likey; Yeh, J.-T.

2007-01-01

Recently, triphenylamine (TPA), 4,4'-bis(phenyl-m-tolylamino)biphenyl (TPD), 4,4'-bis(1-naphthylphenylamino)biphenyl (NPB) and their derivatives are widely used in the organic light-emitting diode (OLED) devices as a hole-transporting material (HTM) layer. We have optimized twenty different structures of HTM materials by using density functional theory (DFT), B3LYP/6-31G method. All these different structures contain mono-amine and diamine TPA derivatives. The energies of highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) along with molecular orbitals for these HTMs are also determined. We have found that the central amine nitrogen atom and the phenyl ring, which is next to the central amine nitrogen atom, show significant contribution to the HOMO and LUMO, respectively. The sum of the calculated bond angles (α+β+γ) of the central amine nitrogen atom has been applied to describe the bonding and the energy difference for HOMO and LUMO in these TPA derivatives. Electronic structure calculations have been performed for these TPA derivatives. Again, the LCAO-MO patterns of HOMO and LUMO levels of these derivatives are used to investigate their electron density. A series of electron-transporting steps are predicted for these compounds employing these calculated results

A study of the valence shell electronic states of s-triazine by photoabsorption spectroscopy and ab initio calculations

DEFF Research Database (Denmark)

Holland, D.M.P.; Shaw, D.A.; Stener, Mauro

2016-01-01

absorption bands due to excitation from the 1e00 or 6e0 orbitals. The interpretation of the experimental spectrum has been guided by transition energies and oscillator strengths, for Rydberg and valence states, calculated with the time-dependent version of density functional theory and with the coupled...... cluster linear response approach. The theoretical studies indicate that Rydberg/Rydberg and Rydberg/valence mixing is important....

Hamiltonian description of the ideal fluid

International Nuclear Information System (INIS)

Morrison, P.J.

1994-01-01

Fluid mechanics is examined from a Hamiltonian perspective. The Hamiltonian point of view provides a unifying framework; by understanding the Hamiltonian perspective, one knows in advance (within bounds) what answers to expect and what kinds of procedures can be performed. The material is organized into five lectures, on the following topics: rudiments of few-degree-of-freedom Hamiltonian systems illustrated by passive advection in two-dimensional fluids; functional differentiation, two action principles of mechanics, and the action principle and canonical Hamiltonian description of the ideal fluid; noncanonical Hamiltonian dynamics with examples; tutorial on Lie groups and algebras, reduction-realization, and Clebsch variables; and stability and Hamiltonian systems

XZP + 1d and XZP + 1d-DKH basis sets for second-row elements: application to CCSD(T) zero-point vibrational energy and atomization energy calculations.

Science.gov (United States)

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).

The spectral distribution of intermediate L-K molecular-orbital radiation in symmetric heavy-ion collisions

International Nuclear Information System (INIS)

Heinig, K.-H.; Jager, H.-U.; Richter, H.; Woittennek, H.; Frank, W.; Gippener, P.; Kaun, K.-H.; Manfrass, P.

1977-01-01

Two distinct x-ray continua C1 and C2 above the characteristic lines are observed in high-energy collisions between atoms with atomic numbers of 28 to 57. This structure is explained by a superposition of K molecular-orbital (KMO) radiation and of an intermediate L-K molecular-orbital (ILKMO) radiation of high intensity which is due to 2psigma vacancies. In the framework of the dynamical theory of intermediate molecular phenomena and using a scaling of the H 2 + correlation diagram with screened state-dependent charges good agreement between the shapes of the measured and calculated spectra is obtained. (author)

Symplectic Geometric Algorithms for Hamiltonian Systems

CERN Document Server

Feng, Kang

2010-01-01

"Symplectic Geometry Algorithms for Hamiltonian Systems" will be useful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics, etc. The book generalizes and develops the generating function and Hamilton-Jacobi equation theory from the perspective of the symplectic geometry and symplectic algebra. It will be a useful resource for engineers and scientists in the fields of quantum theory, astrophysics, atomic and molecular dynamics, climate prediction, oil exploration, etc. Therefore a systematic research and development

K- and L-edge X-ray Absorption Spectroscopy (XAS) and Resonant Inelastic X-ray Scattering (RIXS) Determination of Differential Orbital Covalency (DOC) of Transition Metal Sites.

Science.gov (United States)

Baker, Michael L; Mara, Michael W; Yan, James J; Hodgson, Keith O; Hedman, Britt; Solomon, Edward I

2017-08-15

Continual advancements in the development of synchrotron radiation sources have resulted in X-ray based spectroscopic techniques capable of probing the electronic and structural properties of numerous systems. This review gives an overview of the application of metal K-edge and L-edge X-ray absorption spectroscopy (XAS), as well as K resonant inelastic X-ray scattering (RIXS), to the study of electronic structure in transition metal sites with emphasis on experimentally quantifying 3d orbital covalency. The specific sensitivities of K-edge XAS, L-edge XAS, and RIXS are discussed emphasizing the complementary nature of the methods. L-edge XAS and RIXS are sensitive to mixing between 3d orbitals and ligand valence orbitals, and to the differential orbital covalency (DOC), that is, the difference in the covalencies for different symmetry sets of the d orbitals. Both L-edge XAS and RIXS are highly sensitive to and enable separation of and donor bonding and back bonding contributions to bonding. Applying ligand field multiplet simulations, including charge transfer via valence bond configuration interactions, DOC can be obtained for direct comparison with density functional theory calculations and to understand chemical trends. The application of RIXS as a probe of frontier molecular orbitals in a heme enzyme demonstrates the potential of this method for the study of metal sites in highly covalent coordination sites in bioinorganic chemistry.

GAUSSIAN 76: an ab initio molecular orbital program

International Nuclear Information System (INIS)

Binkley, J.S.; Whiteside, R.; Hariharan, P.C.; Seeger, R.; Hehre, W.J.; Lathan, W.A.; Newton, M.D.; Ditchfield, R.; Pople, J.A.

Gaussian 76 is a general-purpose computer program for ab initio Hartree-Fock molecular orbital calculations. It can handle basis sets involving s, p and d-type gaussian functions. Certain standard sets (STO-3G, 4-31G, 6-31G*, etc.) are stored internally for easy use. Closed shell (RHF) or unrestricted open shell (UHF) wave functions can be obtained. Facilities are provided for geometry optimization to potential minima and for limited potential surface scans

Spin Relaxation and Manipulation in Spin-orbit Qubits

Science.gov (United States)

Borhani, Massoud; Hu, Xuedong

2012-02-01

We derive a generalized form of the Electric Dipole Spin Resonance (EDSR) Hamiltonian in the presence of the spin-orbit interaction for single spins in an elliptic quantum dot (QD) subject to an arbitrary (in both direction and magnitude) applied magnetic field. We predict a nonlinear behavior of the Rabi frequency as a function of the magnetic field for sufficiently large Zeeman energies, and present a microscopic expression for the anisotropic electron g-tensor. Similarly, an EDSR Hamiltonian is devised for two spins confined in a double quantum dot (DQD). Finally, we calculate two-electron-spin relaxation rates due to phonon emission, for both in-plane and perpendicular magnetic fields. Our results have immediate applications to current EDSR experiments on nanowire QDs, g-factor optimization of confined carriers, and spin decay measurements in DQD spin-orbit qubits.

Mixed-Valence Molecular Unit for Quantum Cellular Automata: Beyond the Born-Oppenheimer Paradigm through the Symmetry-Assisted Vibronic Approach.

Science.gov (United States)

Clemente-Juan, Juan Modesto; Palii, Andrew; Coronado, Eugenio; Tsukerblat, Boris

2016-08-09

In this article, we focus on the electron-vibrational problem of the tetrameric mixed-valence (MV) complexes proposed for implementation as four-dot molecular quantum cellular automata (mQCA).1 Although the adiabatic approximation explored in ref 2 is an appropriate tool for the qualitative analysis of the basic characteristics of mQCA, like vibronic trapping of the electrons encoding binary information and cell-cell response, it loses its accuracy providing moderate vibronic coupling and fails in the description of the discrete pattern of the vibronic levels. Therefore, a precise solution of the quantum-mechanical vibronic problem is of primary importance for the evaluation of the shapes of the electron transfer optical absorption bands and quantitative analysis of the main parameters of tetrameric quantum cells. Here, we go beyond the Born-Oppenheimer paradigm and present a solution of the quantum-mechanical pseudo Jahn-Teller (JT) vibronic problem in bielectronic MV species (exemplified by the tetra-ruthenium complexes) based on the recently developed symmetry-assisted approach.3,4 The mathematical approach to the vibronic eigenproblem takes into consideration the point symmetry basis, and therefore, the total matrix of the JT Hamiltonian is blocked to the maximum extent. The submatrices correspond to the irreducible representations (irreps) of the point group. With this tool, we also extend the theory of the mQCA cell beyond the limit of prevailing Coulomb repulsion in the electronic pair (adopted in ref 2), and therefore, the general pseudo-JT problems for spin-singlet ((1)B1g, 2(1)A1g, (1)B2g, (1)Eu) ⊗ (b1g + eu) and spin-triplet states ((3)A2g, (3)B1g, 2(3)Eu) ⊗ (b1g + eu) in a square-planar bielectronic system are solved. The obtained symmetry-adapted electron-vibrational functions are employed for the calculation of the profiles (shape functions) of the charge transfer absorption bands in the tetrameric MV complexes and for the discussion of the

Valence evaluation with approaching or withdrawing cues: directly testing valence-arousal conflict theory.

Science.gov (United States)

Wang, Yan Mei; Li, Ting; Li, Lin

2017-07-19

The valence-arousal conflict theory assumes that both valence and arousal will trigger approaching or withdrawing tendencies. It also predicts that the speed of processing emotional stimuli will depend on whether valence and arousal trigger conflicting or congruent motivational tendencies. However, most previous studies have provided evidence of the interaction between valence and arousal only, and have not provided direct proof of the interactive links between valence, arousal and motivational tendencies. The present study provides direct evidence for the relationship between approach-withdrawal tendencies and the valence-arousal conflict. In an empirical test, participants were instructed to judge the valence of emotional words after visual-spatial cues that appeared to be either approaching or withdrawing from participants. A three-way interaction (valence, arousal, and approach-withdrawal tendency) was observed such that the response time was shorter if participants responded to a negative high-arousal stimulus after a withdrawing cue, or to a positive low-arousal stimulus after an approaching cue. These findings suggest that the approach-withdrawal tendency indeed plays a crucial role in valence-arousal conflict, and that the effect depends on the congruency of valence, arousal and tendency at an early stage of processing.

Valence band structure of InAs(1-x)Bi(x) and InSb(1-x)Bi(x) alloy semiconductors calculated using valence band anticrossing model.

Science.gov (United States)

Samajdar, D P; Dhar, S

2014-01-01

The valence band anticrossing model has been used to calculate the heavy/light hole and spin-orbit split-off energies in InAs(1-x)Bi(x) and InSb(1-x)Bi(x) alloy systems. It is found that both the heavy/light hole, and spin-orbit split E + levels move upwards in energy with an increase in Bi content in the alloy, whereas the split E - energy for the holes shows a reverse trend. The model is also used to calculate the reduction of band gap energy with an increase in Bi mole fraction. The calculated values of band gap variation agree well with the available experimental data.

Competition of multiplet and spin-orbit splitting in open-shells

Energy Technology Data Exchange (ETDEWEB)

Zhang, Qian; Koch, Erik [Institute for Advanced Simulation, Forschungszentrum Juelich (Germany)

2016-07-01

To study the trends in the spectra of open-shells across the periodic table, we perform density functional calculations for atoms and ions. We collect the Slater-Condon and spin-orbit parameters from the resulting self-consistent radial wave functions and potentials. To make these easily accessible, we provide a simple least squares fitting formula in the spirit of Slater's rules. Given these parameters we calculate the many-body spectra in LS-, intermediate-, and jj-coupling. To assess the relative importance of Coulomb and spin-orbit interactions, we estimate the width of the spectra by calculating the eigen-energy variance of the corresponding Hamiltonian using a simple formula that does not require diagonalizing a complicated many-body Hamiltonian.

Systems of transversal sections near critical energy levels of hamiltonian systems in $Mathbb{R}^{4}$

CERN Document Server

de, Naiara V

2018-01-01

In this article the authors study Hamiltonian flows associated to smooth functions H:\\mathbb R^4 \\to \\mathbb R restricted to energy levels close to critical levels. They assume the existence of a saddle-center equilibrium point p_c in the zero energy level H^{-1}(0). The Hamiltonian function near p_c is assumed to satisfy Moser's normal form and p_c is assumed to lie in a strictly convex singular subset S_0 of H^{-1}(0). Then for all E \\gt 0 small, the energy level H^{-1}(E) contains a subset S_E near S_0, diffeomorphic to the closed 3-ball, which admits a system of transversal sections \\mathcal F_E, called a 2-3 foliation. \\mathcal F_E is a singular foliation of S_E and contains two periodic orbits P_2,E\\subset \\partial S_E and P_3,E\\subset S_E\\setminus \\partial S_E as binding orbits. P_2,E is the Lyapunoff orbit lying in the center manifold of p_c, has Conley-Zehnder index 2 and spans two rigid planes in \\partial S_E. P_3,E has Conley-Zehnder index 3 and spans a one parameter family of planes in S_E \\setmin...

Peptide Free Energy Landscapes Calibrated by Molecular Orbital Calculations

OpenAIRE

Ono, S.; Kuroda, M.; Higo, J.; Kamiya, N.; Nakajima, N.; Nakamura, H.

2002-01-01

Free energy landscapes of peptide conformations werecalibrated by ab initiomolecular orbital calculations, after enhancedconformational sampling using the multicanonical molecular dynamicssimulations. Three different potentials of mean force for an isolateddipeptide were individually obtained using the conventional force fields,AMBER parm94, AMBER parm96, and CHARMm22. Each potential ofmean force was calibrated based on the umbrella sampling algorithm fromthe adiabatic energy map that was cal...

Intermediate valence spectroscopy

International Nuclear Information System (INIS)

Gunnarsson, O.; Schoenhammer, K.

1987-01-01

Spectroscopic properties of intermediate valence compounds are studied using the Anderson model. Due to the large orbital and spin degeneracy N/sub f/ of the 4f-level, 1/N/sub f/ can be treated as a small parameter. This approach provides exact T = 0 results for the Anderson impurity model in the limit N/sub f/ → ∞, and by adding 1/N/sub f/ corrections some properties can be calculated accurately even for N/sub f/ = 1 or 2. In particular valence photoemission and resonance photoemission spectroscopies are studied. A comparison of theoretical and experimental spectra provides an estimate of the parameters in the model. Core level photoemission spectra provide estimates of the coupling between the f-level and the conduction states and of the f-level occupancy. With these parameters the model gives a fair description of other electron spectroscopies. For typical parameters the model predicts two structures in the f-spectrum, namely one structure at the f-level and one at the Fermi energy. The resonance photoemission calculation gives a photon energy dependence for these two peaks in fair agreement with experiment. The peak at the Fermi energy is partly due to a narrow Kondo resonance, resulting from many-body effects and the presence of a continuous, partly filled conduction band. This resonance is related to a large density of low-lying excitations, which explains the large susceptibility and specific heat observed for these systems at low temperatures. 38 references, 11 figures, 2 tables

Multiple multi-orbit fermionic and bosonic pairing and rotational SU(3) algebras

International Nuclear Information System (INIS)

Kota, V.K.B.

2017-01-01

In nuclei with valence nucleons that are identical nucleons and occupy r number of j-orbits, there will be 2 r-1 number of multiple pairing (quasi-spin) SU(2) algebras with the generalized pair creation operator S + being a sum of single-j pair creation operators with arbitrary phases. Also, for each set of phases there will be a corresponding Sp(2Ω) algebra in U(2Ω) ⊃ Sp(2Ω); Ω = ∑ (2j+1)/2. Using this correspondence, derived is the condition for a general one-body operator of angular momentum rank k to be a quasi-spin scalar or a vector vis-a-vis the phases in S + . These will give special seniority selection rules for electromagnetic transitions. We found that the phase choice advocated by Arvieu and Moszkowski gives pairing Hamiltonians having maximum correlation with well known effective interactions. All the results derived for identical fermion systems are shown to extend to identical boson systems such as sd, sp, sdg and sdpf interacting boson models (IBM's) with SU(2) → SU(1,1) and Sp(2/Omega) → SO(2Ω). Going beyond pairing, for a given set of oscillator orbits, there are multiple rotational SU(3) algebras both in shell model and IBM's. Different SU(3) algebras in IBM's are shown, using sdg IBM as an example, to give different geometric shapes.

Quantum Hamiltonian reduction and conformal field theories

International Nuclear Information System (INIS)

Bershadsky, M.

1991-01-01

It is proved that irreducible representation of the Virasoro algebra can be extracted from an irreducible representation space of the SL (2, R) current algebra by putting a constraint on the latter using the BRST formalism. Thus there is a SL(2, R) symmetry in the Virasoro algebra which is gauged and hidden. This construction of the Virasoro algebra is the quantum analog of the Hamiltonian reduction. The author then naturally leads to consider an SL(2, R) Wess-Zumino-Witten model. This system is related to the quantum field theory of the coadjoint orbit of the Virasoro group. Based on this result he presents the canonical derivation of the SL(2, R) current algebra in Polyakov's theory of two dimensional gravity; it is manifestation of the SL(2, R) symmetry in the conformal field theory hidden by the quantum Hamiltonian reduction. He discusses the quantum Hamiltonian reduction of the SL(n, R) current algebra for the general type of constraints labeled by index 1 ≤ l ≤ (n - 1) and claim that it leads to the new extended conformal algebras W n l . For l = 1 he recovers the well known W n algebra introduced by A. Zamolodchikov. For SL(3, R) Wess-Zumino-Witten model there are two different possibilities of constraining it. The first possibility gives the W 3 algebra, while the second leads to the new chiral algebra W 3 2 generated by the stress-energy tensor, two bosonic supercurrents with spins 3/2 and the U(1) current. He conjectures a Kac formula that describes the highly reducible representation for this algebra. He also makes some speculations concerning the structure of W gravity

Schwinger variational principle applied to molecular photoionization

International Nuclear Information System (INIS)

Smith, M.E.

1985-01-01

A method based upon the Schwinger variational principle was developed to study molecular photoionization and electron-molecule scattering. Exact static-exchange solutions to the equations for the continuum orbitals are obtained within the Hartree-Fock approximation; and from these cross sections and angular distributions are derived for both of the above processes. This method was applied to photoionization of the valence levels of three different systems. The first application of this method is a study of the photoionization of the valence levels of NO. Next, vibrationally resolved branching ratios and vibrational state-specific asymmetry parameters for photoionization of the 5sigma level of CO are presented. Finally, a study of the photoionization of the 5sigma level of CO absorbed on a nickel surface is reported. Approximating this system by the linear triatomic molecule NiCO leads to cross sections and angular distributions which are in good agreement with experimental data

Gelfand-Dikii Hamiltonian operator and co-ad joint representation of the Volterra group

International Nuclear Information System (INIS)

Lebedev, D.R.; Manin, Yu.I.

1978-01-01

It is shown that the Gelfand-Dikii Hamiltonian structure is an analogue of a very special class of finite-dimensional symplectic structures, namely, the Kirillow structures on the orbits of the co-adjoint representation of the Lie groups. The Lie group is represented by the Volterra operators. The main interest lies in the possibility of application of the ideology of ''geometric quantization'' to the Lax equations

Ab initio study of isomerism in molecular ions Li2AB+ with 10 valence electrons

International Nuclear Information System (INIS)

Charkin, O.P.; Mak-Ki, M.L.; Shlojer, P.R.

1997-01-01

Ab initio calculations of surfaces of Li 2 AB + molecular ion potential energy with biatomic anions AB - with 10 valence electrons have been made in the framework of approximations MP2/6-31G 1 /HF/6-31G*+ZPE(HF/6-31G*) and MP4SDTQ/631G*//MP2/6-31G*+ZPE(MP2/6-31G*). Influence of electron correlation on the accuracy of calculations of their structural and vibrational characteristics is studied. The following most favourable structures have been found: linear for Li 2 BO + , Li 2 CN + , and bent one for Li 2 BS + , with cations coordinated at different anion atoms; onium one for AlOLi 2 + , AlSLi 2 + , SiNLi 2 + and SiPLi 2 + with both cations at electronegative atom of anion

Effect of the density of the electronic states at the valence orbital of the bridge redox molecule on the dependence of the tunnel current on the overvoltage in the case of fully adiabatic electron transition

International Nuclear Information System (INIS)

Medvedev, Igor G.

2008-01-01

Effect of the density of the electronic states at the valence orbital of the bridge redox molecule on the dependence of the tunnel current on the overvoltage and on the width at half maximum of the current-overvoltage curve is studied. A number of the approximate expressions for the density of states, the tunnel current and the width are obtained in the fully adiabatic limit for different particular cases. It is shown that at small values of the coupling of the electronic levels of the electrodes with the valence orbital of the redox molecule and the small values of the bias voltage two regions of the reorganization Gibbs energy exist with different dependence of the width on the reorganization Gibbs energy. The results of calculations of the density of states, the tunnel current and the width are presented and used for the interpretation of the experimental data [N.G. Tao, Phys. Rev. Lett. 76 (1996) 4066, I. Visoly-Fisher, K. Daie, Y. Terazono, C. Herrero, F. Fungo, L. Otero, E. Durantini, J.J. Silber, L. Sereno, D. Gust, T.A. Moore, A.L. Moore, S.M. Lindsay, PNAS 103 (2006) 8686

Newton algorithm for Hamiltonian characterization in quantum control

International Nuclear Information System (INIS)

Ndong, M; Sugny, D; Salomon, J

2014-01-01

We propose a Newton algorithm to characterize the Hamiltonian of a quantum system interacting with a given laser field. The algorithm is based on the assumption that the evolution operator of the system is perfectly known at a fixed time. The computational scheme uses the Crank–Nicholson approximation to explicitly determine the derivatives of the propagator with respect to the Hamiltonians of the system. In order to globalize this algorithm, we use a continuation method that improves its convergence properties. This technique is applied to a two-level quantum system and to a molecular one with a double-well potential. The numerical tests show that accurate estimates of the unknown parameters are obtained in some cases. We discuss the numerical limits of the algorithm in terms of the basin of convergence and the non-uniqueness of the solution. (paper)

X-ray photoelectron spectra structure and chemical bonding in AmO2

Directory of Open Access Journals (Sweden)

Teterin Yury A.

2015-01-01

Full Text Available Quantitative analysis was done of the X-ray photoelectron spectra structure in the binding energy range of 0 eV to ~35 eV for americium dioxide (AmO2 valence electrons. The binding energies and structure of the core electronic shells (~35 eV-1250 eV, as well as the relativistic discrete variation calculation results for the Am63O216 and AmO8 (D4h cluster reflecting Am close environment in AmO2 were taken into account. The experimental data show that the many-body effects and the multiplet splitting contribute to the spectral structure much less than the effects of formation of the outer (0-~15 eV binding energy and the inner (~15 eV-~35 eV binding energy valence molecular orbitals. The filled Am 5f electronic states were shown to form in the AmO2 valence band. The Am 6p electrons participate in formation of both the inner and the outer valence molecular orbitals (bands. The filled Am 6p3/2 and the O 2s electronic shells were found to make the largest contributions to the formation of the inner valence molecular orbitals. Contributions of electrons from different molecular orbitals to the chemical bond in the AmO8 cluster were evaluated. Composition and sequence order of molecular orbitals in the binding energy range 0-~35 eV in AmO2 were established. The experimental and theoretical data allowed a quantitative scheme of molecular orbitals for AmO2, which is fundamental for both understanding the chemical bond nature in americium dioxide and the interpretation of other X-ray spectra of AmO2.

General technique to produce isochronous Hamiltonians

International Nuclear Information System (INIS)

Calogero, F; Leyvraz, F

2007-01-01

We introduce a new technique-characterized by an arbitrary positive constant Ω, with which we associate the period T = 2π/Ω-to 'Ω-modify' a Hamiltonian so that the new Hamiltonian thereby obtained is entirely isochronous, namely it yields motions all of which (except possibly for a lower dimensional set of singular motions) are periodic with the same fixed period T in all their degrees of freedom. This technique transforms real autonomous Hamiltonians into Ω-modified Hamiltonians which are also real and autonomous, and it is widely applicable, for instance, to the most general many-body problem characterized by Newtonian equations of motion ('acceleration equal force') provided it is translation invariant. The Ω-modified Hamiltonians are of course not translation invariant, but for Ω = 0 they reduce (up to marginal changes) to the unmodified Hamiltonians they were obtained from. Hence, when this technique is applied to translation-invariant Hamiltonians yielding, in their center-of-mass systems, chaotic motions with a natural time scale much smaller than T, the corresponding Ω-modified Hamiltonians shall display a chaotic behavior for quite some time before the isochronous character of the motions takes over. We moreover show that the quantized versions of these Ω-modified Hamiltonians feature equispaced spectra

Relaxation and cross section effects in valence band photoemission spectroscopy

International Nuclear Information System (INIS)

McFeely, F.R.

