Lie-series for orbital elements -- II. The spatial case
Pál, András
2016-01-01
If one has to attain high accuracy over long timescales during the numerical computation of the N-body problem, the method called Lie-integration is one of the most effective algorithms. In this paper we present a set of recurrence relations with which the coefficients needed by the Lie-integration of the orbital elements related to the spatial N-body problem can be derived up to arbitrary order. Similarly to the planar case, these formulae yields identically zero series in the case of no perturbations. In addition, the derivation of the formulae has two stages, analogously to the planar problem. Namely, the formulae are obtained to the first order, and then, higher order relations are expanded by involving directly the multilinear and fractional properties of the Lie-operator.
Xiao, Shengqiang; Stuart, Andrew C; Liu, Shubin; You, Wei
2009-07-01
Fusing bithiophene units with a benzo moiety, benzo[2,1-b:3,4-b']dithiophene (BDT), was projected by theoretical calculations to lower the highest occupied molecular orbital (HOMO) energy level of the resulting polymers compared with that of the bithiophene unit, which would enhance the open circuit voltage of bulk heterojunction photovoltaic cells fabricated from BDT-based polymers blended with PCBM. The homopolymer of BDT (HMPBDT) and alternating copolymer of BDT with 2,1,3-benzothiadiazole (PBDT-BT) were therefore synthesized and fully characterized. Both the homopolymer (HMPBDT) and the copolymer (PBDT-BT) were experimentally confirmed to have low HOMO energy levels (-5.70 eV for HMPBDT and -5.34 eV for PBDT-BT). Introducing the acceptor moiety (2,1,3-benzothiadiazole) successfully lowered the optical band gap of the copolymer from 2.31 eV (HMPBDT) to 1.78 eV (PBDT-BT). Bulk heterojunction photovoltaic devices were fabricated from blends of these structurally related polymers with PBCM to investigate the photovoltaic performances. The optimized device of HMPBDT:PCBM (1:3, 180 nm) exhibited an improved open circuit voltage (V(oc)) of 0.76 V, a short circuit current (J(sc)) of 0.34 mA/cm(2), and a fill factor (FF) of 0.40, offering an overall efficiency of 0.10%. The observed large phase separation of the thin film by AFM and the large band gap were accountable for the small current. The optimized device of PBDT-BT:PCBM (1:3, 55 nm) demonstrated a better efficiency of 0.6%, with V(oc) = 0.72 V, J(sc) = 2.06 mA/cm(2), and FF = 0.42. The much improved current was attributed to the lower bandgap and better film morphology. However, the low hole mobility limited the thickness of the PBDT-BT:PCBM film, making inaccessible the thicker film which would utilize more light and enhance the current. Further improvements are expected if the mobility and film morphology can be improved by the new materials design, together with low band gap and low HOMO energy level.
Coadjoint orbits of reductive type of seaweed Lie algebras
Moreau, Anne
2011-01-01
A connected algebraic group Q defined over a field of characteristic zero is quasi-reductive if there is an element of its dual of reductive type, that is such that the quotient of its stabiliser by the centre of Q is a reductive subgroup of GL(q), where q=Lie(Q). Due to results of M. Duflo, coadjoint representation of a quasi-reductive Q possesses a so called maximal reductive stabiliser and knowing this subgroup, defined up to a conjugation in Q, one can describe all coadjoint orbits of reductive type. In this paper, we consider quasi-reductive parabolic subalgebras of simple complex Lie algebras as well as all seaweed subalgebras of gl(n) and describe the classes of their maximal reductive stabilisers.
Chaos Behaviour of Molecular Orbit
Institute of Scientific and Technical Information of China (English)
LIU Shu-Tang; SUN Fu-Yan; SHEN Shu-Lan
2007-01-01
Based on H(u)ckel's molecular orbit theory,the chaos and;bifurcation behaviour of a molecular orbit modelled by a nonlinear dynamic system is studied.The relationship between molecular orbit and its energy level in the nonlinear dynamic system is obtained.
Diffractive molecular-orbital tomography
Zhai, Chunyang; Zhu, Xiaosong; Lan, Pengfei; Wang, Feng; He, Lixin; Shi, Wenjing; Li, Yang; Li, Min; Zhang, Qingbin; Lu, Peixiang
2017-03-01
High-order-harmonic generation in the interaction of femtosecond lasers with atoms and molecules opens the path to molecular-orbital tomography and to probe the electronic dynamics with attosecond-Ångström resolutions. Molecular-orbital tomography requires both the amplitude and phase of the high-order harmonics. Yet the measurement of phases requires sophisticated techniques and represents formidable challenges at present. Here we report a scheme, called diffractive molecular-orbital tomography, to retrieve the molecular orbital solely from the amplitude of high-order harmonics without measuring any phase information. We have applied this method to image the molecular orbitals of N2, CO2, and C2H2 . The retrieved orbital is further improved by taking account the correction of Coulomb potential. The diffractive molecular-orbital tomography scheme, removing the roadblock of phase measurement, significantly simplifies the molecular-orbital tomography procedure and paves an efficient and robust way to the imaging of more complex molecules.
Yao, Jinping; Jia, Xinyan; Hao, Xiaolei; Zeng, Bin; Jing, Chenrui; Chu, Wei; Ni, Jielei; Zhang, Haisu; Xie, Hongqiang; Zhang, Chaojin; Zhao, Zengxiu; Chen, Jing; Liu, Xiaojun; Cheng, Ya; Xu, Zhizhan
2013-01-01
We show that fluorescence emission induced by strong field tunnel ionization of carbon dioxide from its lower-lying orbitals exhibits a peculiar molecular alignment dependence. The experimentally measured alignment-dependence of the fluorescence agrees with the alignment-dependence of the ionization probability calculated in the framework of the strong field approximation. Our results demonstrate the feasibility of an all-optical approach for shedding more light on the ionization mechanisms of molecules from their lower-lying orbitals in tunnel ionization regime.
On sheets of orbit covers for classical semisimple Lie groups
Institute of Scientific and Technical Information of China (English)
LIANG; Ke梁科; Hou; zixin侯自新; Lu; Linyuan岳临渊
2002-01-01
David Vogan gave programmatic conjectures about the Dixmier's map and he made two conjectures that induction may be independent of the choice of parabolic group used and the sheets of orbit data are conjugated or disjointed[1]. In our previous paper, we gave a geometric version of the parabolic induction of the geometric orbit datum (i.e. orbit covers), and proved Vogan's first conjecture for geometric orbit datum:the parabolic induction of the geometric orbit datum is independent of the choice of parabolic group. In this paper, we will prove the other Vogan's conjecture, that is, the sheets are conjugated or disjointed for classical semisimple complex groups.``
Orbit structure of Hamiltonian systems arising from Lie transformation group actions
Garzia, M. R.; Loparo, K. A.; Martin, C. F.
1983-01-01
This paper associates the Riccati group and its group action on linear-quadratic optimal control problems to the action of a Lie transformation group on a set of Hamiltonian matrices. In this Lie theoretic setting results are presented concerning the associated orbit structure and the structure of the group itself. These results are of importance in understanding the solution structure of matrix Riccati differential equations, and thus also of importance in linear-quadratic optimal control.
Orbit structure of Hamiltonian systems arising from Lie transformation group actions
Garzia, M. R.; Loparo, K. A.; Martin, C. F.
This paper associates the Riccati group and its group action on linear-quadratic optimal control problems to the action of a Lie transformation group on a set of Hamiltonian matrices. In this Lie theoretic setting results are presented concerning the associated orbit structure and the structure of the group itself. These results are of importance in understanding the solution structure of matrix Riccati differential equations, and thus also of importance in linear-quadratic optimal control.
Super-atom molecular orbital excited states of fullerenes.
Johansson, J Olof; Bohl, Elvira; Campbell, Eleanor E B
2016-09-13
Super-atom molecular orbitals are orbitals that form diffuse hydrogenic excited electronic states of fullerenes with their electron density centred at the centre of the hollow carbon cage and a significant electron density inside the cage. This is a consequence of the high symmetry and hollow structure of the molecules and distinguishes them from typical low-lying molecular Rydberg states. This review summarizes the current experimental and theoretical studies related to these exotic excited electronic states with emphasis on femtosecond photoelectron spectroscopy experiments on gas-phase fullerenes.This article is part of the themed issue 'Fullerenes: past, present and future, celebrating the 30th anniversary of Buckminster Fullerene'.
Molecular orbital imaging for partially aligned molecules
Qin, Meiyan; Zhu, Xiaosong
2017-01-01
We investigate molecular orbital reconstruction using high-order harmonic emissions from partially aligned molecular ensembles. By carrying out the reconstruction procedure using the harmonic sampling with or without the spectral minimum, the roles of the harmonic phase and amplitude modulation due to the partial alignment can be separately studied. It is found that with the prior knowledge of the orbital symmetry, the reconstructed result is very sensitive to the modulation of the harmonic phase for the πg orbital, while in the case of σg orbital, the reconstructed result is mainly determined by the harmonic amplitude. These results can provide an important reference for the future experiment of molecular orbital imaging.
A Simple Huckel Molecular Orbital Plotter
Ramakrishnan, Raghunathan
2013-01-01
A program is described and presented to readily plot the molecular orbitals from a Huckel calculation. The main features of the program and the scope of its applicability are discussed through some example organic molecules. (Contains 2 figures.)
Apparent Reversal of Molecular Orbitals Reveals Entanglement
Yu, Ping; Kocić, Nemanja; Repp, Jascha; Siegert, Benjamin; Donarini, Andrea
2017-08-01
The frontier orbital sequence of individual dicyanovinyl-substituted oligothiophene molecules is studied by means of scanning tunneling microscopy. On NaCl /Cu (111 ) , the molecules are neutral, and the two lowest unoccupied molecular states are observed in the expected order of increasing energy. On NaCl /Cu (311 ) , where the molecules are negatively charged, the sequence of two observed molecular orbitals is reversed, such that the one with one more nodal plane appears lower in energy. These experimental results, in open contradiction with a single-particle interpretation, are explained by a many-body theory predicting a strongly entangled doubly charged ground state.
Molecular orbital calculations using chemical graph theory
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...
Laser-Induced Electron Diffraction: Inversion of Photoelectron Spectra for Molecular Orbital Imaging
Puthumpally-Joseph, R; Peters, M; Nguyen-Dang, T T; Atabek, O; Charron, E
2016-01-01
In this paper, we discuss the possibility of imaging molecular orbitals from photoelectron spectra obtained via Laser Induced Electron Diffraction (LIED) in linear molecules. This is an extension of our work published recently in Physical Review A \\textbf{94}, 023421 (2016) to the case of the HOMO-1 orbital of the carbon dioxide molecule. We show that such an imaging technique has the potential to image molecular orbitals at different internuclear distances in a sub-femtosecond time scale and with a resolution of a fraction of an Angstr\\"om.
The H2+ molecular ion: Low-lying states
Olivares-Pilón, Horacio; Turbiner, Alexander V.
2016-10-01
Matching for a wavefunction the WKB expansion at large distances and Taylor expansion at small distances leads to a compact, few-parametric uniform approximation found in Turbiner and Olivares-Pilon (2011). The ten low-lying eigenstates of H2+ of the quantum numbers (n , m , Λ , ±) with n = m = 0 at Λ = 0 , 1 , 2, with n = 1, m = 0 and n = 0, m = 1 at Λ = 0 of both parities are explored for all interproton distances R. For all these states this approximation provides the relative accuracy ≲ 10-5 (not less than 5 s.d.) locally, for any real coordinate x in eigenfunctions, when for total energy E(R) it gives 10-11 s.d. for R ∈ [ 0 , 50 ] a.u. Corrections to the approximation are evaluated in the specially-designed, convergent perturbation theory. Separation constants are found with not less than 8 s.d. The oscillator strength for the electric dipole transitions E 1 is calculated with not less than 6 s.d. A dramatic dip in the E 1 oscillator strength f 1 sσg - 3 pσu at R ∼Req is observed. The magnetic dipole and electric quadrupole transitions are calculated for the first time with not less than 6 s.d. in oscillator strength. For two lowest states (0 , 0 , 0 , ±) (or, equivalently, 1 sσg and 2 pσu states) the potential curves are checked and confirmed in the Lagrange mesh method within 12 s.d. Based on them the Energy Gap between 1 sσg and 2 pσu potential curves is approximated with modified Pade Re-R [ Pade(8 / 7) ] (R) with not less than 4-5 figures at R ∈ [ 0 , 40 ] a.u. Sum of potential curves E1sσg +E2pσu is approximated by Pade 1 / R [ Pade(5 / 8) ] (R) in R ∈ [ 0 , 40 ] a.u. with not less than 3-4 figures.
Molecular diagnosis of orbital inflammatory disease.
Rosenbaum, James T; Choi, Dongseok; Wilson, David J; Grossniklaus, Hans E; Sibley, Cailin H; Harrington, Christina A; Planck, Stephen R
2015-04-01
Orbital inflammatory diseases include thyroid eye disease (TED), granulomatosis with polyangiitis (GPA), sarcoidosis, and nonspecific orbital inflammation (NSOI). Histopathological diagnosis usually relies on the clinical context and is not always definitive. Gene expression profiling provides diagnostic and therapeutic information in several malignancies, but its role in evaluating nonmalignant disease is relatively untested. We hypothesized that gene expression profiling could provide diagnostic information for NSOI. We collected formalin-fixed, paraffin-embedded orbital biopsies from 10 institutions and 83 subjects including 25 with thyroid eye disease, 25 nonspecific orbital inflammation, 20 healthy controls, 6 with granulomatosis with polyangiitis, and 7 with sarcoidosis. Tissues were divided into discovery and validation sets. Gene expression was quantified using Affymetrix U133 Plus 2.0 microarrays. A random forest statistical algorithm based on data from 39 probe sets identified controls, GPA, or TED with an average accuracy of 76% (p=0.02). Random forest analysis indicated that 52% of tissues from patients with nonspecific inflammation were consistent with a diagnosis of GPA. Molecular diagnosis by gene expression profiling will augment clinical data and histopathology in differentiating forms of orbital inflammatory disease.
Kobori, Tomoki; Sodeyama, Keitaro; Otsuka, Takao; Tateyama, Yoshitaka; Tsuneyuki, Shinji
2013-09-07
The fragment molecular orbital (FMO)-linear combination of molecular orbitals (LCMO) method incorporates as an efficient post-process calculation of one-electron orbitals of the whole system after the FMO total energy calculation. A straightforward way to increase the accuracy is inclusion of the trimer effect. Here, we derive a comprehensive formulation called the FMO3-LCMO method. To keep the computational costs of the trimer term low enough, we use a matrix-size reduction technique. We evaluated the accuracy and efficiency of the FMO3-LCMO scheme in model biological systems (alanine oligomer and chignolin). The results show that delocalized electronic orbitals with covalent and hydrogen bonds are better described at the trimer level, and the FMO3-LCMO method is applicable to quantitative evaluations of a wide range of frontier orbitals in large biosystems.
Molecular integrals for exponential-type orbitals using hyperspherical harmonics
DEFF Research Database (Denmark)
Avery, James Emil; Avery, John Scales
2015-01-01
Exponential-type orbitals are better suited to calculations of molecular electronic structure than are Gaussians, since ETO's can accurately represent the behavior of molecular orbitals near to atomic nuclei, as well as their long-distance exponential decay. Orbitals based on Gaussians fail in bo...
Theoretical study of nonlinear triatomic molecular potential energy surfaces:Lie algebraic method
Institute of Scientific and Technical Information of China (English)
郑雨军; 丁世良
2000-01-01
Triatomic molecular potential energy surfaces (PES) are obtained by using coherent state to take the classical limits of algebraic Hamiltonian. The algebraic Hamiltonian for bent tria-tomic molecules can be obtained using Lie algebraic method (the expansion coefficients are obtained by fitting spectroscopic data). This PES is applied to H2O molecule, and good results are obtained.
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.
Local Molecular Orbitals from a Projection onto Localized Centers.
Heßelmann, Andreas
2016-06-14
A localization method for molecular orbitals is presented which exploits the locality of the eigenfunctions associated with the largest eigenvalues of the matrix representation of spatially localized functions. Local molecular orbitals are obtained by a projection of the canonical orbitals onto the set of the eigenvectors which correspond to the largest eigenvalues of these matrices. Two different types of spatially localized functions were chosen in this work, a two-parameter smooth-step-type function and the weight functions determined by a Hirshfeld partitioning of the molecular volume. It is shown that the method can provide fairly local occupied molecular orbitals if the positions of the set of local functions are set to the molecular bond centers. The method can also yield reasonably well-localized virtual molecular orbitals, but here, a sensible choice of the positions of the functions are the atomic sites and the locality then depends more strongly on the shape of the set of local functions. The method is tested for a range of polypeptide molecules in two different conformations, namely, a helical and a β-sheet conformation. Futhermore, it is shown that an adequate locality of the occupied and virtual orbitals can also be obtained for highly delocalized systems.
Conformation effects on the molecular orbitals of serine
Institute of Scientific and Technical Information of China (English)
Wang Ke-Dong; Ma Peng-Fei; Shan Xu
2011-01-01
This paper calculates the five most stable conformers of serine with Hartree-Fock theory, density functional theory (B3LYP), M0ller-Plesset perturbation theory (MP4(SDQ)) and electron propagation theory with the 6-311++G(2d,2p) basis set. The calculated vertical ionization energies for the valence molecular orbitals of each conformer are in agreement with the experimental data, indicating that a range of molecular conformations would coexist in an equilibrium sample. Information of the five outer valence molecular orbitals for each conformer is explored in coordinate and momentum spaces using dual space analysis to investigate the conformational processes, which are generated from the global minimum conformer Serl by rotation of C2-C3 (Ser4), C1-C2 (Ser5) and C1-O2 (Ser2 and Ser3). Orbitals 28a, 27a and 26a are identified as the fingerprint orbitals for all the conformational processes.
Tada, Tomofumi; Yoshizawa, Kazunari
2015-12-28
In this study, we report our viewpoint of single molecular conductance in terms of frontier orbitals. The orbital rule derived from orbital phase and amplitude is a powerful guideline for the qualitative understanding of molecular conductance in both theoretical and experimental studies. The essence of the orbital rule is the phase-related quantum interference, and on the basis of this rule a constructive or destructive pathway for electron transport is easily predicted. We have worked on the construction of the orbital rule for more than ten years and recently found from its application that π-stacked molecular junctions fabricated experimentally are in line with the concept for conductance-decay free junctions. We explain the orbital rule using benzene molecular junctions with the para-, meta- and ortho-connections and discuss linear π-conjugated chains and π-stacked molecular junctions with respect to their small decay factors in this manuscript.
Imaging the Temporal Evolution of Molecular Orbitals during Ultrafast Dissociation
Sann, H.; Havermeier, T.; Müller, C.; Kim, H.-K.; Trinter, F.; Waitz, M.; Voigtsberger, J.; Sturm, F.; Bauer, T.; Wallauer, R.; Schneider, D.; Weller, M.; Goihl, C.; Tross, J.; Cole, K.; Wu, J.; Schöffler, M. S.; Schmidt-Böcking, H.; Jahnke, T.; Simon, M.; Dörner, R.
2016-12-01
We investigate the temporal evolution of molecular frame angular distributions of Auger electrons emitted during ultrafast dissociation of HCl following a resonant single-photon excitation. The electron emission pattern changes its shape from that of a molecular σ orbital to that of an atomic p state as the system evolves from a molecule into two separated atoms.
Zhang, Xiaomei; Liu, Xiaoting; Liang, Guiying; Li, Rui; Xu, Haifeng; Yan, Bing
2016-01-01
The potential energy curves (PECs) of the 22 Λ-S states of the phosphorus monoiodide (PI) molecule have been calculated at the level of MRCI+Q method with correlation-consistent quadruple-ζ quality basis set. The spectroscopic constants of the bound states are determined, which well reproduce the available measurements. The metastable a1Δ state has been reported for the first time, which lies between the X3Σ- and b1Σ+ states and have much deeper well than the ground state. The R-dependent spin-orbit (SO) matrix elements are calculated with the full-electron Breit-Pauli operator. Based on the SO matrix elements, the perturbations that the 23Π state may suffer from are analyzed in detail. The SOC effect makes the original Λ-S states split into 51 Ω states. In the zero-field splitting of the ground state X3Σ-, the spin-spin coupling contribution (2.23 cm-1) is found to be much smaller compared to the spin-orbit coupling contribution (50 cm-1). The avoided crossings between the Ω states lead to much shallower potential wells and the change of dissociation relationships of the states. The Ω-state wavefunctions are analyzed depending on their Λ-S compositions, showing the strong interactions among several quasidegenerate Λ-S states of the same total SO symmetry. The transition properties including electric dipole (E1), magnetic dipole (M1), and electric quadrupole (E2) transition moments (TMs), the Franck-Condon factors, the transition probabilities and the radiative lifetimes are computed for the transitions between Ω components of a1Δ and b1Σ+ states and ground state. The transition probabilities induced by the E1, E2, and M1 transitions are evaluated. The E2 makes little effect on transition probabilities. In contrast, the E1 transition makes the main contribution to the transition probability and the M1 transition also brings the influence that cannot be neglected. Finally, the radiative lifetimes are determined with the transition moments including E
Molecular Orbital Based Design Guidelines for Hypergolic Energetic Ionic Liquids
2015-01-01
should be synthesized to further validate our probabilistic approach for identifying EIL hypergols. DMP is one anion that has a lower “energy gap”, but...orbitals (HOMO) of the anions for a series of ionic liquids and the lowest occupied molecular orbital (LUMO) of HNO3, and variation in the computed...relative heats of formation, DHf, of these anions to develop correlations to predict hypergol activity between an ionic liquid fuel and nitric acid as
Tailoring approach for obtaining molecular orbitals of large systems
Indian Academy of Sciences (India)
Anuja P Rahalkar; Shridhar R Gadre
2012-01-01
Molecular orbitals (MO’s) within Hartree-Fock (HF) theory are of vital importance as they provide preliminary information of bonding and features such as electron localization and chemical reactivity. The contemporary literature treats the Kohn-Sham orbitals within density functional theory (DFT) equivalently to the MO's obtained within HF framework. The high scaling order of ab initio methods is the main hurdle in obtaining the MO's for large molecular systems. With this view, an attempt is made in the present work to employ molecular tailoring approach (MTA) for obtaining the complete set of MO's including occupied and virtual orbitals, for large molecules at HF and B3LYP levels of theory. The energies of highest occupied and lowest unoccupied molecular orbitals, and hence the band gaps, are accurately estimated by MTA for most of the test cases benchmarked in this study, which include -conjugated molecules. Typically, the root mean square errors of valence MO's are in range of 0.001 to 0.010 a.u. for all the test cases examined. MTA shows a time advantage factor of 2 to 3 over the corresponding actual calculation, for many of the systems reported.
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 ...
Iuchi, Satoru; Koga, Nobuaki
2014-01-14
With the aim of exploring excited state dynamics, a model electronic Hamiltonian for several low-lying d-d states of [Fe(bpy)3](2+) complex [S. Iuchi, J. Chem. Phys. 136, 064519 (2012)] is refined using density-functional theory calculations of singlet, triplet, and quintet states as benchmarks. Spin-orbit coupling elements are also evaluated within the framework of the model Hamiltonian. The accuracy of the developed model Hamiltonian is determined by examining potential energies and spin-orbit couplings at surface crossing regions between different spin states. Insights into the potential energy surfaces around surface crossing regions are also provided through molecular dynamics simulations. The results demonstrate that the constructed model Hamiltonian can be used for studies on the d-d excited state dynamics of [Fe(bpy)3](2+).
Inversion of Strong Field Photoelectron Spectra for Molecular Orbital Imaging
Puthumpally-Joseph, R; Peters, M; Nguyen-Dang, T T; Atabek, O; Charron, E
2016-01-01
Imaging structures at the molecular level is a fast developing interdisciplinary research field that spans across the boundaries of physics and chemistry. High spatial resolution images of molecules can be obtained with photons or ultrafast electrons. In addition, images of valence molecular orbitals can be extracted via tomographic techniques based on the coherent XUV radiation emitted by a molecular gas exposed to an intense ultra-short infrared laser pulse. In this paper, we demonstrate that similar information can be obtained by inverting energy resolved photoelectron spectra using a simplified analytical model.
On the physical interpretation of the nuclear molecular orbital energy.
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.