1976-09-01

Various problems relating to the interpretation of valence band x-ray photoemission (XPS) spectra of solids are discussed. The experiments and calculations reported herein deal with the following questions: (1) To what extent do many-body effects manifest themselves in an XPS valence band spectrum, and thus invalidate a direct comparison between the photoemission energy distribution, I(E), and the density of states, N(E), calculated on the basis of ground-state one-electron theory. (2) The effect of the binding-energy-dependent photoemission cross section on I(E) at XPS energies. (3) In favorable cases indicated by (1) and (2) we examine the effect of the interaction of the crystal field with the apparent spin-orbit splittings of core levels observed in XPS spectra. (4) The use of tight binding band structure calculations to parameterize the electronic band structure from XPS and other data is described. (5) The use of high energy angle-resolved photoemission on oriented single crystals to gain orbital symmetry information is discussed. (6) The evolution of the shape of the photoemission energy distribution (of polycrystalline Cu) as a function of photon energy from 50 less than or equal h ω less than or equal 175 is discussed

Valence Band Structure of InAs1−xBix and InSb1−xBix Alloy Semiconductors Calculated Using Valence Band Anticrossing Model

Science.gov (United States)

Samajdar, D. P.; Dhar, S.

2014-01-01

The valence band anticrossing model has been used to calculate the heavy/light hole and spin-orbit split-off energies in InAs1−xBix and InSb1−xBix alloy systems. It is found that both the heavy/light hole, and spin-orbit split E + levels move upwards in energy with an increase in Bi content in the alloy, whereas the split E − energy for the holes shows a reverse trend. The model is also used to calculate the reduction of band gap energy with an increase in Bi mole fraction. The calculated values of band gap variation agree well with the available experimental data. PMID:24592181

Reactivity of etoricoxib based on computational study of molecular orbitals, molecular electrostatic potential surface and Mulliken charge analysis

Science.gov (United States)

Sachdeva, Ritika; Soni, Abhinav; Singh, V. P.; Saini, G. S. S.

2018-05-01

Etoricoxib is one of the selective cyclooxygenase inhibitor drug which plays a significant role in the pharmacological management of arthritis and pain. The theoretical investigation of its reactivity is done using Density Functional Theory calculations. Molecular Electrostatic Potential Surface of etoricoxib and its Mulliken atomic charge distribution are used for the prediction of its electrophilic and nucleophilic sites. The detailed analysis of its frontier molecular orbitals is also done.

A parallel algorithm for Hamiltonian matrix construction in electron-molecule collision calculations: MPI-SCATCI

Science.gov (United States)

Al-Refaie, Ahmed F.; Tennyson, Jonathan

2017-12-01

Construction and diagonalization of the Hamiltonian matrix is the rate-limiting step in most low-energy electron - molecule collision calculations. Tennyson (1996) implemented a novel algorithm for Hamiltonian construction which took advantage of the structure of the wavefunction in such calculations. This algorithm is re-engineered to make use of modern computer architectures and the use of appropriate diagonalizers is considered. Test calculations demonstrate that significant speed-ups can be gained using multiple CPUs. This opens the way to calculations which consider higher collision energies, larger molecules and / or more target states. The methodology, which is implemented as part of the UK molecular R-matrix codes (UKRMol and UKRMol+) can also be used for studies of bound molecular Rydberg states, photoionization and positron-molecule collisions.

Transition from direct to inverted charge transport Marcus regions in molecular junctions via molecular orbital gating

Science.gov (United States)

Yuan, Li; Wang, Lejia; Garrigues, Alvar R.; Jiang, Li; Annadata, Harshini Venkata; Anguera Antonana, Marta; Barco, Enrique; Nijhuis, Christian A.

2018-04-01

Solid-state molecular tunnel junctions are often assumed to operate in the Landauer regime, which describes essentially activationless coherent tunnelling processes. In solution, on the other hand, charge transfer is described by Marcus theory, which accounts for thermally activated processes. In practice, however, thermally activated transport phenomena are frequently observed also in solid-state molecular junctions but remain poorly understood. Here, we show experimentally the transition from the Marcus to the inverted Marcus region in a solid-state molecular tunnel junction by means of intra-molecular orbital gating that can be tuned via the chemical structure of the molecule and applied bias. In the inverted Marcus region, charge transport is incoherent, yet virtually independent of temperature. Our experimental results fit well to a theoretical model that combines Landauer and Marcus theories and may have implications for the interpretation of temperature-dependent charge transport measurements in molecular junctions.

The analytic gradient with a reduced molecular orbital space for the equation-of-motion coupled-cluster theory: systematic study of the magnitudes and trends in simple molecules

International Nuclear Information System (INIS)

Baeck, Kyoung K.; Jeon, Sang Il

2000-01-01

The analytic gradient method for the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) energy has been extended to employ a reduced molecular orbital (MO) space. Not only the innermost core MO s but also some of the outermost virtual MO s can be dropped in the reduced MO space, and a substantial amount of computation time can be reduced without deteriorating the results. In order to study the magnitudes and trends of the effects of the dropped MO s , the geometries and vibrational properties of the ground and excited states of BF, CO, CN, N 2 , AlCl, SiS, P 2 , BCl, AlF, CS, SiO, PN and GeSe are calculated with different sizes of molecular orbital space. The 6-31G and the aug-cc-pVTZ basis sets are employed for all molecules except GeSe for which the 6-311 G and the TZV+f basis sets are used. It is shown that the magnitudes of the drop MO effects are about 0.005 A in bond lengths and about 1% on harmonic frequencies and IR intensities provided that the dropped MO s correspond to (1s), (1s,2s,2p), and (1s,2s,2p,3s,3p) atomic orbitals of the first, the second, and the third row atoms, respectively. The geometries and vibrational properties of the first and the second excited states of HCN and HCN are calculated by using a drastically reduced virtual MO space as well as with the well defined frozen core MO space. The results suggest the possibility of using a very small MO space for qualitative study of valence excited states

B-site cation order/disorder and their valence states in Ba3MnNb2O9 perovskite oxide

Science.gov (United States)

Xin, Yan; Huang, Qing; Shafieizadeh, Zahra; Zhou, Haidong

2018-06-01

Polycrystalline samples Ba3MnNb2O9 synthesized by solid state reaction and single crystal samples grown by optical floating zone have been characterized using scanning transmission electron microscopy and electron energy loss spectroscopy. Three types of B-site Mn and Nb ordering phase are observed: fully ordered 1Mn:2Nb; fully disordered; nano-sized 1Mn:1Nb ordered. No electronic structure change for crystals with different ordering/disordering. The Mn valence is determined to be 2+, and Nb valence is 5+. Oxygen 2p orbitals hybridize with Mn 3d and Nb 4d orbitals. Factors that affect the electron energy loss near edge structures of transition metal white-lines in electron energy loss spectroscopy are explicitly illustrated and discussed.

Spin manipulation and relaxation in spin-orbit qubits

Science.gov (United States)

Borhani, Massoud; Hu, Xuedong

2012-03-01

We derive a generalized form of the electric dipole spin resonance (EDSR) Hamiltonian in the presence of the spin-orbit interaction for single spins in an elliptic quantum dot (QD) subject to an arbitrary (in both direction and magnitude) applied magnetic field. We predict a nonlinear behavior of the Rabi frequency as a function of the magnetic field for sufficiently large Zeeman energies, and present a microscopic expression for the anisotropic electron g tensor. Similarly, an EDSR Hamiltonian is devised for two spins confined in a double quantum dot (DQD), where coherent Rabi oscillations between the singlet and triplet states are induced by jittering the inter-dot distance at the resonance frequency. Finally, we calculate two-electron-spin relaxation rates due to phonon emission, for both in-plane and perpendicular magnetic fields. Our results have immediate applications to current EDSR experiments on nanowire QDs, g-factor optimization of confined carriers, and spin decay measurements in DQD spin-orbit qubits.

Valencies of the lanthanides

OpenAIRE

Johnson, David A.; Nelson, Peter G.

2018-01-01

The valencies of the lanthanides vary more than was once thought. In addition to valencies associated with a half-full shell, there are valencies associated with a quarter- and three-quarter-full shell. This can be explained on the basis of Slater’s theory of many-electron atoms. The same theory explains the variation in complexing constants in the trivalent state (the “tetrad effect”). Valency in metallic and organometallic compounds is also discussed.

Exact and Optimal Quantum Mechanics/Molecular Mechanics Boundaries.

Science.gov (United States)

Sun, Qiming; Chan, Garnet Kin-Lic

2014-09-09

Motivated by recent work in density matrix embedding theory, we define exact link orbitals that capture all quantum mechanical (QM) effects across arbitrary quantum mechanics/molecular mechanics (QM/MM) boundaries. Exact link orbitals are rigorously defined from the full QM solution, and their number is equal to the number of orbitals in the primary QM region. Truncating the exact set yields a smaller set of link orbitals optimal with respect to reproducing the primary region density matrix. We use the optimal link orbitals to obtain insight into the limits of QM/MM boundary treatments. We further analyze the popular general hybrid orbital (GHO) QM/MM boundary across a test suite of molecules. We find that GHOs are often good proxies for the most important optimal link orbital, although there is little detailed correlation between the detailed GHO composition and optimal link orbital valence weights. The optimal theory shows that anions and cations cannot be described by a single link orbital. However, expanding to include the second most important optimal link orbital in the boundary recovers an accurate description. The second optimal link orbital takes the chemically intuitive form of a donor or acceptor orbital for charge redistribution, suggesting that optimal link orbitals can be used as interpretative tools for electron transfer. We further find that two optimal link orbitals are also sufficient for boundaries that cut across double bonds. Finally, we suggest how to construct "approximately" optimal link orbitals for practical QM/MM calculations.

A study of the valence shell spectroscopic and thermodynamic properties of trifluoronitrosomethane cations

International Nuclear Information System (INIS)

Graham, D.M.; Powis, I.; Underwood, J.G.; Shaw, D.A.; Holland, D.M.P.

2012-01-01

Highlights: ► Fragmentation processes in CF 3 NO have been studied using mass spectrometry. ► Singly charged atomic fragments have been observed. ► Experimental appearance energies have been compared to thermochemical estimates. ► Hartree Fock transition energies and oscillator strengths have been calculated. - Abstract: A time-of-flight mass spectrometry study has been carried out to investigate the fragmentation processes occurring in trifluoronitrosomethane (CF 3 NO) as a result of valence shell photoionisation. Synchrotron radiation has been used to record spectra in the photon energy range ∼10–42 eV, and appearance energies have been determined for 10 fragment ions. At high excitation energies, singly charged atomic fragments have been observed. For the main dissociation channels, leading to the formation of NO + , CF 2 + or CF 3 + , the experimental appearance energies have been compared with thermochemical estimates, and a satisfactory agreement has been found. Structure observed in the total ion yield curve has been interpreted with the aid of excited state transition energies and oscillator strengths obtained in a time-dependent Hartree Fock calculation. The theoretical results show that configuration interaction strongly affects many of the valence states. A HeI excited photoelectron spectrum of CF 3 NO has been measured and the orbital ionisation energies have been compared with theoretical values computed using the Outer Valence Green’s Function approach. A large Franck–Condon gap is observed between the 12a′ (n - ) and the 11a ′ state bands, in accord with the calculated vertical ionisation energies of 10.87 and 16.32 eV for the 12a′ (n − ) and the 11a′ (n + ) orbitals, respectively. In the ion yield curve, the corresponding energy range is strongly influenced by autoionising valence states.

Renormalization of Hamiltonian QCD

International Nuclear Information System (INIS)

Andrasi, A.; Taylor, John C.

2009-01-01

We study to one-loop order the renormalization of QCD in the Coulomb gauge using the Hamiltonian formalism. Divergences occur which might require counter-terms outside the Hamiltonian formalism, but they can be cancelled by a redefinition of the Yang-Mills electric field.

Valence effects of sorption: laboratory control of valence state

International Nuclear Information System (INIS)

Meyer, R.E.; Arnold, W.D.; Case, F.I.

1984-01-01

Estimation of the rates of migration of nuclides from nuclear waste repositories required knowledge of the interaction of these nuclides with the components of the geological formations in the path of the migration. These interactions will be dependent upon the valence state and speciation of the nuclide. If the valence state is not known, then there can be little confidence in use of the data for safety analysis. An electrochemical method of valence state control was developed which makes use of a porous electrode in a flow system containing a column of the adsorbent. By use of this method and solvent extraction analyses of the valence states, a number of reactions of interest to HLW repositories were investigated. These include the reduction of Np(V) and Tc(VII) by crushed basalt and other minerals. For the reduction of Np(V) by basalt, the experiments indicate that sorption on basalt increases with pH and that most of the Np is reduced to Np(IV). The adsorbed Np(IV) is very difficult to remove from the basalt. For the experiments with Tc(VII), the results are considerably more complicated. The results of these experiments are used to assess some of the techniques and methods currently used in safety analyses of proposed HLW repositories. Perhaps the most important consideration is that predictive modeling of valence change reactions, such as the reduction of Np(V) and Tc(VII), must be used with considerable caution, and the occurrence of such reactions should be verified as best as possible with experiments using valence state control and analyses. 13 references, 3 figures, 1 table

Geometry of Hamiltonian chaos

DEFF Research Database (Denmark)

Horwitz, Lawrence; Zion, Yossi Ben; Lewkowicz, Meir

2007-01-01

The characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian is extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce ...

Magnetic field line Hamiltonian

International Nuclear Information System (INIS)

Boozer, A.H.

1984-03-01

The magnetic field line Hamiltonian and the associated canonical form for the magnetic field are important concepts both for understanding toroidal plasma physics and for practical calculations. A number of important properties of the canonical or Hamiltonian representation are derived and their importance is explained

Periodic orbits near the particle resonance in galaxies

CERN Document Server

Contopoulos, George

1978-01-01

Near the particle resonance of a spiral galaxy the almost circular periodic orbits that exist inside the resonance (direct) or outside it (retrograde) are replaced by elongated trapped orbits around the maxima of the potential L/sub 4/ and L/sub 5/. These are the long- period trapped periodic orbits. The long-period orbits shrink to the points L/sub 4/, L/sub 5/ for a critical value of the Hamiltonian h. For still larger h, a family of short-period trapped orbits appears, with continuously growing size. The evolution of the periodic orbits with h is followed, theoretically and numerically, from the untrapped orbits to the long-periodic orbits and then to the short-periodic orbits, mainly in the case of a bar. In a tight spiral case an explanation of the asymmetric periodic and banana orbits is given, and an example of short-period orbits not surrounding L/sub 4/ or L/sub 5/ is provided. Another family of periodic orbits reaching corotation is trapped at the inner Lindblad resonance. (5 refs).

Development of constraint algorithm for the number of electrons in molecular orbitals consisting mainly 4f atomic orbitals of rare-earth elements and its introduction to tight-binding quantum chemical molecular dynamics method

International Nuclear Information System (INIS)

Endou, Akira; Onuma, Hiroaki; Jung, Sun-ho

2007-01-01

Our original tight-binding quantum chemical molecular dynamics code, Colors', has been successfully applied to the theoretical investigation of complex materials including rare-earth elements, e.g., metal catalysts supported on a CeO 2 surface. To expand our code so as to obtain a good convergence for the electronic structure of a calculation system including a rare-earth element, we developed a novel algorithm to provide a constraint condition for the number of electrons occupying the selected molecular orbitals that mainly consist of 4f atomic orbitals of the rare-earth element. This novel algorithm was introduced in Colors. Using Colors, we succeeded in obtaining the classified electronic configurations of the 4f atomic orbitals of Ce 4+ and reduced Ce ions in a CeO 2 bulk model with one oxygen defect, which makes it difficult to obtain a good convergence using a conventional first-principles quantum chemical calculation code. (author)

Canonical transformations and hamiltonian path integrals

International Nuclear Information System (INIS)

Prokhorov, L.V.

1982-01-01

Behaviour of the Hamiltonian path integrals under canonical transformations produced by a generator, is investigated. An exact form is determined for the kernel of the unitary operator realizing the corresponding quantum transformation. Equivalence rules are found (the Hamiltonian formalism, one-dimensional case) enabling one to exclude non-standard terms from the action. It is shown that the Hamiltonian path integral changes its form under cononical transformations: in the transformed expression besides the classical Hamiltonian function there appear some non-classical terms

Perspective: Quantum Hamiltonians for optical interactions

Science.gov (United States)

Andrews, David L.; Jones, Garth A.; Salam, A.; Woolley, R. Guy

2018-01-01

The multipolar Hamiltonian of quantum electrodynamics is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.

Effects of spin–orbit coupling and many-body correlations in STM transport through copper phthalocyanine

Directory of Open Access Journals (Sweden)

Benjamin Siegert

2015-12-01

Full Text Available The interplay of exchange correlations and spin–orbit interaction (SOI on the many-body spectrum of a copper phtalocyanine (CuPc molecule and their signatures in transport are investigated. We first derive a minimal model Hamiltonian in a basis of frontier orbitals that is able to reproduce experimentally observed singlet–triplet splittings. In a second step SOI effects are included perturbatively. Major consequences of the SOI are the splitting of former degenerate levels and a magnetic anisotropy, which can be captured by an effective low-energy spin Hamiltonian. We show that scanning tunneling microscopy-based magnetoconductance measurements can yield clear signatures of both these SOI-induced effects.

Pressure induced valence transitions in the Anderson lattice model

International Nuclear Information System (INIS)

Bernhard, B.H.; Coqblin, B.

2009-01-01

We apply the equation of motion method to the Anderson lattice model, which describes the physical properties of heavy fermion compounds. In particular, we focus here on the variation of the number of f electrons with pressure, associated to the crossover from the Kondo regime to the intermediate valence regime. We treat here the non-magnetic case and introduce an improved approximation, which consists of an alloy analogy based decoupling for the Anderson lattice model. It is implemented by partial incorporation of the spatial correlations contained in higher-order Green's functions involved in the problem that have been formerly neglected. As it has been verified in the framework of the Hubbard model, the alloy analogy avoids the breakdown of sum rules and is more appropriate to explore the asymmetric case of the periodic Anderson Hamiltonian. The densities of states for a simple cubic lattice are calculated for various values of the model parameters V, t, E f , and U.

Molecular cluster theory of chemical bonding in actinide oxide

International Nuclear Information System (INIS)

Ellis, D.E.; Gubanov, V.A.; Rosen, A.

1978-01-01

The electronic structure of actinide monoxides AcO and dioxides AcO 2 , where Ac = Th, U, Np, Pu, Am, Cm and Bk has been studied by molecular cluster methods based on the first-principles one-electron local density theory. Molecular orbitals for nearest neighbor clusters AcO 10- 6 and AcO 12- 8 representative of monoxide and dioxide lattices were obtained using non-relativistic spin-restricted and spin-polarized Hartree-Fock-Slater models for the entire series. Fully relativistic Dirac-Slater calculations were performed for ThO, UO and NpO in order to explore magnitude of spin-orbit splittings and level shifts in valence structure. Self-consistent iterations were carried out for NpO, in which the NpO 6 cluster was embedded in the molecular field of the solid. Finally, a ''moment polarized'' model which combines both spin-polarization and relativistic effects in a consistent fashion was applied to the NpO system. Covalent mixing of oxygen 2p and Ac 5f orbitals was found to increase rapidly across the actinide series; metal s,p,d covalency was found to be nearly constant. Mulliken atomic population analysis of cluster eigenvectors shows that free-ion crystal field models are unreliable, except for the light actinides. X-ray photoelectron line shapes have been calculated and are found to compare rather well with experimental data on the dioxides

Notch filters for port-Hamiltonian systems

NARCIS (Netherlands)

Dirksz, D.A.; Scherpen, J.M.A.; van der Schaft, A.J.; Steinbuch, M.

2012-01-01

In this paper a standard notch filter is modeled in the port-Hamiltonian framework. By having such a port-Hamiltonian description it is proven that the notch filter is a passive system. The notch filter can then be interconnected with another (nonlinear) port-Hamiltonian system, while preserving the

Noncanonical Hamiltonian methods in plasma dynamics

International Nuclear Information System (INIS)

Kaufman, A.N.

1981-11-01

A Hamiltonian approach to plasma dynamics has numerous advantages over equivalent formulations which ignore the underlying Hamiltonian structure. In addition to achieving a deeper understanding of processes, Hamiltonian methods yield concise expressions (such as the Kubo form for linear susceptibility), greatly shorten the length of calculations, expose relationships (such as between the ponderomotive Hamiltonian and the linear susceptibility), determine invariants in terms of symmetry operations, and cover situations of great generality. In addition, they yield the Poincare invariants, in particular Liouville volume and adiabatic actions

Electrostatics of proteins in dielectric solvent continua. II. Hamiltonian reaction field dynamics

Energy Technology Data Exchange (ETDEWEB)

Bauer, Sebastian; Tavan, Paul; Mathias, Gerald, E-mail: gerald.mathias@physik.uni-muenchen.de [Lehrstuhl für BioMolekulare Optik, Ludig-Maximilians Universität München, Oettingenstr. 67, 80538 München (Germany)

2014-03-14

In Paper I of this work [S. Bauer, G. Mathias, and P. Tavan, J. Chem. Phys. 140, 104102 (2014)] we have presented a reaction field (RF) method, which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of polarizable molecular mechanics (MM) force fields. Building upon these results, here we suggest a method for linearly scaling Hamiltonian RF/MM molecular dynamics (MD) simulations, which we call “Hamiltonian dielectric solvent” (HADES). First, we derive analytical expressions for the RF forces acting on the solute atoms. These forces properly account for all those conditions, which have to be self-consistently fulfilled by RF quantities introduced in Paper I. Next we provide details on the implementation, i.e., we show how our RF approach is combined with a fast multipole method and how the self-consistency iterations are accelerated by the use of the so-called direct inversion in the iterative subspace. Finally we demonstrate that the method and its implementation enable Hamiltonian, i.e., energy and momentum conserving HADES-MD, and compare in a sample application on Ac-Ala-NHMe the HADES-MD free energy landscape at 300 K with that obtained in Paper I by scanning of configurations and with one obtained from an explicit solvent simulation.

Theory of collective Hamiltonian

Energy Technology Data Exchange (ETDEWEB)

Zhang Qingying

1982-02-01

Starting from the cranking model, we derive the nuclear collective Hamiltonian. We expand the total energy of the collective motion of the ground state of even--even nuclei in powers of the deformation parameter ..beta... In the first approximation, we only take the lowest-order non-vanished terms in the expansion. The collective Hamiltonian thus obtained rather differs from the A. Bohr's Hamiltonian obtained by the irrotational incompressible liquid drop model. If we neglect the coupling term between ..beta..-and ..gamma..-vibration, our Hamiltonian then has the same form as that of A. Bohr. But there is a difference between these collective parameters. Our collective parameters are determined by the state of motion of the nucleous in the nuclei. They are the microscopic expressions. On the contrary, A. Bohr's collective parameters are only the simple functions of the microscopic physical quantities (such as nuclear radius and surface tension, etc.), and independent of the state of motion of the nucleons in the nuclei. Furthermore, there exist the coupling term between ..beta..-and ..gamma..-vibration and the higher-order terms in our expansion. They can be treated as the perturbations. There are no such terms in A. Bohr's Hamiltonian. These perturbation terms will influence the rotational, vibrational spectra and the ..gamma..-transition process, etc.

Generalizing the classical fixed-centres problem in a non-Hamiltonian way

International Nuclear Information System (INIS)

Albouy, A; Stuchi, T J

2004-01-01

The problem of two gravitational (or Coulombian) fixed centres is a classical integrable problem, stated and integrated by Euler in 1760. The integrability is due to the unexpected first integral G. We introduce some straightforward generalizations of the problem that still have the generalization of G as a first integral, but do not possess the energy integral. We present some numerical integrations showing the main features of their dynamics. In the domain of bounded orbits the behaviour of these a priori non-Hamiltonian systems is very similar to the behaviour of usual near-integrable systems

Synchronisation in coupled quantum Hamiltonian superconducting oscillator via a control potential

International Nuclear Information System (INIS)

Al-Khawaja, Sameer

2009-01-01

This paper presents chaos synchronisation in a SQUID device mutually coupled to a resonant LC classical circuit. Via the Hamiltonian of the coupled quantum-classical system and by means of a 'control potential' in the form of a double-well, measure synchronisation has been found to exist. A transition from quasi-periodic to chaotically synchronised orbits in the phase space has been observed, as the strength of coupling is increased between both oscillators. The system reaches a non-synchronised state if the choice of the control potential were to render both oscillators non-identical.

Multiplet effects in the electronic structure of intermediate-valence compounds

DEFF Research Database (Denmark)

Thunström, P.; Di Marco, I.; Grechnev, A.

2009-01-01

We present an implementation of the Hubbard-I approximation based on the exact solution of the atomic many-body problem incorporated in a full-potential linear muffin-tin orbital method of density-functional theory. Comparison between calculated and measured x-ray photoemission spectra reveal a g...... a good agreement for intermediate valence systems in open crystal structures such as YbInCu4, SmB6, and YbB12. Spectral features of the unoccupied states of SmB6 are predicted....

Collective Hamiltonians for dipole giant resonances

International Nuclear Information System (INIS)

Weiss, L.I.

1991-07-01

The collective hamiltonian for the Giant Dipole resonance (GDR), in the Goldhaber-Teller-Model, is analytically constructed using the semiclassical and generator coordinates method. Initially a conveniently parametrized set of many body wave functions and a microscopic hamiltonian, the Skyrme hamiltonian - are used. These collective Hamiltonians are applied to the investigation of the GDR, in He 4 , O 16 and Ca 40 nuclei. Also the energies and spectra of the GDR are obtained in these nuclei. The two sets of results are compared, and the zero point energy effects analysed. (author)

Implementation of surface hopping molecular dynamics using semiempirical methods

International Nuclear Information System (INIS)

Fabiano, E.; Keal, T.W.; Thiel, W.

2008-01-01

A molecular dynamics driver and surface hopping algorithm for nonadiabatic dynamics has been implemented in a development version of the MNDO semiempirical electronic structure package. The required energies, gradients and nonadiabatic couplings are efficiently evaluated on the fly using semiempirical configuration interaction methods. The choice of algorithms for the time evolution of the nuclear motion and quantum amplitudes is discussed, and different schemes for the computation of nonadiabatic couplings are analysed. The importance of molecular orbital tracking and electronic state following is underlined in the context of configuration interaction calculations. The method is applied to three case studies (ethylene, methaniminium ion, and methanimine) using the orthogonalization corrected OM2 Hamiltonian. In all three cases decay times and dynamics paths similar to high-level ab initio results are obtained

On the domain of the Nelson Hamiltonian

Science.gov (United States)

Griesemer, M.; Wünsch, A.

2018-04-01

The Nelson Hamiltonian is unitarily equivalent to a Hamiltonian defined through a closed, semibounded quadratic form, the unitary transformation being explicitly known and due to Gross. In this paper, we study the mapping properties of the Gross-transform in order to characterize the regularity properties of vectors in the form domain of the Nelson Hamiltonian. Since the operator domain is a subset of the form domain, our results apply to vectors in the domain of the Hamiltonian as well. This work is a continuation of our previous work on the Fröhlich Hamiltonian.

Geometric Hamiltonian structures and perturbation theory

International Nuclear Information System (INIS)

Omohundro, S.

1984-08-01

We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging

Time dependent drift Hamiltonian

International Nuclear Information System (INIS)

Boozer, A.H.

1982-04-01

The motion of individual charged particles in a given magnetic and an electric fields is discussed. An idea of a guiding center distribution function f is introduced. The guiding center distribution function is connected to the asymptotic Hamiltonian through the drift kinetic equation. The general non-stochastic magnetic field can be written in a contravariant and a covariant forms. The drift Hamiltonian is proposed, and the canonical gyroradius is presented. The proposed drift Hamiltonian agrees with Alfven's drift velocity to lowest non-vanishing order in the gyroradius. The relation between the exact, time dependent equations of motion and the guiding center equation is clarified by a Lagrangian analysis. The deduced Lagrangian represents the drift motion. (Kato, T.)

Entangled trajectories Hamiltonian dynamics for treating quantum nuclear effects

Science.gov (United States)

Smith, Brendan; Akimov, Alexey V.

2018-04-01

A simple and robust methodology, dubbed Entangled Trajectories Hamiltonian Dynamics (ETHD), is developed to capture quantum nuclear effects such as tunneling and zero-point energy through the coupling of multiple classical trajectories. The approach reformulates the classically mapped second-order Quantized Hamiltonian Dynamics (QHD-2) in terms of coupled classical trajectories. The method partially enforces the uncertainty principle and facilitates tunneling. The applicability of the method is demonstrated by studying the dynamics in symmetric double well and cubic metastable state potentials. The methodology is validated using exact quantum simulations and is compared to QHD-2. We illustrate its relationship to the rigorous Bohmian quantum potential approach, from which ETHD can be derived. Our simulations show a remarkable agreement of the ETHD calculation with the quantum results, suggesting that ETHD may be a simple and inexpensive way of including quantum nuclear effects in molecular dynamics simulations.

Magnetic field line Hamiltonian

International Nuclear Information System (INIS)

Boozer, A.H.

1985-02-01

The basic properties of the Hamiltonian representation of magnetic fields in canonical form are reviewed. The theory of canonical magnetic perturbation theory is then developed and applied to the time evolution of a magnetic field embedded in a toroidal plasma. Finally, the extension of the energy principle to tearing modes, utilizing the magnetic field line Hamiltonian, is outlined

Hamiltonian closures in fluid models for plasmas

Science.gov (United States)

Tassi, Emanuele

2017-11-01

This article reviews recent activity on the Hamiltonian formulation of fluid models for plasmas in the non-dissipative limit, with emphasis on the relations between the fluid closures adopted for the different models and the Hamiltonian structures. The review focuses on results obtained during the last decade, but a few classical results are also described, in order to illustrate connections with the most recent developments. With the hope of making the review accessible not only to specialists in the field, an introduction to the mathematical tools applied in the Hamiltonian formalism for continuum models is provided. Subsequently, we review the Hamiltonian formulation of models based on the magnetohydrodynamics description, including those based on the adiabatic and double adiabatic closure. It is shown how Dirac's theory of constrained Hamiltonian systems can be applied to impose the incompressibility closure on a magnetohydrodynamic model and how an extended version of barotropic magnetohydrodynamics, accounting for two-fluid effects, is amenable to a Hamiltonian formulation. Hamiltonian reduced fluid models, valid in the presence of a strong magnetic field, are also reviewed. In particular, reduced magnetohydrodynamics and models assuming cold ions and different closures for the electron fluid are discussed. Hamiltonian models relaxing the cold-ion assumption are then introduced. These include models where finite Larmor radius effects are added by means of the gyromap technique, and gyrofluid models. Numerical simulations of Hamiltonian reduced fluid models investigating the phenomenon of magnetic reconnection are illustrated. The last part of the review concerns recent results based on the derivation of closures preserving a Hamiltonian structure, based on the Hamiltonian structure of parent kinetic models. Identification of such closures for fluid models derived from kinetic systems based on the Vlasov and drift-kinetic equations are presented, and

Single-particle dynamics - Hamiltonian formulation

International Nuclear Information System (INIS)

Montague, B.W.

1977-01-01

In this paper the Hamiltonian formalism is applied to the linear theory of accelerator dynamics. The reasons for the introduction of this method rather than the more straightforward use of second order differential equations of motion are briefly discussed. An outline of Lagrangian and Hamiltonian formalism is given, some properties of the Hamiltonian are discussed and canonical transformations are illustrated. The methods are demonstrated using elementary examples such as the simple pendulum and the procedures adopted to handle specific problems in accelerator theory are indicated. (B.D.)

FOB-SH: Fragment orbital-based surface hopping for charge carrier transport in organic and biological molecules and materials

Energy Technology Data Exchange (ETDEWEB)

Spencer, J.; Gajdos, F.; Blumberger, J., E-mail: j.blumberger@ucl.ac.uk [Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT (United Kingdom)

2016-08-14

We introduce a fragment orbital-based fewest switches surface hopping method, FOB-SH, designed to efficiently simulate charge carrier transport in strongly fluctuating condensed phase systems such as organic semiconductors and biomolecules. The charge carrier wavefunction is expanded and the electronic Hamiltonian constructed in a set of singly occupied molecular orbitals of the molecular sites that mediate the charge transfer. Diagonal elements of the electronic Hamiltonian (site energies) are obtained from a force field, whereas the off-diagonal or electronic coupling matrix elements are obtained using our recently developed analytic overlap method. We derive a general expression for the exact forces on the adiabatic ground and excited electronic state surfaces from the nuclear gradients of the charge localized electronic states. Applications to electron hole transfer in a model ethylene dimer and through a chain of ten model ethylenes validate our implementation and demonstrate its computational efficiency. On the larger system, we calculate the qualitative behaviour of charge mobility with change in temperature T for different regimes of the intermolecular electronic coupling. For small couplings, FOB-SH predicts a crossover from a thermally activated regime at low temperatures to a band-like transport regime at higher temperatures. For higher electronic couplings, the thermally activated regime disappears and the mobility decreases according to a power law. This is interpreted by a gradual loss in probability for resonance between the sites as the temperature increases. The polaron hopping model solved for the same system gives a qualitatively different result and underestimates the mobility decay at higher temperatures. Taken together, the FOB-SH methodology introduced here shows promise for a realistic investigation of charge carrier transport in complex organic, aqueous, and biological systems.

FOB-SH: Fragment orbital-based surface hopping for charge carrier transport in organic and biological molecules and materials

Science.gov (United States)

Spencer, J.; Gajdos, F.; Blumberger, J.

2016-08-01

We introduce a fragment orbital-based fewest switches surface hopping method, FOB-SH, designed to efficiently simulate charge carrier transport in strongly fluctuating condensed phase systems such as organic semiconductors and biomolecules. The charge carrier wavefunction is expanded and the electronic Hamiltonian constructed in a set of singly occupied molecular orbitals of the molecular sites that mediate the charge transfer. Diagonal elements of the electronic Hamiltonian (site energies) are obtained from a force field, whereas the off-diagonal or electronic coupling matrix elements are obtained using our recently developed analytic overlap method. We derive a general expression for the exact forces on the adiabatic ground and excited electronic state surfaces from the nuclear gradients of the charge localized electronic states. Applications to electron hole transfer in a model ethylene dimer and through a chain of ten model ethylenes validate our implementation and demonstrate its computational efficiency. On the larger system, we calculate the qualitative behaviour of charge mobility with change in temperature T for different regimes of the intermolecular electronic coupling. For small couplings, FOB-SH predicts a crossover from a thermally activated regime at low temperatures to a band-like transport regime at higher temperatures. For higher electronic couplings, the thermally activated regime disappears and the mobility decreases according to a power law. This is interpreted by a gradual loss in probability for resonance between the sites as the temperature increases. The polaron hopping model solved for the same system gives a qualitatively different result and underestimates the mobility decay at higher temperatures. Taken together, the FOB-SH methodology introduced here shows promise for a realistic investigation of charge carrier transport in complex organic, aqueous, and biological systems.

Symplectic manifolds, coadjoint orbits, and Mean Field Theory

International Nuclear Information System (INIS)

Rosensteel, G.

1986-01-01

Mean field theory is given a geometrical interpretation as a Hamiltonian dynamical system. The Hartree-Fock phase space is the Grassmann manifold, a symplectic submanifold of the projective space of the full many-fermion Hilbert space. The integral curves of the Hartree-Fock vector field are the time-dependent Hartree-Fock solutions, while the critical points of the energy function are the time-independent states. The mean field theory is generalized beyond determinants to coadjoint orbit spaces of the unitary group; the Grassmann variety is the minimal coadjoint orbit

Polaronic and dressed molecular states in orbital Feshbach resonances

Science.gov (United States)

Xu, Junjun; Qi, Ran

2018-04-01

We consider the impurity problem in an orbital Feshbach resonance (OFR), with a single excited clock state | e ↑⟩ atom immersed in a Fermi sea of electronic ground state | g ↓⟩. We calculate the polaron effective mass and quasi-particle residue, as well as the polaron to molecule transition. By including one particle-hole excitation in the molecular state, we find significant correction to the transition point. This transition point moves toward the BCS side for increasing particle densities, which suggests that the corresponding many-body physics is similar to a narrow resonance.

The Hamiltonian of QED. Zero mode

International Nuclear Information System (INIS)

Zastavenko, L.G.

1990-01-01

We start with the standard QED Lagrangian. New derivation of the spinor QED Hamiltonian is given. We have taken into account the zero mode. Our derivation is faultless from the point of view of gauge invariance. It gives important corrections to the standard QED Hamiltonian. Our derivation of the Hamiltonian can be generalized to the case of QCD. 5 refs

The use of symmetrized valence and relative motion coordinates for crystal potentials

DEFF Research Database (Denmark)

McMurry, H. L.; Hansen, Flemming Yssing

1980-01-01

Symmetrized valence coordinates are linear combinations of conventional valence coordinates which display the symmetry of a set of atoms bound by the valence bonds. Relative motion coordinates are relative translations, or relative rotations, of two or more strongly bonded groups of atoms among...... which relatively weak forces act. They are useful for expressing interactions between molecules in molecular crystals and should be chosen, also, to reflect the symmetry of the interacting groups. Since coordinates defined by these procedures possess elements of symmetry in common with the bonding...... interaction constants coupling coordinates of unlike symmetry with regard to the crystal point group are necessarily zero. They may be small, also, for coordinates which belong to different representations of the local symmetry when this is not the same as for the crystal. Procedures are given for defining...

Investigations of the valence-shell excitations of molecular ethane by high-energy electron scattering

Science.gov (United States)

Xu, Wei-Qing; Xu, Long-Quan; Qi, De-Guang; Chen, Tao; Liu, Ya-Wei; Zhu, Lin-Fan

2018-04-01

The differential cross sections and generalized oscillator strengths for the low-lying excitations of the valence-shell 1eg orbital electron in ethane have been measured for the first time at a high incident electron energy of 1500 eV and a scattering angular range of 1.5°-10°. A weak feature, termed X here, with a band center of about 7.5 eV has been observed, which was also announced by the previous experimental and theoretical studies. The dynamic behaviors of the generalized oscillator strengths for the 3s (8.7 eV), 3s+3p (9.31 eV, 9.41 eV), and X (˜7.5 eV) transitions on the momentum transfer squared have been obtained. The integral cross sections of these transitions from their thresholds to 5000 eV have been obtained with the aid of the BE-scaling (B is the binding energy and E is the excitation energy) method. The optical oscillator strengths of the above transitions determined by extrapolating their generalized oscillator strengths to the limit of the squared momentum transfer K2 → 0 are in good agreement with the ones from the photoabsorption spectrum [J. W. Au et al., Chem. Phys. 173, 209 (1993)], which indicates that the present differential cross sections, generalized oscillator strengths, and integral cross sections can serve as benchmark data.

Simulating Valence-to-Core X-ray Emission Spectroscopy of Transition Metal Complexes with Time-Dependent Density Functional Theory.

Science.gov (United States)

Zhang, Yu; Mukamel, Shaul; Khalil, Munira; Govind, Niranjan

2015-12-08

Valence-to-core (VtC) X-ray emission spectroscopy (XES) has emerged as a powerful technique for the structural characterization of complex organometallic compounds in realistic environments. Since the spectrum represents electronic transitions from the ligand molecular orbitals to the core holes of the metal centers, the approach is more chemically sensitive to the metal-ligand bonding character compared with conventional X-ray absorption techniques. In this paper we study how linear-response time-dependent density functional theory (LR-TDDFT) can be harnessed to simulate K-edge VtC X-ray emission spectra reliably. LR-TDDFT allows one to go beyond the single-particle picture that has been extensively used to simulate VtC-XES. We consider seven low- and high-spin model complexes involving chromium, manganese, and iron transition metal centers. Our results are in good agreement with experiment.

Spectroscopic mapping and selective electronic tuning of molecular orbitals in phosphorescent organometallic complexes – a new strategy for OLED materials

Directory of Open Access Journals (Sweden)

Pascal R. Ewen

2014-11-01

Full Text Available The improvement of molecular electronic devices such as organic light-emitting diodes requires fundamental knowledge about the structural and electronic properties of the employed molecules as well as their interactions with neighboring molecules or interfaces. We show that highly resolved scanning tunneling microscopy (STM and spectroscopy (STS are powerful tools to correlate the electronic properties of phosphorescent complexes (i.e., triplet emitters with their molecular structure as well as the local environment around a single molecule. We used spectroscopic mapping to visualize several occupied and unoccupied molecular frontier orbitals of Pt(II complexes adsorbed on Au(111. The analysis showed that the molecules exhibit a peculiar localized strong hybridization that leads to partial depopulation of a dz² orbital, while the ligand orbitals are almost unchanged. We further found that substitution of functional groups at well-defined positions can alter specific molecular orbitals without influencing the others. The results open a path toward the tailored design of electronic and optical properties of triplet emitters by smart ligand substitution, which may improve the performance of future OLED devices.

Dissipative systems and Bateman's Hamiltonian

International Nuclear Information System (INIS)

Pedrosa, I.A.; Baseia, B.

1983-01-01

It is shown, by using canonical transformations, that one can construct Bateman's Hamiltonian from a Hamiltonian for a conservative system and obtain a clear physical interpretation which explains the ambiguities emerging from its application to describe dissipative systems. (Author) [pt

Spin-Orbit Coupling for Photons and Polaritons in Microstructures

Directory of Open Access Journals (Sweden)

V. G. Sala

2015-03-01

Full Text Available We use coupled micropillars etched out of a semiconductor microcavity to engineer a spin-orbit Hamiltonian for photons and polaritons in a microstructure. The coupling between the spin and orbital momentum arises from the polarization-dependent confinement and tunneling of photons between adjacent micropillars arranged in the form of a hexagonal photonic molecule. It results in polariton eigenstates with distinct polarization patterns, which are revealed in photoluminescence experiments in the regime of polariton condensation. Thanks to the strong polariton nonlinearities, our system provides a photonic workbench for the quantum simulation of the interplay between interactions and spin-orbit effects, particularly when extended to two-dimensional lattices.

Diagonalization of Hamiltonian; Diagonalization of Hamiltonian

Energy Technology Data Exchange (ETDEWEB)

Garrido, L M; Pascual, P

1960-07-01

We present a general method to diagonalized the Hamiltonian of particles of arbitrary spin. In particular we study the cases of spin 0,1/2, 1 and see that for spin 1/2 our transformation agrees with Foldy's and obtain the expression for different observables for particles of spin C and 1 in the new representation. (Author) 7 refs.

Recent achievements in the Hamiltonian treatment of the dynamics and motion of compact binaries in general relativity

International Nuclear Information System (INIS)

Schäfer, Gerhard

2014-01-01

The current knowledge in the post-Newtonian (PN) dynamics and motion of non-spinning and spinning compact binaries will be presented based on the Arnowitt-Deser-Misner Hamiltonian approach to general relativity. The presentation will cover the binary dynamics with non-spinning components up to the 4PN order and for spinning binaries up to the next-to-next-to-leading order in the spin-orbit and spin-spin couplings. Radiation reaction will be treated for both non-spinning and spinning binaries. Explicit analytic expressions for the motion will be given, innermost stable circular orbits will be discussed

Squeezed states from a quantum deformed oscillator Hamiltonian

Energy Technology Data Exchange (ETDEWEB)

Ramírez, R. [IFLP, CONICET–Department of Mathematics, University of La Plata c.c. 67 1900, La Plata (Argentina); Reboiro, M., E-mail: marta.reboiro@gmail.com [IFLP, CONICET–Department of Physics, University of La Plata c.c. 67 1900, La Plata (Argentina)

2016-03-11

The spectrum and the time evolution of a system, which is modeled by a non-hermitian quantum deformed oscillator Hamiltonian, is analyzed. The proposed Hamiltonian is constructed from a non-standard realization of the algebra of Heisenberg. We show that, for certain values of the coupling constants and for a range of values of the deformation parameter, the deformed Hamiltonian is a pseudo-hermitic Hamiltonian. We explore the conditions under which the Hamiltonian is similar to a Swanson Hamiltonian. Also, we show that the lowest eigenstate of the system is a squeezed state. We study the time evolution of the system, for different initial states, by computing the corresponding Wigner functions. - Highlights: • A generalization of the squeezed harmonic oscillator is constructed from a non-standard realization of the Heisenberg algebra. • It is proved that, for certain values of the parameters of the model, the Hamiltonian is a pseudo-hermitian Hamiltonian. • It is shown that the lowest eigenstate of the Hamiltonian is a squeezed state. • The squeezing behavior of the associated Gazeau–Klauder state, as a function of time, is discussed.

Correlation consistent basis sets for actinides. II. The atoms Ac and Np-Lr.

Science.gov (United States)

Feng, Rulin; Peterson, Kirk A

2017-08-28

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 PuO 2 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 IP 0 for PuO 2 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

The chemical bond in inorganic chemistry the bond valence model

CERN Document Server

Brown, I David

2016-01-01

The bond valence model is a version of the ionic model in which the chemical constraints are expressed in terms of localized chemical bonds formed by the valence charge of the atoms. Theorems derived from the properties of the electrostatic flux predict the rules obeyed by both ionic and covalent bonds. They make quantitative predictions of coordination number, crystal structure, bond lengths and bond angles. Bond stability depends on the matching of the bonding strengths of the atoms, while the conflicting requirements of chemistry and space lead to the structural instabilities responsible for the unusual physical properties displayed by some materials. The model has applications in many fields ranging from mineralogy to molecular biology.

Spin-dependent electron-phonon coupling in the valence band of single-layer WS₂

DEFF Research Database (Denmark)

Hinsche, Nicki Frank; Ngankeu, Arlette S.; Guilloy, Kevin

2017-01-01

The absence of inversion symmetry leads to a strong spin-orbit splitting of the upper valence band of semiconducting single-layer transition-metal dichalchogenides such as MoS2 or WS2. This permits a direct comparison of the electron-phonon coupling strength in states that only differ by their spin....... Here, the electron-phonon coupling in the valence band maximum of single-layer WS2 is studied by first-principles calculations and angle-resolved photoemission. The coupling strength is found to be drastically different for the two spin-split branches, with calculated values of λK=0.0021 and 0.......40 for the upper and lower spin-split valence band of the freestanding layer, respectively. This difference is somewhat reduced when including scattering processes involving the Au(111) substrate present in the experiment but it remains significant, in good agreement with the experimental results....

Interatomic decay of inner-valence ionized states in ArXe clusters: Relativistic approach

International Nuclear Information System (INIS)

Fasshauer, Elke; Pernpointner, Markus; Gokhberg, Kirill

2013-01-01

In this work we investigate interatomic electronic decay processes taking place in mixed argon-xenon clusters upon the inner-valence ionization of an argon center. We demonstrate that both interatomic Coulombic decay and electron-transfer mediated decay (ETMD) are important in larger rare gas clusters as opposed to dimers. Calculated secondary electron spectra are shown to depend strongly on the spin-orbit coupling in the final states of the decay as well as the presence of polarizable environment. It follows from our calculations that ETMD is a pure interface process taking place between the argon-xenon layers. The interplay of all these effects is investigated in order to arrive at a suitable physical model for the decay of inner-valence vacancies taking place in mixed ArXe clusters.

Quantum Hamiltonian reduction in superspace formalism

International Nuclear Information System (INIS)

Madsen, J.O.; Ragoucy, E.

1994-02-01

Recently the quantum Hamiltonian reduction was done in the case of general sl(2) embeddings into Lie algebras and superalgebras. The results are extended to the quantum Hamiltonian reduction of N=1 affine Lie superalgebras in the superspace formalism. It is shown that if we choose a gauge for the supersymmetry, and consider only certain equivalence classes of fields, then our quantum Hamiltonian reduction reduces to quantum Hamiltonian reduction of non-supersymmetric Lie superalgebras. The super energy-momentum tensor is constructed explicitly as well as all generators of spin 1 (and 1/2); thus all generators in the superconformal, quasi-superconformal and Z 2 *Z 2 superconformal algebras are constructed. (authors). 21 refs

Discrete Hamiltonian evolution and quantum gravity

International Nuclear Information System (INIS)

Husain, Viqar; Winkler, Oliver

2004-01-01

We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong conditions on both allowable discretizations and Hamiltonians. These conditions permit time discretizations for a limited class of Hamiltonians, which does not include homogeneous cosmological models. We also present two general classes of implicit discretizations which preserve Poisson brackets for any Hamiltonian. Both types of discretizations generically do not preserve first class constraint algebras. Using this observation, we show that time discretization provides a complicated time gauge fixing for quantum gravity models, which may be compared with the alternative procedure of gauge fixing before discretization

Valence-bond theory of linear Hubbard and Pariser-Parr-Pople models

Science.gov (United States)

Soos, Z. G.; Ramasesha, S.

1984-05-01

The ground and low-lying states of finite quantum-cell models with one state per site are obtained exactly through a real-space basis of valence-bond (VB) diagrams that explicitly conserve the total spin. Regular and alternating Hubbard and Pariser-Parr-Pople (PPP) chains and rings with Ne electrons on N(PPP models, but differ from mean-field results. Molecular PPP parameters describe well the excitations of finite polyenes, odd polyene ions, linear cyanine dyes, and slightly overestimate the absorption peaks in polyacetylene (CH)x. Molecular correlations contrast sharply with uncorrelated descriptions of topological solitons, which are modeled by regular polyene radicals and their ions for both wide and narrow alternation crossovers. Neutral solitons have no midgap absorption and negative spin densities, while the intensity of the in-gap excitation of charged solitons is not enhanced. The properties of correlated states in quantum-cell models with one valence state per site are discussed in the adiabatic limit for excited-state geometries and instabilities to dimerization.