Study on the construction of satisfactory nonorthogonal localized molecular orbitals
Institute of Scientific and Technical Information of China (English)
FENG; Huasheng; BIAN; Jiang; LI; Lemin
2004-01-01
Comparing to orthogonal localized molecular orbitals (OLMO), the nonorthogonal localized molecular orbitals (NOLMO) exhibit bonding pictures more accordant with those in the traditional chemistry. They are more contracted, so that they have a better transferability and better performances for the calculation of election correlation energies and for the linear scaling algorithms of large systems. The satisfactory NOLMOs should be as contracted as possible while their shapes and spatial distribution keep in accordance with the traditional chemical bonding picture. It is found that the spread of NOLMOs is a monotonic decreasing function of their orthogonality, and it may reduce to any extent as the orthogonality descends. However, when the orthogonality descends to some point, the shapes and spatial distribution of the NOLMOs deviate drastically from the traditional chemical bonding picture, and finally the NOLMOs tend to linear dependence. Without the requirement of orthogonalization, some other constraints have to be imposed for constructing satisfactory NOLMOs by minimizing their spread functional. It is shown that satisfactory results can be generated by coupling the minimization of orbital spread functionals with the maximization of the distances between orbital centroids.
Laser induced electron diffraction: a tool for molecular orbital imaging
Peters, Michel; Charron, Eric; Keller, Arne; Atabek, Osman
2012-01-01
We explore the laser-induced ionization dynamics of N2 and CO2 molecules subjected to a few-cycle, linearly polarized, 800\\,nm laser pulse using effective two-dimensional single active electron time-dependent quantum simulations. We show that the electron recollision process taking place after an initial tunnel ionization stage results in quantum interference patterns in the energy resolved photo-electron signals. If the molecule is initially aligned perpendicular to the field polarization, the position and relative heights of the associated fringes can be related to the molecular geometrical and orbital structure, using a simple inversion algorithm which takes into account the symmetry of the initial molecular orbital from which the ionized electron is produced. We show that it is possible to extract inter-atomic distances in the molecule from an averaged photon-electron signal with an accuracy of a few percents.
GAUSSIAN 76: An ab initio Molecular Orbital Program
Binkley, J. S.; Whiteside, R.; Hariharan, P. C.; Seeger, R.; Hehre, W. J.; Lathan, W. A.; Newton, M. D.; Ditchfield, R.; Pople, J. A.
1978-01-01
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.
Efficient construction of nonorthogonal localized molecular orbitals in large systems.
Cui, Ganglong; Fang, Weihai; Yang, Weitao
2010-08-26
Localized molecular orbitals (LMOs) are much more compact representations of electronic degrees of freedom than canonical molecular orbitals (CMOs). The most compact representation is provided by nonorthogonal localized molecular orbitals (NOLMOs), which are linearly independent but are not orthogonal. Both LMOs and NOLMOs are thus useful for linear-scaling calculations of electronic structures for large systems. Recently, NOLMOs have been successfully applied to linear-scaling calculations with density functional theory (DFT) and to reformulating time-dependent density functional theory (TDDFT) for calculations of excited states and spectroscopy. However, a challenge remains as NOLMO construction from CMOs is still inefficient for large systems. In this work, we develop an efficient method to accelerate the NOLMO construction by using predefined centroids of the NOLMO and thereby removing the nonlinear equality constraints in the original method ( J. Chem. Phys. 2004 , 120 , 9458 and J. Chem. Phys. 2000 , 112 , 4 ). Thus, NOLMO construction becomes an unconstrained optimization. Its efficiency is demonstrated for the selected saturated and conjugated molecules. Our method for fast NOLMO construction should lead to efficient DFT and NOLMO-TDDFT applications to large systems.
Molecular orbital theory of ballistic electron transport through molecules
Ernzerhof, Matthias; Rocheleau, Philippe; Goyer, Francois
2009-03-01
Electron transport through molecules occurs, for instance, in STM imaging and in conductance measurements on molecular electronic devices (MEDs). To model these phenomena, we use a non-Hermitian model Hamiltonian [1] for the description of open systems that exchange current density with their environment. We derive qualitative, molecular-orbital-based rules relating molecular structure and conductance. We show how side groups attached to molecular conductors [2] can completely suppress the conductance. We discuss interference effects in aromatic molecules [3] that can also inhibit electron transport. Rules are developed [1] for the prediction of Fano resonances. All these phenomena are explained with a molecular orbital theory [1,4] for molecules attached to macroscopic reservoirs. [1] F. Goyer, M. Ernzerhof, and M. Zhuang, JCP 126, 144104 (2007); M. Ernzerhof, JCP 127, 204709 (2007). [2] M. Ernzerhof, M. Zhuang, and P. Rocheleau, JCP 123, 134704 (2005); G. C. Solomon, D Q. Andrews, R P. Van Duyne, and M A. Ratner, JACS 130, 7788 (2008). [3] M. Ernzerhof, H. Bahmann, F. Goyer, M. Zhuang, and P. Rocheleau, JCTC 2, 1291 (2006); G. C. Solomon, D. Q. Andrews, R. P. Van Duyne, and M. A. Ratner, JCP 129, 054701 (2008). [4] B.T. Pickup, P.W. Fowler, CPL 459, 198 (2008); P. Rocheleau and M. Ernzerhof, JCP, submitted.
Polarized Molecular Orbital Model Chemistry. II. The PMO Method.
Zhang, Peng; Fiedler, Luke; Leverentz, Hannah R; Truhlar, Donald G; Gao, Jiali
2011-04-12
We present a new semiempirical molecular orbital method based on neglect of diatomic differential overlap. This method differs from previous NDDO-based methods in that we include p orbitals on hydrogen atoms to provide a more realistic modeling of polarizability. As in AM1-D and PM3-D, we also include damped dispersion. The formalism is based on the original MNDO one, but in the process of parameterization we make some specific changes to some of the functional forms. The present article is a demonstration of the capability of the new approach, and it presents a successful parametrization for compounds composed only of hydrogen and oxygen atoms, including the important case of water clusters.
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)
Localization of molecular orbitals: from fragments to molecule.
Li, Zhendong; Li, Hongyang; Suo, Bingbing; Liu, Wenjian
2014-09-16
Conspectus Localized molecular orbitals (LMO) not only serve as an important bridge between chemical intuition and molecular wave functions but also can be employed to reduce the computational cost of many-body methods for electron correlation and excitation. Therefore, how to localize the usually completely delocalized canonical molecular orbitals (CMO) into confined physical spaces has long been an important topic: It has a long history but still remains active to date. While the known LMOs can be classified into (exact) orthonormal and nonorthogonal, as well as (approximate) absolutely localized MOs, the ways for achieving these can be classified into two categories, a posteriori top-down and a priori bottom-up, depending on whether they invoke the global CMOs (or equivalently the molecular density matrix). While the top-down approaches have to face heavy tasks of minimizing or maximizing a given localization functional typically of many adjacent local extrema, the bottom-up ones have to invoke some tedious procedures for first generating a local basis composed of well-defined occupied and unoccupied subsets and then maintaining or resuming the locality when solving the Hartree-Fock/Kohn-Sham (HF/KS) optimization condition. It is shown here that the good of these kinds of approaches can be combined together to form a very efficient hybrid approach that can generate the desired LMOs for any kind of gapped molecules. Specifically, a top-down localization functional, applied to individual small subsystems only, is minimized to generate an orthonormal local basis composed of functions centered on the preset chemical fragments. The familiar notion for atomic cores, lone pairs, and chemical bonds emerges here automatically. Such a local basis is then employed in the global HF/KS calculation, after which a least action is taken toward the final orthonormal localized molecular orbitals (LMO), both occupied and virtual. This last step is very cheap, implying that, after
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...... determine the reaction barrier of chorismate mutase to be [Formula: see text] kcal mol(-1) for MP2/cc-pVDZ and [Formula: see text] for MP2/cc-pVTZ in an ONIOM approach using EFMO-RHF/6-31G(d) for the high and low layers, respectively....
Tuning the effective spin-orbit coupling in molecular semiconductors
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.
Alpha cluster states and molecular orbitals in sd-shell nuclei
Energy Technology Data Exchange (ETDEWEB)
Kimura, M. [Creative Research Institution Sousei Research Department, Hokkaido University, Sapporo 001-0021 (Japan); Furutachi, N. [Meme Media Laboratory, Hokkaido University, Sapporo 060-8628 (Japan); Kanada-En' yo, Y. [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)
2010-03-01
The alpha-clustering and molecular-orbitals of {sup 22}Ne and F isotopes are investigated based on antisymmetrized molecular dynamics (AMD). The observed candidates for the alpha cluster state of {sup 22}Ne are understood as the molecular-orbital states and alpha+{sup 18}O di-nuclei states. The presence of the molecular-orbital states in the O and F isotopes and the drastic reduction of their excitation energy near the neutron-drip line are predicted.
Directory of Open Access Journals (Sweden)
Sri Mursiti
2010-06-01
Full Text Available The research of Computer Asissted Instruction with animation and simulation was used to misconception remediation of atomic orbital, molecular orbital, and hibridiziation concepts. The applicated instruction model was focused on concept approach with macromedia flash player and power point programme. The subject of this research were the 2nd semestre students of Chemistry Department. The data were collected by using of true-false pre-test and post- test followed by the reason of its. The analysis reveals that the Computer Asissted Instruction with animation and simulation model increased the understanding of atomic orbital, molecular orbital, and hibridiziation concepts or remediation of concepts missconception, shown by the significant score gained between before and after the implementation of Computer Asissted Instruction with animation and simulation model. The instruction model developed the students's generic skills too. Keywords: animation simulation,misconception remediation, orbital, hibridization
Ab initio Path Integral Molecular Dynamics Based on Fragment Molecular Orbital Method
Fujita, Takatoshi; Watanabe, Hirofumi; Tanaka, Shigenori
2009-10-01
We have developed an ab initio path integral molecular dynamics method based on the fragment molecular orbital method. This “FMO-PIMD” method can treat both nuclei and electrons quantum mechanically, and is useful to simulate large hydrogen-bonded systems with high accuracy. After a benchmark calculation for water monomer, water trimer and glycine pentamer have been studied using the FMO-PIMD method to investigate nuclear quantum effects on structure and molecular interactions. The applicability of the present approach is demonstrated through a number of test calculations.
Molecular electric moments calculated by using natural orbital functional theory
Mitxelena, Ion
2016-01-01
The molecular electric dipole, quadrupole and octupole moments of a selected set of 21 spin-compensated molecules are determined employing the extended version of the Piris natural orbital functional 6 (PNOF6), using the triple-$\\zeta$ Gaussian basis set with polarization functions developed by Sadlej, at the experimental geometries. The performance of the PNOF6 is established by carrying out a statistical analysis of the mean absolute errors with respect to the experiment. The calculated PNOF6 electric moments agree satisfactorily with the corresponding experimental data, and are in good agreement with the values obtained by accurate ab initio methods, namely, the coupled-cluster single and doubles (CCSD) and multi-reference single and double excitation configuration interaction (MRSD-CI) methods.
Sulfur at nickel-alumina interfaces - Molecular orbital theory
Hong, S. Y.; Anderson, Alfred B.; Smialek, James L.
1990-01-01
Previous studies on Al-Ni alloys containing sulfur as an impurity suggest that, when S is in the interface between a metal and an oxide scale, it weakens the chemical bonding between them. This paper investigates factors responsible for this effect, using a molecular orbital theory to predict sulfur structures and electronic properties on the Ni-Al2O3 interface. It is shown that, in absence of S, the basal plane of Al2O3 will bind strongly through the Al(3+) cation surface to Ni (111). When segregated S impurity is present on the Ni surface, there are too few interfacial AlS bonds to effect good adhesion, leading to an inhibition of the oxide scale adhesion in NiCrAl alloys.
Energy Technology Data Exchange (ETDEWEB)
Zhou, Xin [Pennsylvania State Univ., University Park, PA (United States)
1998-11-30
Photoemission intensities from the molecular orbitals of c(2x2)CO/Pt(111) over a wide photon energy range were measured and analyzed by the same methods developed for structural studies using core levels. The 4{sigma} orbital center of gravity is found to be concentrated between the C and O atoms, while that of the 5{sigma} orbital lies between the C atom and the Pt surface. The C 1s photoelectron diffraction was used to determine the adsorption geometry. The earlier ambiguity that multiple scattering is needed to correctly model a {chi} curve while single scattering is sufficient for understanding major peaks in the ARPEFS-FTS is clarified by studying the clean Ni(111) surface. In the normal emission case, several different combinations of scattering events have similar path length differences (PLDs), and can either cancel each other or enhance the corresponding FT peak. In the off-normal case the degeneracy is greatly reduced due to the lower degree of symmetry. In normal emission AR PEFS, up to third order multiple scattering is needed to describe fully both the {chi} curve and its FT spectrum. To improve the spectral resolution in the ARPEFS-FT analysis, several new spectral analysis methods are introduced. With both autocorrelation autoregression (ACAR) and autocorrelation eigenvector (ACE), we can produce a reliable power spectrum by following the order-closing procedure. The best spectra are usually obtained when the autocorrelation sequence is computed with lags up to half the data range. A simple way of determining surface adsorption sites is proposed as follows: First use a single scattering cluster for possible adsorption sites to construct the geometrical PLDs from the strong backscattering events; then compare these PLDs with those obtained from the ARPEFS-FT analysis of the experimental data. After the preferred adsorption site is determined, fine tune the interlayer distances according to the positional R-factor.
Jacobson, Nathan
1979-01-01
Lie group theory, developed by M. Sophus Lie in the 19th century, ranks among the more important developments in modern mathematics. Lie algebras comprise a significant part of Lie group theory and are being actively studied today. This book, by Professor Nathan Jacobson of Yale, is the definitive treatment of the subject and can be used as a textbook for graduate courses.Chapter I introduces basic concepts that are necessary for an understanding of structure theory, while the following three chapters present the theory itself: solvable and nilpotent Lie algebras, Carlan's criterion and its
Suzuki, Hiroshi
1967-01-01
Electronic Absorption Spectra and Geometry of Organic Molecules: An Application of Molecular Orbital Theory focuses on electronic absorption spectra of organic compounds and molecules. The book begins with the discussions on molecular spectra, electronic absorption spectra of organic compounds, and practical measures of absorption intensity. The text also focuses on molecular orbital theory and group theory. Molecular state functions; fundamental postulates of quantum theory; representation of symmetry groups; and symmetry operations and symmetry groups are described. The book also dis
Spectroscopic Parameter and Molecular Constant Investigations on Low-Lying States of BeF Radical
Directory of Open Access Journals (Sweden)
Jin Feng Sun
2012-02-01
Full Text Available The potential energy curves (PECs of X2Σ+, A2Πr and B2Σ+ states of BeF radical have been investigated using the complete active space self-consistent-field (CASSCF method, followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI approach at the correlation-consistent basis sets, cc-pV5Z for Be and aug-cc-pV6Z for F. Based on the PECs of X2Σ+, A2Πr and B2Σ+ states, the spectroscopic parameters (De, Re, ωe, ωeχe, αe and Be have also been determined in the present work. With the PECs determined at the present level of theory, vibrational states have been predicted for each state when the rotational quantum number J equals zero (J = 0. The vibrational levels, inertial rotation and centrifugal distortion constants are determined for the three states, and the classical turning points are also calculated for the X2Σ+ state. Compared with the available experiments and other theories, it can be seen that the present spectroscopic parameter and molecular constant results are more fully in agreement with the experimental findings.
Orbital-Free Molecular Dynamics Simulations at Extreme Conditions
Kress, J. D.; Collins, L. A.; Ticknor, C.
2015-06-01
Large-scale molecular dynamics (MD) simulations in an orbital-free (OF) density-functional theory (DFT) formulation have been performed for pure and mixed species over a broad range of temperatures (T) and densities (ρ) that includes the warm, dense matter and high-energy density physics regimes. A finite-temperature Thomas-Fermi-Dirac form with a local-density exchange-correlation potential and a regularized electron-ion interaction represents the quantum nature of the electrons. In particular, we examine the efficacy of the OFMD approach as an effective bridge between Kohn-Sham DFT MD at low temperatures and simple, fully-ionized plasma models at high temperatures. Comparisons against intermediate-range constructions such as the Yukawa and one-component plasmas are also made. We examine the mass transport (diffusion, viscosity) properties of various systems, ranging from light to heavy elements, including lithium hydride (LiH), mixtures of LiH with uranium, mixtures of deuterium-tritium (DT) with plutonium and mixtures of DT with plastic (CH). The OFMD mass transport results have been fitted to simple functions of ρ and T suitable for use in hydrodynamics simulation codes.
Papi, Paolo; Advances in Lie Superalgebras
2014-01-01
The volume is the outcome of the conference "Lie superalgebras," which was held at the Istituto Nazionale di Alta Matematica, in 2012. The conference gathered many specialists in the subject, and the talks held provided comprehensive insights into the newest trends in research on Lie superalgebras (and related topics like vertex algebras, representation theory and supergeometry). The book contains contributions of many leading esperts in the field and provides a complete account of the newest trends in research on Lie Superalgebras.
Gilbert, Kathleen M.; Skawinski, William J.; Misra, Milind; Paris, Kristina A.; Naik, Neelam H.; Buono, Ronald A.; Deutsch, Howard M.; Venanzi, Carol A.
2004-11-01
Methylphenidate (MP) binds to the cocaine binding site on the dopamine transporter and inhibits reuptake of dopamine, but does not appear to have the same abuse potential as cocaine. This study, part of a comprehensive effort to identify a drug treatment for cocaine abuse, investigates the effect of choice of calculation technique and of solvent model on the conformational potential energy surface (PES) of MP and a rigid methylphenidate (RMP) analogue which exhibits the same dopamine transporter binding affinity as MP. Conformational analysis was carried out by the AM1 and AM1/SM5.4 semiempirical molecular orbital methods, a molecular mechanics method (Tripos force field with the dielectric set equal to that of vacuum or water) and the HF/6-31G* molecular orbital method in vacuum phase. Although all three methods differ somewhat in the local details of the PES, the general trends are the same for neutral and protonated MP. In vacuum phase, protonation has a distinctive effect in decreasing the regions of space available to the local conformational minima. Solvent has little effect on the PES of the neutral molecule and tends to stabilize the protonated species. The random search (RS) conformational analysis technique using the Tripos force field was found to be capable of locating the minima found by the molecular orbital methods using systematic grid search. This suggests that the RS/Tripos force field/vacuum phase protocol is a reasonable choice for locating the local minima of MP. However, the Tripos force field gave significantly larger phenyl ring rotational barriers than the molecular orbital methods for MP and RMP. For both the neutral and protonated cases, all three methods found the phenyl ring rotational barriers for the RMP conformers/invertamers (denoted as cte, tte, and cta) to be: cte, tte> MP > cta. Solvation has negligible effect on the phenyl ring rotational barrier of RMP. The B3LYP/6-31G* density functional method was used to calculate the phenyl
Xu, Guochang
2008-01-01
This is the first book of the satellite era which describes orbit theory with analytical solutions of the second order with respect to all possible disturbances. Based on such theory, the algorithms of orbits determination are completely revolutionized.
Orbital-Free Density Functional Theory for Molecular Structure Calculations
Institute of Scientific and Technical Information of China (English)
Huajie Chen; Aihui Zhou
2008-01-01
We give here an overview of the orbital-free density functional theory that is used for modeling atoms and molecules. We review typical approximations to the kinetic energy, exchange-correlation corrections to the kinetic and Hartree energies, and constructions of the pseudopotentials. We discuss numerical discretizations for the orbital-free methods and include several numerical results for illustrations.
Polarized Molecular Orbital Model Chemistry 3. The PMO Method Extended to Organic Chemistry.
Isegawa, Miho; Fiedler, Luke; Leverentz, Hannah R; Wang, Yingjie; Nachimuthu, Santhanamoorthi; Gao, Jiali; Truhlar, Donald G
2013-01-08
The polarized molecular orbital (PMO) method, a neglect-of-diatomic-differential-overlap (NDDO) semiempirical molecular orbital method previously parameterized for systems composed of O and H, is here extended to carbon. We modified the formalism and optimized all the parameters in the PMO Hamiltonian by using a genetic algorithm and a database containing both electrostatic and energetic properties; the new parameter set is called PMO2. The quality of the resulting predictions is compared to results obtained by previous NDDO semiempirical molecular orbital methods, both including and excluding dispersion terms. We also compare the PMO2 properties to SCC-DFTB calculations. Within the class of semiempirical molecular orbital methods, the PMO2 method is found to be especially accurate for polarizabilities, atomization energies, proton transfer energies, noncovalent complexation energies, and chemical reaction barrier heights and to have good across-the-board accuracy for a range of other properties, including dipole moments, partial atomic charges, and molecular geometries.
Polarized Molecular Orbital Model Chemistry 3. The PMO Method Extended to Organic Chemistry
Isegawa, Miho; Fiedler, Luke; Leverentz, Hannah R.; Wang, Yingjie; Nachimuthu, Santhanamoorthi; Gao, Jiali; Truhlar, Donald G.
2013-01-01
The polarized molecular orbital (PMO) method, a neglect-of-diatomic-differential-overlap (NDDO) semiempirical molecular orbital method previously parameterized for systems composed of O and H, is here extended to carbon. We modified the formalism and optimized all the parameters in the PMO Hamiltonian by using a genetic algorithm and a database containing both electrostatic and energetic properties; the new parameter set is called PMO2. The quality of the resulting predictions is compared to results obtained by previous NDDO semiempirical molecular orbital methods, both including and excluding dispersion terms. We also compare the PMO2 properties to SCC-DFTB calculations. Within the class of semiempirical molecular orbital methods, the PMO2 method is found to be especially accurate for polarizabilities, atomization energies, proton transfer energies, noncovalent complexation energies, and chemical reaction barrier heights and to have good across-the-board accuracy for a range of other properties, including dipole moments, partial atomic charges, and molecular geometries. PMID:23704835
A unified scheme for ab initio molecular orbital theory and path integral molecular dynamics
Shiga, Motoyuki; Tachikawa, Masanori; Miura, Shinichi
2001-11-01
We present a general approach for accurate calculation of chemical substances which treats both nuclei and electrons quantum mechanically, adopting ab initio molecular orbital theory for the electronic structure and path integral molecular dynamics for the nuclei. The present approach enables the evaluation of physical quantities dependent on the nuclear configuration as well as the electronic structure, within the framework of Born-Oppenheimer adiabatic approximation. As an application, we give the path integral formulation of electric response properties—dipole moment and polarizability, which characterize the changes both in electronic structure and nuclear configuration at a given temperature when uniform electrostatic field is present. We also demonstrate the calculation of a water molecule using the present approach and the result of temperature and isotope effects is discussed.
Casida, Mark E.; Jamorski, Christine; Casida, Kim C.; Salahub, Dennis R.
1998-03-01
This paper presents an evaluation of the performance of time-dependent density-functional response theory (TD-DFRT) for the calculation of high-lying bound electronic excitation energies of molecules. TD-DFRT excitation energies are reported for a large number of states for each of four molecules: N2, CO, CH2O, and C2H4. In contrast to the good results obtained for low-lying states within the time-dependent local density approximation (TDLDA), there is a marked deterioration of the results for high-lying bound states. This is manifested as a collapse of the states above the TDLDA ionization threshold, which is at -ɛHOMOLDA (the negative of the highest occupied molecular orbital energy in the LDA). The -ɛHOMOLDA is much lower than the true ionization potential because the LDA exchange-correlation potential has the wrong asymptotic behavior. For this reason, the excitation energies were also calculated using the asymptotically correct potential of van Leeuwen and Baerends (LB94) in the self-consistent field step. This was found to correct the collapse of the high-lying states that was observed with the LDA. Nevertheless, further improvement of the functional is desirable. For low-lying states the asymptotic behavior of the exchange-correlation potential is not critical and the LDA potential does remarkably well. We propose criteria delineating for which states the TDLDA can be expected to be used without serious impact from the incorrect asymptotic behavior of the LDA potential.
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.
Isomorphism of Intransitive Linear Lie Equations
Directory of Open Access Journals (Sweden)
Jose Miguel Martins Veloso
2009-11-01
Full Text Available We show that formal isomorphism of intransitive linear Lie equations along transversal to the orbits can be extended to neighborhoods of these transversal. In analytic cases, the word formal is dropped from theorems. Also, we associate an intransitive Lie algebra with each intransitive linear Lie equation, and from the intransitive Lie algebra we recover the linear Lie equation, unless of formal isomorphism. The intransitive Lie algebra gives the structure functions introduced by É. Cartan.
NEW METHOD FOR CALCULATING MOLECULAR ORBITALS WITH APPLICATION TO CYCLIC SYSTEMS,
New method for calculating molecular orbitals with application to cyclic systems: Stud; of the quantum mechanical problem of an electron bound to a configuration of N overlapping potentials. Reprinted from ’The Physical Review ’.