Orbital and spin dynamics of intraband electrons in quantum rings driven by twisted light.

Science.gov (United States)

Quinteiro, G F; Tamborenea, P I; Berakdar, J

2011-12-19

We theoretically investigate the effect that twisted light has on the orbital and spin dynamics of electrons in quantum rings possessing sizable Rashba spin-orbit interaction. The system Hamiltonian for such a strongly inhomogeneous light field exhibits terms which induce both spin-conserving and spin-flip processes. We analyze the dynamics in terms of the perturbation introduced by a weak light field on the Rasha electronic states, and describe the effects that the orbital angular momentum as well as the inhomogeneous character of the beam have on the orbital and the spin dynamics.

Generalized oscillator representations for Calogero Hamiltonians

International Nuclear Information System (INIS)

Tyutin, I V; Voronov, B L

2013-01-01

This paper is a natural continuation of the previous paper (Gitman et al 2011 J. Phys. A: Math. Theor. 44 425204), where oscillator representations for nonnegative Calogero Hamiltonians with coupling constant α ⩾ − 1/4 were constructed. In this paper, we present generalized oscillator representations for all Calogero Hamiltonians with α ⩾ − 1/4. These representations are generally highly nonunique, but there exists an optimum representation for each Hamiltonian. (comment)

Constructing Dense Graphs with Unique Hamiltonian Cycles

Science.gov (United States)

Lynch, Mark A. M.

2012-01-01

It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…

On the physical applications of hyper-Hamiltonian dynamics

International Nuclear Information System (INIS)

Gaeta, Giuseppe; Rodriguez, Miguel A

2008-01-01

An extension of Hamiltonian dynamics, defined on hyper-Kahler manifolds ('hyper-Hamiltonian dynamics') and sharing many of the attractive features of standard Hamiltonian dynamics, was introduced in previous work. In this paper, we discuss applications of the theory to physically interesting cases, dealing with the dynamics of particles with spin 1/2 in a magnetic field, i.e. the Pauli and the Dirac equations. While the free Pauli equation corresponds to a hyper-Hamiltonian flow, it turns out that the hyper-Hamiltonian description of the Dirac equation, and of the full Pauli one, is in terms of two commuting hyper-Hamiltonian flows. In this framework one can use a factorization principle discussed here (which is a special case of a general phenomenon studied by Walcher) and provide an explicit description of the resulting flow. On the other hand, by applying the familiar Foldy-Wouthuysen and Cini-Tousheck transformations (and the one recently introduced by Mulligan) which separate-in suitable limits-the Dirac equation into two equations, each of these turn out to be described by a single hyper-Hamiltonian flow. Thus the hyper-Hamiltonian construction is able to describe the fundamental dynamics for particles with spin

Oscillator representations for self-adjoint Calogero Hamiltonians

Energy Technology Data Exchange (ETDEWEB)

Gitman, D M [Institute of Physics, University of Sao Paulo (Brazil); Tyutin, I V; Voronov, B L, E-mail: gitman@dfn.if.usp.br, E-mail: tyutin@lpi.ru, E-mail: voronov@lpi.ru [Lebedev Physical Institute, Moscow (Russian Federation)

2011-10-21

In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = {alpha}x{sup -2}. We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation H=-d{sub x}{sup 2}+{alpha}x{sup -2} for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representations for the Calogero Hamiltonians. As is known, operators of the form N-hat = a-hat{sup +} a-hat and A-hat = a-hat a-hat{sup +} are called operators of oscillator type. Oscillator-type operators possess a number of useful properties in the case when the elementary operators a-hat are closed. It turns out that some s.a. Calogero Hamiltonians allow oscillator-type representations. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators a-hat and a-hat{sup +}. An oscillator-type representation for a given Hamiltonian is generally not unique. (paper)

Oscillator representations for self-adjoint Calogero Hamiltonians

International Nuclear Information System (INIS)

Gitman, D M; Tyutin, I V; Voronov, B L

2011-01-01

In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = αx -2 . We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation H=-d x 2 +αx -2 for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representations for the Calogero Hamiltonians. As is known, operators of the form N-hat = a-hat + a-hat and A-hat = a-hat a-hat + are called operators of oscillator type. Oscillator-type operators possess a number of useful properties in the case when the elementary operators a-hat are closed. It turns out that some s.a. Calogero Hamiltonians allow oscillator-type representations. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators a-hat and a-hat + . An oscillator-type representation for a given Hamiltonian is generally not unique. (paper)

EMR-related problems at the interface between the crystal field Hamiltonians and the zero-field splitting Hamiltonians

Directory of Open Access Journals (Sweden)

Rudowicz Czesław

2015-07-01

Full Text Available The interface between optical spectroscopy, electron magnetic resonance (EMR, and magnetism of transition ions forms the intricate web of interrelated notions. Major notions are the physical Hamiltonians, which include the crystal field (CF (or equivalently ligand field (LF Hamiltonians, and the effective spin Hamiltonians (SH, which include the zero-field splitting (ZFS Hamiltonians as well as to a certain extent also the notion of magnetic anisotropy (MA. Survey of recent literature has revealed that this interface, denoted CF (LF ↔ SH (ZFS, has become dangerously entangled over the years. The same notion is referred to by three names that are not synonymous: CF (LF, SH (ZFS, and MA. In view of the strong need for systematization of nomenclature aimed at bringing order to the multitude of different Hamiltonians and the associated quantities, we have embarked on this systematization. In this article, we do an overview of our efforts aimed at providing a deeper understanding of the major intricacies occurring at the CF (LF ↔ SH (ZFS interface with the focus on the EMR-related problems for transition ions.

Theoretical study of spin–orbit and Coriolis coupling among the low-lying states of Rb{sub 2} and Cs{sub 2}

Energy Technology Data Exchange (ETDEWEB)

Pazyuk, Elena A.; Revina, Elena I.; Stolyarov, Andrey V., E-mail: avstol@phys.chem.msu.ru

2015-11-25

Highlights: • Spin–orbit and angular coupling matrix elements of Rb{sub 2} and Cs{sub 2} were ab initio calculated. • The predicted molecular parameters agree well with the most experimental counterparts. • Non-adiabatic treatment of Rb{sub 2} and Cs{sub 2} properties could be accomplished with high accuracy. - Abstract: The spin–orbit (SO) and angular (Coriolis) coupling matrix elements of rubidium and cesium dimers have been calculated between the states converging to the lowest three dissociation limits. The relevant quasi-relativistic matrix elements were evaluated for a wide range of internuclear distances and density grid in the basis of the spin-averaged wave functions corresponding to pure Hund’s coupling case (a). Both shape and energy consistent small (9-electrons) effective core pseudopotentials were used to monitor a sensitivity of the matrix elements to the particular basis set. The dynamic correlation has been taken accounted by a large scale multi-reference configuration interaction method which was applied for only two valence electrons. The l-independent core-polarization potentials were employed to take into account the residual core-valence effect. The assessment of current accuracy of the present ab initio functions is discussed by a comparison with preceding calculations and their empirical counterparts.

Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets

Science.gov (United States)

Yuzbashyan, Emil A.

2018-05-01

We solve the non-stationary Schrödinger equation for several time-dependent Hamiltonians, such as the BCS Hamiltonian with an interaction strength inversely proportional to time, periodically driven BCS and linearly driven inhomogeneous Dicke models as well as various multi-level Landau-Zener tunneling models. The latter are Demkov-Osherov, bow-tie, and generalized bow-tie models. We show that these Landau-Zener problems and their certain interacting many-body generalizations map to Gaudin magnets in a magnetic field. Moreover, we demonstrate that the time-dependent Schrödinger equation for the above models has a similar structure and is integrable with a similar technique as Knizhnik-Zamolodchikov equations. We also discuss applications of our results to the problem of molecular production in an atomic Fermi gas swept through a Feshbach resonance and to the evaluation of the Landau-Zener transition probabilities.

Hamiltonian Dynamics of Spider-Type Multirotor Rigid Bodies Systems

International Nuclear Information System (INIS)

Doroshin, Anton V.

2010-01-01

This paper sets out to develop a spider-type multiple-rotor system which can be used for attitude control of spacecraft. The multirotor system contains a large number of rotor-equipped rays, so it was called a 'Spider-type System', also it can be called 'Rotary Hedgehog'. These systems allow using spinups and captures of conjugate rotors to perform compound attitude motion of spacecraft. The paper describes a new method of spacecraft attitude reorientation and new mathematical model of motion in Hamilton form. Hamiltonian dynamics of the system is investigated with the help of Andoyer-Deprit canonical variables. These variables allow obtaining exact solution for hetero- and homoclinic orbits in phase space of the system motion, which are very important for qualitative analysis.

Valence shell photoionization energies and cross-sections of NF sub 3 and PF sub 3

CERN Document Server

Jürgensen, A

2003-01-01

Relative outer valence shell ionization potentials and cross-sections were determined for the isostructural, Group 15, trifluorides NF sub 3 and PF sub 3 in the gas phase using synchrotron radiation. Excitation photon energies ranged from 70 to 160 eV. The experimental spectra were assigned and cross-sections analyzed with the aid of both MS-X alpha and ab initio calculations. Spectral differences in peak energies and relative intensities are related to structural and electronic differences between these two fluoride molecules. Valence shell ionization potentials were compared to calculated values obtained by several different methods. The partial photoionization cross-sections for each orbital were obtained as a function of excitation energy and compared to theoretical results obtained with the X alpha method.

Relativistic non-Hamiltonian mechanics

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2010-01-01

Relativistic particle subjected to a general four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u μ u μ + c 2 = 0, where c is the speed of light in vacuum. In the general case, four-forces are non-potential, and the relativistic particle is a non-Hamiltonian system in four-dimensional pseudo-Euclidean space-time. We consider non-Hamiltonian and dissipative systems in relativistic mechanics. Covariant forms of the principle of stationary action and the Hamilton's principle for relativistic mechanics of non-Hamiltonian systems are discussed. The equivalence of these principles is considered for relativistic particles subjected to potential and non-potential forces. We note that the equations of motion which follow from the Hamilton's principle are not equivalent to the equations which follow from the variational principle of stationary action. The Hamilton's principle and the principle of stationary action are not compatible in the case of systems with nonholonomic constraint and the potential forces. The principle of stationary action for relativistic particle subjected to non-potential forces can be used if the Helmholtz conditions are satisfied. The Hamilton's principle and the principle of stationary action are equivalent only for a special class of relativistic non-Hamiltonian systems.

Chromatic roots and hamiltonian paths

DEFF Research Database (Denmark)

Thomassen, Carsten

2000-01-01

We present a new connection between colorings and hamiltonian paths: If the chromatic polynomial of a graph has a noninteger root less than or equal to t(n) = 2/3 + 1/3 (3)root (26 + 6 root (33)) + 1/3 (3)root (26 - 6 root (33)) = 1.29559.... then the graph has no hamiltonian path. This result...

Hamiltonian structure of the Lotka-Volterra equations

Science.gov (United States)

Nutku, Y.

1990-03-01

The Lotka-Volterra equations governing predator-prey relations are shown to admit Hamiltonian structure with respect to a generalized Poisson bracket. These equations provide an example of a system for which the naive criterion for the existence of Hamiltonian structure fails. We show further that there is a three-component generalization of the Lotka-Volterra equations which is a bi-Hamiltonian system.

Boson mapping and the microscopic collective nuclear Hamiltonian

International Nuclear Information System (INIS)

Dobes, J.; Ivanova, S.P.; Dzholos, R.V.; Pedrosa, R.

1990-01-01

Starting with the mapping of the quadrupole collective states in the fermion space onto the boson space, the fermion nuclear problem is transformed into the boson one. The boson images of the bifermion operators and of the fermion Hamiltonian are found. Recurrence relations are used to obtain approximately the norm matrix which appears in the boson-fermion mapping. The resulting boson Hamiltonian contains terms which go beyond the ordinary SU(6) symmetry Hamiltonian of the interacting boson model. Calculations, however, suggest that on the phenomenological level the differences between the mapped Hamiltonian and the SU(6) Hamiltonian are not too important. 18 refs.; 2 figs

On integrable Hamiltonians for higher spin XXZ chain

International Nuclear Information System (INIS)

Bytsko, Andrei G.

2003-01-01

Integrable Hamiltonians for higher spin periodic XXZ chains are constructed in terms of the spin generators; explicit examples for spins up to (3/2) are given. Relations between Hamiltonians for some U q (sl 2 )-symmetric and U(1)-symmetric universal r-matrices are studied; their properties are investigated. A certain modification of the higher spin periodic chain Hamiltonian is shown to be an integrable U q (sl 2 )-symmetric Hamiltonian for an open chain

Hamiltonian ABC

NARCIS (Netherlands)

Meeds, E.; Leenders, R.; Welling, M.; Meila, M.; Heskes, T.

2015-01-01

Approximate Bayesian computation (ABC) is a powerful and elegant framework for performing inference in simulation-based models. However, due to the difficulty in scaling likelihood estimates, ABC remains useful for relatively lowdimensional problems. We introduce Hamiltonian ABC (HABC), a set of

Accurate Valence Ionization Energies from Kohn-Sham Eigenvalues with the Help of Potential Adjustors.

Science.gov (United States)

Thierbach, Adrian; Neiss, Christian; Gallandi, Lukas; Marom, Noa; Körzdörfer, Thomas; Görling, Andreas

2017-10-10

An accurate yet computationally very efficient and formally well justified approach to calculate molecular ionization potentials is presented and tested. The first as well as higher ionization potentials are obtained as the negatives of the Kohn-Sham eigenvalues of the neutral molecule after adjusting the eigenvalues by a recently [ Görling Phys. Rev. B 2015 , 91 , 245120 ] introduced potential adjustor for exchange-correlation potentials. Technically the method is very simple. Besides a Kohn-Sham calculation of the neutral molecule, only a second Kohn-Sham calculation of the cation is required. The eigenvalue spectrum of the neutral molecule is shifted such that the negative of the eigenvalue of the highest occupied molecular orbital equals the energy difference of the total electronic energies of the cation minus the neutral molecule. For the first ionization potential this simply amounts to a ΔSCF calculation. Then, the higher ionization potentials are obtained as the negatives of the correspondingly shifted Kohn-Sham eigenvalues. Importantly, this shift of the Kohn-Sham eigenvalue spectrum is not just ad hoc. In fact, it is formally necessary for the physically correct energetic adjustment of the eigenvalue spectrum as it results from ensemble density-functional theory. An analogous approach for electron affinities is equally well obtained and justified. To illustrate the practical benefits of the approach, we calculate the valence ionization energies of test sets of small- and medium-sized molecules and photoelectron spectra of medium-sized electron acceptor molecules using a typical semilocal (PBE) and two typical global hybrid functionals (B3LYP and PBE0). The potential adjusted B3LYP and PBE0 eigenvalues yield valence ionization potentials that are in very good agreement with experimental values, reaching an accuracy that is as good as the best G 0 W 0 methods, however, at much lower computational costs. The potential adjusted PBE eigenvalues result in

Hamiltonian quantum simulation with bounded-strength controls

International Nuclear Information System (INIS)

Bookatz, Adam D; Wocjan, Pawel; Viola, Lorenza

2014-01-01

We propose dynamical control schemes for Hamiltonian simulation in many-body quantum systems that avoid instantaneous control operations and rely solely on realistic bounded-strength control Hamiltonians. Each simulation protocol consists of periodic repetitions of a basic control block, constructed as a modification of an ‘Eulerian decoupling cycle,’ that would otherwise implement a trivial (zero) target Hamiltonian. For an open quantum system coupled to an uncontrollable environment, our approach may be employed to engineer an effective evolution that simulates a target Hamiltonian on the system while suppressing unwanted decoherence to the leading order, thereby allowing for dynamically corrected simulation. We present illustrative applications to both closed- and open-system simulation settings, with emphasis on simulation of non-local (two-body) Hamiltonians using only local (one-body) controls. In particular, we provide simulation schemes applicable to Heisenberg-coupled spin chains exposed to general linear decoherence, and show how to simulate Kitaev's honeycomb lattice Hamiltonian starting from Ising-coupled qubits, as potentially relevant to the dynamical generation of a topologically protected quantum memory. Additional implications for quantum information processing are discussed. (papers)

Mathematical Modeling of Constrained Hamiltonian Systems

NARCIS (Netherlands)

Schaft, A.J. van der; Maschke, B.M.

1995-01-01

Network modelling of unconstrained energy conserving physical systems leads to an intrinsic generalized Hamiltonian formulation of the dynamics. Constrained energy conserving physical systems are directly modelled as implicit Hamiltonian systems with regard to a generalized Dirac structure on the

Lagrangian and Hamiltonian dynamics

CERN Document Server

Mann, Peter

2018-01-01

An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers. Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications. The book contains some unusual topics for a classical mechanics textbook. Mo...

Investigation of the intermediate LK molecular orbital radiation in heavy ion-atom collisions

International Nuclear Information System (INIS)

Frank, W.; Kaun, K.-H.; Manfrass, P.

1981-01-01

The continuum consisting of an intensive low-energy and a high-energy components in heavy-ion atom collision systems with atomic numbers Z 1 , Z 2 > 28 is studied. The aim of the study is to prove that the C1 continuum cannot be caused by ridiative electron capture (REC) being molecular orbital (MO) radiation to the 2ptau level. It is shown that the comparison of the C1 yields obtained in Kr+Nb asymmetric collisions in gas and solid targets is associated with the formation of vacancies in the lower-Z collision partner and can be interpreted as quasimolecular radiation to the 2ptau orbital level. The strong suppression of the C2 component in the gas target experimets indicates that the MO radiation to the 1stau orbit is emitted preferentially in the two-collision process in symmetric and near-symmetric systems with Z 1 , Z 2 [ru

Relativistic magnetohydrodynamics as a Hamiltonian system

International Nuclear Information System (INIS)

Holm, D.D.; Kupershmidt, A.

1985-01-01

The equations of ideal relativistic magnetohydrodynamics in the laboratory frame form a noncanonical Hamiltonian system with the same Poisson bracket as for the nonrelativistic system, but with dynamical variables and Hamiltonian obtained via a regular deformation of their nonrelativistic counterparts [fr

Ab initio study of isomerism in molecular Li2AB+ ions with 12 and 14 valence electrons

International Nuclear Information System (INIS)

Charkin, O.P.; Klimenko, N.M.; Mak-Ki, M.L.; Shlojer, P.R.

1997-01-01

Ab initio calculations of potential energy surfaces (PES) of molecular ions Li 2 AB + with 12 and 14 valence electrons have been made in the framework of approximations MP2/6-31G*//HF/6-31G*+ZPE(HF/6-31G*) and MP4SDTQ/6-31*//MP2/6-31G*+ZPE(MP2/6-31G*). The following most favourable structures have been found: a double-terminal linear for LiNO + (a triplet); a plane bicyclic one for Li 2 OF + , Li 2 SCl + , Li 2 NO + (a singlet) and Li 2 PS + (a singlet), where both cations are coordinated to A-B bond; rectangular (T-shaped) for Li 2 OCl + and SFLi + , as well as for LiNS + and POLi 2 + ions in singlet and triplet states; in the form of a half-opened butterfly for Li 2 PS + (a triplet) and Li 2 SCl +

Localized orbitals vs. pseudopotential-plane waves basis sets: performances and accuracy for molecular magnetic systems

International Nuclear Information System (INIS)

Massobrio, C.; Ruiz, E.

2003-01-01

Density functional theory, in combination with a) a careful choice of the exchange-correlation part of the total energy and b) localized basis sets for the electronic orbital, has become the method of choice for calculating the exchange-couplings in magnetic molecular complexes. Orbital expansion on plane waves can be seen as an alternative basis set especially suited to allow optimization of newly synthesized materials of unknown geometries. However, little is known on the predictive power of this scheme to yield quantitative values for exchange coupling constants J as small as a few hundredths of eV (50-300 cm -1 ). We have used density functional theory and a plane waves basis set to calculate the exchange couplings J of three homodinuclear Cu-based molecular complexes with experimental values ranging from +40 cm -1 to -300 cm -1 . The plane waves basis set proves as accurate as the localized basis set, thereby suggesting that this approach can be reliably employed to predict and rationalize the magnetic properties of molecular-based materials. (author)

Noncanonical Hamiltonian mechanics

International Nuclear Information System (INIS)

Litteljohn, R.G.

1986-01-01

Noncanonical variables in Hamiltonian mechanics were first used by Lagrange in 1808. In spite of this, most work in Hamiltonian mechanics has been carried out in canonical variables, up to this day. One reason for this is that noncanonical coordinates are seldom needed for mechanical problems based on Lagrangians of the form L = T - V, where T is the kinetic energy and V is the potential energy. Of course, such Lagrangians arise naturally in celestial mechanics, and as a result they form the paradigms of nineteenth-century mechanics and have become enshrined in all the mechanics textbooks. Certain features of modern problems, however, lead to the use of noncanonical coordinates. Among these are issues of gauge invariance and singular Lagrange a Poisson structures. In addition, certain problems, like the flow of magnetic-field lines in physical space, are naturally formulated in terms of noncanonical coordinates. None of these features is present in the nineteenth-century paradigms of mechanics, but they do arise in problems involving particle motion in the presence of magnetic fields. For example, the motion of a particle in an electromagnetic wave is an important one in plasma physics, but the usual Hamiltonian formulation is gauge dependent. For this problem, noncanonical approaches based on Lagrangians in phase space lead to powerful computational techniques which are gauge invariant. In the limit of strong magnetic fields, particle motion becomes 'guiding-center motion'. Guiding-center motion is also best understood in terms of noncanonical coordinates. Finally the flow of magnetic-field lines through physical space is a Hamiltonian system which is best understood with noncanonical coordinates. No doubt many more systems will arise in the future for which these noncanonical techniques can be applied. (author)

Variational identities and Hamiltonian structures

International Nuclear Information System (INIS)

Ma Wenxiu

2010-01-01

This report is concerned with Hamiltonian structures of classical and super soliton hierarchies. In the classical case, basic tools are variational identities associated with continuous and discrete matrix spectral problems, targeted to soliton equations derived from zero curvature equations over general Lie algebras, both semisimple and non-semisimple. In the super case, a supertrace identity is presented for constructing Hamiltonian structures of super soliton equations associated with Lie superalgebras. We illustrate the general theories by the KdV hierarchy, the Volterra lattice hierarchy, the super AKNS hierarchy, and two hierarchies of dark KdV equations and dark Volterra lattices. The resulting Hamiltonian structures show the commutativity of each hierarchy discussed and thus the existence of infinitely many commuting symmetries and conservation laws.

Carbon dioxide sorption in a nanoporous octahedral molecular sieve

Science.gov (United States)

Williamson, Izaak; Nelson, Eric B.; Li, Lan

2015-08-01

We have performed first-principles density functional theory calculations, incorporated with van der Waals interactions, to study CO2 adsorption and diffusion in nanoporous solid—OMS-2 (Octahedral Molecular Sieve). We found the charge, type, and mobility of a cation, accommodated in a porous OMS-2 material for structural stability, can affect not only the OMS-2 structural features but also CO2 sorption performance. This paper targets K+, Na+, and Ba2+ cations. First-principles energetics and electronic structure calculations indicate that Ba2+ has the strongest interaction with the OMS-2 porous surface due to valence electrons donation to the OMS-2 and molecular orbital hybridization. However, the Ba-doped OMS-2 has the worst CO2 uptake capacity. We also found evidence of sorption hysteresis in the K- and Na-doped OMS-2 materials.

Mesoscopic rings with spin-orbit interactions

Energy Technology Data Exchange (ETDEWEB)

Berche, Bertrand; Chatelain, Christophe; Medina, Ernesto, E-mail: berche@lpm.u-nancy.f [Statistical Physics Group, Institut Jean Lamour, UMR CNRS No 7198, Universite Henri Poincare, Nancy 1, B.P. 70239, F-54506 Vandoeuvre les Nancy (France)

2010-09-15

A didactic description of charge and spin equilibrium currents on mesoscopic rings in the presence of spin-orbit interaction is presented. Emphasis is made on the non-trivial construction of the correct Hamiltonian in polar coordinates, the calculation of eigenvalues and eigenfunctions and the symmetries of the ground-state properties. Spin currents are derived following an intuitive definition, and then a more thorough derivation is built upon the canonical Lagrangian formulation that emphasizes the SU(2) gauge structure of the transport problem of spin-1/2 fermions in spin-orbit active media. The quantization conditions that follow from the constraint of single-valued Pauli spinors are also discussed. The targeted students are those of a graduate condensed matter physics course.

Chaos and nonlinear dynamics of single-particle orbits in a magnetotaillike magnetic field

Science.gov (United States)

Chen, J.; Palmadesso, P. J.

1986-01-01

The properties of charged-particle motion in Hamiltonian dynamics are studied in a magnetotaillike magnetic field configuration. It is shown by numerical integration of the equation of motion that the system is generally nonintegrable and that the particle motion can be classified into three distinct types of orbits: bounded integrable orbits, unbounded stochastic orbits, and unbounded transient orbits. It is also shown that different regions of the phase space exhibit qualitatively different responses to external influences. The concept of 'differential memory' in single-particle distributions is proposed. Physical implications for the dynamical properties of the magnetotail plasmas and the possible generation of non-Maxwellian features in the distribution functions are discussed.

A localized orbital description of ideal vacancies in GaP and GaSb

International Nuclear Information System (INIS)

Erbarut, E.; Tomak, M.

1986-10-01

Gaussian orbitals of s and p symmetry and an empirical pseudopotential Hamiltonian is employed for the study of electronic structures of ideal vacancies in GaP and GaSb. A reasonably accurate description of band structures and densities of states are attained. (author)

NATO Advanced Study Institute on Mixed-Valence Compounds : Theory and Applications in Chemistry, Physics, Geology, and Biology

CERN Document Server

1980-01-01

It has been a decade since two seminal reviews demonstrated that mixed-valence compounds share many unique and fascinating features. The insight pro­ vided by those early works has promoted a great deal of both experimental and theoretical study. As a result of extensive efforts, our understanding of the bonding and properties of mixed-valence compounds has advanced substantially. There has been no compre­ hensive treatment of mixed-valence compounds since 1967, and the meeting convened at Oxford in September, 1979, provided a unique opportunity to examine the subject and its many ramifications. Mixed-valence compounds play an important role in many fields. Although the major impact of the subject has been in chemistry, its importance has become increasingly clear in solid state physics, geology, and biology. Extensive interest and effort in the field of molecular metals has demonstrated that mixed-valency is a prerequisite for high elec­ trical conductivity. The intense colors of many minerals have been s...

Introductory Molecular Orbital Theory: An Honors General Chemistry Computational Lab as Implemented Using Three-Dimensional Modeling Software

Science.gov (United States)

Ruddick, Kristie R.; Parrill, Abby L.; Petersen, Richard L.

2012-01-01

In this study, a computational molecular orbital theory experiment was implemented in a first-semester honors general chemistry course. Students used the GAMESS (General Atomic and Molecular Electronic Structure System) quantum mechanical software (as implemented in ChemBio3D) to optimize the geometry for various small molecules. Extended Huckel…

Modeling Photodetachment from HO2- Using the pd Case of the Generalized Mixed Character Molecular Orbital Model

Science.gov (United States)

Blackstone, Christopher C.; Sanov, Andrei

2016-06-01

Using the generalized model for photodetachment of electrons from mixed-character molecular orbitals, we gain insight into the nature of the HOMO of HO2- by treating it as a coherent superpostion of one p- and one d-type atomic orbital. Fitting the pd model function to the ab initio calculated HOMO of HO2- yields a fractional d-character, γp, of 0.979. The modeled curve of the anisotropy parameter, β, as a function of electron kinetic energy for a pd-type mixed character orbital is matched to the experimental data.

Quantization of a relativistic particle on the SL(2.R) manifold based on Hamiltonian reduction

International Nuclear Information System (INIS)

Jorjadze, G.; O'Raifeartaigh, L.; Tsutsui, I.

1994-07-01

A quantum theory is constructed for the system of a relativistic particle with mass m moving freely on the SL(2.R) group manifold. Applied to the cotangent bundle of SL(2.R). the method of Hamiltonian reduction allows us to split the reduced system into two coadjoint orbits of the group. We find that the Hilbert space consists of states given by the discrete series of the unitary irreducible representations of SL(2.R). and with a positive-definite, discrete spectrum. (author)

Almost periodic Hamiltonians: an algebraic approach

International Nuclear Information System (INIS)

Bellissard, J.

1981-07-01

We develop, by analogy with the study of periodic potential, an algebraic theory for almost periodic hamiltonians, leading to a generalized Bloch theorem. This gives rise to results concerning the spectral measures of these operators in terms of those of the corresponding Bloch hamiltonians

Scattering theory for Stark Hamiltonians

International Nuclear Information System (INIS)

Jensen, Arne

1994-01-01

An introduction to the spectral and scattering theory for Schroedinger operators is given. An abstract short range scattering theory is developed. It is applied to perturbations of the Laplacian. Particular attention is paid to the study of Stark Hamiltonians. The main result is an explanation of the discrepancy between the classical and the quantum scattering theory for one-dimensional Stark Hamiltonians. (author). 47 refs

Indirect quantum tomography of quadratic Hamiltonians

Energy Technology Data Exchange (ETDEWEB)

Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)

2011-01-15

A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.

Sdg interacting boson hamiltonian in the seniority scheme

Energy Technology Data Exchange (ETDEWEB)

Yoshinaga, N.

1989-03-06

The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagnoalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.

sdg Interacting boson hamiltonian in the seniority scheme

Science.gov (United States)

Yoshinaga, N.

1989-03-01

The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagonalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.

Dopamine and Caffeine Encapsulation within Boron Nitride (14,0) Nanotubes: Classical Molecular Dynamics and First Principles Calculations.

Science.gov (United States)

García-Toral, Dolores; González-Melchor, Minerva; Rivas-Silva, Juan F; Meneses-Juárez, Efraín; Cano-Ordaz, José; H Cocoletzi, Gregorio

2018-06-07

Classical molecular dynamics (MD) and density functional theory (DFT) calculations are developed to investigate the dopamine and caffeine encapsulation within boron nitride (BN) nanotubes (NT) with (14,0) chirality. Classical MD studies are done at canonical and isobaric-isothermal conditions at 298 K and 1 bar in explicit water. Results reveal that both molecules are attracted by the nanotube; however, only dopamine is able to enter the nanotube, whereas caffeine moves in its vicinity, suggesting that both species can be transported: the first by encapsulation and the second by drag. Findings are analyzed using the dielectric behavior, pair correlation functions, diffusion of the species, and energy contributions. The DFT calculations are performed according to the BLYP approach and applying the atomic base of the divided valence 6-31g(d) orbitals. The geometry optimization uses the minimum-energy criterion, accounting for the total charge neutrality and multiplicity of 1. Adsorption energies in the dopamine encapsulation indicate physisorption, which induces the highly occupied molecular orbital-lower unoccupied molecular orbital gap reduction yielding a semiconductor behavior. The charge redistribution polarizes the BNNT/dopamine and BNNT/caffeine structures. The work function decrease and the chemical potential values suggest the proper transport properties in these systems, which may allow their use in nanobiomedicine.

Numerical Investigations of Post-Newtonian Hamiltonian Dynamics for Spinning Compact Binaries

Science.gov (United States)

Zhong, S. Y.

2012-03-01

Spinning compact binaries, consisting of neutron stars or black holes, not only have rich dynamic phenomena of resonance and chaos, but also are the most promising source for detecting gravitational waves. There should be a certain relation between the dynamics of the gravitational bodies and the gravitational waveforms. Based on the least-squares correction, several manifold correction schemes like the single-scaling method and the dual-scaling method are designed to suppress numerical errors from 6 integrals of motion in a conservative post-Newtonian (PN) Hamiltonian of spinning compact binaries. Taking a fifth order Runge-Kutta algorithm as a basic integrator, we wonder whether the PN contributions, the spin effects, and the classification of orbits exert some influences on these correction schemes and the Nacozy's approach. It is found that they are almost the same in correcting the integrals for the pure Kepler problem. Once the third-order PN contributions are added to the pure orbital part, there are explicit differences of correction effectiveness among these methods. As an interesting case, the efficiency of correction is better for chaotic eccentric orbits than for quasicircular regular ones. In all cases tested, the new momentum-position dual-scaling scheme does always have the optimal performance. It costs a little but not much expensive additional computational cost when the spin effects exist, and several time-saving techniques are used. The corrected numerical results are more accurate than the uncorrected ones, so that chaos from the numerical errors can be avoided. See Phys. Rev. D 81, 104037 (2010) for more details. Lubich et al. (Phys. Rev. D 81, 104025 (2010)) presented a noncanonically symplectic integrator for the PN Hamiltonian of a spinning compact binary. However, the Euler mixed integrator is problematic because of its bad numerical stability.We improved the work by constructing the second-order and the fourth-order fixed symplectic

Spin-orbit scattering in superconducting nanoparticles

Energy Technology Data Exchange (ETDEWEB)

Alhassid, Y. [Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut, 06520 (United States); Nesterov, K.N. [Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin, 53706 (United States)

2017-06-15

We review interaction effects in chaotic metallic nanoparticles. Their single-particle Hamiltonian is described by the proper random-matrix ensemble while the dominant interaction terms are invariants under a change of the single-particle basis. In the absence of spin-orbit scattering, the nontrivial invariants consist of a pairing interaction, which leads to superconductivity in the bulk, and a ferromagnetic exchange interaction. Spin-orbit scattering breaks spin-rotation invariance and when it is sufficiently strong, the only dominant nontrivial interaction is the pairing interaction. We discuss how the magnetic response of discrete energy levels of the nanoparticle (which can be measured in single-electron tunneling spectroscopy experiments) is affected by such pairing correlations and how it can provide a signature of pairing correlations. We also consider the spin susceptibility of the nanoparticle and discuss how spin-orbit scattering changes the signatures of pairing correlations in this observable. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Dynamical decoupling of unbounded Hamiltonians

Science.gov (United States)

Arenz, Christian; Burgarth, Daniel; Facchi, Paolo; Hillier, Robin

2018-03-01

We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, is known to work for bounded interactions, but physical environments such as bosonic heat baths are usually modeled with unbounded interactions; hence, here, we initiate a systematic study of dynamical decoupling for unbounded operators. We develop a sufficient decoupling criterion for arbitrary Hamiltonians and a necessary decoupling criterion for semibounded Hamiltonians. We give examples for unbounded Hamiltonians where decoupling works and the limiting evolution as well as the convergence speed can be explicitly computed. We show that decoupling does not always work for unbounded interactions and we provide both physically and mathematically motivated examples.

Predicting Near Edge X-ray Absorption Spectra with the Spin-Free Exact-Two-Component Hamiltonian and Orthogonality Constrained Density Functional Theory.

Science.gov (United States)

Verma, Prakash; Derricotte, Wallace D; Evangelista, Francesco A

2016-01-12

Orthogonality constrained density functional theory (OCDFT) provides near-edge X-ray absorption (NEXAS) spectra of first-row elements within one electronvolt from experimental values. However, with increasing atomic number, scalar relativistic effects become the dominant source of error in a nonrelativistic OCDFT treatment of core-valence excitations. In this work we report a novel implementation of the spin-free exact-two-component (X2C) one-electron treatment of scalar relativistic effects and its combination with a recently developed OCDFT approach to compute a manifold of core-valence excited states. The inclusion of scalar relativistic effects in OCDFT reduces the mean absolute error of second-row elements core-valence excitations from 10.3 to 2.3 eV. For all the excitations considered, the results from X2C calculations are also found to be in excellent agreement with those from low-order spin-free Douglas-Kroll-Hess relativistic Hamiltonians. The X2C-OCDFT NEXAS spectra of three organotitanium complexes (TiCl4, TiCpCl3, TiCp2Cl2) are in very good agreement with unshifted experimental results and show a maximum absolute error of 5-6 eV. In addition, a decomposition of the total transition dipole moment into partial atomic contributions is proposed and applied to analyze the nature of the Ti pre-edge transitions in the three organotitanium complexes.

Unifying perspective: Solitary traveling waves as discrete breathers in Hamiltonian lattices and energy criteria for their stability

Science.gov (United States)

Cuevas-Maraver, Jesús; Kevrekidis, Panayotis G.; Vainchtein, Anna; Xu, Haitao

2017-09-01

In this work, we provide two complementary perspectives for the (spectral) stability of solitary traveling waves in Hamiltonian nonlinear dynamical lattices, of which the Fermi-Pasta-Ulam and the Toda lattice are prototypical examples. One is as an eigenvalue problem for a stationary solution in a cotraveling frame, while the other is as a periodic orbit modulo shifts. We connect the eigenvalues of the former with the Floquet multipliers of the latter and using this formulation derive an energy-based spectral stability criterion. It states that a sufficient (but not necessary) condition for a change in the wave stability occurs when the functional dependence of the energy (Hamiltonian) H of the model on the wave velocity c changes its monotonicity. Moreover, near the critical velocity where the change of stability occurs, we provide an explicit leading-order computation of the unstable eigenvalues, based on the second derivative of the Hamiltonian H''(c0) evaluated at the critical velocity c0. We corroborate this conclusion with a series of analytically and numerically tractable examples and discuss its parallels with a recent energy-based criterion for the stability of discrete breathers.

Matchings Extend to Hamiltonian Cycles in 5-Cube

Directory of Open Access Journals (Sweden)

Wang Fan

2018-02-01

Full Text Available Ruskey and Savage asked the following question: Does every matching in a hypercube Qn for n ≥ 2 extend to a Hamiltonian cycle of Qn? Fink confirmed that every perfect matching can be extended to a Hamiltonian cycle of Qn, thus solved Kreweras’ conjecture. Also, Fink pointed out that every matching can be extended to a Hamiltonian cycle of Qn for n ∈ {2, 3, 4}. In this paper, we prove that every matching in Q5 can be extended to a Hamiltonian cycle of Q5.

Dynamics of High-Order Spin-Orbit Couplings about Linear Momenta in Compact Binary Systems*

International Nuclear Information System (INIS)

Huang Li; Wu Xin; Huang Guo-Qing; Mei Li-Jie

2017-01-01

This paper relates to the post-Newtonian Hamiltonian dynamics of spinning compact binaries, consisting of the Newtonian Kepler problem and the leading, next-to-leading and next-to-next-to-leading order spin-orbit couplings as linear functions of spins and momenta. When this Hamiltonian form is transformed to a Lagrangian form, besides the terms corresponding to the same order terms in the Hamiltonian, several additional terms, third post-Newtonian (3PN), 4PN, 5PN, 6PN and 7PN order spin-spin coupling terms, yield in the Lagrangian. That means that the Hamiltonian is nonequivalent to the Lagrangian at the same PN order but is exactly equivalent to the full Lagrangian without any truncations. The full Lagrangian without the spin-spin couplings truncated is integrable and regular. Whereas it is non-integrable and becomes possibly chaotic when any one of the spin-spin terms is dropped. These results are also supported numerically. (paper)

Electron-correlated fragment-molecular-orbital calculations for biomolecular and nano systems.

Science.gov (United States)

Tanaka, Shigenori; Mochizuki, Yuji; Komeiji, Yuto; Okiyama, Yoshio; Fukuzawa, Kaori

2014-06-14

Recent developments in the fragment molecular orbital (FMO) method for theoretical formulation, implementation, and application to nano and biomolecular systems are reviewed. The FMO method has enabled ab initio quantum-mechanical calculations for large molecular systems such as protein-ligand complexes at a reasonable computational cost in a parallelized way. There have been a wealth of application outcomes from the FMO method in the fields of biochemistry, medicinal chemistry and nanotechnology, in which the electron correlation effects play vital roles. With the aid of the advances in high-performance computing, the FMO method promises larger, faster, and more accurate simulations of biomolecular and related systems, including the descriptions of dynamical behaviors in solvent environments. The current status and future prospects of the FMO scheme are addressed in these contexts.

Thermal conductivity of magnetic insulators with strong spin-orbit coupling

Science.gov (United States)

Stamokostas, Georgios; Lapas, Panteleimon; Fiete, Gregory A.

We study the influence of spin-orbit coupling on the thermal conductivity of various types of magnetic insulators. In the absence of spin-orbit coupling and orbital-degeneracy, the strong-coupling limit of Hubbard interactions at half filling can often be adequately described in terms of a pure spin Hamiltonian of the Heisenberg form. However, in the presence of spin-orbit coupling the resulting exchange interaction can become highly anisotropic. The effect of the atomic spin-orbit coupling, taken into account through the effect of magnon-phonon interactions and the magnetic order and excitations, on the lattice thermal conductivity of various insulating magnetic systems is studied. We focus on the regime of low temperatures where the dominant source of scattering is two-magnon scattering to one-phonon processes. The thermal current is calculated within the Boltzmann transport theory. We are grateful for financial support from NSF Grant DMR-0955778.

Hamiltonian Approach to 2+1 Dimensional Gravity

Science.gov (United States)

Cantini, L.; Menotti, P.; Seminara, D.

2002-12-01

It is shown that the reduced particle dynamics of 2+1 dimensional gravity in the maximally slicing gauge has hamiltonian form. We give the exact diffeomorphism which transforms the spinning cone metric in the Deser, Jackiw, 't Hooft gauge to the maximally slicing gauge. It is explicitly shown that the boundary term in the action, written in hamiltonian form gives the hamiltonian for the reduced particle dynamics. The quantum mechanical translation of the two particle hamiltonian gives rise to the logarithm of the Laplace-Beltrami operator on a cone whose angular deficit is given by the total energy of the system irrespective of the masses of the particles thus proving at the quantum level a conjecture by 't Hooft on the two particle dynamics.

Mapping enzymatic catalysis using the effective fragment molecular orbital method

DEFF Research Database (Denmark)

Svendsen, Casper Steinmann; Fedorov, Dmitri G.; Jensen, Jan Halborg

2013-01-01

We extend the Effective Fragment Molecular Orbital (EFMO) method to the frozen domain approach where only the geometry of an active part is optimized, while the many-body polarization effects are considered for the whole system. The new approach efficiently mapped out the entire reaction path...... of chorismate mutase in less than four days using 80 cores on 20 nodes, where the whole system containing 2398 atoms is treated in the ab initio fashion without using any force fields. The reaction path is constructed automatically with the only assumption of defining the reaction coordinate a priori. We...

A Direct Method of Hamiltonian Structure

International Nuclear Information System (INIS)

Li Qi; Chen Dengyuan; Su Shuhua

2011-01-01

A direct method of constructing the Hamiltonian structure of the soliton hierarchy with self-consistent sources is proposed through computing the functional derivative under some constraints. The Hamiltonian functional is related with the conservation densities of the corresponding hierarchy. Three examples and their two reductions are given. (general)

On Distributed Port-Hamiltonian Process Systems

NARCIS (Netherlands)

Lopezlena, Ricardo; Scherpen, Jacquelien M.A.

2004-01-01

In this paper we use the term distributed port-Hamiltonian Process Systems (DPHPS) to refer to the result of merging the theory of distributed Port-Hamiltonian systems (DPHS) with the theory of process systems (PS). Such concept is useful for combining the systematic interconnection of PHS with the

A diagrammatic construction of formal E-independent model hamiltonian

International Nuclear Information System (INIS)

Kvasnicka, V.

1977-01-01

A diagrammatic construction of formal E-independent model interaction (i.e., without second-quantization formalism) is suggested. The construction starts from the quasi-degenerate Brillouin-Wigner perturbation theory, in the framework of which an E-dependent model Hamiltonian is simply constructed. Applying the ''E-removing'' procedure to this E-dependent model Hamiltonian, the E-independent formal model Hamiltonian either Hermitian or non-Hermitian can diagrammatically be easily derived. For the formal E-independent model Hamiltonian the separability theorem is proved, which can be profitably used for a rather ''formalistic ''construction of a many-body E-independent model Hamiltonian

Molecular-orbital and structural descriptors in theoretical investigation of electroreduction of nitrodiazoles

Directory of Open Access Journals (Sweden)

BRANKO KOLARIC

2005-07-01

Full Text Available It is shown how a simple theoretical approach can be used for the investigation of electro-organic reactions.Mononitroimidazoles and mononitropyrazoles were studied by the semiempirical MNDO-PM3 molecular orbital method. The electrochemical reduction potentials of diazoles have been correlated with the energy of the lowest unoccupied molecular orbital (LUMO. It was found that an admirable correlation could be obtained by the introduction of simple structural descriptors as a correction to the energy of the LUMO. The interaction of a molecule with its surrounding depends on electrostatic potential and on steric hindrance. Most of these steric effects are taken into account using two parameters having a very limited set of integer values. The first (b is the position of a ring substituent regarding ring nitrogens, which accounts for the different orientations of dipole moments and for the different shape of the electrostatic potential. The second (structural parameter (t is the type of the ring, which accounts mostly for different modes of electrode approach, and for different charge polarization patterns in two diazole rings. The extended correlation with ELUMO, b and t, is very good, having a regression coefficient r = 0.991. The intrinsic importance of b and t is exemplified by their high statistical weight.

Molecular dynamics simulation based on the multi-component molecular orbital method: Application to H5O2+,D5O2+,andT5O2+

International Nuclear Information System (INIS)

Ishimoto, Takayoshi; Koyama, Michihisa

2012-01-01

Graphical abstract: Molecular dynamics method based on multi-component molecular orbital method was applied to basic hydrogen bonding systems, H 5 O 2 + , and its isotopomers (D 5 O 2 + andT 5 O 2 + ). Highlights: ► Molecular dynamics method with nuclear quantum effect was developed. ► Multi-component molecular orbital method was used as ab initio MO calculation. ► Developed method applied to basic hydrogen bonding system, H 5 O 2 + , and isotopomers. ► O ⋯ O vibrational stretching reflected to the distribution of protonic wavefunctions. ► H/D/T isotope effect was also analyzed. - Abstract: We propose a molecular dynamics (MD) method based on the multi-component molecular orbital (MC M O) method, which takes into account the quantum effect of proton directly, for the detailed analyses of proton transfer in hydrogen bonding system. The MC M O based MD (MC M O-MD) method is applied to the basic structures, H 5 O 2 + (called “Zundel ion”), and its isotopomers (D 5 O 2 + andT 5 O 2 + ). We clearly demonstrate the geometrical difference of hydrogen bonded O ⋯ O distance induced by H/D/T isotope effect because the O ⋯ O in H-compound was longer than that in D- or T-compound. We also find the strong relation between stretching vibration of O ⋯ O and the distribution of hydrogen bonded protonic wavefunction because the protonic wavefunction tends to delocalize when the O ⋯ O distance becomes short during the dynamics. Our proposed MC M O-MD simulation is expected as a powerful tool to analyze the proton dynamics in hydrogen bonding systems.

Port Hamiltonian modeling of Power Networks

NARCIS (Netherlands)

van Schaik, F.; van der Schaft, Abraham; Scherpen, Jacquelien M.A.; Zonetti, Daniele; Ortega, R

2012-01-01

In this talk a full nonlinear model for the power network in port–Hamiltonian framework is derived to study its stability properties. For this we use the modularity approach i.e., we first derive the models of individual components in power network as port-Hamiltonian systems and then we combine all

Hamiltonian Cycles on Random Eulerian Triangulations

DEFF Research Database (Denmark)

Guitter, E.; Kristjansen, C.; Nielsen, Jakob Langgaard

1998-01-01

. Considering the case n -> 0, this implies that the system of random Eulerian triangulations equipped with Hamiltonian cycles describes a c=-1 matter field coupled to 2D quantum gravity as opposed to the system of usual random triangulations equipped with Hamiltonian cycles which has c=-2. Hence, in this case...

Quantum dynamics of a vibronically coupled linear chain using a surrogate Hamiltonian approach

Energy Technology Data Exchange (ETDEWEB)

Lee, Myeong H., E-mail: myeong.lee@warwick.ac.uk; Troisi, Alessandro [Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL (United Kingdom)

2016-06-07

Vibronic coupling between the electronic and vibrational degrees of freedom has been reported to play an important role in charge and exciton transport in organic photovoltaic materials, molecular aggregates, and light-harvesting complexes. Explicitly accounting for effective vibrational modes rather than treating them as a thermal environment has been shown to be crucial to describe the effect of vibronic coupling. We present a methodology to study dissipative quantum dynamics of vibronically coupled systems based on a surrogate Hamiltonian approach, which is in principle not limited by Markov approximation or weak system-bath interaction, using a vibronic basis. We apply vibronic surrogate Hamiltonian method to a linear chain system and discuss how different types of relaxation process, intramolecular vibrational relaxation and intermolecular vibronic relaxation, influence population dynamics of dissipative vibronic systems.

Chemical insight from density functional modeling of molecular adsorption: Tracking the bonding and diffusion of anthracene derivatives on Cu(111) with molecular orbitals

Science.gov (United States)

Wyrick, Jonathan; Einstein, T. L.; Bartels, Ludwig

2015-03-01

We present a method of analyzing the results of density functional modeling of molecular adsorption in terms of an analogue of molecular orbitals. This approach permits intuitive chemical insight into the adsorption process. Applied to a set of anthracene derivates (anthracene, 9,10-anthraquinone, 9,10-dithioanthracene, and 9,10-diselenonanthracene), we follow the electronic states of the molecules that are involved in the bonding process and correlate them to both the molecular adsorption geometry and the species' diffusive behavior. We additionally provide computational code to easily repeat this analysis on any system.