Institute of Scientific and Technical Information of China (English)
Metin Orbay; Telhat Ozdogan
2003-01-01
In this paper, the symmetry properties of linear combination coefficients for molecular orbitals of diatomicmolecules, using Slater type orbitals, are presented with the help of the symmetry operations in group theory. In order totest the presented symmetry properties, the linear combination coefficients of molecular orbitalsfor the ground electronicstate of pilot molecules F2 and CO are calculated using constructed computer programs for Hartree-Fock-Roothaanequation. It is seen that the obtained computing results satisfy the presented symmetry properties.
Shiga, Motoyuki; Tachikawa, Masanori; Miura, Shinichi
2000-12-01
We present an accurate calculational scheme for many-body systems composed of electrons and nuclei, by path integral molecular dynamics technique combined with the ab initio molecular orbital theory. Based upon the scheme, the simulation of a water molecule at room temperature is demonstrated, applying all-electron calculation at the Hartree-Fock level of theory.
Balachandran, Janakiraman; Reddy, Pramod; Dunietz, Barry; Gavini, Vikram
2014-03-01
The frontier molecular orbital (FMO) reorganization and in turn on the thermopower of the aromatic molecules trapped between metal electrodes (aka molecular junctions) depends on two effects namely (1) the stabilization effect - due to the physical presence of the metal electrode atoms and (2) change in e-e interactions - due to end-group mediated charge transfer. The stabilization effect always reduces the FMO energies. The charge transfer effect increases the FMO energies in charge-gaining molecules, which in turn opposes the stabilization effect resulting in a small overall shift. However, the charge transfer effect decreases the FMO energies in charge-losing molecules, which in turn complements the stabilization effect resulting in a large overall downward shift. This hypothesis is validated by delineating the shifts due to stabilization and charge-transfer effects independently. Further we also demonstrate the generality of the hypothesis by applying it on a wide range of aromatic molecules with different length and end-groups. Finally, we also present computationally efficient strategies, based on the proposed mechanism, to quantitatively compute the FMO reorganization which in turn has potential for high throughput analysis of molecular junctions.
Energy Technology Data Exchange (ETDEWEB)
Pruitt, Spencer R.; Nakata, Hiroya; Nagata, Takeshi; Mayes, Maricris; Alexeev, Yuri; Fletcher, Graham D.; Fedorov, Dmitri G; Kitaura, Kazuo; Gordon, M
2016-04-12
The analytic first derivative with respect to nuclear coordinates is formulated and implemented in the framework of the three-body fragment molecular orbital (FMO) method. The gradient has been derived and implemented for restricted Hartree-Fock, second-order Møller-Plesset perturbation, and density functional theories. The importance of the three-body fully analytic gradient is illustrated through the failure of the two-body FMO method during molecular dynamics simulations of a small water cluster. The parallel implementation of the fragment molecular orbital method, its parallel efficiency, and its scalability on the Blue Gene/Q architecture up to 262,144 CPU cores, are also discussed.
Tomographic imaging of asymmetric molecular orbitals with a two-color multicycle laser field
Qin, Meiyan; Zhang, Qingbin; Lu, Peixiang
2013-01-01
We theoretically demonstrate a scheme for tomographic reconstruction of asymmetric molecular orbitals based on high-order harmonic generation with a two-color multicycle laser field. It is shown that by adjusting the relative phase of the two fields, the returning electrons can be forced to recollide from one direction for all the orientations of molecules. Thus the reconstruction of the asymmetric orbitals can be carried out with multicycle laser field. This releases the stringent requirement of a single-cycle pulse with a stabilized and controllable carrier-envelop phase for the tomographic imaging of asymmetric molecular orbitals.
Spin-orbit coupled molecular quantum magnetism realized in inorganic solid.
Park, Sang-Youn; Do, S-H; Choi, K-Y; Kang, J-H; Jang, Dongjin; Schmidt, B; Brando, Manuel; Kim, B-H; Kim, D-H; Butch, N P; Lee, Seongsu; Park, J-H; Ji, Sungdae
2016-09-21
Molecular quantum magnetism involving an isolated spin state is of particular interest due to the characteristic quantum phenomena underlying spin qubits or molecular spintronics for quantum information devices, as demonstrated in magnetic metal-organic molecular systems, the so-called molecular magnets. Here we report the molecular quantum magnetism realized in an inorganic solid Ba3Yb2Zn5O11 with spin-orbit coupled pseudospin-½ Yb(3+) ions. The magnetization represents the magnetic quantum values of an isolated Yb4 tetrahedron with a total (pseudo)spin 0, 1 and 2. Inelastic neutron scattering results reveal that a large Dzyaloshinsky-Moriya interaction originating from strong spin-orbit coupling of Yb 4f is a key ingredient to explain magnetic excitations of the molecular magnet states. The Dzyaloshinsky-Moriya interaction allows a non-adiabatic quantum transition between avoided crossing energy levels, and also results in unexpected magnetic behaviours in conventional molecular magnets.
Spin–orbit coupled molecular quantum magnetism realized in inorganic solid
Park, Sang-Youn; Do, S.-H.; Choi, K.-Y.; Kang, J.-H.; Jang, Dongjin; Schmidt, B.; Brando, Manuel; Kim, B.-H.; Kim, D.-H.; Butch, N. P.; Lee, Seongsu; Park, J.-H.; Ji, Sungdae
2016-01-01
Molecular quantum magnetism involving an isolated spin state is of particular interest due to the characteristic quantum phenomena underlying spin qubits or molecular spintronics for quantum information devices, as demonstrated in magnetic metal–organic molecular systems, the so-called molecular magnets. Here we report the molecular quantum magnetism realized in an inorganic solid Ba3Yb2Zn5O11 with spin–orbit coupled pseudospin-½ Yb3+ ions. The magnetization represents the magnetic quantum values of an isolated Yb4 tetrahedron with a total (pseudo)spin 0, 1 and 2. Inelastic neutron scattering results reveal that a large Dzyaloshinsky–Moriya interaction originating from strong spin–orbit coupling of Yb 4f is a key ingredient to explain magnetic excitations of the molecular magnet states. The Dzyaloshinsky–Moriya interaction allows a non-adiabatic quantum transition between avoided crossing energy levels, and also results in unexpected magnetic behaviours in conventional molecular magnets. PMID:27650796
Kruijssen, J M Diederik; Longmore, Steven N
2014-01-01
We recently proposed that the star-forming potential of dense molecular clouds in the Central Molecular Zone (CMZ, i.e. the central few 100 pc) of the Milky Way is linked to their orbital dynamics, potentially giving rise to an absolute-time sequence of star-forming clouds. In this paper, we present an orbital model for the gas stream(s) observed in the CMZ. The model is obtained by integrating orbits in the observed gravitational potential and represents a good fit to the distribution of dense gas, reproducing all of its key properties. The orbit is also consistent with observational constraints not included in the fitting process, such as the velocities of Sgr B2 and the Arches and Quintuplet clusters. It differs from previous models: (1) the orbit is open rather than closed due to the extended mass distribution in the CMZ, (2) its orbital velocity is twice as high as in previous models, and (3) Sgr A$^*$ coincides with the focus of the (eccentric) orbit rather than being offset. Our orbital solution suppor...
Image-charge-induced localization of molecular orbitals at metal-molecule interfaces
DEFF Research Database (Denmark)
Strange, M.; Thygesen, K. S.
2012-01-01
-conjugated molecular wire in contact with a metal surface. We find that image charge effects pull the frontier molecular orbitals toward the metal surface, while orbitals with higher or lower energy are pushed away. This affects both the size of the energetic image charge shifts and the coupling of the individual......Quasiparticle (QP) wave functions, also known as Dyson orbitals, extend the concept of single-particle states to interacting electron systems. Here we employ many-body perturbation theory in the GW approximation to calculate the QP wave functions for a semiempirical model describing a pi...... orbitals to the metal substrate. Full diagonalization of the QP equation and, to some extent, self-consistency in the GW self-energy, is important to describe the effect, which is not captured by standard density functional theory or Hartree-Fock. These results should be important for the understanding...
Diels−Alder Reactions of Acyclic 2-Azadienes: A Semiempirical Molecular Orbital Study
Teresa M. V. D. Pinho e Melo; Fausto, Rui; Gonsalves, António M. d'A. Rocha
1998-01-01
Molecular orbital calculations (AM1) have been performed to obtain the frontier orbitals' (HOMO and LUMO) energies and polarization of a series of acyclic 2-azadienes. The results are used to rationalize the reactivity of the compounds studied with both electron-rich and electron-deficient dienophiles as well as the observed regioselectivity of the corresponding Diels−Alder reactions. http://dx.doi.org/10.1021/jo980090e
Solution of multi-center molecular integrals of Slater-type orbitals
Tai, H.
1989-01-01
The troublesome multi-center molecular integrals of Slater-type orbitals (STO) in molecular physics calculations can be evaluated by using the Fourier transform and proper coupling of the two center exchange integrals. A numerical integration procedure is then readily rendered to the final expression in which the integrand consists of well known special functions of arguments containing the geometrical arrangement of the nuclear centers and the exponents of the atomic orbitals. A practical procedure was devised for the calculation of a general multi-center molecular integrals coupling arbitrary Slater-type orbitals. Symmetry relations and asymptotic conditions are discussed. Explicit expressions of three-center one-electron nuclear-attraction integrals and four-center two-electron repulsion integrals for STO of principal quantum number n=2 are listed. A few numerical results are given for the purpose of comparison.
Intramolecular charge ordering in the multi molecular orbital system (TTM-TTP)I3
Bonnet, Marie-Laure; Robert, Vincent; Tsuchiizu, Masahisa; Omori, Yukiko; Suzumura, Yoshikazu
2010-06-01
Starting from the structure of the (TTM-TTP)I3 molecular-based material, we examine the characteristics of frontier molecular orbitals using ab initio (CASSCF/CASPT2) configurations interaction calculations. It is shown that the singly occupied and second-highest-occupied molecular orbitals are close to each other, i.e., this compound should be regarded as a two-orbital system. By dividing virtually the [TTM-TTP] molecule into three fragments, an effective model is constructed to rationalize the origin of this picture. In order to investigate the low-temperature, symmetry breaking experimentally observed in the crystal, the electronic distribution in a pair of [TTM-TTP] molecules is analyzed from CASPT2 calculations. Our inspection supports and explains the speculated intramolecular charge ordering which is likely to give rise to low-energy magnetic properties.
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.
Roskop, Luke; Fedorov, Dmitri G.; Gordon, Mark S.
2013-07-01
The fragment molecular orbital (FMO) method is used to model truncated portions of mesoporous silica nanoparticle (MSN) pores. The application of the FMO/RHF (restricted Hartree-Fock) method to MCM-41 type MSNs is discussed and an error analysis is given. The FMO/RHF method is shown to reliably approximate the RHF energy (error ∼0.2 kcal/mol), dipole moment (error ∼0.2 debye) and energy gradient (root mean square [RMS] error ∼0.2 × 10-3 a.u./bohr). Several FMO fragmentation schemes are employed to provide guidance for future applications to MSN models. An MSN pore model is functionalised with (phenyl)propyl substituents and the diffusion barrier for benzene passing through the pore is computed by the FMO/RHF-D method with the Grimme dispersion correction (RHF-D). For the reaction coordinates examined here, the maximum FMO/RHF-D interaction energies range from -0.3 to -5.8 kcal/mol.
Canning, A.; Galli, G.; Mauri, F.; De Vita, A.; Car, R.
1996-04-01
The implementation of an O( N) tight-binding molecular dynamics code on the Cray T3D parallel computer is discussed. The O( N) energy functional depends on non-orthogonal, localised orbitals and a chemical potential parameter which determines the number of electrons in the system. The localisation introduces a sparse nature to the orbital data and Hamiltonian matrix, greatly changing the coding on parallel machines compared to non-localised systems. The data distribution, communication routines and dynamic load-balancing scheme of the program are presented in detail together with the speed and scaling of the code on various homogeneous and inhomogeneous physical systems. Performance results will be presented for systems of 2048 to 32768 atoms on 32 to 512 processors. We discuss the relevance to quantum molecular dynamics simulations with localised orbitals, of techniques used for programming short-range classical molecular dynamics simulations on parallel machines. The absence of global communications and the localised nature of the orbitals makes these algorithms extremely scalable in terms of memory and speed on parallel systems with fast communications. The main aim of this article is to present in detail all the new concepts and programming techniques that localisation of the orbitals introduces which scientists, coming from a background in non-localised quantum molecular dynamics simulations, may be unfamiliar with.
Graph of atomic orbitals and the molecular structure-descriptors based on it
Directory of Open Access Journals (Sweden)
ANDREY A. TOROPOV
2005-04-01
Full Text Available The graph of atomic orbitals (GAO is a novel type of molecular graph, recently proposed by one of the authors. Various molecular structure-descriptors computed for GAO are compared with their analogs computed for ordinary molecular graphs. The quality of these structure-descriptors was tested for correlation with the normal boiling points of alkanes and cycloalkanes. In all the studied cases, the results based on GAO are similar to, and usually slightly better than, those obtained by means of ordinary molecular graps.
Luther, George W., III
1987-01-01
In this paper, molecular orbital theory is used to explain a heterogeneous reaction mechanism for both pyrite oxidation and reduction. The mechanism demonstrates that the oxidation of FeS2 by Fe(3+) may occur as a result of three important criteria: (1) the presence of a suitable oxidant having a vacant orbital (in case of liquid phase) or site (solid phase) to bind to the FeS2 via sulfur; (2) the initial formation of a persulfido (disulfide) bridge between FeS2 and the oxidant, and (3) an electron transfer from a pi(asterisk) orbital in S2(2-) to a pi or pi(asterisk) orbital of the oxidant.
Orenha, Renato P.; Galembeck, Sérgio E.
2014-01-01
This computational experiment presents qualitative molecular orbital (QMO) and computational quantum chemistry exercises of NO, NO[superscript+], and NO[superscript-]. Initially students explore several properties of the target molecules by Lewis diagrams and the QMO theory. Then, they compare qualitative conclusions with EHT and DFT calculations…
1984-10-19
a molecular orbital approximation to the electron delocalization energy.1 8 The ASED theory is derived from the Hellmann- Feynman formula for...34 . . 4.•" " ., .7% . r .- - - . , .-. - . . _ .-.- :.- .- . v ._ . _ . " - . ’ " _ _ 12. Wheeler , B. L.; Nagasubramanian, G.; Bard, A. J
Li, M. Y.; Liu, Z. T.; Zhou, W.; Yang, H. F.; Shen, D. W.; Li, W.; Jiang, J.; Niu, X. H.; Xie, B. P.; Sun, Y.; Fan, C. C.; Yao, Q.; Liu, J. S.; Shi, Z. X.; Xie, X. M.
2015-01-01
We report a systematic polarization-dependent angle-resolved photoemission spectroscopy study of the three-dimensional electronic structure of the recently discovered 112-type iron-based superconductor Ca1 -xLaxFeAs2 (x =0.1 ). Besides the commonly reported three holelike and two electronlike bands in iron-based superconductors, we resolve one additional holelike band around the zone center and one more fast-dispersing band near the X point in the vicinity of the Fermi level. By tuning the polarization and the energy of incident photons, we are able to identify the specific orbital character and the kz dependence of all bands. Combining these results with band calculations, we find that As 4 pz and 4 px(4 py) orbitals contribute significantly to the additional three-dimensional holelike band and the narrow band, respectively. Also, there is considerable hybridization between the As 4 pz and Fe 3 d orbitals in the additional holelike band, which suggests strong coupling between the unique arsenic zigzag bond layers and the FeAs layers therein. Our findings provide a comprehensive picture of the orbital character of the low-lying band structure of 112-type iron-based superconductors, which can be a starting point for the further understanding of their unconventional superconductivity.
Espinosa-Garciá, Joaquín; Rangel, Cipriano; Navarrete, Marta; Corchado, José C
2004-09-15
A computational approach to calculating potential energy surfaces for reactive systems is presented and tested. This hybrid approach is based on integrated methods where calculations for a small model system are performed by using analytical potential energy surfaces, and for the real system by using molecular orbital or molecular mechanics methods. The method is tested on a hydrogen abstraction reaction by using the variational transition-state theory with multidimensional tunneling corrections. The agreement between the calculated and experimental information depends on the quality of the method chosen for the real system. When the real system is treated by accurate quantum mechanics methods, the rate constants are in excellent agreement with the experimental measurements over a wide temperature range. When the real system is treated by molecular mechanics methods, the results are still good, which is very encouraging since molecular mechanics itself is not at all capable of describing this reactive system. Since no experimental information or additional fits are required to apply this method, it can be used to improve the accuracy of molecular orbital methods or to extend the molecular mechanics method to treat any reactive system with the single constraint of the availability of an analytical potential energy surface that describes the model system.
Lie groups and Lie algebras for physicists
Das, Ashok
2015-01-01
The book is intended for graduate students of theoretical physics (with a background in quantum mechanics) as well as researchers interested in applications of Lie group theory and Lie algebras in physics. The emphasis is on the inter-relations of representation theories of Lie groups and the corresponding Lie algebras.
Proppe, Jonny; Herrmann, Carmen
2015-02-05
Common trends in communication through molecular bridges are ubiquitous in chemistry, such as the frequently observed exponential decay of conductance/electron transport and of exchange spin coupling with increasing bridge length, or the increased communication through a bridge upon closing a diarylethene photoswitch. For antiferromagnetically coupled diradicals in which two equivalent spin centers are connected by a closed-shell bridge, the molecular orbitals (MOs) whose energy splitting dominates the coupling strength are similar in shape to the MOs of the dithiolated bridges, which in turn can be used to rationalize conductance. Therefore, it appears reasonable to expect the observed common property trends to result from common orbital trends. We illustrate based on a set of model compounds that this assumption is not true, and that common property trends result from either different pairs of orbitals being involved, or from orbital energies not being the dominant contribution to property trends. For substituent effects, an effective modification of the π system can make a comparison difficult.
Attia, Ali Kamal; Souaya, Eglal R; Soliman, Ethar A
2015-11-01
Thermal analysis techniques have been used to study the thermal behavior of dapoxetine and vardenafil hydrochlorides and confirmed using semi-empirical molecular orbital calculations. Thermogravimetric analysis, derivative thermogravimetry, differential thermal analysis and differential scanning calorimetry were used to determine the thermal behavior and purity of the drugs under investigation. Thermodynamic parameters such as activation energy, enthalpy, entropy and Gibbs free energy were calculated. Thermal behavior of DAP and VAR were confirmed using by semi-empirical molecular orbital calculations. The purity values were found to be 99.97% and 99.95% for dapoxetine and vardenafil hydrochlorides, respectively. The purity of dapoxetine and vardenafil hydrochlorides is similar to that found by reported methods according to DSC data. Thermal analysis justifies its application in quality control of pharmaceutical compounds due to its simplicity, sensitivity and low operational costs.
Mass transport properties of Pu/DT mixtures from orbital free molecular dynamics simulations
Energy Technology Data Exchange (ETDEWEB)
Kress, Joel David [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ticknor, Christopher [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Collins, Lee A. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-09-16
Mass transport properties (shear viscosity and diffusion coefficients) for Pu/DT mixtures were calculated with Orbital Free Molecular Dynamics (OFMD). The results were fitted to simple functions of mass density (for ρ=10.4 to 62.4 g/cm^{3}) and temperature (for T=100 up to 3,000 eV) for Pu/DT mixtures consisting of 100/0, 25/75, 50/50, and 75/25 by number.
Pseudo-symmetry analysis of the d-block molecular orbitals in four-coordinate complexes.
Falceto, Andrés; Casanova, David; Alemany, Pere; Alvarez, Santiago
2013-06-03
A rigorous definition of the concept of pseudo-symmetry, which is as important to chemistry as the concepts of symmetry implemented through group theory, should allow us to apply those group theoretical tools to molecules that are significantly distorted from those ideal symmetries best known and understood by the chemical community. In this paper, we consider four-coordinate transition-metal complexes with geometries along the interconversion path between the square and the tetrahedron and show how their molecular orbitals can be expressed in terms of either the tetrahedral or tetragonal symmetry groups. Furthermore, we analyze how the intensity of a d-d absorption band can be related to the degree of symmetry loss of the d-block molecular orbitals by means of their decomposition in terms of contributions from different pseudo-symmetry representations. As a final example, we also show how the substitution of a single ligand in a square planar complex affects the symmetry of the molecular orbitals and the absorption intensity associated to an electronic transition.
Ab initio derivation of multi-orbital extended Hubbard model for molecular crystals
Tsuchiizu, Masahisa; Omori, Yukiko; Suzumura, Yoshikazu; Bonnet, Marie-Laure; Robert, Vincent
2012-01-01
From configuration interaction (CI) ab initio calculations, we derive an effective two-orbital extended Hubbard model based on the gerade (g) and ungerade (u) molecular orbitals (MOs) of the charge-transfer molecular conductor (TTM-TTP)I3 and the single-component molecular conductor [Au(tmdt)2]. First, by focusing on the isolated molecule, we determine the parameters for the model Hamiltonian so as to reproduce the CI Hamiltonian matrix. Next, we extend the analysis to two neighboring molecule pairs in the crystal and we perform similar calculations to evaluate the inter-molecular interactions. From the resulting tight-binding parameters, we analyze the band structure to confirm that two bands overlap and mix in together, supporting the multi-band feature. Furthermore, using a fragment decomposition, we derive the effective model based on the fragment MOs and show that the staking TTM-TTP molecules can be described by the zig-zag two-leg ladder with the inter-molecular transfer integral being larger than the intra-fragment transfer integral within the molecule. The inter-site interactions between the fragments follow a Coulomb law, supporting the fragment decomposition strategy.
Directory of Open Access Journals (Sweden)
ZHANG Jingtao
2015-08-01
Full Text Available High-order harmonics generated from aligned molecules are studied by a nonperturbative QED theory and the effect of the multiple molecular orbits is included.The harmonic spectra generated from single molecular orbit exhibit an interference minimum which is induced by the molecular structure.The location of the spectral minimum shifts with the laser intensity in long laser pulses,but is fixed in ultrashort laser pulses.This difference is owed to the quiver motion of the electron in the laser pulses.The maximal shift of the spectral minimum equals to the increment of the ponderomotive energy and depends linearly on the laser intensity.The interference between the harmonics generated from multiple molecular orbits has two principal effects:one is obscuring the deep minima in the overall harmonic spectrum,the other is manifesting the phase jump in the harmonics generated from single molecular orbit.
Weak Lie symmetry and extended Lie algebra
Energy Technology Data Exchange (ETDEWEB)
Goenner, Hubert [Institute for Theoretical Physics, Friedrich-Hund-Platz 1, University of Goettingen, D-37077 Gottingen (Germany)
2013-04-15
The concept of weak Lie motion (weak Lie symmetry) is introduced. Applications given exhibit a reduction of the usual symmetry, e.g., in the case of the rotation group. In this context, a particular generalization of Lie algebras is found ('extended Lie algebras') which turns out to be an involutive distribution or a simple example for a tangent Lie algebroid. Riemannian and Lorentz metrics can be introduced on such an algebroid through an extended Cartan-Killing form. Transformation groups from non-relativistic mechanics and quantum mechanics lead to such tangent Lie algebroids and to Lorentz geometries constructed on them (1-dimensional gravitational fields).
Institute of Scientific and Technical Information of China (English)
白瑞蒲; 程宇; 李佳倩; 孟伟
2014-01-01
3-Lie algebras have close relationships with many important fields in mathemat-ics and mathematical physics. This article concerns 3-Lie algebras. The concepts of 3-Lie coalgebras and 3-Lie bialgebras are given. The structures of such categories of algebras and the relationships with 3-Lie algebras are studied. And the classification of 4-dimensional 3-Lie coalgebras and 3-dimensional 3-Lie bialgebras over an algebraically closed field of char-acteristic zero are provided.
Many-body expansion of the Fock matrix in the fragment molecular orbital method
Fedorov, Dmitri G.; Kitaura, Kazuo
2017-09-01
A many-body expansion of the Fock matrix in the fragment molecular orbital method is derived up to three-body terms for restricted Hartree-Fock and density functional theory in the atomic orbital basis and compared to the expansion in the basis of fragment molecular orbitals (MOs). The physical nature of many-body corrections is revealed in terms of charge transfer terms. An improvement of the fragment MO expansion is proposed by adding exchange to the embedding. The accuracy of all developed methods is demonstrated in comparison to unfragmented results for polyalanines, a water cluster, Trp-cage (PDB: 1L2Y) and crambin (PDB: 1CRN) proteins, a zeolite cluster, a Si nano-wire, and a boron nitride ribbon. The physical nature of metallicity is discussed, and it is shown what kinds of metallic systems can be treated by fragment-based methods. The density of states is calculated for a fully closed and a partially open nano-ring of boron nitride with a diameter of 105 nm.