Wigner-Smith delay times and the non-Hermitian Hamiltonian for the HOCl molecule

International Nuclear Information System (INIS)

Barr, A.M.; Reichl, L.E.

2013-01-01

We construct the scattering matrix for a two-dimensional model of a Cl atom scattering from an OH dimer. We show that the scattering matrix can be written in terms of a non-Hermitian Hamiltonian whose complex energy eigenvalues can be used to compute Wigner-Smith delay times for the Cl-OH scattering process. We compute the delay times for a range of energies, and show that the scattering states with the longest delay times are strongly influenced by unstable periodic orbits in the classical dynamics. (Copyright copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Study of unstable valences of cadmium and samarium by pulse radiolysis. Influence of complexation by some synthetical ionophores

International Nuclear Information System (INIS)

Lerat-Parizot, O.

1992-01-01

Instable valences of cations in solution are evidenced by pulse radiolysis, in spite of a lifetime often lower than a milli-second they participate to electron transfer reactions, owing to their redox potential. In this work are studied Cd + and Sm 2+ obtained respectively by reduction of Cd 2+ and Sm 3+ by a solvated electron. The reactivity of Cd + in a cryptand and in a coronand is studied; it is a powerful reducing agent (redox potential -2V) going back to the stable valence by electron transfer to an acceptor. Transfer kinetics is studied by reduction of organic molecules, effect of solvents and ligands is also examined. For samarium the reduction kinetics by hydrated electrons is increased when the ion is in a cryptand in agreement with electrochemical observations, showing that the valence 2+ is stabilized in respect to the valence 3+ for lanthanides. The difference of behaviour between Cd + and Sm 2+ is probably due to the fact that for Cd the transferred electron comes from the external layer and for Sm it is a f electron protected by the 5s and 5p orbitals

Kohn-Sham orbitals and potentials from quantum Monte Carlo molecular densities

International Nuclear Information System (INIS)

Varsano, Daniele; Barborini, Matteo; Guidoni, Leonardo

2014-01-01

In this work we show the possibility to extract Kohn-Sham orbitals, orbital energies, and exchange correlation potentials from accurate Quantum Monte Carlo (QMC) densities for atoms (He, Be, Ne) and molecules (H 2 , Be 2 , H 2 O, and C 2 H 4 ). The Variational Monte Carlo (VMC) densities based on accurate Jastrow Antisymmetrised Geminal Power wave functions are calculated through different estimators. Using these reference densities, we extract the Kohn-Sham quantities with the method developed by Zhao, Morrison, and Parr (ZMP) [Phys. Rev. A 50, 2138 (1994)]. We compare these extracted quantities with those obtained form CISD densities and with other data reported in the literature, finding a good agreement between VMC and other high-level quantum chemistry methods. Our results demonstrate the applicability of the ZMP procedure to QMC molecular densities, that can be used for the testing and development of improved functionals and for the implementation of embedding schemes based on QMC and Density Functional Theory

Incomplete Dirac reduction of constrained Hamiltonian systems

Energy Technology Data Exchange (ETDEWEB)

Chandre, C., E-mail: chandre@cpt.univ-mrs.fr

2015-10-15

First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac’s theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson brackets between the constraints, we show that a Dirac–Poisson bracket can be constructed, even if it corresponds to an incomplete reduction of the original Hamiltonian system. The uniqueness of Dirac brackets is discussed. The relevance of this procedure for infinite dimensional Hamiltonian systems is exemplified.

Spectral and resonance properties of the Smilansky Hamiltonian

Energy Technology Data Exchange (ETDEWEB)

Exner, Pavel [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic); Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University, Břehová 7, 11519 Prague (Czech Republic); Lotoreichik, Vladimir [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic); Tater, Miloš, E-mail: tater@ujf.cas.cz [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic)

2017-02-26

We analyze the Hamiltonian proposed by Smilansky to describe irreversible dynamics in quantum graphs and studied further by Solomyak and others. We derive a weak-coupling asymptotics of the ground state and add new insights by finding the discrete spectrum numerically in the subcritical case. Furthermore, we show that the model then has a rich resonance structure. - Highlights: • We derive conditions on bound states and on resonances of the Smilansky Hamiltonian. • Using these conditions we find numerically discrete spectrum and resonances of this Hamiltonian. • Our numerical tests confirm known properties of the Hamiltonian and allow us to conjecture new ones.

Optimal adaptive control for quantum metrology with time-dependent Hamiltonians

Science.gov (United States)

Pang, Shengshi; Jordan, Andrew N.

2017-01-01

Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case. PMID:28276428

Optimal adaptive control for quantum metrology with time-dependent Hamiltonians.

Science.gov (United States)

Pang, Shengshi; Jordan, Andrew N

2017-03-09

Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T 2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T 4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case.

Hamiltonian representation of divergence-free fields

International Nuclear Information System (INIS)

Boozer, A.H.

1984-11-01

Globally divergence-free fields, such as the magnetic field and the vorticity, can be described by a two degree of freedom Hamiltonian. The Hamiltonian function provides a complete topological description of the field lines. The formulation also separates the dissipative and inertial time scale evolution of the magnetic and the vorticity fields

Quantum simulator for spin-orbital magnetism

International Nuclear Information System (INIS)

Buehler, Adam

2016-01-01

In this dissertation we focus on many-body phenomena on a quantum level. In particular fermionic quantum gases in a temperature regime approaching absolute zero. Ultracold quantum gases have proven to be a versatile framework for Theorists and Experimentalists to probe many-body quantum mechanics. They also serve to quantum simulate solid state problems in a clean and controllable environment. The use of optical lattices include the advantage of tuning the required lattice structure nearly at will and lack the experimental shortcomings compared to the solid state, like the presence of lattice dislocations. The relevant lattice parameters can be easily tuned without changing the setup. In recent years many goals within theory and experiments of ultracold quantum gases in optical lattices were achieved. This emphasizes the significance of ongoing research with ultracold quantum gases on optical lattices. We present two aspects of modern theory of ultracold quantum gases in optical lattices. On the one hand, we implement orbital physics in a setup of optical lattices and on the other, we find elusive Majorana fermions in a setup with ultracold fermionic gases. Both aspects are well-known in solid state systems, but did not make the step towards ultracold quantum gases so far. We propose and investigate setups to quantum simulate these challenges in the framework of optical lattices. The first part of this work concerns the implementation of orbital physics in optical lattices. The orbital structure of atoms reveals novel phenomena in solid state systems. This raises the interest in creating optical lattice systems exhibiting analog behavior, as dictated by the orbitals in the solid state. We derive the microscopic Hamiltonian for a p-orbital system and investigate it in detail. For this Hamiltonian we perform a mean-field treatment and discover novel phase transitions including a possible tricritical point. In the analysis of the strong coupling regime we find an

Valence photoelectron spectra of alkali bromides calculated within the propagator theory

DEFF Research Database (Denmark)

Karpenko, Alexander; Iablonskyi, Denys; Aksela, Helena

2013-01-01

The valence ionization spectra covering the binding energy range 0-45 eV of alkali bromide XBr (X = Li, Na, K, Rb) vapors are studied within the framework of the propagator theory. Relativistic Algebraic Diagrammatic Construction calculations have been carried out in order to investigate photoion...... photoionization processes and to describe molecular electronic structure. Theoretical results are compared with available experimental data....

Orbital stability of solitary waves for Kundu equation

Science.gov (United States)

Zhang, Weiguo; Qin, Yinghao; Zhao, Yan; Guo, Boling

In this paper, we consider the Kundu equation which is not a standard Hamiltonian system. The abstract orbital stability theory proposed by Grillakis et al. (1987, 1990) cannot be applied directly to study orbital stability of solitary waves for this equation. Motivated by the idea of Guo and Wu (1995), we construct three invariants of motion and use detailed spectral analysis to obtain orbital stability of solitary waves for Kundu equation. Since Kundu equation is more complex than the derivative Schrödinger equation, we utilize some techniques to overcome some difficulties in this paper. It should be pointed out that the results obtained in this paper are more general than those obtained by Guo and Wu (1995). We present a sufficient condition under which solitary waves are orbitally stable for 2c+sυ1995) only considered the case 2c+sυ>0. We obtain the results on orbital stability of solitary waves for the derivative Schrödinger equation given by Colin and Ohta (2006) as a corollary in this paper. Furthermore, we obtain orbital stability of solitary waves for Chen-Lee-Lin equation and Gerdjikov-Ivanov equation, respectively.

Hamiltonian structures of some non-linear evolution equations

International Nuclear Information System (INIS)

Tu, G.Z.

1983-06-01

The Hamiltonian structure of the O(2,1) non-linear sigma model, generalized AKNS equations, are discussed. By reducing the O(2,1) non-linear sigma model to its Hamiltonian form some new conservation laws are derived. A new hierarchy of non-linear evolution equations is proposed and shown to be generalized Hamiltonian equations with an infinite number of conservation laws. (author)

Numerical determination of the magnetic field line Hamiltonian

International Nuclear Information System (INIS)

Kuo-Petravic, G.; Boozer, A.H.

1986-03-01

The structure of a magnetic field is determined by a one-degree of freedom, time-dependent Hamiltonian. This Hamiltonian is evaluated for a given field in a perturbed action-angle form. The location and the size of magnetic islands in the given field are determined from Hamiltonian perturbation theory and from an ordinary Poincare plot of the field line trajectories

Valence skipping driven superconductivity and charge Kondo effect

International Nuclear Information System (INIS)

Yanagisawa, Takashi; Hase, Izumi

2013-01-01

Highlights: •Valence skipping in metallic compounds can give rise to an unconventional superconductivity. •Several elements in the periodic table show valence skipping (or valence missing), for example, Bi forms the compounds in valence states +3 and +5. •The doping of valence skipping elements will induce superconductivity and this will lead to a possibility of high temperature superconductivity. •We consider the Wolf model with negative-U impurities, and show a phase diagram including superconducting phase. •There is a high temperature region near the boundary. -- Abstract: Valence skipping in metallic compounds can give rise to an unconventional superconductivity. Several elements in the periodic table show valence skipping (or valence missing), for example, Bi forms the compounds in valence states +3 and +5. The doping of valence skipping elements will induce superconductivity and this will lead to a possibility of high temperature superconductivity. We consider the Wolf model with negative-U impurities, and show a phase diagram including superconducting phase. The superconducting state is changed into a metallic state with a local singlet as the attractive interaction |U| increases. There is a high temperature region near the boundary

Potential energy surfaces for electron dynamics modeled by floating and breathing Gaussian wave packets with valence-bond spin-coupling: An analysis of high-harmonic generation spectrum

Science.gov (United States)

Ando, Koji

2018-03-01

A model of localized electron wave packets (EWPs), floating and breathing Gaussians with non-orthogonal valence-bond spin-coupling, is applied to compute the high-harmonic generation (HHG) spectrum from a LiH molecule induced by an intense laser pulse. The characteristic features of the spectrum, a plateau up to 50 harmonic-order and a cutoff, agreed well with those from the previous time-dependent complete active-space self-consistent-field calculation [T. Sato and K. L. Ishikawa, Phys. Rev. A 91, 023417 (2015)]. In contrast to the conventional molecular orbital picture in which the Li 2s and H 1s atomic orbitals are strongly mixed, the present calculation indicates that an incoherent sum of responses of single electrons reproduces the HHG spectrum, in which the contribution from the H 1s electron dominates the plateau and cutoff, whereas the Li 2s electron contributes to the lower frequency response. The results are comprehensive in terms of the shapes of single-electron potential energy curves constructed from the localized EWP model.

Consistent gaussian basis sets of double- and triple-zeta valence with polarization quality of the fifth period for solid-state calculations.

Science.gov (United States)

Laun, Joachim; Vilela Oliveira, Daniel; Bredow, Thomas

2018-02-22

Consistent basis sets of double- and triple-zeta valence with polarization quality for the fifth period have been derived for periodic quantum-chemical solid-state calculations with the crystalline-orbital program CRYSTAL. They are an extension of the pob-TZVP basis sets, and are based on the full-relativistic effective core potentials (ECPs) of the Stuttgart/Cologne group and on the def2-SVP and def2-TZVP valence basis of the Ahlrichs group. We optimized orbital exponents and contraction coefficients to supply robust and stable self-consistent field (SCF) convergence for a wide range of different compounds. The computed crystal structures are compared to those obtained with standard basis sets available from the CRYSTAL basis set database. For the applied hybrid density functional PW1PW, the average deviations of calculated lattice constants from experimental references are smaller with pob-DZVP and pob-TZVP than with standard basis sets. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.

Simultaneous conditioning of valence and arousal.

Science.gov (United States)

Gawronski, Bertram; Mitchell, Derek G V

2014-01-01

Evaluative conditioning (EC) refers to the change in the valence of a conditioned stimulus (CS) due to its pairing with a positive or negative unconditioned stimulus (US). To the extent that core affect can be characterised by the two dimensions of valence and arousal, EC has important implications for the origin of affective responses. However, the distinction between valence and arousal is rarely considered in research on EC or conditioned responses more generally. Measuring the subjective feelings elicited by a CS, the results from two experiments showed that (1) repeated pairings of a CS with a positive or negative US of either high or low arousal led to corresponding changes in both CS valence and CS arousal, (2) changes in CS arousal, but not changes in CS valence, were significantly related to recollective memory for CS-US pairings, (3) subsequent presentations of the CS without the US reduced the conditioned valence of the CS, with conditioned arousal being less susceptible to extinction and (4) EC effects were stronger for high arousal than low arousal USs. The results indicate that the conditioning of affective responses can occur simultaneously along two independent dimensions, supporting evidence in related areas that calls for a consideration of both valence and arousal. Implications for research on EC and the acquisition of emotional dispositions are discussed.

Hamiltonian analysis of transverse dynamics in axisymmetric rf photoinjectors

International Nuclear Information System (INIS)

Wang, C.-x.

2006-01-01

A general Hamiltonian that governs the beam dynamics in an rf photoinjector is derived from first principles. With proper choice of coordinates, the resulting Hamiltonian has a simple and familiar form, while taking into account the rapid acceleration, rf focusing, magnetic focusing, and space-charge forces. From the linear Hamiltonian, beam-envelope evolution is readily obtained, which better illuminates the theory of emittance compensation. Preliminary results on the third-order nonlinear Hamiltonian will be given as well.

Frustration-free Hamiltonians supporting Majorana zero edge modes

International Nuclear Information System (INIS)

Jevtic, Sania; Barnett, Ryan

2017-01-01

A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs. (paper)

Frustration-free Hamiltonians supporting Majorana zero edge modes

Science.gov (United States)

Jevtic, Sania; Barnett, Ryan

2017-10-01

A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs.

Capillary wave Hamiltonian for the Landau–Ginzburg–Wilson density functional

International Nuclear Information System (INIS)

Chacón, Enrique; Tarazona, Pedro

2016-01-01

We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau–Ginzburg–Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers. (paper)

Dirac Hamiltonian and Reissner-Nordström metric: Coulomb interaction in curved space-time

Science.gov (United States)

Noble, J. H.; Jentschura, U. D.

2016-03-01

We investigate the spin-1 /2 relativistic quantum dynamics in the curved space-time generated by a central massive charged object (black hole). This necessitates a study of the coupling of a Dirac particle to the Reissner-Nordström space-time geometry and the simultaneous covariant coupling to the central electrostatic field. The relativistic Dirac Hamiltonian for the Reissner-Nordström geometry is derived. A Foldy-Wouthuysen transformation reveals the presence of gravitational and electrogravitational spin-orbit coupling terms which generalize the Fokker precession terms found for the Dirac-Schwarzschild Hamiltonian, and other electrogravitational correction terms to the potential proportional to αnG , where α is the fine-structure constant and G is the gravitational coupling constant. The particle-antiparticle symmetry found for the Dirac-Schwarzschild geometry (and for other geometries which do not include electromagnetic interactions) is shown to be explicitly broken due to the electrostatic coupling. The resulting spectrum of radially symmetric, electrostatically bound systems (with gravitational corrections) is evaluated for example cases.

Mapping Enzymatic Catalysis Using the Effective Fragment Molecular Orbital Method: Towards all ab initio Biochemistry

DEFF Research Database (Denmark)

Svendsen, Casper Steinmann; Jensen, Jan; Fedorov, Dmitri

2013-01-01

We extend the Effective Fragment Molecular Orbital (EFMO) method to the frozen domain approach where only the geometry of an active part is optimized, while the many-body polarization effects are considered for the whole system. The new approach efficiently mapped out the entire reaction path of ...

Quantum entangling power of adiabatically connected Hamiltonians

International Nuclear Information System (INIS)

Hamma, Alioscia; Zanardi, Paolo

2004-01-01

The space of quantum Hamiltonians has a natural partition in classes of operators that can be adiabatically deformed into each other. We consider parametric families of Hamiltonians acting on a bipartite quantum state space. When the different Hamiltonians in the family fall in the same adiabatic class, one can manipulate entanglement by moving through energy eigenstates corresponding to different values of the control parameters. We introduce an associated notion of adiabatic entangling power. This novel measure is analyzed for general dxd quantum systems, and specific two-qubit examples are studied

A parcel formulation for Hamiltonian layer models

NARCIS (Netherlands)

Bokhove, Onno; Oliver, M.

Starting from the three-dimensional hydrostatic primitive equations, we derive Hamiltonian N-layer models with isentropic tropospheric and isentropic or isothermal stratospheric layers. Our construction employs a new parcel Hamiltonian formulation which describes the fluid as a continuum of

Band nesting, massive Dirac fermions, and valley Landé and Zeeman effects in transition metal dichalcogenides: A tight-binding model

Science.gov (United States)

Bieniek, Maciej; Korkusiński, Marek; Szulakowska, Ludmiła; Potasz, Paweł; Ozfidan, Isil; Hawrylak, Paweł

2018-02-01

We present here the minimal tight-binding model for a single layer of transition metal dichalcogenides (TMDCs) MX 2(M , metal; X , chalcogen) which illuminates the physics and captures band nesting, massive Dirac fermions, and valley Landé and Zeeman magnetic field effects. TMDCs share the hexagonal lattice with graphene but their electronic bands require much more complex atomic orbitals. Using symmetry arguments, a minimal basis consisting of three metal d orbitals and three chalcogen dimer p orbitals is constructed. The tunneling matrix elements between nearest-neighbor metal and chalcogen orbitals are explicitly derived at K ,-K , and Γ points of the Brillouin zone. The nearest-neighbor tunneling matrix elements connect specific metal and sulfur orbitals yielding an effective 6 ×6 Hamiltonian giving correct composition of metal and chalcogen orbitals but not the direct gap at K points. The direct gap at K , correct masses, and conduction band minima at Q points responsible for band nesting are obtained by inclusion of next-neighbor Mo-Mo tunneling. The parameters of the next-nearest-neighbor model are successfully fitted to MX 2(M =Mo ; X =S ) density functional ab initio calculations of the highest valence and lowest conduction band dispersion along K -Γ line in the Brillouin zone. The effective two-band massive Dirac Hamiltonian for MoS2, Landé g factors, and valley Zeeman splitting are obtained.

Effective Hamiltonians in quantum physics: resonances and geometric phase

International Nuclear Information System (INIS)

Rau, A R P; Uskov, D

2006-01-01

Effective Hamiltonians are often used in quantum physics, both in time-dependent and time-independent contexts. Analogies are drawn between the two usages, the discussion framed particularly for the geometric phase of a time-dependent Hamiltonian and for resonances as stationary states of a time-independent Hamiltonian

Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions

Science.gov (United States)

Scazza, F.; Hofrichter, C.; Höfer, M.; de Groot, P. C.; Bloch, I.; Fölling, S.

2014-10-01

Spin-exchanging interactions govern the properties of strongly correlated electron systems such as many magnetic materials. When orbital degrees of freedom are present, spin exchange between different orbitals often dominates, leading to the Kondo effect, heavy fermion behaviour or magnetic ordering. Ultracold ytterbium or alkaline-earth ensembles have attracted much recent interest as model systems for these effects, with two (meta-) stable electronic configurations representing independent orbitals. We report the observation of spin-exchanging contact interactions in a two-orbital SU(N)-symmetric quantum gas realized with fermionic 173Yb. We find strong inter-orbital spin exchange by spectroscopic characterization of all interaction channels and demonstrate SU(N = 6) symmetry within our measurement precision. The spin-exchange process is also directly observed through the dynamic equilibration of spin imbalances between ensembles in separate orbitals. The realization of an SU(N)-symmetric two-orbital Hubbard Hamiltonian opens the route to quantum simulations with extended symmetries and with orbital magnetic interactions, such as the Kondo lattice model.

Quantum chemical approaches: semiempirical molecular orbital and hybrid quantum mechanical/molecular mechanical techniques.

Science.gov (United States)

Bryce, Richard A; Hillier, Ian H

2014-01-01

The use of computational quantum chemical methods to aid drug discovery is surveyed. An overview of the various computational models spanning ab initio, density function theory, semiempirical molecular orbital (MO), and hybrid quantum mechanical (QM)/molecular mechanical (MM) methods is given and their strengths and weaknesses are highlighted, focussing on the challenge of obtaining the accuracy essential for them to make a meaningful contribution to drug discovery. Particular attention is given to hybrid QM/MM and semiempirical MO methods which have the potential to yield the necessary accurate predictions of macromolecular structure and reactivity. These methods are shown to have advanced the study of many aspects of substrate-ligand interactions relevant to drug discovery. Thus, the successful parametrization of semiempirical MO methods and QM/MM methods can be used to model noncovalent substrate-protein interactions, and to lead to improved scoring functions. QM/MM methods can be used in crystal structure refinement and are particularly valuable for modelling covalent protein-ligand interactions and can thus aid the design of transition state analogues. An extensive collection of examples from the areas of metalloenzyme structure, enzyme inhibition, and ligand binding affinities and scoring functions are used to illustrate the power of these techniques.

Study on the ionization of 1sσ molecular orbital in slow asymmetric collisions

International Nuclear Information System (INIS)

Sigaud, G.M.

1985-01-01

A model, based on the adiabatic perturbation theory, is proposed to the ionization of the 1sσ molecular orbital in slow asymmetric collisions. The extension of the model to less adiabatic collisions is made by imposing an asymptotic matching with the semiclassical approximation. The transient molecular state wavefunction is evaluated using an effective charge, which is dependent on the internuclear separation distance, for the projectile-target-atom-system. This procedure simulates both the screening due to the external electrons and the modifications on the electronic wavefunction due to the nuclei relative motion. The direct Coulomb ionization cross-section of the 1sσ molecular orbital is calculated for projectiles following hyperbolic paths in terms of this effective charge. At the same time, X-rays production cross-sections for the K-shell of thick targets of Ti and Fe are determined for incident beams of D, He, C, N and O, with energy range between 0,20 and 4,00 MeV. The comparison between the proposed model and the obtained experimental data shows that, for this energy range, two other processes, besides direct ionization, contribute to X-rays production. These processes, namely the recoil of the target-atom in its matrix and the electron capture by the projectile, are discussed in the light of theoretical models existent in the literature. (author)

In search for an optimal methodology to calculate the valence electron affinities of temporary anions.

Science.gov (United States)

Puiatti, Marcelo; Vera, D Mariano A; Pierini, Adriana B

2009-10-28

Recently, we have proposed an approach for finding the valence anion ground state, based on the stabilization exerted by a polar solvent; the methodology used standard DFT methods and relatively inexpensive basis sets and yielded correct electron affinity (EA) values by gradually decreasing the dielectric constant of the medium. In order to address the overall performance of the new methodology, to find the best conditions for stabilizing the valence state and to evaluate its scope and limitations, we gathered a pool of 60 molecules, 25 of them bearing the conventional valence state as the ground anion and 35 for which the lowest anion state found holds the extra electron in a diffuse orbital around the molecule (non valence state). The results obtained by testing this representative set suggest a very good performance for most species having an experimental EA less negative than -3.0 eV; the correlation at the B3LYP/6-311+G(2df,p) level being y = 1.01x + 0.06, with a correlation index of 0.985. As an alternative, the time dependent DFT (TD-DFT) approach was also tested with both B3LYP and PBE0 functionals. The methodology we proposed shows a comparable or better accuracy with respect to TD-DFT, although the TD-DFT approach with the PBE0 functional is suggested as a suitable estimate for species with the most negative EAs (ca.-2.5 to -3.5 eV), for which stabilization strategies can hardly reach the valence state. As an application, a pool of 8 compounds of key biological interest with EAs which remain unknown or unclear were predicted using the new methodology.