Electronic structures of TiN and TiC-Extension of Molecular Orbital Method into Crystals
Institute of Scientific and Technical Information of China (English)
Bin Song; Gaoling Zhao
2000-01-01
Density of states and theoretical X-ray emission spectra for the valence bands of TiN and TiC are obtained with a molecular orbital method. In order to describe electronic structures of crystals, local clusters for the molecular orbital calculations are extended, including the effects from the outside of the cluster in the crystal. The theoretical results are in good agreement with the experimental ones.
Takada, Tatsuo; Hayase, Yuji; Miyake, Hiroaki; Tanaka, Yasuhiro; Yoshida, Masafumi
This paper reports an examination of hetero-space charge trapping site in cross linked polyethylene (XLPE) using Molecular Orbital calculation. We chose a simple model for polyethylene (C24H50) with one molecular of acetophenone (one of cross linking byproducts), for the examination of XLPE sample. Molecular Orbital calculation can give the microscopic information of electron energy levels, electron density distributions and electro-static potential maps for the simple molecular mode of XLPE. It is presumed that the negative hetero-space charge (electron) and positive hetero-space charge (hole) were trapped at the permanent dipole of acetophenone, and the hole carrier could move in the polyethylene chain.
Empirical LCAO parameters for \\pi molecular orbitals in planar organic molecules
Hawke, Laurence; Simserides, Constantinos
2008-01-01
We present a simplified LCAO model for the description of \\pi molecular orbitals in organic molecules containing \\pi-bonds between carbon, nitrogen, or oxygen atoms with sp2 hybridization, which we show to be quite accurate in predicting the energy of the highest occupied \\pi orbital and the first \\pi-\\pi* transition energy of a large set of organic compounds. We provide four empirical parameter values for the diagonal matrix elements of the LCAO description, corresponding to atoms of carbon, nitrogen with one pz electron, nitrogen with two pz electrons, and oxygen. The bond-distance dependent formula (proportional to 1/d^2) of Harrison is used for the non-diagonal matrix elements between neighboring atoms. The predictions of our calculations have been tested against available experimental results in more than sixty organic molecules, including benzene and its derivatives, polyacenes, aromatic hydrocarbons of various geometries, polyenes, ketones, aldehydes, azabenzenes, nucleic acids bases and others. The co...
Highest Occupied Molecular Orbital of Cyclopentanone by Binary (e, 2e) Spectroscopy
Institute of Scientific and Technical Information of China (English)
ZHANG Shu-Feng; NING Chuan-Gang; DENG Jing-Kang; REN Xue-Guang; SU Guo-Lin; YANG Tie-Cheng; HUANG Yan-Ru
2006-01-01
@@ We report the first measurements of the momentum profiles of highest occupied molecular orbital (HOMO) and the complete valence shell binding energy spectra of cyclopentanone with impact energies of 600 and 1200 eV by a binary (e, 2e) spectrometer. The experimental momentum profiles of the HOMO orbital are compared with the theoretical momentum distribution calculated using the Hartree-Fock and density functional theory methods with various basis sets. However, none of these calculations gives a completely satisfactory description of the momentum distributions of the HOMO 7b2. The inadequacy of the calculations could result in the intensity difference of the second maximum at p ～l.2a.u. between the experiment and the theory. The discrepancy between experimental and theoretical data in the low-momentum region is explained with the distorted wave effect.
Directory of Open Access Journals (Sweden)
Anwar S. El-Shahawy
2004-12-01
Full Text Available Through CNDO/SCF molecular orbital calculations, the structure of 4,4’-dimethoxy- diquinone (DQ has been discussed and compared with some related compounds. The electron transfer between DQ and uracil was studied in ethanol as an interaction medium. The ionization potentials and the electron affinities of the studied molecules have been calculated in addition to their charge densities giving the columbic potential energy of the donor and acceptor. The experimental charge transfer band lies at 500 nm. The electronic transitions have been calculated for the singlet and triplet transitions in uracil and DQ molecules using the SCF eigenvectors of the two HOMO’s, ψn-1 and ψ n, and the two LUMO’s, ψ n+1 and ψ n+2, using CI theory. The calculated electronic transitions are compared with those of the experimental data to verify the non-planar structure of the DQ molecule.
Multi-Orbital Molecular Compound (TTM-TTP)I3: Effective Model and Fragment Decomposition
Tsuchiizu, Masahisa; Omori, Yukiko; Suzumura, Yoshikazu; Bonnet, Marie-Laure; Robert, Vincent; Ishibashi, Shoji; Seo, Hitoshi
2011-01-01
The electronic structure of the molecular compound (TTM-TTP)I3, which exhibits a peculiar intra-molecular charge ordering, has been studied using multi-configuration ab initio calculations. First we derive an effective Hubbard-type model based on the molecular orbitals (MOs) of TTM-TTP; we set up a two-orbital Hamiltonian for the two MOs near the Fermi energy and determine its full parameters: the transfer integrals, the Coulomb and exchange interactions. The tight-binding band structure obtained from these transfer integrals is consistent with the result of the direct band calculation based on density functional theory. Then, by decomposing the frontier MOs into two parts, i.e., fragments, we find that the stacked TTM-TTP molecules can be described by a two-leg ladder model, while the inter-fragment Coulomb energies are scaled to the inverse of their distances. This result indicates that the fragment picture that we proposed earlier [M.-L. Bonnet et al.: J. Chem. Phys. 132 (2010) 214705] successfully describes the low-energy properties of this compound.
Solvable quadratic Lie algebras
Institute of Scientific and Technical Information of China (English)
ZHU; Linsheng
2006-01-01
A Lie algebra endowed with a nondegenerate, symmetric, invariant bilinear form is called a quadratic Lie algebra. In this paper, the author investigates the structure of solvable quadratic Lie algebras, in particular, the solvable quadratic Lie algebras whose Cartan subalgebras consist of semi-simple elements, the author presents a procedure to construct a class of quadratic Lie algebras from the point of view of cohomology and shows that all solvable quadratic Lie algebras can be obtained in this way.
Covalent features in the hydrogen bond of a water dimer: molecular orbital analysis
Wang, Bo; Dai, Xing; Gao, Yang; Wang, Zhigang; Zhang, Rui-Qin
2015-01-01
The covalent-like characteristics of hydrogen bonds offer a new perspective on intermolecular interactions. Here, using density functional theory and post-Hartree-Fock methods, we reveal that there are two bonding molecular orbitals (MOs) crossing the O and H atoms of the hydrogen-bond in water dimer. Energy decomposition analysis also shows a non-negligible contribution of the induction term. These results illustrate the covalent-like character of the hydrogen bond between water molecules, which contributes to the essential understanding of ice, liquid water, related materials, and life sciences.
Path Integral Molecular Dynamics for Hydrogen with Orbital-Free Density Functional Theory
Runge, Keith; Karasiev, Valentin; Deymier, Pierre
2014-03-01
The computational bottleneck for performing path-integral molecular dynamics (PIMD) for nuclei on a first principles electronic potential energy surface has been the speed with which forces from the electrons can be generated. Recent advances in orbital-free density functional theory (OF-DFT) not only allow for faster generation of first principles forces but also include the effects of temperature on the electron density. We will present results of calculations on hydrogen in warm dense matter conditions where the protons are described by PIMD and the electrons by OF-DFT. Work supported by U.S. Dept. of Energy, grant DE-SC0002139.
Hybrid RHF/MP2 geometry optimizations with the effective fragment molecular orbital method
DEFF Research Database (Denmark)
Christensen, Anders Steen; Svendsen, Casper Steinmann; Fedorov, Dmitri G
2014-01-01
The frozen domain effective fragment molecular orbital method is extended to allow for the treatment of a single fragment at the MP2 level of theory. The approach is applied to the conversion of chorismate to prephenate by Chorismate Mutase, where the substrate is treated at the MP2 level of theory...... while the rest of the system is treated at the RHF level. MP2 geometry optimization is found to lower the barrier by up to 3.5 kcal/mol compared to RHF optimzations and ONIOM energy refinement and leads to a smoother convergence with respect to the basis set for the reaction profile. For double zeta...
Multicenter molecular integrals for Slater orbitals of higher principal quantum numbers
Tai, H.
1989-01-01
As was shown earlier by Tai (1979), by using the Fourier-transform technique and properly coupling a pair of two-center exchange integrals, the multicenter molecular integrals can be cast into a simple expression upon which numerical procedures can be directly applied. In this paper, the procedure of Tai is extended to integrals involving orbitals with arbitrarily higher principal quantum number. The derivation is outlined, and the explicit expressions are presented for a three-center nuclear attraction integral and a four-center two-electron Coulomb repulsion integral of arbitrary higher states.
Fedorov, Dmitri G; Kitaura, Kazuo
2009-11-01
We have examined the role of the exchange in describing the electrostatic potential in the fragment molecular orbital method and showed that it should be included in the total Fock matrix to obtain an accurate one-electron spectrum; however, adding it to the Fock matrices of individual fragments and pairs leads to very large errors. For the error analysis we have used the virial theorem; numerical tests have been performed for solvated phenol at the Hartree-Fock level with the 6-31G( *) and 6-311G( * *) basis sets.
Fu, Zhendong; Xiao, Yinguo; Su, Yixi; Zheng, Yanzhen; Kögerler, Paul; Brückel, Thomas
2015-10-01
Low-temperature heat capacity measurements were performed on the molecular nanomagnet \\text{K}6[\\text{V}15\\text{As}6\\text{O}42(\\text{H}2\\text{O})] \\cdot8\\text{H}2{\\text{O}} (V15). The low-lying magnetic excitations are clearly evidenced by the Schottky anomalies in the specific-heat data. The energy levels determined from the low-temperature observables agree well with the three-spin model for V15. The magnetocaloric effect of V15 is examined. The maximum entropy change of 5.31 \\text{Jkg}-1\\text{K}-1 is found for a field change of Δ H =(8-0.5) \\text{T} at ˜1.5 \\text{K} . In spite of the low ground-state spin of V15, a drastic entropy change of 4.12 \\text{Jkg}-1\\text{K}-1 is observed for a field change of Δ H = (8-0.05) \\text{T} at 0.4 K, which is comparable to the entropy change of some high-spin sub-kelvin magnetic coolers at such low temperatures. Anisotropy and consequent zero-field splitting result in this characteristic of V15 and may open new possibilities in the design of ultra-low-temperature molecular coolers.
Nozaki, Daijiro; Lücke, Andreas; Schmidt, Wolf Gero
2017-02-16
Destructive quantum interference (QI) in molecular junctions has attracted much attention in recent years. It can tune the conductance of molecular devices dramatically, which implies numerous potential applications in thermoelectric and switching applications. There are several schemes that address and rationalize QI in single molecular devices. Dimers play a particular role in this respect because the QI signal may disappear, depending on the dislocation of monomers. We derive a simple rule that governs the occurrence of QI in weakly coupled dimer stacks of both alternant and nonalternant polyaromatic hydrocarbons (PAHs) and extends the Tada-Yoshizawa scheme. Starting from the Green's function formalism combined with the molecular orbital expansion approach, it is shown that QI-induced antiresonances and their energies can be predicted from the amplitudes of the respective monomer terminal molecular orbitals. The condition is illustrated for a toy model consisting of two hydrogen molecules and applied within density functional calculations to alternant dimers of oligo(phenylene-ethynylene) and nonalternant PAHs. Minimal dimer structure modifications that require only a few millielectronvolts and lead to an energy crossing of the essentially preserved monomer orbitals are shown to result in giant conductance switching ratios.
A Simple Molecular Orbital Treatment of the Barrier to Internal Rotation in the Ethane Molecule
Smith, Derek W.
1998-07-01
The origin of the barrier to internal rotation in the ethane molecule is explored in terms of elementary molecular orbital (MO) considerations. Emphasis is placed on the antibonding effect, i.e. the result that an antibonding MO is more destabilized than its bonding counterpart is stabilized, relative to the parent atomic orbitals (AOs). It is shown that, in the case of two equivalent AOs, this effect is approximately proportional to the square of the overlap integral. By constructing the ethane Mos from those of two methyl fragments, it is shown that the most important orbital energy changes consequent upon rotation about the C-C bond can be expressed in terms of the antibonding effect arising from the filled twofold-degenerate p-bonding and -antibonding MOs. This can be reduced to the dependence on the rotation angle of the vicinal H-H overlap integrals, which are calculated explicitly, showing that the antibonding effect is minimised in the staggered conformation. A letter from Lawrence J. Sacks in our April 2000 issue addresses the above.
Gao, Chang; Zhang, Shen; Kang, Wei; Wang, Cong; Zhang, Ping; He, X. T.
2016-11-01
With 6LiD as an example, we show that the applicable region of the orbital-free molecular dynamics (OFMD) method in a large temperature range is determined by the thermal ionization process of bound electrons in shell structures. The validity boundary of the OFMD method is defined roughly by the balance point of the average thermal energy of an electron and the ionization energy of the lowest localized electronic state. This theoretical proposition is based on the observation that the deviation of the OFMD method originates from its less accurate description to the charge density in partially ionized shells, as compared with the results of the extended first-principles molecular dynamics method, which well reproduces the charge density of shell structures.
Liquid Be, Ca and Ba. An orbital-free ab-initio molecular dynamics study
Energy Technology Data Exchange (ETDEWEB)
Rio, B. G. del; González, L. E. [Departamento de Física Teórica, Atómica y Óptica, Universidad de Valladolid, 47011 Valladolid (Spain)
2015-08-17
Several static and dynamic properties of liquid beryllium (l-Be), liquid calcium (l-Ca) and liquid barium (l-Ba) near their triple point have been evaluated by the orbital-free ab initio molecular dynamics method (OF-AIMD), where the interaction between valence electrons and ions is described by means of local pseudopotentials. These local pseudopotentials used were constructed through a force-matching process with those obtained from a Kohn-Sham ab initio molecular dynamics study (KS-AIMD) of a reduced system with non-local pseudopotentials. The calculated static structures show good agreement with the available experimental data, including an asymmetric second peak in the structure factor which has been linked to the existence of a marked icosahedral short-range order in the liquid. As for the dynamic properties, we obtain collective density excitations whose associated dispersion relations exhibit a positive dispersion.
Spin-orbit force, recoil corrections, and possible BB¯* and DD¯* molecular states
Zhao, Lu; Ma, Li; Zhu, Shi-Lin
2014-05-01
In the framework of the one-boson exchange model, we have calculated the effective potentials between two heavy mesons BB¯* and DD¯* from the t- and u-channel π-, η-, ρ-, ω-, and σ-meson exchanges with four kinds of quantum number: I=0, JPC=1++; I =0, JPC=1+-; I =1, JPC=1++; I =1, JPC=1+-. We keep the recoil corrections to the BB¯* and DD¯* systems up to O(1/M2). The spin-orbit force appears at O(/1M), which turns out to be important for the very loosely bound molecular states. Our numerical results show that the momentum-related corrections are unfavorable to the formation of the molecular states in the I =0, JPC=1++ and I =1, JPC=1+- channels in the DD¯* system.
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…
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.
Superconductivity, Mott-Hubbard states, and molecular orbital order in intercalated fullerides
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...
Molecular orbital studies of gas-phase interactions between complex molecules.
Gaudreault, Roger; Whitehead, M A; van de Ven, Theo G M
2006-03-16
Describing interactions among large molecules theoretically is a challenging task. As an example, we investigated gas-phase interactions between a linear nonionic oligomer and various model compounds (cofactors), which have been reported to associate experimentally, using PM3 semiempirical molecular orbital theory. As oligomer, we studied the hexamer of poly(ethylene oxide) (PEO), and as cofactors, we studied corilagin and related compounds containing phenolic groups (R-OH). These systems are of interest because they are models for PEO/cofactor flocculation systems, used in industrial applications. The PM3 delocalized molecular orbitals (DLMO) describe the bonding between (PEO)6 and cofactors, and some of them cover the complete complex. The DLMOs which cover the traditionally considered hydrogen bonds R-OH...O or R-CH...O show a distinct "pinch", a decrease of the electron density, between the H...O atoms. Calculations of Gibbs free energy, entropy, and enthalpy show that the PEO/cofactor complexes do not form at room temperature, because the loss of entropy exceeds the increase in enthalpy. The change in enthalpy is linearly related to the change in entropy for the different complexes. Even though bond lengths, bond angles, DLMOs, and electron densities for the PEO/cofactor complexes are consistent with the definition of hydrogen bonds, the number of intermolecular R-OH...O and R-CH...O bonds does not correlate with the enthalpy of association, indicating that the bonding mechanism for these systems is the sum of many small contributions of many delocalized orbitals.
Jaeger, C.R.; Debowski, M.A.; Manners, I.; Vancso, G.J.
1999-01-01
Ab initio molecular orbital calculations at the MP2/6-31G* level of theory have been used to study the molecular geometry, electronic structure, and the thermal stability of six-membered phosphazene and heterophosphazene rings. The studies included the phosphazene ring [NPCl2]3, the carbophosphazene
Stochastic Lie group integrators
Malham, Simon J A
2007-01-01
We present Lie group integrators for nonlinear stochastic differential equations with non-commutative vector fields whose solution evolves on a smooth finite dimensional manifold. Given a Lie group action that generates transport along the manifold, we pull back the stochastic flow on the manifold to the Lie group via the action, and subsequently pull back the flow to the corresponding Lie algebra via the exponential map. We construct an approximation to the stochastic flow in the Lie algebra via closed operations and then push back to the Lie group and then to the manifold, thus ensuring our approximation lies in the manifold. We call such schemes stochastic Munthe-Kaas methods after their deterministic counterparts. We also present stochastic Lie group integration schemes based on Castell--Gaines methods. These involve using an underlying ordinary differential integrator to approximate the flow generated by a truncated stochastic exponential Lie series. They become stochastic Lie group integrator schemes if...
Genoni, Alessandro
2013-07-09
Following the X-ray constrained wave function approach proposed by Jayatilaka, we have devised a new technique that allows to extract molecular orbitals strictly localized on small molecular fragments from sets of experimental X-ray structure factors amplitudes. Since the novel strategy enables to obtain electron distributions that have quantum mechanical features and that can be easily interpreted in terms of traditional chemical concepts, the method can be also considered as a new useful tool for the determination and the analysis of charge densities from high-resolution X-ray experiments. In this paper, we describe in detail the theory of the new technique, which, in comparison to our preliminary work, has been improved both treating the effects of isotropic secondary extinctions and introducing a new protocol to halt the fitting procedure against the experimental X-ray scattering data. The performances of the novel strategy have been studied both in function of the basis-sets flexibility and in function of the quality of the considered crystallographic data. The tests performed on four different systems (α-glycine, l-cysteine, (aminomethyl)phosphonic acid and N-(trifluoromethyl)formamide) have shown that the achievement of good statistical agreements with the experimental measures mainly depends on the quality of the crystal structures (i.e., geometry positions and thermal parameters) used in the X-ray constrained calculations. Finally, given the reliable transferability of the obtained Extremely Localized Molecular Orbitals (ELMOs), we envisage to exploit the novel approach to construct new ELMOs databases suited to the development of linear-scaling methods for the refinement of macromolecular crystal structures.
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.
Orbital-free molecular dynamics simulations of transport properties in dense-plasma uranium
Kress, J. D.; Cohen, James S.; Kilcrease, D. P.; Horner, D. A.; Collins, L. A.
2011-09-01
We have calculated the self-diffusion coefficients and shear viscosity of dense-plasma uranium using orbital-free molecular dynamics (OFMD) at the Thomas-Fermi-Dirac level. The transport properties of uranium in this regime have not previously been investigated experimentally or theoretically. The OFMD calculations were performed for temperatures from 50 to 5000 eV and densities from ambient to 10 times compressed. The results are compared with the one-component-plasma (OCP) model, using effective charges given by the average-atom code INFERNO and by the regularization procedure from the OFMD method. The latter generally showed better agreement with the OFMD for viscosity and the former for diffusion. A Stokes-Einstein relationship of the OFMD viscosities and diffusion coefficients is found to hold fairly well with a constant of 0.075 ± 0.10, while the OCP/INFERNO model yields 0.13 ± 0.10.
Molecular orbital ab initio and density functional theoretical study on reaction between PH2 and NO
Institute of Scientific and Technical Information of China (English)
HU; Zhengfa(胡正发); WANG; Zhenya(王振亚); LI; Haiyang(李海洋); ZHOU; Shikang(周士康)
2002-01-01
The theoretical study of reaction between PH2 and NO on the ground state potential energy surface is reported by using molecular orbital ab initio calculation and density function theory (DFT). Equilibrium structural parameters, harmonic vibrational frequencies, total energies and zero point energies of all species during reaction are computed by HF, MP2 (full) and B3LYP theory levels with the medium basis set 6-31G*. Theoretical results indicate that intermediate IM1(H2PNO) is firstly formed by overcoming a small energy barrier TS1, and then two four-membered ring transient states TS2 and TS5, with energy barriers 103.3 and 102.6 kJ/mol respectively,then H-migration and isomerization are completed and the products PN and H2O are formed. The reaction is exothermic one with -189.6 k J/mol released.
Oxygen evolution on a SrFeO3 anode - Mechanistic considerations from molecular orbital theory
Mehandru, S. P.; Anderson, Alfred B.
1989-01-01
Various pathways proposed in the literature for the evolution of O2 in electrochemical oxidations are explored using the atom superposition and electron delocalization molecular orbital (ASED-MO) theory and the cluster models of the SrFeO3 surface as a prototype material. Calculations indicate that oxygen atoms can be easily formed on the (100) surface as well as on the edge cation sites of a SrFeO3 anode by the discharge of OH(-), followed by its deprotonation and electron transfer to the electrode. The O atoms can form O2 on the edge and corner sites, where the Fe(4+) is coordinated to four and three bulk oxygen anions, respectively. The calculations strongly disfavor mechanisms involving coupling of oxygen atoms adsorbed on different cations as well as a mechanism featuring an ozone intermediate.
Collado, J. R. Alvarez
A previous self-consistent field molecular orbital method, able to describe systems having a large number of unpaired electrons, n, is reviewed and improved. This method is applied to the study of paramagnetism in large (1,000-16,000 atoms) zigzag carbon nanotubes, represented by their n values. The computational scheme is based on the Hückel neglect differential overlap approach. It is shown that dependence of n on the semiempirical parameters is very small, and so they can be removed from the calculation. Enhancement of the paramagnetism (increase of n), by use of a strong external magnetic field, is also studied. Finally, the dependence of the Fermi one-electron potential energies and the spin atomic densities on both the parameters and the shape of the nanotubes is analyzed.0
Analytic second derivatives of the energy in the fragment molecular orbital method.
Nakata, Hiroya; Nagata, Takeshi; Fedorov, Dmitri G; Yokojima, Satoshi; Kitaura, Kazuo; Nakamura, Shinichiro
2013-04-28
We developed the analytic second derivatives of the energy for the fragment molecular orbital (FMO) method. First we derived the analytic expressions and then introduced some approximations related to the first and second order coupled perturbed Hartree-Fock equations. We developed a parallel program for the FMO Hessian with approximations in GAMESS and used it to calculate infrared (IR) spectra and Gibbs free energies and to locate the transition states in SN2 reactions. The accuracy of the Hessian is demonstrated in comparison to ab initio results for polypeptides and a water cluster. By using the two residues per fragment division, we achieved the accuracy of 3 cm(-1) in the reduced mean square deviation of vibrational frequencies from ab initio for all three polyalanine isomers, while the zero point energy had the error not exceeding 0.3 kcal/mol. The role of the secondary structure on IR spectra, zero point energies, and Gibbs free energies is discussed.
Steinmann, Casper; Fedorov, Dmitri G; Jensen, Jan H
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 determine the reaction barrier of chorismate mutase to be [Formula: see text] kcal mol(-1) for MP2/cc-pVDZ and [Formula: see text] for MP2/cc-pVTZ in an ONIOM approach using EFMO-RHF/6-31G(d) for the high and low layers, respectively.
The Effective Fragment Molecular Orbital Method for Fragments Connected by Covalent Bonds
Steinmann, Casper; Fedorov, Dmitri G.; Jensen, Jan H.
2012-01-01
We extend the effective fragment molecular orbital method (EFMO) into treating fragments connected by covalent bonds. The accuracy of EFMO is compared to FMO and conventional ab initio electronic structure methods for polypeptides including proteins. Errors in energy for RHF and MP2 are within 2 kcal/mol for neutral polypeptides and 6 kcal/mol for charged polypeptides similar to FMO but obtained two to five times faster. For proteins, the errors are also within a few kcal/mol of the FMO results. We developed both the RHF and MP2 gradient for EFMO. Compared to ab initio, the EFMO optimized structures had an RMSD of 0.40 and 0.44 Å for RHF and MP2, respectively. PMID:22844433
The McClelland approximation and the distribution of π-electron molecular orbital energy levels
Directory of Open Access Journals (Sweden)
IVAN GUTMAN
2007-10-01
Full Text Available The total π-electron energy E of a conjugated hydrocarbon with n carbon atoms and m carbon–carbon bonds can be approximately calculated by means of the McClelland formula E = g SQRT(2mr, where g is an empirical ﬁtting constant, g ≈ 0.9. It was claimed that the good quality of the McClelland approximation is a consequence of the fact that the π-electron molecular orbital energy levels are distributed in a nearly uniform manner. It will now be shown that the McClelland approximation does not depend on the nature of the distribution of energy levels, i.e., that it is compatible with a large variety of such distributions.
Monmonier, Mark
2005-01-01
Darrell Huff’s How to Lie with Statistics was the inspiration for How to Lie with Maps, in which the author showed that geometric distortion and graphic generalization of data are unavoidable elements of cartographic representation. New examples of how ill-conceived or deliberately contrived statistical maps can greatly distort geographic reality demonstrate that lying with maps is a special case of lying with statistics. Issues addressed include the effects of map scale on geometry and featu...
Heyman, Gail D.; Luu, Diem H.; Lee, Kang
2009-01-01
The present set of studies identifies the phenomenon of "parenting by lying", in which parents lie to their children as a means of influencing their emotional states and behaviour. In Study 1, undergraduates (n = 127) reported that their parents had lied to them while maintaining a concurrent emphasis on the importance of honesty. In Study 2 (n =…
Institute of Scientific and Technical Information of China (English)
曹泽星; 吴玮; 张乾二
1997-01-01
Based on the correspondence of the molecular orbital theory and valence bond theory to the description of chemical bonds,the ah imtio valence bond (VB) calculations of the low-lying states of diatomic molecules arc realized.The calculation results for the low-lying states of B2 show that the VB calculation has clear-cut physical significance,and its simulation of the behavior of the potential energy surface about the equilibrium position is superior to that of the molecular orbital theory.The valence bond calculation involving only a few bonded tableaus can correctly re fleet the effect of electronic correlation.
Velasco, A. M.; Lavín, C.; Díaz-Tinoco, Manuel; Ortiz, J. V.
2017-01-01
In this work, electron-propagator methods are applied to the calculation of the ionization potential and vertical excitation energies for several Rydberg series of the CaH molecule. The present calculations cover more highly excited states than those previously reported. In particular, excitation energies for ns (n>5), np (n>5), nd (n>4) and nf Rydberg states are given. Oscillator strengths for electronic transitions involving Rydberg states of CaH, as well as photoionization cross sections for Rydberg channels, also have been determined by using the Molecular Quantum Defect Orbital approach. Good agreement has been found with the scarce comparative data that are available for oscillator strengths. To our knowledge, predictions of photoionization cross sections from the outermost orbital of CaH are made here for the first time. A Cooper minimum and mixed atomic orbital character in some of the Dyson orbitals are among the novel features of these present calculations.
Institute of Scientific and Technical Information of China (English)
Guseinov I. Israfil; Erturk Murat
2008-01-01
Using complete orthonormal sets of Ψα -exponential type orbitals in single exponent approximation the new approach has been suggested for construction of different kinds of functions which can be useful in the theory of linear combination of atomic orbitals. These functions can be chosen properly according to the nature of the problems under consideration. This is rather important because the choice of the basis set may be play a crucial role in applications to atomic and molecular problems. As an example of application, different atomic orbitals for the ground states of the neutral and the first ten cationic members of the isoelectronic series of He atom are constructed by the solution of Hartree-Fock Roothaan equations using Ψ1, Ψ0 and Ψ-1 basis sets. The calculated results are close to the numerical Hartree-Fock values. The total energy, expansion coefficients, orbital exponents and virial ratio for each atom are presented.
Magnetic pseudo-differential Weyl calculus on nilpotent Lie groups
Beltita, Ingrid
2009-01-01
We develop a pseudo-differential Weyl calculus on nilpotent Lie groups which allows one to deal with magnetic perturbations of right invariant vector fields. For this purpose we investigate an infinite-dimensional Lie group constructed as the semidirect product of a nilpotent Lie grup and an appropriate function space thereon. We single out an appropriate coadjoint orbit in the semidirect product and construct our pseudo-differential calculus as a Weyl quantization of that orbit.
Habeeb, Moustafa M; Al-Attas, Amirah S; Al-Raimi, Doaa S
2015-05-05
Charge transfer (CT) interaction between 3,5-dimethylpyrazole (DMP) with the π-acceptor 2,3-dichloro-5,6-dicyano-p-benzoquinon (DDQ) has been investigated spectrophotometrically in acetonitrile (AN). Simultaneous reddish brown color has been observed upon mixing donor with acceptor solutions attributing to CT complex formation. The electronic spectra of the formed complex exhibited multi-charge transfer bands at 429, 447, 506, 542 and 589nm, respectively. Job(')s method of continuous variations and spectrophotometric titration methods confirmed the formation of the studied complex in 1:2 ratio between DMP and DDQ. Benesi-Hildebrand equation has been applied to calculate the stability constant of the formed complex where it recorded high value supporting formation of stable complex. Molecular orbital calculations using MM2 method and GAMESS (General Atomic and Molecular Electronic Structure System) interface computations as a package of ChemBio3D Ultra12 software were carried out for more analysis of the formed complex in the gas phase. The computational analysis included energy minimisation, stabilisation energy, molecular geometry, Mullikan charges, molecular electrostatic potential (MEP) surfaces of reactants and complex as well as characterization of the higher occupied molecular orbitals (HOMO) and lower unoccupied molecular orbitals (LUMO) surfaces of the complex. A good consistency between experimental and theoretical results has been recorded.
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.
Litofsky, Joshua; Viswanathan, Rama
2015-01-01
Matrix diagonalization, the key technique at the heart of modern computational chemistry for the numerical solution of the Schrödinger equation, can be easily introduced in the physical chemistry curriculum in a pedagogical context using simple Hückel molecular orbital theory for p bonding in molecules. We present details and results of…
Energy Technology Data Exchange (ETDEWEB)
Zheng, Y.; Brion, C.E. [British Columbia Univ., Vancouver, BC (Canada). Dept. of Chemistry; Brunger, M.J.; Zhao, K.; Grisogono, A.M.; Braidwood, S.; Weigold, E. [Flinders Univ. of South Australia, Adelaide, SA (Australia). Electronic Structure of Materials Centre; Chakravorty, S.J.; Davidson, E.R. [Indiana Univ., Bloomington, IN (United States). Dept. of Chemistry; Sgamellotti, A. [Univ di Perugia (Italy). Dipartimento di Chimica; von Niessen, W. [Technische Univ. Braunschweig (Germany). Inst fuer Physikalische
1996-01-01
The first electronic structural study of the complete valence shell binding energy spectrum of molecular fluorine, encompassing both the outer and inner valence regions, is reported. These binding energy spectra as well as the individual orbital momentum profiles have been measured using an energy dispersive multichannel electron momentum spectrometer at a total energy of 1500 eV, with an energy resolution of 1.5 eV and a momentum resolution of 0.1 a.u. The measured binding energy spectra in the energy range of 14-60 eV are compared with the results of ADC(4) many-body Green`s function and also direct-Configuration Interaction (CI) and MRSD-CI calculations. The experimental orbital electron momentum profiles are compared with SCF theoretical profiles calculated using the target Hartree-Fock approximation with a range of basis sets and with Density Functional Theory predictions in the target Kohn-Sham approximation with non-local potentials. The truncated (aug-cc-pv5z) Dunning basis sets were used for the Density Functional Theory calculations which also include some treatment of correlation via the exchange and correlation potentials. Comparisons are also made with the full ion-neutral overlap amplitude calculated with MRSD-CI wave functions. Large, saturated basis sets (199-GTO) were employed for both the high level SCF near Hartree-Fock limit and MRSD-CI calculations to investigate the effects of electron correlation and relaxation. 66 refs., 9 tabs., 9 figs.
Additive Lie ($\\xi$-Lie) Derivations and Generalized Lie ($\\xi$-Lie) Derivations on Prime Algebras
Qi, Xiaofei
2010-01-01
The additive (generalized) $\\xi$-Lie derivations on prime algebras are characterized. It is shown, under some suitable assumption, that an additive map $L$ is an additive (generalized) Lie derivation if and only if it is the sum of an additive (generalized) derivation and an additive map from the algebra into its center vanishing all commutators; is an additive (generalized) $\\xi$-Lie derivation with $\\xi\
Lombardi, James C
2015-01-01
The present investigation relates the orbital radii of regular satellites of Uranus, Jupiter, Neptune, and Saturn to photon energies in the spectra of atomic and molecular hydrogen. To explain these observations a model is developed involving stimulated radiative molecular association (SRMA) reactions among the photons and atoms in the protosatellite disks of the planets. In this model thermal energy is extracted from each disk due to a resonance at radii where there is a match between the temperature in the disk and a photon energy. Matter accumulates at these radii, and satellites and rings are ultimately formed. Orbital radii of satellites of Uranus, Jupiter, and Neptune are related to photon energies ($E_{PM}$ values) in the spectrum of molecular hydrogen. Orbital radii of satellites of Saturn are related to photon energies ($E_{PA}$ values) in the spectrum of atomic hydrogen. The first hint that such relationships exist is found in the linearity of the graphs of orbital radii of uranian satellites vs. or...
Kirker, Ian; Kaltsoyannis, Nikolas
2011-01-07
The title compounds are studied with scalar relativistic, gradient-corrected (PBE) and hybrid (PBE0) density functional theory. The metal-Cp centroid distances shorten from ThCp(3) to NpCp(3), but lengthen again from PuCp(3) to CmCp(3). Examination of the valence molecular orbital structures reveals that the highest-lying Cp π(2,3)-based orbitals transform as 1e + 2e + 1a(1) + 1a(2). Above these levels come the predominantly metal-based 5f orbitals, which stabilise across the actinide series such that in CmCp(3) the 5f manifold is at more negative energy than the Cp π(2,3)-based levels. Mulliken population analysis shows metal d orbital participation in the e symmetry Cp π(2,3)-based orbitals. Metal 5f character is found in the 1a(1) and 1a(2) levels, and this contribution increases significantly from ThCp(3) to AmCp(3). This is in agreement with the metal spin densities, which are enhanced above their formal value in NpCp(3), PuCp(3) and especially AmCp(3) with both PBE and PBE0. However, atoms-in-molecules analysis of the electron densities indicates that the An-Cp bonding is very ionic, increasingly so as the actinide becomes heavier. It is concluded that the large metal orbital contributions to the Cp π(2,3)-based levels, and enhanced metal spin densities toward the middle of the actinide series arise from a coincidental energy match of metal and ligand orbitals, and do not reflect genuinely increased covalency (in the sense of appreciable overlap between metal and ligand levels and a build up of electron density in the region between the actinide and carbon nuclei).
Energy Technology Data Exchange (ETDEWEB)
Wyrick, Jonathan; Bartels, Ludwig, E-mail: ludwig.bartels@ucr.edu [Pierce Hall, University of California-Riverside, Riverside, California 92521 (United States); Einstein, T. L. [Department of Physics and Condensed Matter Theory Center, University of Maryland, College Park, Maryland 20742-4111 (United States)
2015-03-14
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.
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.
Cahill, Katharine J; Johnson, Richard P
2013-03-01
Polar bimolecular reactions often begin as charge-transfer complexes and may proceed with a high degree of electron transfer character. Frontier molecular orbital (FMO) theory is predicated in part on this concept. We have developed an electron transfer model (ETM) in which we systematically transfer one electron between reactants and then use density functional methods to model the resultant radical or radical ion intermediates. Sites of higher reactivity are revealed by a composite spin density map (SDM) of odd electron character on the electron density surface, assuming that a new two-electron bond would occur preferentially at these sites. ETM correctly predicts regio- and stereoselectivity for a broad array of reactions, including Diels-Alder, dipolar and ketene cycloadditions, Birch reduction, many types of nucleophilic additions, and electrophilic addition to aromatic rings and polyenes. Conformational analysis of radical ions is often necessary to predict reaction stereochemistry. The electronic and geometric changes due to one-electron oxidation or reduction parallel the reaction coordinate for electrophilic or nucleophilic addition, respectively. The effect is more dramatic for one-electron reduction.
Verschuere, B.; Spruyt, A.; Meijer, E.H.; Otgaar, H.
2011-01-01
Brain imaging studies suggest that truth telling constitutes the default of the human brain and that lying involves intentional suppression of the predominant truth response. By manipulating the truth proportion in the Sheffield lie test, we investigated whether the dominance of the truth response i
Verschuere, B.; Spruyt, A.; Meijer, E.H.; Otgaar, H.
2011-01-01
Brain imaging studies suggest that truth telling constitutes the default of the human brain and that lying involves intentional suppression of the predominant truth response. By manipulating the truth proportion in the Sheffield lie test, we investigated whether the dominance of the truth response
Vermillion, Marti
1985-01-01
Lying is a symptom of a much broader problem. Primary motivations are need for acceptance, fear of punishment, and desire for attention. Children learn about honesty through observation, both directly and indirectly. Admitting mistakes, especially to children, is invaluable and can help break the lying syndrome. (MT)
Medicine, lies and deceptions.
Benn, P
2001-04-01
This article offers a qualified defence of the view that there is a moral difference between telling lies to one's patients, and deceiving them without lying. However, I take issue with certain arguments offered by Jennifer Jackson in support of the same conclusion. In particular, I challenge her claim that to deny that there is such a moral difference makes sense only within a utilitarian framework, and I cast doubt on the aptness of some of her examples of non-lying deception. But I argue that lies have a greater tendency to damage trust than does non-lying deception, and suggest that since many doctors do believe there is a moral boundary between the two types of deception, encouraging them to violate that boundary may have adverse general effects on their moral sensibilities.
Evasive Lying in Strategic Communication
Khalmetski, Kiryl; Rockenbach, Bettina; Werner, Peter
2017-01-01
In a sender-receiver game we investigate if sanctions for lying induce more truth-telling. Senders may not only choose between truth-telling and (explicit) lying, but may also engage in evasive lying by credibly pretending not to know. Sanctions promote truth-telling if senders cannot engage in evasive lying. If evasive lying is possible, explicit lying is largely substituted by evasive lying, in line with the notion that evasive lying is perceived as sufficiently less psychologically costly.
Findlater, Alexander D; Zahariev, Federico; Gordon, Mark S
2015-04-16
The local correlation "cluster-in-molecule" (CIM) method is combined with the fragment molecular orbital (FMO) method, providing a flexible, massively parallel, and near-linear scaling approach to the calculation of electron correlation energies for large molecular systems. Although the computational scaling of the CIM algorithm is already formally linear, previous knowledge of the Hartree-Fock (HF) reference wave function and subsequent localized orbitals is required; therefore, extending the CIM method to arbitrarily large systems requires the aid of low-scaling/linear-scaling approaches to HF and orbital localization. Through fragmentation, the combined FMO-CIM method linearizes the scaling, with respect to system size, of the HF reference and orbital localization calculations, achieving near-linear scaling at both the reference and electron correlation levels. For the 20-residue alanine α helix, the preliminary implementation of the FMO-CIM method captures 99.6% of the MP2 correlation energy, requiring 21% of the MP2 wall time. The new method is also applied to solvated adamantine to illustrate the multilevel capability of the FMO-CIM method.
Directory of Open Access Journals (Sweden)
M.A. Zayed
2017-03-01
Full Text Available Naproxen (C14H14O3 is a non-steroidal anti-inflammatory drug (NSAID. It is important to investigate its structure to know the active groups and weak bonds responsible for medical activity. In the present study, naproxen was investigated by mass spectrometry (MS, thermal analysis (TA measurements (TG/DTG and DTA and confirmed by semi empirical molecular orbital (MO calculation, using PM3 procedure. These calculations included, bond length, bond order, bond strain, partial charge distribution, ionization energy and heat of formation (ΔHf. The mass spectra and thermal analysis fragmentation pathways were proposed and compared to select the most suitable scheme representing the correct fragmentation pathway of the drug in both techniques. The PM3 procedure reveals that the primary cleavage site of the charged molecule is the rupture of the COOH group (lowest bond order and high strain which followed by CH3 loss of the methoxy group. Thermal analysis of the neutral drug reveals a high response to the temperature variation with very fast rate. It decomposed in several sequential steps in the temperature range 80–400 °C. These mass losses appear as two endothermic and one exothermic peaks which required energy values of 255.42, 10.67 and 371.49 J g−1 respectively. The initial thermal ruptures are similar to that obtained by mass spectral fragmentation (COOH rupture. It was followed by the loss of the methyl group and finally by ethylene loss. Therefore, comparison between MS and TA helps in selection of the proper pathway representing its fragmentation. This comparison is successfully confirmed by MO-calculation.
Pharmacophore modeling for anti-Chagas drug design using the fragment molecular orbital method.
Directory of Open Access Journals (Sweden)
Ryunosuke Yoshino
Full Text Available Chagas disease, caused by the parasite Trypanosoma cruzi, is a neglected tropical disease that causes severe human health problems. To develop a new chemotherapeutic agent for the treatment of Chagas disease, we predicted a pharmacophore model for T. cruzi dihydroorotate dehydrogenase (TcDHODH by fragment molecular orbital (FMO calculation for orotate, oxonate, and 43 orotate derivatives.Intermolecular interactions in the complexes of TcDHODH with orotate, oxonate, and 43 orotate derivatives were analyzed by FMO calculation at the MP2/6-31G level. The results indicated that the orotate moiety, which is the base fragment of these compounds, interacts with the Lys43, Asn67, and Asn194 residues of TcDHODH and the cofactor flavin mononucleotide (FMN, whereas functional groups introduced at the orotate 5-position strongly interact with the Lys214 residue.FMO-based interaction energy analyses revealed a pharmacophore model for TcDHODH inhibitor. Hydrogen bond acceptor pharmacophores correspond to Lys43 and Lys214, hydrogen bond donor and acceptor pharmacophores correspond to Asn67 and Asn194, and the aromatic ring pharmacophore corresponds to FMN, which shows important characteristics of compounds that inhibit TcDHODH. In addition, the Lys214 residue is not conserved between TcDHODH and human DHODH. Our analysis suggests that these orotate derivatives should preferentially bind to TcDHODH, increasing their selectivity. Our results obtained by pharmacophore modeling provides insight into the structural requirements for the design of TcDHODH inhibitors and their development as new anti-Chagas drugs.
Bridgeman, Adam J.; Schmidt, Timothy W.; Young, Nigel A.
2013-01-01
The stretching modes of ML[subscript "x"] complexes have the same symmetry as the atomic orbitals on M that are used to form its s bonds. In the exercise suggested here, the atomic orbitals are used to derive the form of the stretching modes without the need for formal group theory. The analogy allows students to help understand many…
Bridgeman, Adam J.; Schmidt, Timothy W.; Young, Nigel A.
2013-01-01
The stretching modes of ML[subscript "x"] complexes have the same symmetry as the atomic orbitals on M that are used to form its s bonds. In the exercise suggested here, the atomic orbitals are used to derive the form of the stretching modes without the need for formal group theory. The analogy allows students to help understand many…
Roemelt, Michael
2015-07-01
Spin Orbit Coupling (SOC) is introduced to molecular ab initio density matrix renormalization group (DMRG) calculations. In the presented scheme, one first approximates the electronic ground state and a number of excited states of the Born-Oppenheimer (BO) Hamiltonian with the aid of the DMRG algorithm. Owing to the spin-adaptation of the algorithm, the total spin S is a good quantum number for these states. After the non-relativistic DMRG calculation is finished, all magnetic sublevels of the calculated states are constructed explicitly, and the SOC operator is expanded in the resulting basis. To this end, spin orbit coupled energies and wavefunctions are obtained as eigenvalues and eigenfunctions of the full Hamiltonian matrix which is composed of the SOC operator matrix and the BO Hamiltonian matrix. This treatment corresponds to a quasi-degenerate perturbation theory approach and can be regarded as the molecular equivalent to atomic Russell-Saunders coupling. For the evaluation of SOC matrix elements, the full Breit-Pauli SOC Hamiltonian is approximated by the widely used spin-orbit mean field operator. This operator allows for an efficient use of the second quantized triplet replacement operators that are readily generated during the non-relativistic DMRG algorithm, together with the Wigner-Eckart theorem. With a set of spin-orbit coupled wavefunctions at hand, the molecular g-tensors are calculated following the scheme proposed by Gerloch and McMeeking. It interprets the effective molecular g-values as the slope of the energy difference between the lowest Kramers pair with respect to the strength of the applied magnetic field. Test calculations on a chemically relevant Mo complex demonstrate the capabilities of the presented method.
Institute of Scientific and Technical Information of China (English)
胡式贤; 刘晓平; 赵洪刚; 曹阳
2000-01-01
The tree graph method of evaluating the local molecular moment is proposed. By applying this method and the molecular moment formula of π-electron energy in the molecular orbital graph theory, a topological method of using the molecular moment to judge the relatively reactive point of even AH is achieved.
Bakhurst, D
1992-06-01
This article challenges Jennifer Jackson's recent defence of doctors' rights to deceive patients. Jackson maintains there is a general moral difference between lying and intentional deception: while doctors have a prima facie duty not to lie, there is no such obligation to avoid deception. This paper argues 1) that an examination of cases shows that lying and deception are often morally equivalent, and 2) that Jackson's position is premised on a species of moral functionalism that misconstrues the nature of moral obligation. Against Jackson, it is argued that both lying and intentional deception are wrong where they infringe a patient's right to autonomy or his/her right to be treated with dignity. These rights represent 'deontological constraints' on action, defining what we must not do whatever the functional value of the consequences. Medical ethics must recognise such constraints if it is to contribute to the moral integrity of medical practice.
Iachello, Francesco
2015-01-01
This course-based primer provides an introduction to Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. In the first part, it concisely presents the basic concepts of Lie algebras, their representations and their invariants. The second part includes a description of how Lie algebras are used in practice in the treatment of bosonic and fermionic systems. Physical applications considered include rotations and vibrations of molecules (vibron model), collective modes in nuclei (interacting boson model), the atomic shell model, the nuclear shell model, and the quark model of hadrons. One of the key concepts in the application of Lie algebraic methods in physics, that of spectrum generating algebras and their associated dynamic symmetries, is also discussed. The book highlights a number of examples that help to illustrate the abstract algebraic definitions and includes a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators...
Additive Lie (ζ-Lie) Derivations and Generalized Lie (ζ-Lie)Derivations on Prime Algebras
Institute of Scientific and Technical Information of China (English)
Xiao Fei QI; Jin Chuan HOU
2013-01-01
The additive (generalized) ζ-Lie derivations on prime algebras are characterized.It is shown,under some suitable assumptions,that an additive map L is an additive generalized Lie derivation if and only if it is the sum of an additive generalized derivation and an additive map from the algebra into its center vanishing all commutators; is an additive (generalized) ζ-Lie derivation with ζ ≠ 1 if and only if it is an additive (generalized) derivation satisfying L(ζA) =ζL(A) for all A.These results are then used to characterize additive (generalized) ζ-Lie derivations on several operator algebras such as Banach space standard operator algebras and von Neumman algebras.
Lying, honor, and contradiction
National Research Council Canada - National Science Library
Michael Gilsenan
2016-01-01
.... +Superscript 1 -Superscript With a particular concentration on the manifold practices of what will be called "lying," I shall try to show the way in which individuals in a Lebanese village negotiate...
Baeck, Kyoung K.; Watts, John D.; Bartlett, Rodney J.
1997-09-01
Analytic coupled-cluster (CC) and many-body perturbation theory (MBPT) energy gradient methods with restricted Hartree-Fock (RHF), unrestricted Hartree-Fock (UHF), restricted open-shell Hartree-Fock (ROHF), and quasi-RHF(QRHF) reference functions are extended to permit dopping core and excited orbitals. By using the canonical property of the semicanonical ROHF orbitals and the RHF orbitals from which the QRHF reference function is constructed, it is shown that a general procedure can be established not only for RHF and UHF, but also for ROHF and QRHF reference functions. The basic theory and implementation are reported. To provide a systematic study of the trends and magnitudes of the effects of dropped molecular orbitals (MOs) on the structures, harmonic frequencies, and ir intensities, we study HCN, C2H2, CO2, HO2, and C2H4 at increasing levels of correlation and basis sets. The effects of the dropped MOs with the largest basis sets are about 0.003 Å and 0.1° in structures and about 1% on harmonic frequencies and ir intensities. The magnitude and the direction of the drop-MO effect tend to be almost constant from MBPT(2) to CCSD(T) methods. The two isomers of S3 are studied by the drop-MO-method, yielding very accurate results.