A generalized AKNS hierarchy and its bi-Hamiltonian structures

International Nuclear Information System (INIS)

Xia Tiecheng; You Fucai; Chen Dengyuan

2005-01-01

First we construct a new isospectral problem with 8 potentials in the present paper. And then a new Lax pair is presented. By making use of Tu scheme, a class of new soliton hierarchy of equations is derived, which is integrable in the sense of Liouville and possesses bi-Hamiltonian structures. After making some reductions, the well-known AKNS hierarchy and other hierarchies of evolution equations are obtained. Finally, in order to illustrate that soliton hierarchy obtained in the paper possesses bi-Hamiltonian structures exactly, we prove that the linear combination of two-Hamiltonian operators admitted are also a Hamiltonian operator constantly. We point out that two Hamiltonian operators obtained of the system are directly derived from a recurrence relations, not from a recurrence operator

Gravitational surface Hamiltonian and entropy quantization

Directory of Open Access Journals (Sweden)

Ashish Bakshi

2017-02-01

Full Text Available The surface Hamiltonian corresponding to the surface part of a gravitational action has xp structure where p is conjugate momentum of x. Moreover, it leads to TS on the horizon of a black hole. Here T and S are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos–Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics.

First principles of Hamiltonian medicine.

Science.gov (United States)

Crespi, Bernard; Foster, Kevin; Úbeda, Francisco

2014-05-19

We introduce the field of Hamiltonian medicine, which centres on the roles of genetic relatedness in human health and disease. Hamiltonian medicine represents the application of basic social-evolution theory, for interactions involving kinship, to core issues in medicine such as pathogens, cancer, optimal growth and mental illness. It encompasses three domains, which involve conflict and cooperation between: (i) microbes or cancer cells, within humans, (ii) genes expressed in humans, (iii) human individuals. A set of six core principles, based on these domains and their interfaces, serves to conceptually organize the field, and contextualize illustrative examples. The primary usefulness of Hamiltonian medicine is that, like Darwinian medicine more generally, it provides novel insights into what data will be productive to collect, to address important clinical and public health problems. Our synthesis of this nascent field is intended predominantly for evolutionary and behavioural biologists who aspire to address questions directly relevant to human health and disease.

Quantum Statistical Operator and Classically Chaotic Hamiltonian ...

African Journals Online (AJOL)

Quantum Statistical Operator and Classically Chaotic Hamiltonian System. ... Journal of the Nigerian Association of Mathematical Physics ... In a Hamiltonian system von Neumann Statistical Operator is used to tease out the quantum consequence of (classical) chaos engendered by the nonlinear coupling of system to its ...

Noise-induced phase space transport in two-dimensional Hamiltonian systems.

Science.gov (United States)

Pogorelov, I V; Kandrup, H E

1999-08-01

First passage time experiments were used to explore the effects of low amplitude noise as a source of accelerated phase space diffusion in two-dimensional Hamiltonian systems, and these effects were then compared with the effects of periodic driving. The objective was to quantify and understand the manner in which "sticky" chaotic orbits that, in the absence of perturbations, are confined near regular islands for very long times, can become "unstuck" much more quickly when subjected to even very weak perturbations. For both noise and periodic driving, the typical escape time scales logarithmically with the amplitude of the perturbation. For white noise, the details seem unimportant: Additive and multiplicative noise typically have very similar effects, and the presence or absence of a friction related to the noise by a fluctuation-dissipation theorem is also largely irrelevant. Allowing for colored noise can significantly decrease the efficacy of the perturbation, but only when the autocorrelation time, which vanishes for white noise, becomes so large that there is little power at frequencies comparable to the natural frequencies of the unperturbed orbit. Similarly, periodic driving is relatively inefficient when the driving frequency is not comparable to these natural frequencies. This suggests that noise-induced extrinsic diffusion, like modulational diffusion associated with periodic driving, is a resonance phenomenon. The logarithmic dependence of the escape time on amplitude reflects the fact that the time required for perturbed and unperturbed orbits to diverge a given distance scales logarithmically in the amplitude of the perturbation.

Orbital Resonances in the Vinti Solution

Science.gov (United States)

Zurita, L. D.

As space becomes more congested, contested, and competitive, high-accuracy orbital predictions become critical for space operations. Current orbit propagators use the two-body solution with perturbations added, which have significant error growth when numerically integrated for long time periods. The Vinti Solution is a more accurate model than the two-body problem because it also accounts for the equatorial bulge of the Earth. Unfortunately, the Vinti solution contains small divisors near orbital resonances in the perturbative terms of the Hamiltonian, which lead to inaccurate orbital predictions. One approach to avoid the small divisors is to apply transformation theory, which is presented in this research. The methodology of this research is to identify the perturbative terms of the Vinti Solution, perform a coordinate transformation, and derive the new equations of motion for the Vinti system near orbital resonances. An analysis of these equations of motion offers insight into the dynamics found near orbital resonances. The analysis in this research focuses on the 2:1 resonance, which includes the Global Positioning System. The phase portrait of a nominal Global Positioning System satellite orbit is found to contain a libration region and a chaotic region. Further analysis shows that the dynamics of the 2:1 resonance affects orbits with semi-major axes ranging from -5.0 to +5.4 kilometers from an exactly 2:1 resonant orbit. Truth orbits of seven Global Positioning System satellites are produced for 10 years. Two of the satellites are found to be outside of the resonance region and three are found to be influenced by the libration dynamics of the resonance. The final satellite is found to be influenced by the chaotic dynamics of the resonance. This research provides a method of avoiding the small divisors found in the perturbative terms of the Vinti Solution near orbital resonances.

Generalized Hubbard Hamiltonian: renormalization group approach

International Nuclear Information System (INIS)

Cannas, S.A.; Tamarit, F.A.; Tsallis, C.

1991-01-01

We study a generalized Hubbard Hamiltonian which is closed within the framework of a Quantum Real Space Renormalization Group, which replaces the d-dimensional hypercubic lattice by a diamond-like lattice. The phase diagram of the generalized Hubbard Hamiltonian is analyzed for the half-filled band case in d = 2 and d = 3. Some evidence for superconductivity is presented. (author). 44 refs., 12 figs., 2 tabs

Influence of the spin-orbit coupling on nuclear superfluidity along the N=Z line

International Nuclear Information System (INIS)

Juillet, O.; Josse, S.

2000-01-01

We show that the spin-orbit potential of the nuclear mean field destroys isoscalar superfluid correlations in self-conjugate nuclei. Using group theory and boson mapping techniques on a Hamiltonian including single particle splittings and a SO ST (8) pairing interaction, we give analytical expression for the spin-orbit dependence of some N =Z properties such as the relative position of T = 0 and T = 1 states in odd-odd systems or double binding-energy differences of even-even nuclei. (authors)

Local Hamiltonians for maximally multipartite-entangled states

Science.gov (United States)

Facchi, P.; Florio, G.; Pascazio, S.; Pepe, F.

2010-10-01

We study the conditions for obtaining maximally multipartite-entangled states (MMESs) as nondegenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 3 to 5) and show some example Hamiltonians with MMESs as eigenstates.

Local Hamiltonians for maximally multipartite-entangled states

International Nuclear Information System (INIS)

Facchi, P.; Florio, G.; Pascazio, S.; Pepe, F.

2010-01-01

We study the conditions for obtaining maximally multipartite-entangled states (MMESs) as nondegenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 3 to 5) and show some example Hamiltonians with MMESs as eigenstates.

Control by damping Injection of Electrodynamic Tether System in an Inclined Orbit

DEFF Research Database (Denmark)

Larsen, Martin Birkelund; Blanke, Mogens

2009-01-01

dynamical system. Based on this model, a nonlinear controller is designed that will make the system asymptotically stable around its open-loop equilibrium. The control scheme handles the time-varying nature of the system in a suitable manner resulting in a large operational region. The performance...... of the closed loop system is treated using Floquet theory, investigating the closed loop properties for their dependency of the controller gain and orbit inclination.......Control of a satellite system with an electrodynamic tether as actuator is a time-periodic and underactuated control problem. This paper considers the tethered satellite in a Hamiltonian framework and determines a port-controlled Hamiltonian formulation that adequately describes the nonlinear...

Greenberger-Horne-Zeilinger States and Few-Body Hamiltonians

Science.gov (United States)

Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Pepe, Francesco V.

2011-12-01

The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an n-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of m-qubit couplings with m≥[(n+1)/2]. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.

Greenberger-Horne-Zeilinger states and few-body Hamiltonians.

Science.gov (United States)

Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Pepe, Francesco V

2011-12-23

The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an n-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of m-qubit couplings with m≥[(n+1)/2]. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.

Lagrangian-Hamiltonian formalism for the gravitational two-body problem with spin and parametrized post-Newtonian parameters γ and β

International Nuclear Information System (INIS)

Barker, B.M.; O'Connell, R.F.

1976-01-01

We generalize the Lagrangian and Hamiltonian of our previous work on the gravitational two-body problem with spin by including the parametrized-post-Newtonian parameters γ and β. By this procedure we are able to obtain the precession of the orbit as well as the precession of the spin. Equations of motion corresponding to an arbitrary-spin supplementary condition are also given. Finally we show how the masses of the binary pulsar PSR 1913 + 16 and its companion are related to the orbit and spin precessions. Combining this with a result derivable from the second-order Doppler effect and the gravitational red-shift, we obtain a relation constraining the values that γ and β can take

Effective Hamiltonian for travelling discrete breathers

Science.gov (United States)

MacKay, Robert S.; Sepulchre, Jacques-Alexandre

2002-05-01

Hamiltonian chains of oscillators in general probably do not sustain exact travelling discrete breathers. However solutions which look like moving discrete breathers for some time are not difficult to observe in numerics. In this paper we propose an abstract framework for the description of approximate travelling discrete breathers in Hamiltonian chains of oscillators. The method is based on the construction of an effective Hamiltonian enabling one to describe the dynamics of the translation degree of freedom of moving breathers. Error estimate on the approximate dynamics is also studied. The concept of the Peierls-Nabarro barrier can be made clear in this framework. We illustrate the method with two simple examples, namely the Salerno model which interpolates between the Ablowitz-Ladik lattice and the discrete nonlinear Schrödinger system, and the Fermi-Pasta-Ulam chain.

Valence effects on adsorption: a preliminary assessment of the effects on valence state control on sorption measurements

International Nuclear Information System (INIS)

Meyer, R.E.; Arnold, W.D.; Case, F.; Shiao, S.Y.; Palmer, D.A.

1983-01-01

Electrochemical arguments are advanced to illustrate that what is usually measured in practice is a mixed potential determined by the kinetics of the electrode processes occurring at the indicator electrode. Valence states can be altered electrochemically or by use of added chemical reagents, including redox couples which can hold the potential to relatively specific potentials. The disadvantage of added chemical reagents is that they may alter the characteristics of the sorption reactions by interaction with the sorbent. Electrochemical methods are versatile and do not add reagents, but in some caes the nuclide can adsorb on the electrode itself. A description is given of the application of the electrochemical method of valence control to determination of sorption of Np(V) on alumina. Valence state control and analysis can be used to study possible redox reactions on materials which might be used as backfill materials. A description is given of survey experiments with a number of sulfides and iron-containing materials. Valence state analysis is used on the initial solutions and leachate from acid leaches of the sorbent after the sorption experiment to help determine whether valence state change is occurring. The preliminary results indicate that on the sulfides tested, sorption occurs both with and without valence state change

Complex Hamiltonian Dynamics

CERN Document Server

Bountis, Tassos

2012-01-01

This book introduces and explores modern developments in the well established field of Hamiltonian dynamical systems. It focuses on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion. The role of nonlinear normal modes is highlighted and the importance of low-dimensional tori in the resolution of the famous FPU paradox is emphasized. Novel powerful numerical methods are used to study localization phenomena and distinguish order from strongly and weakly chaotic regimes. The emerging hierarchy of complex structures in such regimes gives rise to particularly long-lived patterns and phenomena called quasi-stationary states, which are explored in particular in the concrete setting of one-dimensional Hamiltonian lattices and physical applications in condensed matter systems.  The self-contained and pedagogical approach is blended with a unique balance between mathematical rigor, physics insights and concrete applications. End of chapter exercises and (more demanding) res...

Invariant metrics for Hamiltonian systems

International Nuclear Information System (INIS)

Rangarajan, G.; Dragt, A.J.; Neri, F.

1991-05-01

In this paper, invariant metrics are constructed for Hamiltonian systems. These metrics give rise to norms on the space of homeogeneous polynomials of phase-space variables. For an accelerator lattice described by a Hamiltonian, these norms characterize the nonlinear content of the lattice. Therefore, the performance of the lattice can be improved by minimizing the norm as a function of parameters describing the beam-line elements in the lattice. A four-fold increase in the dynamic aperture of a model FODO cell is obtained using this procedure. 7 refs

Approximate symmetries of Hamiltonians

Science.gov (United States)

Chubb, Christopher T.; Flammia, Steven T.

2017-08-01

We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.

Momentum and hamiltonian in complex action theory

DEFF Research Database (Denmark)

Nagao, Keiichi; Nielsen, Holger Frits Bech

2012-01-01

$-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator $\\hat{p}$, in FPI with a starting Lagrangian. Solving the eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led...

Diffeomorphism invariance in the Hamiltonian formulation of General Relativity

International Nuclear Information System (INIS)

Kiriushcheva, N.; Kuzmin, S.V.; Racknor, C.; Valluri, S.R.

2008-01-01

It is shown that when the Einstein-Hilbert Lagrangian is considered without any non-covariant modifications or change of variables, its Hamiltonian formulation leads to results consistent with principles of General Relativity. The first-class constraints of such a Hamiltonian formulation, with the metric tensor taken as a canonical variable, allow one to derive the generator of gauge transformations, which directly leads to diffeomorphism invariance. The given Hamiltonian formulation preserves general covariance of the transformations derivable from it. This characteristic should be used as the crucial consistency requirement that must be met by any Hamiltonian formulation of General Relativity

Covalently bound molecular states in beryllium and carbon isotopes

International Nuclear Information System (INIS)

Wolfram von, Oertzen; Hans-Gerhard, Bohlen; Wolfram von, Oertzen

2003-01-01

Nuclear clustering in N=Z nuclei has been studied since many decades. States close to the decay thresholds, as described by the Ikeda diagram, are of particular interest. Recent studies in loosely bound systems, as observed with neutron-rich nuclei has revived the interest in cluster structures in nuclei, with additional valence neutrons, which give rise to pronounced covalent molecular structures. The Beryllium isotopes represent the first example of such unique states in nuclear physics with extreme deformations. In the deformed shell model these are referred to as super- and hyper-deformation. These states can be described explicitly by molecular concepts, with neutrons in covalent binding orbits. Examples of recent experiments performed at the HMI-Berlin demonstrating the molecular structure of the rotational bands in Beryllium isotopes are presented. Further work on chain states (nuclear polymers) in the carbon isotopes is in progress, these are the first examples of deformed structures in nuclei with an axis ratio of 3:1. A threshold diagram with clusters bound via neutrons in covalent molecular configurations can be established, which can serve as a guideline for future work. (authors)

Spin-orbit interaction effects in zincblende semiconductors: Ab initio pseudopotential calculations

International Nuclear Information System (INIS)

Li, Ming-Fu; Surh, M.P.; Louie, S.G.

1988-06-01

Ab initio band structure calculations have been performed for the spin-orbit interaction effects at the top of the valence bands for GaAs and InSb. Relativistic, norm-conserving pseudopotentials are used with no correction made for the gaps from the local density approximation. The spin-orbit splitting at Γ and linear terms in the /rvec char/k dependence of the splitting are found to be in excellent agreement with existing experiments and previous theoretical results. The effective mass and the cubic splitting terms are also examined. 6 refs., 1 fig., 2 tabs

Grid-based Continual Analysis of Molecular Interior for Drug Discovery, QSAR and QSPR.

Science.gov (United States)

Potemkin, Andrey V; Grishina, Maria A; Potemkin, Vladimir A

2017-01-01

In 1979, R.D.Cramer and M.Milne made a first realization of 3D comparison of molecules by aligning them in space and by mapping their molecular fields to a 3D grid. Further, this approach was developed as the DYLOMMS (Dynamic Lattice- Oriented Molecular Modelling System) approach. In 1984, H.Wold and S.Wold proposed the use of partial least squares (PLS) analysis, instead of principal component analysis, to correlate the field values with biological activities. Then, in 1988, the method which was called CoMFA (Comparative Molecular Field Analysis) was introduced and the appropriate software became commercially available. Since 1988, a lot of 3D QSAR methods, algorithms and their modifications are introduced for solving of virtual drug discovery problems (e.g., CoMSIA, CoMMA, HINT, HASL, GOLPE, GRID, PARM, Raptor, BiS, CiS, ConGO,). All the methods can be divided into two groups (classes):1. Methods studying the exterior of molecules; 2) Methods studying the interior of molecules. A series of grid-based computational technologies for Continual Molecular Interior analysis (CoMIn) are invented in the current paper. The grid-based analysis is fulfilled by means of a lattice construction analogously to many other grid-based methods. The further continual elucidation of molecular structure is performed in various ways. (i) In terms of intermolecular interactions potentials. This can be represented as a superposition of Coulomb, Van der Waals interactions and hydrogen bonds. All the potentials are well known continual functions and their values can be determined in all lattice points for a molecule. (ii) In the terms of quantum functions such as electron density distribution, Laplacian and Hamiltonian of electron density distribution, potential energy distribution, the highest occupied and the lowest unoccupied molecular orbitals distribution and their superposition. To reduce time of calculations using quantum methods based on the first principles, an original quantum

Empirical Hamiltonians

International Nuclear Information System (INIS)

Peggs, S.; Talman, R.

1987-01-01

As proton accelerators get larger, and include more magnets, the conventional tracking programs which simulate them run slower. The purpose of this paper is to describe a method, still under development, in which element-by-element tracking around one turn is replaced by a single man, which can be processed far faster. It is assumed for this method that a conventional program exists which can perform faithful tracking in the lattice under study for some hundreds of turns, with all lattice parameters held constant. An empirical map is then generated by comparison with the tracking program. A procedure has been outlined for determining an empirical Hamiltonian, which can represent motion through many nonlinear kicks, by taking data from a conventional tracking program. Though derived by an approximate method this Hamiltonian is analytic in form and can be subjected to further analysis of varying degrees of mathematical rigor. Even though the empirical procedure has only been described in one transverse dimension, there is good reason to hope that it can be extended to include two transverse dimensions, so that it can become a more practical tool in realistic cases

Molecular orbital evaluation of charge flow dynamics in natural pigments based photosensitizers.

Science.gov (United States)

Heera, Thekinneydath Rajan; Cindrella, Louis

2010-03-01

The relationship between structure and photo electrochemical property of ten natural pigments from plants, insects and microbes has been analyzed using density functional theory (DFT) at the B3LYP/6-31G(d) level. The essential parameters for their photoelectrochemical behaviour such as ground state geometries, electronic transition energies and oxidation potentials are computed. The attachment tendency of the anchoring groups, expressed as the deprotonation order, is determined by calculating the proton affinities at different sites of the molecules. A thorough analysis of the charge flow dynamics in the molecular orbitals (HOMO and LUMO) of these molecules has been carried out and presented to emphasize the role of these orbitals in effective charge separation, the important feature of photosensitizers for DSSC. This study highlights that the flexible spatial orientation provided by the bridging aliphatic unsaturation favours the oscillator strength and the hydroxyl anchor group attached to the ring of delocalized pi electron cloud acts as the effective anchor.

Effective magnetic Hamiltonians

Czech Academy of Sciences Publication Activity Database

Drchal, Václav; Kudrnovský, Josef; Turek, I.

2013-01-01

Roč. 26, č. 5 (2013), s. 1997-2000 ISSN 1557-1939 R&D Projects: GA ČR GA202/09/0775 Institutional support: RVO:68378271 Keywords : effective magnetic Hamiltonian * ab initio * magnetic structure Subject RIV: BE - Theoretical Physics Impact factor: 0.930, year: 2013

Competition Between Two Large-Amplitude Motion Models: New Hybrid Hamiltonian Versus Old Pure-Tunneling Hamiltonian

Science.gov (United States)

Kleiner, Isabelle; Hougen, Jon T.

2017-06-01

In this talk we report on our progress in trying to make the hybrid Hamiltonian competitive with the pure-tunneling Hamiltonian for treating large-amplitude motions in methylamine. A treatment using the pure-tunneling model has the advantages of: (i) requiring relatively little computer time, (ii) working with relatively uncorrelated fitting parameters, and (iii) yielding in the vast majority of cases fits to experimental measurement accuracy. These advantages are all illustrated in the work published this past year on a gigantic v_{t} = 1 data set for the torsional fundamental band in methyl amine. A treatment using the hybrid model has the advantages of: (i) being able to carry out a global fit involving both v_{t} = 0 and v_{t} = 1 energy levels and (ii) working with fitting parameters that have a clearer physical interpretation. Unfortunately, a treatment using the hybrid model has the great disadvantage of requiring a highly correlated set of fitting parameters to achieve reasonable fitting accuracy, which complicates the search for a good set of molecular fitting parameters and a fit to experimental accuracy. At the time of writing this abstract, we have been able to carry out a fit with J up to 15 that includes all available infrared data in the v_{t} = 1-0 torsional fundamental band, all ground-state microwave data with K up to 10 and J up to 15, and about a hundred microwave lines within the v_{t} = 1 torsional state, achieving weighted root-mean-square (rms) deviations of about 1.4, 2.8, and 4.2 for these three categories of data. We will give an update of this situation at the meeting. I. Gulaczyk, M. Kreglewski, V.-M. Horneman, J. Mol. Spectrosc., in Press (2017).

A local inverse spectral theorem for Hamiltonian systems

International Nuclear Information System (INIS)

Langer, Matthias; Woracek, Harald

2011-01-01

We consider (2 × 2)-Hamiltonian systems of the form y'(x) = zJH(x)y(x), x in [s − , s + ). If a system of this form is in the limit point case, an analytic function is associated with it, namely its Titchmarsh–Weyl coefficient q H . The (global) uniqueness theorem due to de Branges says that the Hamiltonian H is (up to reparameterization) uniquely determined by the function q H . In this paper we give a local uniqueness theorem; if the Titchmarsh–Weyl coefficients q H 1 and q H 2 corresponding to two Hamiltonian systems are exponentially close, then the Hamiltonians H 1 and H 2 coincide (up to reparameterization) up to a certain point of their domain, which depends on the quantitative degree of exponential closeness of the Titchmarsh–Weyl coefficients

A Combined Theoretical and Experimental View on Valence and Conduction Band Densities of States of Lead Halide Perovskites

Science.gov (United States)

Kronik, Leeor; Endres, James; Egger, David A.; Kulbak, Michael; Kerner, Ross A.; Zhao, Lianfeng; Silver, Scott H.; Hodes, Gary; Rand, Barry P.; Cahen, David; Kahn, Antoine

We present results for the valence and conduction band density of states (DOS), measured via ultraviolet and inverse photoemission spectroscopies for three lead halide perovskites. Specifically, the DOS of MAPbI3, MAPbBr3, and CsPbBr3, grown on different substrates, are compared. Theoretical DOS, calculated via hybrid density functional theory and including spin-orbit coupling, are compared to experimental data. The agreement between experiment and theory, obtained after correcting the latter for quantitative discrepancies, leads to the identification of valence and conduction band spectral features. In particular, this comparison allows for precise determination of the energy position of the band edges, namely ionization energies and electron affinities of these materials. We find an unusually low DOS at the valence band maximum (VBM) of these systems, which confirms and generalizes previous findings of strong band dispersion and low DOS at the VBM of MAPbI3. This calls for special attention when using electron spectroscopy to determine the frontier electronic states of lead halide perovskites.

Valence band electronic structure of Pd based ternary chalcogenide superconductors

Energy Technology Data Exchange (ETDEWEB)

Lohani, H. [Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005 (India); Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400085 (India); Mishra, P. [Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005 (India); Goyal, R.; Awana, V.P.S. [National Physical Laboratory(CSIR), Dr. K. S. Krishnan Road, New Delhi 110012 (India); Sekhar, B.R., E-mail: sekhar@iopb.res.in [Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005 (India); Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400085 (India)

2016-12-15

Highlights: • VB Photoemission study and DFT calculations on Pd based ternary superconductors are presented. • Nb{sub 2}Pd{sub 0.95}S{sub 5} shows a temperature dependent pseudogap. • VB spectral features of ternary superconductors are correlated to their structural geometry. - Abstract: We present a comparative study of the valence band electronic structure of Pd based ternary chalcogenide superconductors Nb{sub 2}Pd{sub 0.95}S{sub 5}, Ta{sub 2}Pd{sub 0.97}S{sub 6} and Ta{sub 2}Pd{sub 0.97}Te{sub 6} using experimental photoemission spectroscopy and density functional based theoretical calculations. We observe a qualitatively similarity between valence band (VB) spectra of Nb{sub 2}Pd{sub 0.95}S{sub 5} and Ta{sub 2}Pd{sub 0.97}S{sub 6}. Further, we find a pseudogap feature in Nb{sub 2}Pd{sub 0.95}S{sub 5} at low temperature, unlike other two compounds. We have correlated the structural geometry with the differences in VB spectra of these compounds. The different atomic packing in these compounds could vary the strength of inter-orbital hybridization among various atoms which leads to difference in their electronic structure as clearly observed in our DOS calculations.