Nishikawa, Sadakatsu; Kamimura, Eri
2011-02-03
Ultrasonic absorption coefficients in the frequency range of 0.8-220 MHz have been measured in aqueous solution of amitriptyline (3-(10,11-dihydro-5H-dibenzo[a,d]cycloheptene-5-ylidene)-N,N-dimethyl-1-propanamine) in the concentration range from 0.20 to 0.60 mol dm(-3) at 25 °C. A single relaxational phenomenon has been observed, and the relaxation frequency is independent of the concentration. It has been also observed that the amplitude of the relaxational absorption increases linearly with the analytical concentration. From these ultrasonic relaxation data, it has been concluded that the relaxation is associated with a unimolecular reaction due to a conformational change of the solute molecule, such as a structural change due to a rotational motion of a group in the solute molecule. Molecular orbital semiempirical methods using AM1 (Austin model 1) and PM3 (modified neglect of diatomic overlap parametric method 3) have been applied to obtain the standard enthalpy of formation for amitriptyline molecule at various dihedral angles around one of the bonds in alkylamine side chain. The results have shown the two clear minimum standard enthalpies of formation for amitriptyline. From the difference of the two values, the standard enthalpy change between the two stable conformers has been calculated be 2.9 kJ mol(-1). On a rough assumption that the standard enthalpy change reflects the standard free energy change, the equilibrium constant for the rotational isomers has been estimated to be 0.31. Combining this value with the experimental ultrasonic relaxation frequency, the backward and forward rate constants have been evaluated. The standard enthalpy change of the reaction has been also estimated from the concentration dependence of the maximum absorption per wavelength, and it has been close to that calculated by the semiempirical methods. The ultrasonic absorption measurements have been also carried out in amitriptyline solution in the presence of
Phipps, M J S; Fox, T; Tautermann, C S; Skylaris, C-K
2016-07-12
We report the development and implementation of an energy decomposition analysis (EDA) scheme in the ONETEP linear-scaling electronic structure package. Our approach is hybrid as it combines the localized molecular orbital EDA (Su, P.; Li, H. J. Chem. Phys., 2009, 131, 014102) and the absolutely localized molecular orbital EDA (Khaliullin, R. Z.; et al. J. Phys. Chem. A, 2007, 111, 8753-8765) to partition the intermolecular interaction energy into chemically distinct components (electrostatic, exchange, correlation, Pauli repulsion, polarization, and charge transfer). Limitations shared in EDA approaches such as the issue of basis set dependence in polarization and charge transfer are discussed, and a remedy to this problem is proposed that exploits the strictly localized property of the ONETEP orbitals. Our method is validated on a range of complexes with interactions relevant to drug design. We demonstrate the capabilities for large-scale calculations with our approach on complexes of thrombin with an inhibitor comprised of up to 4975 atoms. Given the capability of ONETEP for large-scale calculations, such as on entire proteins, we expect that our EDA scheme can be applied in a large range of biomolecular problems, especially in the context of drug design.
Real-space observation of spin-split molecular orbitals of adsorbed single-molecule magnets
National Research Council Canada - National Science Library
Schwöbel, Jörg; Fu, Yingshuang; Brede, Jens; Dilullo, Andrew; Hoffmann, Germar; Klyatskaya, Svetlana; Ruben, Mario; Wiesendanger, Roland
2012-01-01
A key challenge in the field of molecular spintronics, and for the design of single-molecule magnet-based devices in particular, is the understanding and control of the molecular coupling at the electrode interfaces...
Liquid Water through Density-Functional Molecular Dynamics: Plane-Wave vs Atomic-Orbital Basis Sets
Miceli, Giacomo; Pasquarello, Alfredo
2016-01-01
We determine and compare structural, dynamical, and electronic properties of liquid water at near ambient conditions through density-functional molecular dynamics simulations, when using either plane-wave or atomic-orbital basis sets. In both frameworks, the electronic structure and the atomic forces are self-consistently determined within the same theoretical scheme based on a nonlocal density functional accounting for van der Waals interactions. The overall properties of liquid water achieved within the two frameworks are in excellent agreement with each other. Thus, our study supports that implementations with plane-wave or atomic-orbital basis sets yield equivalent results and can be used indiscriminately in study of liquid water or aqueous solutions.
Chen, Mohan; Xia, Junchao; Huang, Chen; Dieterich, Johannes M.; Hung, Linda; Shin, Ilgyou; Carter, Emily A.
2015-05-01
Orbital-free density functional theory (OFDFT) is a linear-scaling first-principles quantum mechanics method used to calculate the ground-state energy of a given system. Here we present a new version of PRinceton Orbital-Free Electronic Structure Software (PROFESS) with new features. First, PROFESS 3.0 provides a set of new kinetic energy density functionals (KEDFs) which are designed to model semiconductors or transition metals. Specifically, PROFESS 3.0 includes the Huang-Carter (HC) KEDF [1], a density decomposition method with fixed localized electronic density [2], the Wang-Govind-Carter (WGC) decomposition KEDF [3], and the Enhanced von Weizsäcker (EvW)-WGC KEDF [4]. Other major new functions are included, such as molecular dynamics with different statistical mechanical ensembles and spin-polarized density optimizers.
Seron, X
2014-10-01
The issue of lying occurs in neuropsychology especially when examinations are conducted in a forensic context. When a subject intentionally either presents non-existent deficits or exaggerates their severity to obtain financial or material compensation, this behaviour is termed malingering. Malingering is discussed in the general framework of lying in psychology, and the different procedures used by neuropsychologists to evidence a lack of collaboration at examination are briefly presented and discussed. When a lack of collaboration is observed, specific emphasis is placed on the difficulty in unambiguously establishing that this results from the patient's voluntary decision.
Duncan, James A; Calkins, David E G; Chavarha, Mariya
2008-05-28
Results of (10,9)CASSCF/6-31G* and B3LYP/6-31G* level calculations on the potential surface for the electrocyclic ring closure of E-7-azahepta-1,2,4,6-tetraene 3 to 1-aza-6-methylidenecyclohexa-2,4-diene ( 4) are reported, as well as parallel calculations on the electrocyclizations of hepta-1,2,4,6-tetraene 5, hexa-1,3,5-triene 7, Z and E-1-aza-1,3,5-hexatrienes 9 and 10, and Z-7-azahepta-1,2,4,6-tetraene 12 for purposes of careful comparison. The 3 --> 4 rearrangement has been studied computationally with density functional theory (DFT) by others, leading to disagreement over whether it is pseudopericyclic (de Lera, A. R.; Alvarez, R.; Lecea, B.; Torrado, A.; Cossío, F. P. Angew. Chem., Int. Ed. 2001, 40, 557-561; de Lera, A. R.; Cossío, F. P. Angew. Chem., Int. Ed. 2002, 41, 1150-1152) or pericyclic (Rodríguez-Otero, J.; Cabaleiro-Lago, E. Angew. Chem., Int. Ed. 2002, 41, 1147-1150). In accordance with disrotatory motion, the normal mode vectors for TS 3-->4 calculated at the (10,9)CASSCF/6-31G* level show a greater magnitude of rotation of the N1-H group relative to the N1-C2 bond being formed than in TS 3-->4 calculated at the B3LYP/6-31G* level. Furthermore, comparison of orbital correlation diagrams constructed entirely from localized complete active space (CAS) molecular orbitals (MOs) for the electrocyclizations of 3, 5, 7, 9, and 10 suggest that it is the highest occupied delocalized pi-MO of 3 that is primarily responsible for sigma-bond formation in 4, not the terminal allenyl pi-bond MO. However, there does appear to be a special secondary orbital effect role for the nitrogen lone-pair and hence the process is likely neither purely pericyclic nor pseudopericyclic.
Institute of Scientific and Technical Information of China (English)
MAMEDOV,B.A.
2004-01-01
A closed analytical relation is derived for the two-center nuclear attraction integrals over Slater type orbitals (STOs) in terms of binomial coefficients. This formula can be used in highly accurate calculations of the nuclear attraction integrals. The relationships obtained are valid for arbitrary values of quantum numbers and screening constants of STOs and location of nuclei.
Directory of Open Access Journals (Sweden)
G.M. Bhuiyan
2012-10-01
Full Text Available Several static and dynamic properties of liquid Cu, Ag and Au at thermodynamic states near their respective melting points, have been evaluated by means of the orbital free ab-initio molecular dynamics simulation method. The calculated static structure shows good agreement with the available X-ray and neutron diffraction data. As for the dynamic properties, the calculated dynamic structure factors point to the existence of collective density excitations along with a positive dispersion for l-Cu and l-Ag. Several transport coefficients have been obtained which show a reasonable agreement with the available experimental data.
Bhuiyan, G M; González, D J; 10.5488/CMP.15.33604
2012-01-01
Several static and dynamic properties of liquid Cu, Ag and Au at thermodynamic states near their respective melting points, have been evaluated by means of the orbital free ab-initio molecular dynamics simulation method. The calculated static structure shows good agreement with the available X-ray and neutron diffraction data. As for the dynamic properties, the calculated dynamic structure factors point to the existence of collective density excitations along with a positive dispersion for l-Cu and l-Ag. Several transport coefficients have been obtained which show a reasonable agreement with the available experimental data.
Harmonic analysis on exponential solvable Lie groups
Fujiwara, Hidenori
2015-01-01
This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. There still are many interesting open problems, and the book contributes to the future progress of this research field. As well, various related topics are presented to motivate young researchers. The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups. This method tells us that the unitary dual of these groups is realized as the space of their coadjoint orbits. This fact is established using the Mackey theory for induced representations, and that mechanism is explained first. One of the fundamental problems in the representation theory is the irreducible decomposition of induced or restricted representations. Therefore, these decompositions are studied in detail before proceeding to various related problems: the multiplicity formula, Plancherel formulas, intertwining operators, Frobenius reciprocity, and associated alge...
Hirano, Toshiyuki; Sato, Fumitoshi
2014-07-28
We used grid-free modified Cholesky decomposition (CD) to develop a density-functional-theory (DFT)-based method for calculating the canonical molecular orbitals (CMOs) of large molecules. Our method can be used to calculate standard CMOs, analytically compute exchange-correlation terms, and maximise the capacity of next-generation supercomputers. Cholesky vectors were first analytically downscaled using low-rank pivoted CD and CD with adaptive metric (CDAM). The obtained Cholesky vectors were distributed and stored on each computer node in a parallel computer, and the Coulomb, Fock exchange, and pure exchange-correlation terms were calculated by multiplying the Cholesky vectors without evaluating molecular integrals in self-consistent field iterations. Our method enables DFT and massively distributed memory parallel computers to be used in order to very efficiently calculate the CMOs of large molecules.
Zarycz, Natalia; Aucar, Gustavo A
2012-02-02
NMR J-coupling calculations at the second-order of polarization propagator approach, SOPPA, are among the most reliable. They include a high percentage of the total electron correlation effects in saturated and unsaturated molecular systems. Furthermore, J-couplings are quite sensitive to the whole electronic molecular framework. We present in this article the first study of all three response mechanisms, Fermi contact, FC, spin-dipolar, SD and paramagnetic spin-orbital, PSO, for J-couplings with occupied localized molecular orbitals at the SOPPA level of approach. Even though SOPPA results are not invariant under unitary transformations, the difference between results obtained with canonical and localized molecular orbitals, LMOs, are small enough to permit its application with confidence. The following small-size saturated and unsaturated compounds were analyzed: CH(4), CH(3)F, C(2)H(6), NH(3), C(2)H(4), CH(2)NH, H(2)C═CHF, and FHC═CHF. The local character of the FC mechanism that appears in J-couplings of these molecular models is shown through the analysis of contributions from LMOs. The importance of including the electron correlation on the engaged bonding orbitals for one-bond couplings is emphasized. Almost all electron correlation effects are included in such orbitals. Interesting findings were the large contributions by s-type LMOs to the C-H and C-C J-couplings; they are responsible for the variation of (1)J(C-C) when going from ethane to ethene and to 1,2-difluoroethene. The previously proposed hyperconjugative transfer mechanism has been tested. Among other tests we found the difference anti-syn of one-bond (1)J(C-H) in imine as due to both the corresponding σ(C-H) and the lone-pair, LP, contribution. Geminal and vicinal J-couplings were also analyzed. Our findings are in accord with a previous work by Pople and Bothner-by, who considered results taken from calculations or empirical data. For all geminal couplings the pattern of J-couplings, like
H. van Ditmarsch (Hans); D.J.N. van Eijck (Jan); F.A.G. Sietsma (Floor); Y. Wang (Yanjing); D.J.N. van Eijck (Jan); R. Verbrugge
2011-01-01
htmlabstractWe look at lying as an act of communication, where (i) the proposition that is communicated is not true, (ii) the utterer of the lie knows (or believes) that what she communicates is not true, and (iii) the utterer of the lie intends the lie to be taken as truth. Rather than dwell on
Biswas, P K; Gogonea, Valentin
2008-10-21
We present an ab initio polarizable representation of classical molecular mechanics (MM) atoms by employing an angular momentum-based expansion scheme of the point charges into partial wave orbitals. The charge density represented by these orbitals can be fully polarized, and for hybrid quantum-mechanical-molecular-mechanical (QM/MM) calculations, mutual polarization within the QM/MM Hamiltonian can be obtained. We present the mathematical formulation and the analytical expressions for the energy and forces pertaining to the method. We further develop a variational scheme to appropriately determine the expansion coefficients and then validate the method by considering polarizations of ions by the QM system employing the hybrid GROMACS-CPMD QM/MM program. Finally, we present a simpler prescription for adding isotropic polarizability to MM atoms in a QM/MM simulation. Employing this simpler scheme, we present QM/MM energy minimization results for the classic case of a water dimer and a hydrogen sulfide dimer. Also, we present single-point QM/MM results with and without the polarization to study the change in the ionization potential of tetrahydrobiopterin (BH(4)) in water and the change in the interaction energy of solvated BH(4) (described by MM) with the P(450) heme described by QM. The model can be employed for the development of an extensive classical polarizable force-field.
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.
Lie algebraic noncommutative gravity
Banerjee, Rabin; Mukherjee, Pradip; Samanta, Saurav
2007-06-01
We exploit the Seiberg-Witten map technique to formulate the theory of gravity defined on a Lie algebraic noncommutative space-time. Detailed expressions of the Seiberg-Witten maps for the gauge parameters, gauge potentials, and the field strengths have been worked out. Our results demonstrate that notwithstanding the introduction of more general noncommutative structure there is no first order correction, exactly as happens for a canonical (i.e. constant) noncommutativity.
Introduction to quantum Lie algebras
Delius, G W
1996-01-01
Quantum Lie algebras are generalizations of Lie algebras whose structure constants are power series in h. They are derived from the quantized enveloping algebras \\uqg. The quantum Lie bracket satisfies a generalization of antisymmetry. Representations of quantum Lie algebras are defined in terms of a generalized commutator. In this paper the recent general results about quantum Lie algebras are introduced with the help of the explicit example of (sl_2)_h.
Lie groups, lie algebras, and representations an elementary introduction
Hall, Brian
2015-01-01
This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compac...
Molecular quantum magnetism with strong spin-orbit coupling in inorganic solid Ba3Yb2Zn5O11
Park, Sang-Youn; Ji, Sungdae; Park, Jae-Hoon; Do, Seunghwan; Choi, Kwang-Yong; Jang, Dongjin; Schmidt, Burkhard; Brando, Manuel; Butch, Nicholas
The molecular magnet, assembly of finite number of spins which are isolated from environment, is a model system to study the quantum information process such as the qubit or spintronic devices. In past decades, the molecular magnet has been mostly realized in organic material, however, it has difficulty synthesizing materials or controlling their properties, meanwhile tremendous endeavors to search inorganic molecular magnet are continuing. Here, we propose Ba3Yb2Zn5O11 as a candidate of inorganic molecular magnet. This material consists of an alternating 3D-array of small and large tetrahedron containing antiferromagnetically coupled four pseudospin-1/2 Yb ions, and magnetic properties are described by an isolated tetrahedron without long-range magnetic ordering. Inelastic neutron scattering measurement with external magnetic field reveals that extraordinarily huge Dzyaloshinsky-Moriya (DM) interaction originating from strong spin-orbit coupling in Yb isospin is the key to explain energy level of tetrahedron in addition to Heisenberg exchange interaction and Zeeman effect. Magnetization measurement shows the Landau-Zener transition between avoided crossing levels caused by DM interaction.
Liu, Chao-Fei; JuzeliÅ«nas, Gediminas; Liu, W. M.
2017-02-01
Atomic-molecular Bose-Einstein condensates (BECs) offer brand new opportunities to revolutionize quantum gases and probe the variation of fundamental constants with unprecedented sensitivity. The recent realization of spin-orbit coupling (SOC) in BECs provides a new platform for exploring completely new phenomena unrealizable elsewhere. In this study, we find a way of creating a Rashba-Dresselhaus SOC in atomic-molecular BECs by combining the spin-dependent photoassociation and Raman coupling, which can control the formation and distribution of a different type of topological excitation—carbon-dioxide-like skyrmion. This skyrmion is formed by two half-skyrmions of molecular BECs coupling with one skyrmion of atomic BECs, where the two half-skyrmions locate at both sides of one skyrmion. Carbon-dioxide-like skyrmion can be detected by measuring the vortices structures using the time-of-flight absorption imaging technique in real experiments. Furthermore, we find that SOC can effectively change the occurrence of the Chern number in k space, which causes the creation of topological spin textures from some separated carbon-dioxide-like monomers each with topological charge -2 to a polymer chain of the skyrmions. This work helps in creating dual SOC atomic-molecular BECs and opens avenues to manipulate topological excitations.
Xavier, S.; Periandy, S.; Carthigayan, K.; Sebastian, S.
2016-12-01
Vibrational spectral analysis of Diphenyl Carbonate (DPC) is carried out by using FT-IR and FT-Raman spectroscopic techniques. It is found that all vibrational modes are in the expected region. Gaussian computational calculations were performed using B3LYP method with 6-311++G (d, p) basis set. The computed geometric parameters are in good agreement with XRD data. The observation shows that the structure of the carbonate group is unsymmetrical by ∼5° due to the attachment of the two phenyl rings. The stability of the molecule arising from hyperconjugative interaction and charge delocalization are analyzed by Natural Bond Orbital (NBO) study and the results show the lone pair transition has higher stabilization energy compared to all other. The 1H and 13C NMR chemical shifts are calculated using the Gauge-Including Atomic Orbital (GIAO) method with B3LYP/6-311++G (d, p) method. The chemical shifts computed theoretically go very closer to the experimental results. A study on the electronic and optical properties; absorption wavelengths, excitation energy, dipole moment and frontier molecular orbital energies and Molecular electrostatic potential (MEP) exhibit the high reactivity nature of the molecule. The non-linear optical property of the DPC molecule predicted theoretically found to be good candidate for NLO material. TG/DTA analysis was made and decomposition of the molecule with respect to the temperature was studied. DPC having the anthelmintic activity is docked in the Hemoglobin of Fasciola hepatica protein. The DPC has been screened to antimicrobial activity and found to exhibit antibacterial effects.
Lie algebraic Noncommutative Gravity
Banerjee, R; Samanta, S; Banerjee, Rabin; Mukherjee, Pradip; Samanta, Saurav
2007-01-01
The minimal (unimodular) formulation of noncommutative general relativity, based on gauging the Poincare group, is extended to a general Lie algebra valued noncommutative structure. We exploit the Seiberg -- Witten map technique to formulate the theory as a perturbative Lagrangian theory. Detailed expressions of the Seiberg -- Witten maps for the gauge parameters, gauge potentials and the field strengths have been worked out. Our results demonstrate that notwithstanding the introduction of more general noncommutative structure there is no first order correction, exactly as happens for a canonical (i.e. constant) noncommutativity.
Energy Technology Data Exchange (ETDEWEB)
NONE
1996-02-01
The Department of Energy has prepared an Environmental Assessment (DOE/EA-1143) evaluating the construction, equipping and operation of the proposed Lied Transplant Center at the University of Nebraska Medical Center in Omaha, Nebraska. Based on the analysis in the EA, the DOE has determined that the proposed action does not constitute a major federal action significantly affecting the quality of the human environment within the meaning of the National Environmental Policy Act of 1969 (NEPA). Therefore, the preparation of an Environmental Statement in not required.
Police lie detection accuracy: the effect of lie scenario.
O'Sullivan, Maureen; Frank, Mark G; Hurley, Carolyn M; Tiwana, Jaspreet
2009-12-01
Although most people are not better than chance in detecting deception, some groups of police professionals have demonstrated significant lie detection accuracy. One reason for this difference may be that the types of lies police are asked to judge in scientific experiments often do not represent the types of lies they see in their profession. Across 23 studies, involving 31 different police groups in eight countries, police officers tested with lie detection scenarios using high stakes lies (i.e., the lie was personally involving and/or resulted in substantial rewards or punishments for the liar) were significantly more accurate than law enforcement officials tested with low stakes lies. Face validity and construct validity of various lie scenarios are differentiated.
Sk, Mahasin Alam; Chen, Yingqian; Manzhos, Sergei
2016-08-01
We report a qualitative difference in molecular band structures and frontier orbital nodal structures in DFT calculations using GGA vs. hybrid functionals and Hartree Fock in molecules used in electrochemical power sources. This can have a significant effect in applications sensitive to redox potentials and to orbital overlaps (excitations, electron transfer rates) but for which the use of hybrid functionals is impractical, such as solids or interfaces used in electrochemical energy conversion and storage technologies. We show that correct band structures and nodal structures (ordering) of frontier orbitals can be obtained by applying a Hubbard correction to selected atomic states.
Energy Technology Data Exchange (ETDEWEB)
Kortright, Jeffrey B; Kortright, Jeffrey B; Lincoln, Derek M; Edelstein, Ruth Shima; Epstein, Arthur J
2008-05-20
X-ray absorption spectroscopy (XAS) and magnetic circular dichroism (MCD) at the V L2,3 and C and N K edges reveal bonding/backbonding interactions in films of the 400 K magnetic semiconductor V[TCNE]x~;;2. In V spectra, dxy-like orbitals are modeled assuming V2+ in an octahedral ligand field, while dz2 and dx2-y2 orbitals involved in strong covalent bonding cannot be modeled by atomic calculations. C and N MCD, and differences in XAS from neutral TCNE molecules, reveal spin-polarized molecular orbitals in V[TCNE]x~;;2 associated with backbonding interactions that yield its novel properties.
Ohyama, Tatsuya; Hayakawa, Masato; Nishikawa, Shin; Kurita, Noriyuki
2011-06-01
Transcription mechanisms of gene information from DNA to mRNA are essentially controlled by regulatory proteins such as a lactose repressor (LacR) protein and ligand molecules. Biochemical experiments elucidated that a ligand binding to LacR drastically changes the mechanism controlled by LacR, although the effect of ligand binding has not been clarified at atomic and electronic levels. We here investigated the effect of ligand binding on the specific interactions between LacR and operator DNA by the molecular simulations combined with classical molecular mechanics and ab initio fragment molecular orbital methods. The results indicate that the binding of anti-inducer ligand strengthens the interaction between LacR and DNA, which is consistent with the fact that the binding of anti-inducer enhances the repression of gene transcription by LacR. It was also elucidated that hydrating water molecules existing between LacR and DNA contribute to the specific interactions between LacR and DNA. Copyright © 2011 Wiley Periodicals, Inc.
Rings of C2H in the Molecular Disks Orbiting TW Hya and V4046 Sgr
Kastner, J H; Gorti, U; Hily-Blant, P; Oberg, K; Forveille, T; Andrews, S; Wilner, D
2015-01-01
We have used the Submillimeter Array to image, at ~1" resolution, C2H(3-2) emission from the molecule-rich circumstellar disks orbiting the nearby, classical T Tauri star systems TW Hya and V4046 Sgr. The SMA imaging reveals that the C2H emission exhibits a ring-like morphology within each disk, the inner hole radius of the C2H ring within the V4046 Sgr disk (~70 AU) is somewhat larger than than of its counterpart within the TW Hya disk (~45 AU). We suggest that, in each case, the C2H emission likely traces irradiation of the tenuous surface layers of the outer disks by high-energy photons from the central stars.
[Diagnostic imaging of lying].
Lass, Piotr; Sławek, Jarosław; Sitek, Emilia; Szurowska, Edyta; Zimmermann, Agnieszka
2013-01-01
Functional diagnostic imaging has been applied in neuropsychology for more than two decades. Nowadays, the functional magnetic resonance (fMRI) seems to be the most important technique. Brain imaging in lying has been performed and discussed since 2001. There are postulates to use fMRI for forensic purposes, as well as commercially, e.g. testing the loyalty of employees, especially because of the limitations of traditional polygraph in some cases. In USA fMRI is performed in truthfulness/lying assessment by at least two commercial companies. Those applications are a matter of heated debate of practitioners, lawyers and specialists of ethics. The opponents of fMRI use for forensic purposes indicate the lack of common agreement on it and the lack of wide recognition and insufficient standardisation. Therefore it cannot serve as a forensic proof, yet. However, considering the development of MRI and a high failure rate of traditional polygraphy, forensic applications of MRI seem to be highly probable in future.
Telling Lies: The Irrepressible Truth?
Williams, Emma J.; Bott, Lewis A.; Patrick, John; Lewis, Michael B.
2013-01-01
Telling a lie takes longer than telling the truth but precisely why remains uncertain. We investigated two processes suggested to increase response times, namely the decision to lie and the construction of a lie response. In Experiments 1 and 2, participants were directed or chose whether to lie or tell the truth. A colored square was presented and participants had to name either the true color of the square or lie about it by claiming it was a different color. In both experiments we found that there was a greater difference between lying and telling the truth when participants were directed to lie compared to when they chose to lie. In Experiments 3 and 4, we compared response times when participants had only one possible lie option to a choice of two or three possible options. There was a greater lying latency effect when questions involved more than one possible lie response. Experiment 5 examined response choice mechanisms through the manipulation of lie plausibility. Overall, results demonstrate several distinct mechanisms that contribute to additional processing requirements when individuals tell a lie. PMID:23573277
Energy Technology Data Exchange (ETDEWEB)
Chen, Y. [Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States); Zhuang, G.; Ross, P.N. [Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States); Van Hove, M.A.; Fadley, C.S. [Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)]|[Department of Physics, University of California at Davis, Davis, California 95616 (United States)
1998-10-01
The equivalent-core approximation is implemented in a novel way so as to calculate core-level relaxation energies in photoelectron spectroscopy. The method is based on self-consistent field (SCF) Hartree{endash}Fock molecular-orbital calculations via linear combinations of atomic orbitals, and involves evaluating the difference of sums of two-electron Coulomb and exchange integrals, for all electrons in an atom and in its equivalent-core ion. By thus avoiding SCF calculations with a core hole present (the true final state of photoemission), this procedure is shown to significantly save computing time in comparison with an exact SCF direct-hole calculation. Application of the method in single atoms and selected molecules shows about a 10{percent} difference with respect to direct-hole calculation results. The approximation introduces about 1{endash}6 eV errors compared to the experimental results of gas phase molecules. This method thus should be a generally useful procedure for estimating relaxation energies in core spectra. {copyright} {ital 1998 American Institute of Physics.}
Energy Technology Data Exchange (ETDEWEB)
Scholes, G.D.; Fleming, G.R. [Univ. of California, Berkeley, CA (United States). Dept. of Chemistry]|[Lawrence Berkeley National Lab., CA (United States). Physical Biosciences Div.; Gould, I.R. [Imperial Coll. of Science, Technology and Medicine, London (United Kingdom). Dept. of Chemistry; Cogdell, R.J. [Univ. of Glasgow (United Kingdom). Div. of Biochemistry and Molecular Biology
1999-04-01
The results of ab initio molecular orbital calculations of excited states and electronic couplings (for energy transfer) between the B800 and B850 bacteriochlorophyll a (Bchl) chromophores in the peripheral light-harvesting complex (LH2) of the purple photosynthetic bacterium Rhodopseudomonas acidophila are reported. Electronic couplings are estimated from supermolecule calculations of Bchl dimers using the Ci-singles methodology and 3-21G{sup *} or 6-31G{sup *} basis sets. A scheme for dissecting the coupling into contributions from the Coulombic coupling and the short-range coupling (i.e., dependent on interchromophore orbital overlap) is reported. B850 couplings are calculated to be [total (Coulombic + short)]: intrapolypeptide dimer 320 (265 + 55) cm{sup {minus}1} and interpolypeptide dimer 255 (195 + 60) cm{sup {minus}1} at the CIS/6-31G{sup *} level. These results differ significantly from those estimated using the point dipole approximation. The effect of including Mg ligands (His residues) and H-bonding residues (Trp and Tyr) is also investigated. The consequences for superradiance and energy transfer dynamics and mechanism are discussed.
Ilieva, S.; Hadjieva, B.; Galabov, B.
1999-09-01
Ab initio molecular orbital calculations at HF/4-31G level and infrared spectroscopic data for the frequencies are applied to analyse the grouping in a series model aromatic secondary amides: formanilide; acetanilide; o-methylacetanilide; 2,6-dimethylformanilide, 2,6-dimethylacetanilide; N-benzylacetamide and N-benzylformamide. The theoretical and experimental data obtained show that the conformational state of the molecules studied is determined by the fine balance of several intramolecular factors: resonance effect between the amide group and the aromatic ring, steric interaction between various substituents around the -NH-CO- grouping in the aromatic ring, conjugation between the carbonyl bond and the nitrogen lone pair as well as direct field influences inside the amide group.
Energy Technology Data Exchange (ETDEWEB)
Park, Young Ran [Graphene Research Institute, Sejong University, Gwangjin-gu, Seoul 143-747 (Korea, Republic of); Kim, Hyeong Jin; Hong, Young Joon, E-mail: shink@sejong.ac.kr, E-mail: yjhong@sejong.ac.kr [Graphene Research Institute, Sejong University, Gwangjin-gu, Seoul 143-747 (Korea, Republic of); Faculty of Nanotechnology and Advanced Materials Engineering, Sejong University, Gwangjin-gu, Seoul 143-747 (Korea, Republic of); Hybrid Materials Research Center, Sejong University, Gwangjin-gu, Seoul 143-747 (Korea, Republic of); Im, Sungjin; Shin, Koo, E-mail: shink@sejong.ac.kr, E-mail: yjhong@sejong.ac.kr [Graphene Research Institute, Sejong University, Gwangjin-gu, Seoul 143-747 (Korea, Republic of); Department of Chemistry, Sejong University, Gwangjin-gu, Seoul 143-747 (Korea, Republic of); Seo, Sunae [Graphene Research Institute, Sejong University, Gwangjin-gu, Seoul 143-747 (Korea, Republic of); Department of Physics, Sejong University, Gwangjin-gu, Seoul 143-747 (Korea, Republic of); Choi, Won Kook [Materials and Life Science Research Division, Korea Institute of Science and Technology, Hwarang-ro 14-gil, Seoul 136-791 (Korea, Republic of)
2016-01-11
We report the tailoring of the electronic structure of poly(N-vinylcarbazole) (PVK) using a mixture layer of polyaniline:poly(p-styrenesulfonic acid) (PANI:PSS) in organic multilayer PVK/PANI:PSS/poly(3,4-ethylenedioxythiophene):PSS heterojunctions. The overall electronic structure of the PVK overlayer was systematically down-shifted while the work function of PANI:PSS increased as a function of the PSS-to-PANI weight ratio for the ratio range from 1 to 11 in the PANI:PSS film. The down-shift in the highest occupied molecular orbital of PVK markedly reduced the hole injection barrier from PVK to quantum-dot (QD) layers in QD-light emitting diode (QD-LED) structures, resulting in superior electrical and electroluminescent characteristics for QD-LEDs. The influences of PANI:PSS thickness on the electronic structure of PVK and the performance of QD-LEDs are also discussed.
Hohenstein, Edward G.
2016-11-01
The floating occupation molecular orbital complete active space configuration interaction (FOMO-CASCI) method is quite promising for the study of nonadiabatic processes. Use of this method directly in nonadiabatic dynamics simulations has been limited by the lack of available first-order nonadiabatic coupling vectors. Here, an analytic formulation of these derivative coupling vectors is presented for FOMO-CASCI wavefunctions using a simple Lagrangian-based approach. The derivative coupling vectors are applied in the optimization of minimum energy conical intersections of an aqueously solvated model compound for the chromophore of the green fluorescent protein (including 100 water molecules). The computational cost of the FOMO-CASCI derivative coupling vector is shown to scale quadratically, O ( N 2 ) , with system size and is applied to systems with up to 1000 atoms.
The Role of Super-Atom Molecular Orbitals in Doped Fullerenes in a Femtosecond Intense Laser Field.
Xiong, Hui; Mignolet, Benoit; Fang, Li; Osipov, Timur; Wolf, Thomas J A; Sistrunk, Emily; Gühr, Markus; Remacle, Francoise; Berrah, Nora
2017-12-01
The interaction of gas phase endohedral fullerene Ho3N@C80 with intense (0.1-5 × 10(14) W/cm(2)), short (30 fs), 800 nm laser pulses was investigated. The power law dependence of Ho3N@C80(q+), q = 1-2, was found to be different from that of C60. Time-dependent density functional theory computations revealed different light-induced ionization mechanisms. Unlike in C60, in doped fullerenes, the breaking of the cage spherical symmetry makes super atomic molecular orbital (SAMO) states optically active. Theoretical calculations suggest that the fast ionization of the SAMO states in Ho3N@C80 is responsible for the n = 3 power law for singly charged parent molecules at intensities lower than 1.2 × 10(14) W/cm(2).
Orbital-free molecular dynamics simulations of melting in $Na_{8}$ and $Na_{20} melting in steps
Aguado, A; Alonso, J A; Stott, M J; Aguado, Andres; Lopez, Jose M.; Alonso, Julio A.; Stott, Malcolm J.
1999-01-01
The melting-like transitions of Na8 and Na20 are investigated by extensive ab initio constant energy molecular dynamics simulations, using a variant of the Car-Parrinello method which employs an explicit electronic kinetic energy functional of the density, thus avoiding the use of one-particle orbitals. Several melting indicators are evaluated in order to determine the nature of the different transitions, and comparison with other theoretical calculations is made. Both Na8 and Na20 melt over a wide range of temperature. For Na8, a first transition is observed at approx. 110 K, between a rigid phase and a phase involving isomerization between the different permutational isomers of the ground state structure. The ``liquid'' phase is completely established at approx. 220 K. For Na20, three successive transitions are observed: the first phase transition, at approx. 110 K, is associated with isomerization transitions between those permutational isomers of the ground state structure which are obtained by interchang...
Group discussion improves lie detection
National Research Council Canada - National Science Library
Nadav Klein; Nicholas Epley
2015-01-01
... identify when a person is lying. These experiments demonstrate that the group advantage in lie detection comes through the process of group discussion, and is not a product of aggregating individual opinions...
Energy Technology Data Exchange (ETDEWEB)
Thirman, Jonathan, E-mail: thirman@berkeley.edu; Head-Gordon, Martin, E-mail: mhg@cchem.berkeley.edu [Department of Chemistry, Kenneth S. Pitzer Center for Theoretical Chemistry, University of California, Berkeley, Berkeley, California 94720 (United States)
2015-08-28
An energy decomposition analysis (EDA) of intermolecular interactions is proposed for second-order Møller–Plesset perturbation theory (MP2) based on absolutely localized molecular orbitals (ALMOs), as an extension to a previous ALMO-based EDA for self-consistent field methods. It decomposes the canonical MP2 binding energy by dividing the double excitations that contribute to the MP2 wave function into classes based on how the excitations involve different molecules. The MP2 contribution to the binding energy is decomposed into four components: frozen interaction, polarization, charge transfer, and dispersion. Charge transfer is defined by excitations that change the number of electrons on a molecule, dispersion by intermolecular excitations that do not transfer charge, and polarization and frozen interactions by intra-molecular excitations. The final two are separated by evaluations of the frozen, isolated wave functions in the presence of the other molecules, with adjustments for orbital response. Unlike previous EDAs for electron correlation methods, this one includes components for the electrostatics, which is vital as adjustment to the electrostatic behavior of the system is in some cases the dominant effect of the treatment of electron correlation. The proposed EDA is then applied to a variety of different systems to demonstrate that all proposed components behave correctly. This includes systems with one molecule and an external electric perturbation to test the separation between polarization and frozen interactions and various bimolecular systems in the equilibrium range and beyond to test the rest of the EDA. We find that it performs well on these tests. We then apply the EDA to a halogen bonded system to investigate the nature of the halogen bond.
Lying because we care: Compassion increases prosocial lying.
Lupoli, Matthew J; Jampol, Lily; Oveis, Christopher
2017-07-01
Prosocial lies, or lies intended to benefit others, are ubiquitous behaviors that have important social and economic consequences. Though emotions play a central role in many forms of prosocial behavior, no work has investigated how emotions influence behavior when one has the opportunity to tell a prosocial lie-a situation that presents a conflict between two prosocial ethics: lying to prevent harm to another, and honesty, which might also provide benefits to the target of the lie. Here, we examine whether the emotion of compassion influences prosocial lying, and find that compassion causally increases and positively predicts prosocial lying. In Studies 1 and 2, participants evaluated a poorly written essay and provided feedback to the essay writer. Experimentally induced compassion felt toward the essay writer (Study 1) and individual differences in trait compassion (Study 2) were positively associated with inflated feedback to the essay writer. In both of these studies, the relationship between compassion and prosocial lying was partially mediated by an enhanced importance placed on preventing emotional harm. In Study 3, we found moderation such that experimentally induced compassion increased lies that resulted in financial gains for a charity, but not lies that produced financial gains for the self. This research illuminates the emotional underpinnings of the common yet morally complex behavior of prosocial lying, and builds on work highlighting the potentially harmful effects of compassion-an emotion typically seen as socially beneficial. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
H. van Ditmarsch (Hans); D.J.N. van Eijck (Jan); F.A.G. Sietsma (Floor)
2012-01-01
textabstractWe model lying as a communicative act changing the beliefs of the agents in a multi-agent system. With Augustine, we see lying as an utterance believed to be false by the speaker and uttered with the intent to deceive the addressee. The deceit is successful if the lie is believed
Debey, E.; De Houwer, J.; Verschuere, B.
2014-01-01
Cognitive models of deception focus on the conflict-inducing nature of the truth activation during lying. Here we tested the counterintuitive hypothesis that the truth can also serve a functional role in the act of lying. More specifically, we examined whether the construction of a lie can involve a
Debey, E.; De Houwer, J.; Verschuere, B.
2014-01-01
Cognitive models of deception focus on the conflict-inducing nature of the truth activation during lying. Here we tested the counterintuitive hypothesis that the truth can also serve a functional role in the act of lying. More specifically, we examined whether the construction of a lie can involve a
Dotsenko, V.; Shadrin, S.; Vallette, B.
2016-01-01
In this paper, we develop the deformation theory controlled by pre-Lie algebras; the main tool is a new integration theory for preLie algebras. The main field of application lies in homotopy algebra structures over a Koszul operad; in this case, we provide a homotopical description of the associated
Indian Academy of Sciences (India)
M K Subramanian; P M Anbarasan; S Manimegalai
2010-05-01
Quantum mechanical calculations of energies, geometries and vibrational wave numbers of 7-amino-4-trifluoromethyl coumarin (7A4TFMC) were carried out using Hartree–Fock (HF) and density functional theory (DFT) using hybrid functional BLYP and B3LYP with 6-31G(d,p) as basis set. The optimized geometrical parameters obtained by HF and DFT calculations are in good agreement with the experimental X-ray data. The best method to reproduce the experimental wave numbers is B3LYP method with the 6-31G(d,p) basis set. The difference between the observed and scaled wave number values of most of the fundamentals is very small. A detailed interpretation of the infrared spectra of 7A4TFMC was also reported. The entropy of the title compound was also performed at HF using the hybrid functional BLYP and B3LYP with 6-31 G(d,p) as basis set levels of theory. Natural bond orbital (NBO) analysis of the title molecule is also carried out. The theoretical spectrogram for FTIR spectra of the title molecule has been constructed.
Infrared spectroscopy of molecular ions in selected rotational and spin-orbit states
Jacovella, U.; Agner, J. A.; Schmutz, H.; Deiglmayr, J.; Merkt, F.
2016-07-01
First results are presented obtained with an experimental setup developed to record IR spectra of rotationally state-selected ions. The method we use is a state-selective version of a method developed by Schlemmer et al. [Int. J. Mass Spectrom. 185, 589 (1999); J. Chem. Phys. 117, 2068 (2002)] to record IR spectra of ions. Ions are produced in specific rotational levels using mass-analyzed-threshold-ionization spectroscopy. The state-selected ions generated by pulsed-field ionization of Rydberg states of high principal quantum number (n ≈ 200) are extracted toward an octupole ion guide containing a neutral target gas. Prior to entering the octupole, the ions are excited by an IR laser. The target gas is chosen so that only excited ions react to form product ions. These product ions are detected mass selectively as a function of the IR laser wavenumber. To illustrate this method, we present IR spectra of C 2 H2 + in selected rotational levels of the 2Πu,3/2 and 2Πu,1/2 spin-orbit components of the vibronic ground state.
Quantization on nilpotent Lie groups
Fischer, Veronique
2016-01-01
This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on graded Lie groups together with their associated Sobolev spaces. For the specific example of the Heisenberg group the theory is illustrated in detail. In addition, the book features a brief account of the corresponding quantization theory in the setting of compact Lie groups. The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize.
Almarza, Jorge; Rincón, Luis; Bahsas, Alí; Pinto, María Angela; Brito, Francisco
2013-02-01
Understanding of protein-urea interactions is one of the greatest challenges to modern structural protein chemistry. Based in enzyme kinetics experiments and (1)H NMR spectroscopic analysis we proposed that urea, at low concentrations, directly interacts with the protonated histidines of the active center of RNase A, following a simple model of competitive inhibition. These results were supported by theoretical analysis based on the frontier molecular orbital theory and suggest that urea might establish a favorable interaction with the cationic amino acids. Our experimental evidence and theoretical analysis indicate that the initials steps of the molecular mechanism of Urea-RNase A interaction passes through the establishment of a three center four electron adduct. Also, our results would explain the observed disruption of the (1)H NMR signals corresponding to H12 and H119 (involved in catalysis) of the RNase A studied in the presence of urea. Our interaction model of urea-amino acids (cationic) can be extended to explain the inactivation of other enzymes with cationic amino acids at the active site.
Zhao, Lu; Zhu, Shi-Lin
2014-01-01
In the framework of the one boson exchange model, we have calculated the effective potentials between two heavy mesons $B \\bar{B}^{*}$ and $D \\bar{D}^{*}$ from the t- and u-channel $\\pi$, $\\eta$, $\\rho$, $\\omega$ and $\\sigma$ meson exchange with four kinds of quantum number: $I=0$, $J^{PC}=1^{++}$; $I=0$, $J^{PC}=1^{+-}$; $I=1$, $J^{PC}=1^{++}$; $I=1$, $J^{PC}=1^{+-}$. We keep the recoil corrections to the $B \\bar{B}^{*}$ and $D \\bar{D}^{*}$ system up to $O(\\frac{1}{M^2})$. The spin orbit force appears at $O(\\frac{1}{M})$, which turns out to be important for the very loosely bound molecular states. Our numerical results show that the momentum-related corrections are unfavorable to the formation of the molecular states in the $I=0$, $J^{PC}=1^{++}$ and $I=1$, $J^{PC}=1^{+-}$ channels in the $D \\bar{D}^{*}$ systems.
Lyu, Yan; Fang, Yuan; Miao, Qingqing; Zhen, Xu; Ding, Dan; Pu, Kanyi
2016-04-26
Optical theranostic nanoagents that seamlessly and synergistically integrate light-generated signals with photothermal or photodynamic therapy can provide opportunities for cost-effective precision medicine, while the potential for clinical translation requires them to have good biocompatibility and high imaging/therapy performance. We herein report an intraparticle molecular orbital engineering approach to simultaneously enhance photoacoustic brightness and photothermal therapy efficacy of semiconducting polymer nanoparticles (SPNs) for in vivo imaging and treatment of cancer. The theranostic SPNs have a binary optical component nanostructure, wherein a near-infrared absorbing semiconducting polymer and an ultrasmall carbon dot (fullerene) interact with each other to induce photoinduced electron transfer upon light irradiation. Such an intraparticle optoelectronic interaction augments heat generation and consequently enhances the photoacoustic signal and maximum photothermal temperature of SPNs by 2.6- and 1.3-fold, respectively. With the use of the amplified SPN as the theranostic nanoagent, it permits enhanced photoacoustic imaging and photothermal ablation of tumor in living mice. Our study thus not only introduces a category of purely organic optical theranostics but also highlights a molecular guideline to amplify the effectiveness of light-intensive imaging and therapeutic nanosystems.
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.
Nodular Fasciitis of the Orbit: A Case Report Confirmed by Molecular Cytogenetic Analysis.
Anzeljc, Andrew J; Oliveira, Andre M; Grossniklaus, Hans E; Kim, Hee Joon; Hayek, Brent
2016-02-12
Nodular fasciitis is a benign fibroblastic proliferation typically found in the subcutaneous tissue or superficial fascia of the extremities that is often confused for malignancy. These lesions rarely occur on the eyelids and ocular adnexa and are seldom analyzed by ophthalmic pathologists. USP6 gene rearrangement has been recently demonstrated in nodular fasciitis and this rearrangement may lead to the formation of a fusion gene MYH9-USP6 in some cases. Herein, the authors describe a 38-year-old woman with a 6-month history of a progressively enlarging mass beneath her right medial upper eyelid. Histopathologic analysis of the excisional biopsy confirmed classic features of nodular fasciitis. Molecular cytogenetic analysis revealed a rearrangement of the USP6 locus, confirming the diagnosis of benign nodular fasciitis.
Energy Technology Data Exchange (ETDEWEB)
Elston, S.B.
1978-01-01
Inner-shell excitation occurring in low and moderate (keV range) energy collisions between light atomic and ionic systems is frequently describable in terms of molecular promotion mechanisms, which were extensively explored both theoretically and experimentally. The bulk of such studies have concentrated on processes understandable through the use of single- and independent-electron models. Nonetheless, it is possible to find cases of inner-shell excitation in relatively simple collision systems which involve nearly simultaneous multiple-electron transitions and transitions induced by inherently two-electron interactions. Evidence for these many- and nonindependent-electron phenomena in inner-shell excitation processes and the importance of considering such effects in the interpretation of collisionally induced excitation spectra is discussed. 13 references.
Suresh, S; Gunasekaran, S; Srinivasan, S
2014-05-05
The solid phase FT-IR and FT-Raman spectra of 2-[2-[2-[(2,6-dichlorophenyl)amino]phenyl]acetyl] oxyacetic acid (Aceclofenac) have been recorded in the region 4000-400 and 4000-100 cm(-1) respectively. The optimized molecular geometry and fundamental vibrational frequencies are interpreted with the aid of structure optimizations and normal coordinate force field calculations based on density functional theory (DFT) method and a comparative study between Hartree Fork (HF) method 6-311++G(d,p) level basis set. The calculated harmonic vibrational frequencies were scaled and have been compared with experimental by obtained FT-IR and FT-Raman spectra. A detailed interpretation of the vibrational spectra of this compound has been made on the basis of the calculated potential energy distribution (PED). The time dependent DFT method employed to study its absorption energy and oscillator strength. The linear polarizability (α) and the first order hyper polarizability (β) values of the investigated molecule have been computed. The electronic properties, such as HOMO and LUMO energies, molecular electrostatic potential (MESP) were also performed. Stability of the molecule arising from hyper conjugative interaction, charge delocalization has been analyzed using natural bond orbital (NBO) analysis.
Institute of Scientific and Technical Information of China (English)
周泰锦; 莫亦荣
1999-01-01
The symmetry orbital-symmetry orbital tensor method is applied to the evaluation of molecular integrals (one-electron and two-electron integrals) and the symmetry-orbital-tensor and self-consistent-field (SOT-SCF) calculations. A calculation scheme is proposed to simplify the evaluation of integrals and a key equation is derived to reduce the computation efforts in SCF iterations. According to the key equation, compared with the traditional SCF method, the computation efficiencies including CPU timing and external disk (or internal memory) requirement increase in the magnitude of the square of the order of a point group. The new SOT method is expected to be useful in the theoretical calculations of large molecular systems of high point group symmetries.
DEFF Research Database (Denmark)
Zarycz, M. Natalia C.; Sauer, Stephan P. A.; Provasi, Patricio F.