A molecular orbital study on the oxidative decomposition of HFC-32

International Nuclear Information System (INIS)

Mochizuki, Yuji

1999-03-01

A series of ab initio molecular orbital calculations, in which Hartree-Fock, second-order Moeller-Plesset perturbation, density functional (B3LYP and BHandHLYP) levels of theory were used, was performed on the elementary reactions related to the oxidative decomposition of HFC-32 (CH 2 F 2 ) by hydroxyl (OH) radicals in a supercritical water condition (so-called SCWO). The whole process is written as CH 2 F 2 + 4OH → CO 2 + 2H 2 O + 2HF and consists of (1) H abstraction by OH to form H 2 O, (2) OH coupling to C-center, and (3) HF leaving to form C=O bond. Molecular geometries were optimized at each level of theory. The HF leaving was found to be the rate-determining step, but its barrier height was lowered by the reactive solvation with an extra H 2 O. Calculations implied that the SCWO of HFC-32 can proceed efficiently. (author)

Communication: Localized molecular orbital analysis of the effect of electron correlation on the anomalous isotope effect in the NMR spin-spin coupling constant in methane

Energy Technology Data Exchange (ETDEWEB)

Zarycz, M. Natalia C., E-mail: mnzarycz@gmail.com; Provasi, Patricio F., E-mail: patricio@unne.edu.ar [Department of Physics, University of Northeastern - CONICET, Av. Libertad 5500, Corrientes W3404AAS (Argentina); Sauer, Stephan P. A., E-mail: sauer@kiku.dk [Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø (Denmark)

2014-10-21

We discuss the effect of electron correlation on the unexpected differential sensitivity (UDS) in the {sup 1}J(C–H) coupling constant of CH{sub 4} using a decomposition into contributions from localized molecular orbitals and compare with the {sup 1}J(N–H) coupling constant in NH{sub 3}. In particular, we discuss the well known fact that uncorrelated coupled Hartree-Fock (CHF) calculations are not able to reproduce the UDS in methane. For this purpose we have implemented for the first time a localized molecular orbital analysis for the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes—SOPPA(CCSD) in the DALTON program. Comparing the changes in the localized orbital contributions at the correlated SOPPA and SOPPA(CCSD) levels and at the uncorrelated CHF level, we find that the latter overestimates the effect of stretching the bond between the coupled atoms on the contribution to the coupling from the localized bonding orbital between these atoms. This disturbs the subtle balance between the molecular orbital contributions, which lead to the UDS in methane.

Fragment-orbital tunneling currents and electronic couplings for analysis of molecular charge-transfer systems.

Science.gov (United States)

Hwang, Sang-Yeon; Kim, Jaewook; Kim, Woo Youn

2018-04-04

In theoretical charge-transfer research, calculation of the electronic coupling element is crucial for examining the degree of the electronic donor-acceptor interaction. The tunneling current (TC), representing the magnitudes and directions of electron flow, provides a way of evaluating electronic couplings, along with the ability of visualizing how electrons flow in systems. Here, we applied the TC theory to π-conjugated organic dimer systems, in the form of our fragment-orbital tunneling current (FOTC) method, which uses the frontier molecular-orbitals of system fragments as diabatic states. For a comprehensive test of FOTC, we assessed how reasonable the computed electronic couplings and the corresponding TC densities are for the hole- and electron-transfer databases HAB11 and HAB7. FOTC gave 12.5% mean relative unsigned error with regard to the high-level ab initio reference. The shown performance is comparable with that of fragment-orbital density functional theory, which gave the same error by 20.6% or 13.9% depending on the formulation. In the test of a set of nucleobase π stacks, we showed that the original TC expression is also applicable to nondegenerate cases under the condition that the overlap between the charge distributions of diabatic states is small enough to offset the energy difference. Lastly, we carried out visual analysis on the FOTC densities of thiophene dimers with different intermolecular alignments. The result depicts an intimate topological connection between the system geometry and electron flow. Our work provides quantitative and qualitative grounds for FOTC, showing it to be a versatile tool in characterization of molecular charge-transfer systems.

Contact symmetries and Hamiltonian thermodynamics

International Nuclear Information System (INIS)

Bravetti, A.; Lopez-Monsalvo, C.S.; Nettel, F.

2015-01-01

It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production

Generic Local Hamiltonians are Gapless

Science.gov (United States)

Movassagh, Ramis

2017-12-01

We prove that generic quantum local Hamiltonians are gapless. In fact, we prove that there is a continuous density of states above the ground state. The Hamiltonian can be on a lattice in any spatial dimension or on a graph with a bounded maximum vertex degree. The type of interactions allowed for include translational invariance in a disorder (i.e., probabilistic) sense with some assumptions on the local distributions. Examples include many-body localization and random spin models. We calculate the scaling of the gap with the system's size when the local terms are distributed according to a Gaussian β orthogonal random matrix ensemble. As a corollary, there exist finite size partitions with respect to which the ground state is arbitrarily close to a product state. When the local eigenvalue distribution is discrete, in addition to the lack of an energy gap in the limit, we prove that the ground state has finite size degeneracies. The proofs are simple and constructive. This work excludes the important class of truly translationally invariant Hamiltonians where the local terms are all equal.

Localized orbitals vs. pseudopotential-plane waves basis sets: performances and accuracy for molecular magnetic systems

CERN Document Server

Massobrio, C

2003-01-01

Density functional theory, in combination with a) a careful choice of the exchange-correlation part of the total energy and b) localized basis sets for the electronic orbital, has become the method of choice for calculating the exchange-couplings in magnetic molecular complexes. Orbital expansion on plane waves can be seen as an alternative basis set especially suited to allow optimization of newly synthesized materials of unknown geometries. However, little is known on the predictive power of this scheme to yield quantitative values for exchange coupling constants J as small as a few hundredths of eV (50-300 cm sup - sup 1). We have used density functional theory and a plane waves basis set to calculate the exchange couplings J of three homodinuclear Cu-based molecular complexes with experimental values ranging from +40 cm sup - sup 1 to -300 cm sup - sup 1. The plane waves basis set proves as accurate as the localized basis set, thereby suggesting that this approach can be reliably employed to predict and r...

Validations of CNDOL approximate Hamiltonian as a fast and reliable method to obtain vertical excitation energies in polyatomic systems

International Nuclear Information System (INIS)

Montero-Alejo, Ana L.; Gonzalez-Santana, Susana; Montero-Cabrera, Luis A.; Hernandez-Rodriguez, Erix Wiliam; Fuentes-Montero, Maria Elena; Bunge-Molina, Carlos F.; Gonzalez, Augusto

2008-01-01

Theoretical prediction of vertical excitation energies and an estimation of charge distributions of polyatomic systems can be calculated, through the configuration interaction of single (CIS) excited determinants procedure, with the CNDOL (Complete Neglect of Differential Overlap considering the l azimuthal quantum number) Hamiltonians. This method does not use adjusted parameters to fit experimental data and only employ a priori data on atomic orbitals and simple formulas to substitute large computations of electronic integrals. In this sense, different functions for bi-electron integrals have been evaluated in order to improve the approximate Hamiltonian. The reliability of predictions and theoretical consistence has been tested with a benchmark set of organic molecules that covers important classes of chromophores including polyenes and other unsaturated aliphatic compounds, aromatic, hydrocarbons, heterocycles, carbonyl compounds, and nucleobases. The calculations are done at identical geometries (MP2) with the same basis set (6-31G) for these medium-sized molecules and the obtained results were statistically compared with other analogous methods and experimental data. The accuracy of prediction of each CNDOL vertical transitions energy increases while the active space is more complete allowing the best variational optimization of CIS matrices i.e. molecular excited states. Moreover and due to the feasible computation procedure for large polyatomic systems, the studies have been extended, as a preliminary work, in the field of optoelectronic materials for photovoltaic applications. Hence, the excitation energies of different conjugated Phenyl-cored Thiophene Dendrimers optimized by DFT (Density Functional Theory) were calculated and show good agreement with the experiment data. The predicted charge distribution during the excitation contributes to understand the photophysics process on these kind materials. (Full text)

Hamiltonian formulation for the Martin-Taylor model

International Nuclear Information System (INIS)

Vasconcelos, D.B.; Viana, R.L.

1993-01-01

Locally stochastic layer and its optimization are studied. In order to accomplish this task, it is employed a Hamiltonian formulation of magnetic field line flow with a subsequent application of Escande-Doveil renormalization method which have been extensively used to obtain accurate estimates of stochasticity thresholds in systems exhibiting Hamiltonian chaos. (author)

Hamiltonian structure of linearly extended Virasoro algebra

International Nuclear Information System (INIS)

Arakelyan, T.A.; Savvidi, G.K.

1991-01-01

The Hamiltonian structure of linearly extended Virasoro algebra which admits free bosonic field representation is described. An example of a non-trivial extension is found. The hierarchy of integrable non-linear equations corresponding to this Hamiltonian structure is constructed. This hierarchy admits the Lax representation by matrix Lax operator of second order

Valence band structures of InAs/GaAs quantum rings using the Fourier transform method

International Nuclear Information System (INIS)

Jia Boyong; Yu Zhongyuan; Liu Yumin

2009-01-01

The valence band structures of strained InAs/GaAs quantum rings are calculated, with the four-band k · p model, in the framework of effective-mass envelope function theory. When determining the Hamiltonian matrix elements, we develop the Fourier transform method instead of the widely used analytical integral method. Using Fourier transform, we have investigated the energy levels as functions of the geometrical parameters of the rings and compared our results with those obtained by the analytical integral method. The results show that the energy levels in the quantum rings change dramatically with the inner radius, outer radius, average radius, width, height of the ring and the distance between two adjacent rings. Our method can be adopted in low-dimensional structures with arbitrary shape. Our results are consistent with those in the literature and should be helpful for studying and fabricating optoelectronic devices

Relativistic Spin-Orbit Heavy Atom on the Light Atom NMR Chemical Shifts: General Trends Across the Periodic Table Explained.

Science.gov (United States)

Vícha, Jan; Komorovsky, Stanislav; Repisky, Michal; Marek, Radek; Straka, Michal

2018-05-10

The importance of relativistic effects on the NMR parameters in heavy-atom (HA) compounds, particularly the SO-HALA (Spin-Orbit Heavy Atom on the Light Atom) effect on NMR chemical shifts, has been known for about 40 years. Yet, a general correlation between the electronic structure and SO-HALA effect has been missing. By analyzing 1 H NMR chemical shifts of the sixth-period hydrides (Cs-At), we discovered general electronic-structure principles and mechanisms that dictate the size and sign of the SO-HALA NMR chemical shifts. In brief, partially occupied HA valence shells induce relativistic shielding at the light atom (LA) nuclei, while empty HA valence shells induce relativistic deshielding. In particular, the LA nucleus is relativistically shielded in 5d 2 -5d 8 and 6p 4 HA hydrides and deshielded in 4f 0 , 5d 0 , 6s 0 , and 6p 0 HA hydrides. This general and intuitive concept explains periodic trends in the 1 H NMR chemical shifts along the sixth-period hydrides (Cs-At) studied in this work. We present substantial evidence that the introduced principles have a general validity across the periodic table and can be extended to nonhydride LAs. The decades-old question of why compounds with occupied frontier π molecular orbitals (MOs) cause SO-HALA shielding at the LA nuclei, while the frontier σ MOs cause deshielding is answered. We further derive connection between the SO-HALA NMR chemical shifts and Spin-Orbit-induced Electron Deformation Density (SO-EDD), a property that can be obtained easily from differential electron densities and can be represented graphically. SO-EDD provides an intuitive understanding of the SO-HALA effect in terms of the depletion/concentration of the electron density at LA nuclei caused by spin-orbit coupling due to HA in the presence of a magnetic field. Using an analogy between the SO-EDD concept and arguments from classic NMR theory, the complex question of the SO-HALA NMR chemical shifts becomes easily understandable for a wide

Human Amygdala Represents the Complete Spectrum of Subjective Valence

Science.gov (United States)

Jin, Jingwen; Zelano, Christina; Gottfried, Jay A.

2015-01-01

Although the amygdala is a major locus for hedonic processing, how it encodes valence information is poorly understood. Given the hedonic potency of odor stimuli and the amygdala's anatomical proximity to the peripheral olfactory system, we combined high-resolution fMRI with pattern-based multivariate techniques to examine how valence information is encoded in the amygdala. Ten human subjects underwent fMRI scanning while smelling 9 odorants that systematically varied in perceived valence. Representational similarity analyses showed that amygdala codes the entire dimension of valence, ranging from pleasantness to unpleasantness. This unidimensional representation significantly correlated with self-reported valence ratings but not with intensity ratings. Furthermore, within-trial valence representations evolved over time, prioritizing earlier differentiation of unpleasant stimuli. Together, these findings underscore the idea that both spatial and temporal features uniquely encode pleasant and unpleasant odor valence in the amygdala. The availability of a unidimensional valence code in the amygdala, distributed in both space and time, would create greater flexibility in determining the pleasantness or unpleasantness of stimuli, providing a mechanism by which expectation, context, attention, and learning could influence affective boundaries for guiding behavior. SIGNIFICANCE STATEMENT Our findings elucidate the mechanisms of affective processing in the amygdala by demonstrating that this brain region represents the entire valence dimension from pleasant to unpleasant. An important implication of this unidimensional valence code is that pleasant and unpleasant valence cannot coexist in the amygdale because overlap of fMRI ensemble patterns for these two valence extremes obscures their unique content. This functional architecture, whereby subjective valence maps onto a pattern continuum between pleasant and unpleasant poles, offers a robust mechanism by which context

Remarks on Hamiltonian structures in G2-geometry

International Nuclear Information System (INIS)

Cho, Hyunjoo; Salur, Sema; Todd, A. J.

2013-01-01

In this article, we treat G 2 -geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G 2 -structure; in particular, we discuss existence and make a number of identifications of the spaces of Hamiltonian structures associated to the two multisymplectic structures associated to an integrable G 2 -structure. Along the way, we prove some results in multisymplectic geometry that are generalizations of results from symplectic geometry

QCD string with quarks. 2. Light cone Hamiltonian

International Nuclear Information System (INIS)

Dubin, A.Yu.; Kaidalov, A.B.; Simonov, Yu.A.

1994-01-01

The light-cone Hamiltonian is derived from the general gauge - and Lorentz - invariant expression for the qq-bar Green function. The resulting Hamiltonian contains in a non-additive way contributions from quark and string degrees of freedom

Plasticity of 150-loop in influenza neuraminidase explored by Hamiltonian replica exchange molecular dynamics simulations.

Directory of Open Access Journals (Sweden)

Nanyu Han

Full Text Available Neuraminidase (NA of influenza is a key target for antiviral inhibitors, and the 150-cavity in group-1 NA provides new insight in treating this disease. However, NA of 2009 pandemic influenza (09N1 was found lacking this cavity in a crystal structure. To address the issue of flexibility of the 150-loop, Hamiltonian replica exchange molecular dynamics simulations were performed on different groups of NAs. Free energy landscape calculated based on the volume of 150-cavity indicates that 09N1 prefers open forms of 150-loop. The turn A (residues 147-150 of the 150-loop is discovered as the most dynamical motif which induces the inter-conversion of this loop among different conformations. In the turn A, the backbone dynamic of residue 149 is highly related with the shape of 150-loop, thus can function as a marker for the conformation of 150-loop. As a contrast, the closed conformation of 150-loop is more energetically favorable in N2, one of group-2 NAs. The D147-H150 salt bridge is found having no correlation with the conformation of 150-loop. Instead the intimate salt bridge interaction between the 150 and 430 loops in N2 variant contributes the stabilizing factor for the closed form of 150-loop. The clustering analysis elaborates the structural plasticity of the loop. This enhanced sampling simulation provides more information in further structural-based drug discovery on influenza virus.

Restricted Hartree Fock using complex-valued orbitals: A long-known but neglected tool in electronic structure theory

Energy Technology Data Exchange (ETDEWEB)

Small, David W.; Sundstrom, Eric J.; Head-Gordon, Martin [Department of Chemistry, University of California, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)

2015-01-14

Restricted Hartree Fock using complex-valued orbitals (cRHF) is studied. We introduce an orbital pairing theorem, with which we obtain a concise connection between cRHF and real-valued RHF, and use it to uncover the close relationship between cRHF, unrestricted Hartree Fock, and generalized valence bond perfect pairing. This enables an intuition for cRHF, contrasting with the generally unintuitive nature of complex orbitals. We also describe an efficient computer implementation of cRHF and its corresponding stability analysis. By applying cRHF to the Be + H{sub 2} insertion reaction, a Woodward-Hoffmann violating reaction, and a symmetry-driven conical intersection, we demonstrate in genuine molecular systems that cRHF is capable of removing certain potential energy surface singularities that plague real-valued RHF and related methods. This complements earlier work that showed this capability in a model system. We also describe how cRHF is the preferred RHF method for certain radicaloid systems like singlet oxygen and antiaromatic molecules. For singlet O{sub 2}, we show that standard methods fail even at the equilibrium geometry. An implication of this work is that, regardless of their individual efficacies, cRHF solutions to the HF equations are fairly commonplace.

Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces

CERN Document Server

Jacob, Birgit

2012-01-01

This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the fir

Global Melnikov Theory in Hamiltonian Systems with General Time-Dependent Perturbations

Science.gov (United States)

Gidea, Marian; de la Llave, Rafael

2018-04-01

We consider a mechanical system consisting of n-penduli and a d-degree-of-freedom rotator. The phase space of the rotator defines a normally hyperbolic invariant manifold Λ _0 . We apply a time-dependent perturbation, which is not assumed to be either Hamiltonian, or periodic, or quasi-periodic, as we allow for rather general time dependence. The strength of the perturbation is given by a parameter ɛ \\in R . For all |ɛ | sufficiently small, the augmented flow—obtained by making the time into a new variable—has a normally hyperbolic locally invariant manifold \\tilde{Λ }_ɛ . For ɛ =0 , \\tilde{Λ }_0=Λ _0× R . We define a Melnikov-type vector, which gives the first-order expansion of the displacement of the stable and unstable manifolds of \\tilde{Λ }_0 under the perturbation. We provide an explicit formula for the Melnikov vector in terms of convergent improper integrals of the perturbation along homoclinic orbits of the unperturbed system. We show that if the perturbation satisfies some explicit non-degeneracy conditions, then the stable and unstable manifolds of \\tilde{Λ }_ɛ , W^s(\\tilde{Λ }_ɛ ) and W^u(\\tilde{Λ }_ɛ ) , respectively, intersect along a transverse homoclinic manifold, and, moreover, the splitting of W^s(\\tilde{Λ }_ɛ ) and W^u(\\tilde{Λ }_ɛ ) can be explicitly computed, up to the first order, in terms of the Melnikov-type vector. This implies that the excursions along some homoclinic trajectories yield a non-trivial increase of order O(ɛ ) in the action variables of the rotator, for all sufficiently small perturbations. The formulas that we obtain are independent of the unperturbed motions in Λ _0 , and give, at the same time, the effects on periodic, quasi-periodic, or general-type orbits. When the perturbation is Hamiltonian, we express the effects of the perturbation, up to the first order, in terms of a Melnikov potential. In addition, if the perturbation is periodic, we obtain that the non-degeneracy conditions on

Molecular Electronic Terms and Molecular Orbital Configurations.

Science.gov (United States)

Mazo, R. M.

1990-01-01

Discussed are the molecular electronic terms which can arise from a given electronic configuration. Considered are simple cases, molecular states, direct products, closed shells, and open shells. Two examples are provided. (CW)

Finite-dimensional Liouville integrable Hamiltonian systems generated from Lax pairs of a bi-Hamiltonian soliton hierarchy by symmetry constraints

Science.gov (United States)

Manukure, Solomon

2018-04-01

We construct finite-dimensional Hamiltonian systems by means of symmetry constraints from the Lax pairs and adjoint Lax pairs of a bi-Hamiltonian hierarchy of soliton equations associated with the 3-dimensional special linear Lie algebra, and discuss the Liouville integrability of these systems based on the existence of sufficiently many integrals of motion.

Local modular Hamiltonians from the quantum null energy condition

Science.gov (United States)

Koeller, Jason; Leichenauer, Stefan; Levine, Adam; Shahbazi-Moghaddam, Arvin

2018-03-01

The vacuum modular Hamiltonian K of the Rindler wedge in any relativistic quantum field theory is given by the boost generator. Here we investigate the modular Hamiltonian for more general half-spaces which are bounded by an arbitrary smooth cut of a null plane. We derive a formula for the second derivative of the modular Hamiltonian with respect to the coordinates of the cut which schematically reads K''=Tv v . This formula can be integrated twice to obtain a simple expression for the modular Hamiltonian. The result naturally generalizes the standard expression for the Rindler modular Hamiltonian to this larger class of regions. Our primary assumptions are the quantum null energy condition—an inequality between the second derivative of the von Neumann entropy of a region and the stress tensor—and its saturation in the vacuum for these regions. We discuss the validity of these assumptions in free theories and holographic theories to all orders in 1 /N .

Periodic solutions of asymptotically linear Hamiltonian systems without twist conditions

Energy Technology Data Exchange (ETDEWEB)

Cheng Rong [Coll. of Mathematics and Physics, Nanjing Univ. of Information Science and Tech., Nanjing (China); Dept. of Mathematics, Southeast Univ., Nanjing (China); Zhang Dongfeng [Dept. of Mathematics, Southeast Univ., Nanjing (China)

2010-05-15

In dynamical system theory, especially in many fields of applications from mechanics, Hamiltonian systems play an important role, since many related equations in mechanics can be written in an Hamiltonian form. In this paper, we study the existence of periodic solutions for a class of Hamiltonian systems. By applying the Galerkin approximation method together with a result of critical point theory, we establish the existence of periodic solutions of asymptotically linear Hamiltonian systems without twist conditions. Twist conditions play crucial roles in the study of periodic solutions for asymptotically linear Hamiltonian systems. The lack of twist conditions brings some difficulty to the study. To the authors' knowledge, very little is known about the case, where twist conditions do not hold. (orig.)

On local Hamiltonians and dissipative systems

Energy Technology Data Exchange (ETDEWEB)

Castagnino, M. [CONICET-Institutos de Fisica Rosario y de Astronomia y Fisica del Espacio Casilla de Correos 67, Sucursal 28, 1428, Buenos Aires (Argentina); Gadella, M. [Facultad de Ciencias Exactas, Ingenieria y Agrimensura UNR, Rosario (Argentina) and Departamento de Fisica Teorica, Facultad de Ciencias c. Real de Burgos, s.n., 47011 Valladolid (Spain)]. E-mail: manuelgadella@yahoo.com.ar; Lara, L.P. [Facultad de Ciencias Exactas, Ingenieria y Agrimensura UNR, Rosario (Argentina)

2006-11-15

We study a type of one-dimensional dynamical systems on the corresponding two-dimensional phase space. By using arguments related to the existence of integrating factors for Pfaff equations, we show that some one-dimensional non-Hamiltonian systems like dissipative systems, admit a Hamiltonian description by sectors on the phase plane. This picture is not uniquely defined and is coordinate dependent. A simple example is exhaustively discussed. The method, is not always applicable to systems with higher dimensions.

Statistical properties of spectra in harmonically trapped spin-orbit coupled systems

DEFF Research Database (Denmark)

V. Marchukov, O.; G. Volosniev, A.; V. Fedorov, D.

2014-01-01

We compute single-particle energy spectra for a one-body Hamiltonian consisting of a two-dimensional deformed harmonic oscillator potential, the Rashba spin-orbit coupling and the Zeeman term. To investigate the statistical properties of the obtained spectra as functions of deformation, spin......-orbit and Zeeman strengths we examine the distributions of the nearest neighbor spacings. We find that the shapes of these distributions depend strongly on the three potential parameters. We show that the obtained shapes in some cases can be well approximated with the standard Poisson, Brody and Wigner...... distributions. The Brody and Wigner distributions characterize irregular motion and help identify quantum chaotic systems. We present a special choices of deformation and spin-orbit strengths without the Zeeman term which provide a fair reproduction of the fourth-power repelling Wigner distribution. By adding...

The Closed-Orbit Theory for General Rydberg Atoms in External Fields

International Nuclear Information System (INIS)

Carboni, R.

1997-01-01

The photoabsorption spectra of hydrogen Rydberg atoms, as well of model Rydberg atoms in pure magnetic or electric fields have been successfully calculated using the semiclassical closed-orbit theory. The theory relates the resonances of the spectra to closed classical orbits of the excited electron. The dynamics of multielectron atoms is more complicated than the hydrogenic one; additionally, when the atoms are in the presence of perpendicular magnetic and electric fields becomes more complex than when they are in pure fields, due to the fact that the Hamiltonian is non-separable in three degrees of freedom, instead of two non-separable degrees of freedom. In this work, I present an extension of the closed-orbit theory to three degrees of freedom, considering arbitrary quantum defects, i.e., general atoms. (Author) [es

Effective stability around the Cassini state in the spin-orbit problem