2014-01-01
We discuss the effect of electron correlation on the unexpected differential sensitivity (UDS) in the 1J(C-H) coupling constant of CH4 using a decomposition into contributions from localized molecular orbitals and compare with the 1J(N-H) coupling constant in NH3. 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...
Geometric orbit datum and orbit covers
Institute of Scientific and Technical Information of China (English)
LIANG; Ke(
2001-01-01
［1］Vogan, D. , Dixmier algebras, sheets and representation theory (in Actes du colloque en I' honneur de Jacques Dixmier),Progress in Math. 92, Boston: Birkhauser Verlag, 1990, 333－397.［2］McGovern, W., Dixmier Algebras and Orbit Method, Operator Algebras, Unitary Representations and Invariant Theory,Boston: Birkhauser, 1990, 397－416.［3］Liang, K. , Parabolic inductions of nilpotent geometric orbit datum, Chinese Science Bulletin (in Chinese) , 1996, 41 (23):2116－2118.［4］Vogan, D., Representations of Real Reductive Lie Groups, Boston-Basel-Stuttgart: Birkhauser, 1981.［5］Lustig, G., Spaltenstein, N., Induced unipotent class, J. London Math. Soc., 1997, 19. 41－52.［6］Collingwood, D. H. , McGovern, W. M. , Nilpotent Orbits in Semisimple Lie Algebras, New York: Van Nostremt Reinhold,1993.
Lie Subalgebras in a Certain Operator Lie Algebra with Involution
Institute of Scientific and Technical Information of China (English)
Shan Li SUN; Xue Feng MA
2011-01-01
We show in a certain Lie'-algebra,the connections between the Lie subalgebra G+:＝G+G*+[G,G*],generated by a Lie subalgebra G,and the properties of G.This allows us to investigate some useful information about the structure of such two Lie subalgebras.Some results on the relations between the two Lie subalgebras are obtained.As an application,we get the following conclusion:Let A (∪) B(X)be a space of self-adjoint operators and L:＝A ⊕ iA the corresponding complex Lie*-algebra.G+＝G+G*+[G,G*]and G are two LM-decomposable Lie subalgebras of,L with the decomposition G+＝R(G+)+S,G＝RG+SG,and RG (∪) R(C+).Then G+ is ideally finite iff RG+:＝RG+RG*+[RG,RG*]is a quasisolvable Lie subalgebra,SG+:＝SG+SG*+[SG,SG*]is an ideally finite semisimple Lie subalgebra,and [RG,SG]＝[RG*,SG]＝{0}.
Lie algebras determined by finite valued Auslander-Reiten quivers
Institute of Scientific and Technical Information of China (English)
张顺华
1997-01-01
Let r denote a connected valued Auslander-Reiten quiver,let (Γ) denote the free abelian group generated by the vertex set Γ0 and let Γ be the universal cover of Γ with fundamental group G.It is proved that when Γ is a finite connected valued Auslander-Reiten quiver,(Γ) is a Lie subalgebra of (Γ) and is just the "rbit" Lie algebra (Γ)/G,where (Γ)1 is the degenerate Hall algebra of Γ and (Γ)/G is the "orbit" Lie algebra induced by Γ.
Lie groups and automorphic forms
Ji, Lizhen; Xu, H W; Yau, Shing-Tung
2006-01-01
Lie groups are fundamental objects in mathematics. They occur naturally in differential geometry, algebraic geometry, representation theory, number theory, and other areas. Closely related are arithmetic subgroups, locally symmetric spaces and the spectral theory of automorphic forms. This book consists of five chapters which give comprehensive introductions to Lie groups, Lie algebras, arithmetic groups and reduction theories, cohomology of arithmetic groups, and the Petersson and Kuznetsov trace formulas.
Chiu, Ying-Nan
1983-05-01
A new cyclic boundary condition which corresponds to a Möbius strip representation of a one-dimensional crystal is introduced. It is compared with the usual Bloch and Born—von Karman boundary condition which is shown to be a Hückel condition in the sense of LCAO MO treatment of a ring structure. The potential relevance of this Möbius condition to one-dimensional molecular and liquid crystals in which the relative molecular orientation changes during phase transition is alluded to. A comparison of the energies for the twisted and non-twisted form of the linear crystal is derived in the LCAO approximation. The orbital symmetry correlation in the concerted twist of the atomic or molecular orbitals atom! the linear backbone during a rotational polymorphic structural transition is also derived.
Bosonization and Lie Group Structure
Ha, Yuan K
2015-01-01
We introduce a concise quantum operator formula for bosonization in which the Lie group structure appears in a natural way. The connection between fermions and bosons is found to be exactly the connection between Lie group elements and the group parameters. Bosonization is an extraordinary way of expressing the equation of motion of a complex fermion field in terms of a real scalar boson in two dimensions. All the properties of the fermion field theory are known to be preserved under this remarkable transformation with substantial simplification and elucidation of the original theory, much like Lie groups can be studied by their Lie algebras.
Debey, Evelyne; De Houwer, Jan; Verschuere, Bruno
2014-09-01
Cognitive models of deception focus on the conflict-inducing nature of the truth activation during lying. Here we tested the counterintuitive hypothesis that the truth can also serve a functional role in the act of lying. More specifically, we examined whether the construction of a lie can involve a two-step process, where the first step entails activating the truth, based upon which a lie response can be formulated in a second step. To investigate this hypothesis, we tried to capture the covert truth activation in a reaction-time based deception paradigm. Together with each question, we presented either the truth or lie response as distractors. If lying depends on the covert activation of the truth, deceptive responses would thus be facilitated by truth distractors relative to lie distractors. Our results indeed revealed such a "covert congruency" effect, both in errors and reaction times (Experiment 1). Moreover, stimulating participants to use the distractor information by increasing the proportion of truth distractor trials enlarged the "covert congruency" effects, and as such confirmed that the effects operate at a covert response level (Experiment 2). Our findings lend support to the idea that lying relies on a first step of truth telling, and call for a shift in theoretical thinking that highlights both the functional and interfering properties of the truth activation in the lying process. Copyright © 2014 Elsevier B.V. All rights reserved.
Differential geometry on Lie groups
2013-01-01
Resumo: Neste trabalho estudamos os aspectos geométricos dos grupos de Lie do ponto de vista da geometria Riemanniana, geometria Hermitiana e geometria Kähler, através das estruturas geométricas invariantes associadas. Exploramos resultados relacionados às curvaturas da variedade Riemanniana subjacente a um grupo de Lie através do estudo de sua álgebra de Lie correspondente. No contexto da geometria Hermitiana e geometria Kähler, para um caso concreto de grupo de Lie complexo, investigaram su...
Affective Priming Caused by Lying
Directory of Open Access Journals (Sweden)
Megumi Sato
2011-10-01
Full Text Available Typically, arousal increases when telling a lie, as indicated in psychophysiological studies about lie detection. But the emotional valence induced by lying is unknown, though intuition indicates that it may be negative. Indeed, the Electrodermal Activity (EDA, used in such studies, only shows arousal changes during an emotional response. In this study, we examined the emotional valence induced by lying using two tasks. First, in the deceptive task, participants answered “no” to every question regarding the nature of displayed playing cards. Therefore, they told a lie about specific cards. During the task, their EDA was recorded. Secondly, in the figure estimation task, they assessed pictures by “like” or “dislike” after looking at playing cards visibly or subliminally as prime stimuli. We expected them to tend to estimate figures by “dislike” when cards relevant to deception were previously shown. This would mean that an affective priming effect due to telling a lie happened. Actually, this effect was found only when prime stimuli were displayed visibly. This result suggests that lying per se induces negative emotions even without motivation or punishment due to lying. Furthermore, we found that such effect was more blatant in participants whose EDA changes were salient while lying.
On the linearization theorem for proper Lie groupoids
Crainic, Marius
2011-01-01
We revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the the fixed point case (known as Zung's theorem) we give a shorter and more geometric proof, based on a Moser deformation argument. The passing to general orbits (Weinstein) is given a more conceptual interpretation: as a manifestation of Morita invariance. We also clarify the precise conditions needed for the theorem to hold (which often have been misstated in the literature).
Theatres of the lie: 'crazy' deception and lying as drama.
Dongen, Els van
2002-08-01
In this article, the author argues that lying is drama, theatre, which brings about transition, reflection, reversal and involvement of the participants in the drama. By means of ethnographic data of a psychiatric ward, the author shows that lying of mental patients is not pathological, but a ritual of affliction. By using Turner's theory about rituals and performance and Goffman's theory about presentation of the self it will be showed that lying serves the redefinition of reciprocity and solidarity. With the help of Bakhtin's work on Rabelais, the author discusses the nature of the drama of the lie. It is concluded that a perspective on lying as theatre may be of use outside psychiatric wards and will occur in imbalanced power relationships.
Bäppler, Stefanie A.; Plasser, Felix; Wormit, Michael; Dreuw, Andreas
2014-11-01
Exciton sizes and electron-hole binding energies, which are central properties of excited states in extended systems and crucial to the design of modern electronic devices, are readily defined within a quasiparticle framework but are quite challenging to understand in the molecular-orbital picture. The intent of this work is to bridge this gap by providing a general way of extracting the exciton wave function out of a many-body wave function obtained by a quantum chemical excited-state computation. This methodology, which is based on the one-particle transition density matrix, is implemented within the ab initio algebraic diagrammatic construction scheme for the polarization propagator and specifically the evaluation of exciton sizes, i.e., dynamic charge separation distances, is considered. A number of examples are presented. For stacked dimers it is shown that the exciton size for charge separated states corresponds to the intermolecular separation, while it only depends on the monomer size for locally excited states or Frenkel excitons. In the case of conjugated organic polymers, the tool is applied to analyze exciton structure and dynamic charge separation. Furthermore, it is discussed how the methodology may be used for the construction of a charge-transfer diagnostic for time-dependent density-functional theory.
Lv, Xiaoli; Li, Zhuoxin; Li, Songyang; Luan, Guoyou; Liang, Dadong; Tang, Shanshan; Jin, Ruifa
2016-05-13
A series of perylene diimide (PDI) derivatives have been investigated at the CAM-B3LYP/6-31G(d) and the TD-B3LYP/6-31+G(d,p) levels to design solar cell acceptors with high performance in areas such as suitable frontier molecular orbital (FMO) energies to match oligo(thienylenevinylene) derivatives and improved charge transfer properties. The calculated results reveal that the substituents slightly affect the distribution patterns of FMOs for PDI-BI. The electron withdrawing group substituents decrease the FMO energies of PDI-BI, and the electron donating group substituents slightly affect the FMO energies of PDI-BI. The di-electron withdrawing group substituents can tune the FMOs of PDI-BI to be more suitable for the oligo(thienylenevinylene) derivatives. The electron withdrawing group substituents result in red shifts of absorption spectra and electron donating group substituents result in blue shifts for PDI-BI. The -CN substituent can improve the electron transport properties of PDI-BI. The -CH₃ group in different positions slightly affects the electron transport properties of PDI-BI.
Energy Technology Data Exchange (ETDEWEB)
Nakata, Hiroya, E-mail: nakata.h.ab@m.titech.ac.jp [Center for Biological Resources and Informatics, Tokyo Institute of Technology, B-62 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8501 (Japan); RIKEN, Research Cluster for Innovation, Nakamura Lab, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan); Japan Society for the Promotion of Science, Kojimachi Business Center Building, 5-3-1 Kojimachi, Chiyoda-ku, Tokyo 102-0083 (Japan); Fedorov, Dmitri G., E-mail: d.g.fedorov@aist.go.jp [NRI, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568 (Japan); Zahariev, Federico; Schmidt, Michael W.; Gordon, Mark S. [Department of Chemistry and Ames Laboratory, US-DOE, Iowa State University, Ames, Iowa 50011 (United States); Kitaura, Kazuo [Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501 (Japan); Nakamura, Shinichiro [RIKEN, Research Cluster for Innovation, Nakamura Lab, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan)
2015-03-28
Analytic second derivatives of the energy with respect to nuclear coordinates have been developed for spin restricted density functional theory (DFT) based on the fragment molecular orbital method (FMO). The derivations were carried out for the three-body expansion (FMO3), and the two-body expressions can be obtained by neglecting the three-body corrections. Also, the restricted Hartree-Fock (RHF) Hessian for FMO3 can be obtained by neglecting the density-functional related terms. In both the FMO-RHF and FMO-DFT Hessians, certain terms with small magnitudes are neglected for computational efficiency. The accuracy of the FMO-DFT Hessian in terms of the Gibbs free energy is evaluated for a set of polypeptides and water clusters and found to be within 1 kcal/mol of the corresponding full (non-fragmented) ab initio calculation. The FMO-DFT method is also applied to transition states in S{sub N}2 reactions and for the computation of the IR and Raman spectra of a small Trp-cage protein (PDB: 1L2Y). Some computational timing analysis is also presented.
DEFF Research Database (Denmark)
García Lastra, Juan Maria; Cook, P. L.; Himpsel, F. J.
2010-01-01
Porphyrins are widely used as dye molecules in solar cells. Knowing the energies of their frontier orbitals is crucial for optimizing the energy level structure of solar cells. We use near edge x-ray absorption fine structure (NEXAFS) spectroscopy to obtain the energy of the lowest unoccupied...... molecular orbital (LUMO) with respect to the N-1s core level of the molecule. A systematic energy shift of the N-1s to LUMO transition is found along a series of 3d metal octaethylporphyrins and explained by density functional theory. It is mainly due to a shift of the N-1s level rather than a shift...
Park, Hongkun; Zare, Richard N.
1996-03-01
A theoretical formalism is developed for the quantum-state-specific photoelectron angular distributions (PADs) from the direct photoionization of a diatomic molecule in which both the ionizing state and the state of the ion follow Hund's case (b) coupling. The formalism is based on the molecular-orbital decomposition of the ionization continuum and therefore fully incorporates the molecular nature of the photoelectron-ion scattering within the independent electron approximation. The resulting expression for the quantum-state-specific PADs is dependent on two distinct types of dynamical quantities, one that pertains only to the ionization continuum and the other that depends both on the ionizing state and the ionization continuum. Specifically, the electronic dipole-moment matrix element rlλ exp(iηlλ) for the ejection of a photoelectron with orbital angular momentum quantum number l making a projection λ on the internuclear axis is expressed as ΣαλŪlαλλ exp (iπτ¯αλλ) Mαλλ, where Ūλ is the electronic transformation matrix, τ¯αλλ is the scattering phase shift associated with the αλth continuum molecular orbital, and Mαλλ is the real electronic dipole-moment matrix element that connects the ionizing orbital to the αλth continuum molecular orbital. Because Ūλ and τ¯αλλ depend only on the dynamics in the ionization continuum, this formalism allows maximal exploitation of the commonality between photoionization processes from different ionizing states. It also makes possible the direct experimental investigation of scattering matrices for the photoelectron-ion scattering and thus the dynamics in the ionization continuum by studying the quantum-state-specific PADs, as illustrated in the companion article on the photoionization of NO.
Energy Technology Data Exchange (ETDEWEB)
Kido, Kentaro, E-mail: kido.kentaro@jaea.go.jp [Nuclear Safety Research Center, Japan Atomic Energy Agency, 2-4 Shirane, Shirakata, Tokai-mura, Naka-gun, Ibaraki 319-1195 (Japan); Kasahara, Kento [Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510 (Japan); Yokogawa, Daisuke [Department of Chemistry, Graduate School of Science, Nagoya University, Chikusa, Nagoya 464-8602 (Japan); Institute of Transformative Bio-Molecules (WPI-ITbM), Nagoya University, Chikusa, Nagoya 464-8062 (Japan); Sato, Hirofumi [Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510 (Japan); Elements Strategy Institute for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520 (Japan)
2015-07-07
In this study, we reported the development of a new quantum mechanics/molecular mechanics (QM/MM)-type framework to describe chemical processes in solution by combining standard molecular-orbital calculations with a three-dimensional formalism of integral equation theory for molecular liquids (multi-center molecular Ornstein–Zernike (MC-MOZ) method). The theoretical procedure is very similar to the 3D-reference interaction site model self-consistent field (RISM-SCF) approach. Since the MC-MOZ method is highly parallelized for computation, the present approach has the potential to be one of the most efficient procedures to treat chemical processes in solution. Benchmark tests to check the validity of this approach were performed for two solute (solute water and formaldehyde) systems and a simple S{sub N}2 reaction (Cl{sup −} + CH{sub 3}Cl → ClCH{sub 3} + Cl{sup −}) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF.
Deciding isomorphism of Lie algebras
Graaf, W.A. de
2001-01-01
When doing calculations with Lie algebras one of the main problems is to decide whether two given Lie algebras are isomorphic. A partial solution to this problem is obtained by calculating structural invariants. There is also a direct method available which involves the computation of Grobner bases.
The low lying glueball spectrum
Energy Technology Data Exchange (ETDEWEB)
Adam Szczepaniak; Eric Swanson
2003-12-18
The complete low-lying positive charge conjugation glueball spectrum is obtained from QCD. The formalism relies on the construction of an efficient quasiparticle gluon basis for Hamiltonian QCD in Coulomb gauge. The resulting rapidly convergent Fock space expansion is exploited to derive quenched low-lying glueball masses with no free parameters which are in remarkable agreement with lattice gauge theory.
Lie Symmetries of Ishimori Equation
Institute of Scientific and Technical Information of China (English)
SONG Xu-Xia
2013-01-01
The Ishimori equation is one of the most important (2+1)-dimensional integrable models,which is an integrable generalization of (1+1)-dimensional classical continuous Heisenberg ferromagnetic spin equations.Based on importance of Lie symmetries in analysis of differential equations,in this paper,we derive Lie symmetries for the Ishimori equation by Hirota's direct method.
Lying despite telling the truth.
Wiegmann, Alex; Samland, Jana; Waldmann, Michael R
2016-05-01
According to the standard definition of lying an utterance counts as a lie if the agent believes the statement to be false. Thus, according to this view it is possible that a lie states something that happens to be true. This subjective view on lying has recently been challenged by Turri and Turri (2015) who presented empirical evidence suggesting that people only consider statements as lies that are objectively false (objective view). We argue that the presented evidence is in fact consistent with the standard subjective view if conversational pragmatics is taken into account. Three experiments are presented that directly test and support the subjective view. An additional experiment backs up our pragmatic hypothesis by using the uncontroversial case of making a promise.
Group discussion improves lie detection.
Klein, Nadav; Epley, Nicholas
2015-06-16
Groups of individuals can sometimes make more accurate judgments than the average individual could make alone. We tested whether this group advantage extends to lie detection, an exceptionally challenging judgment with accuracy rates rarely exceeding chance. In four experiments, we find that groups are consistently more accurate than individuals in distinguishing truths from lies, an effect that comes primarily from an increased ability to correctly identify when a person is lying. These experiments demonstrate that the group advantage in lie detection comes through the process of group discussion, and is not a product of aggregating individual opinions (a "wisdom-of-crowds" effect) or of altering response biases (such as reducing the "truth bias"). Interventions to improve lie detection typically focus on improving individual judgment, a costly and generally ineffective endeavor. Our findings suggest a cheap and simple synergistic approach of enabling group discussion before rendering a judgment.
Xiao-Hong, Li; Hong-Ling, Cui; Rui-Zhou, Zhang; Xian-Zhou, Zhang
2015-02-01
The vibrational frequencies of (E)-2-cyano-3-(3-hydroxyphenyl)acrylamide (HB-CA) in the ground state have been calculated using density functional method (B3LYP) with B3LYP/6-311++G(d,p) basis set. The analysis of natural bond orbital was also performed. The IR spectra were obtained and interpreted by means of potential energies distributions (PEDs) using MOLVIB program. In addition, the results show that there exists Csbnd H⋯O hydrogen bond in the title compound, which is confirmed by the natural bond orbital analysis. The predicted NLO properties show that the title compound is a good candidate as nonlinear optical material. The analysis of frontier molecular orbitals shows that HB-CA has high excitation energies, good stability and high chemical hardness. The analysis of MEP map shows the negative and the positive potential sites.
Xiao-Hong, Li; Hong-Ling, Cui; Rui-Zhou, Zhang; Xian-Zhou, Zhang
2015-02-25
The vibrational frequencies of (E)-2-cyano-3-(3-hydroxyphenyl)acrylamide (HB-CA) in the ground state have been calculated using density functional method (B3LYP) with B3LYP/6-311++G(d,p) basis set. The analysis of natural bond orbital was also performed. The IR spectra were obtained and interpreted by means of potential energies distributions (PEDs) using MOLVIB program. In addition, the results show that there exists C-H⋯O hydrogen bond in the title compound, which is confirmed by the natural bond orbital analysis. The predicted NLO properties show that the title compound is a good candidate as nonlinear optical material. The analysis of frontier molecular orbitals shows that HB-CA has high excitation energies, good stability and high chemical hardness. The analysis of MEP map shows the negative and the positive potential sites.
Detecting true lies: police officers' ability to detect suspects' lies.
Mann, Samantha; Vrij, Aldert; Bull, Ray
2004-02-01
Ninety-nine police officers, not identified in previous research as belonging to groups that are superior in lie detection, attempted to detect truths and lies told by suspects during their videotaped police interviews. Accuracy rates were higher than those typically found in deception research and reached levels similar to those obtained by specialized lie detectors in previous research. Accuracy was positively correlated with perceived experience in interviewing suspects and with mentioning cues to detecting deceit that relate to a suspect's story. Accuracy was negatively correlated with popular stereotypical cues such as gaze aversion and fidgeting. As in previous research, accuracy and confidence were not significantly correlated, but the level of confidence was dependent on whether officers judged actual truths or actual lies and on the method by which confidence was measured.
Lying aversion and prosocial behaviour
Biziou-van-Pol, Laura; Novaro, Arianna; Liberman, Andrés Occhipinti; Capraro, Valerio
2015-01-01
The focus of this paper is the moral conflict between lying aversion and prosociality. What does telling a white lie signal about a person's prosocial tendencies? How does believing a possibly untruthful message signal about a listener's prosocial tendencies? To answer these questions, we conducted a 2x3 experiment. In the first stage we measured altruistic tendencies using a Dictator Game and cooperative tendencies using a Prisoner's dilemma. In the second stage, we used a sender-receiver game to measure aversion to telling a Pareto white lie (i.e., a lie that helps both the liar and the listener), aversion to telling an altruistic white lie (i.e., a lie that helps the listener at the expense of the liar), and skepticism towards believing a possibly untruthful message. We found three major results: (i) both altruism and cooperation are positively correlated with aversion to telling a Pareto white lie; (ii) neither altruism nor cooperation are significantly correlated with aversion to telling an altruistic wh...
Lies, Calculations and Constructions: Beyond How to Lie with Statistics
Best, Joel
2005-01-01
Darrell Huff’s How to Lie with Statistics remains the best-known, nontechnical call for critical thinking about statistics. However, drawing a distinction between statistics and lying ignores the process by which statistics are socially constructed. For instance, bad statistics often are disseminated by sincere, albeit innumerate advocates (e.g., inflated estimates for the number of anorexia deaths) or through research findings selectively highlighted to attract media coverage (e.g., a recent...
Mignolet, B.; Remacle, F.
2016-12-01
Fullerenes have a dense manifold of excited states composed of valence excited states and Rydberg states. Among Rydberg states, one distinguishes Super Atom Molecular Orbitals (SAMO), excited states in which an electron is promoted to a diffuse nanometer size molecular orbital with a hydrogenic-like character. Unlike typical Rydberg states, the electronic density of the SAMO states is mainly localized inside and in the close vicinity of the fullerene cage. In this proceeding, we propose a time-saving way to compute the electronic structure of the SAMO and Rydberg states of fullerenes at the TDDFT level by limiting the number of excitations allowed to build the excited states. We investigate the effect of limiting the number of excitations in C60 and compare it to the experimental binding energies. We also investigate the effect of the functional and basis set on the binding energies of the SAMO states.
Lombardi, James C
2015-01-01
In a previous investigation, the orbital radii of regular satellites of Uranus, Jupiter, Neptune, and Saturn are shown to be directly related to photon energies in the spectra of atomic and molecular hydrogen. To explain these observations a model was developed involving stimulated radiative molecular association (SRMA) reactions among photons and atoms in the protosatellite disks of the planets. In the present investigation, the previously developed model is applied to the planets and important satellites of the Sun. A key component of the model involves resonance associated with SRMA. Through this resonance, thermal energy is extracted from the protosun's protoplanetary disk at specific distances from the protosun wherever there is a match between the local thermal energy of the disk and the energy of photons impinging on the disk. Orbital radii of the planets and satellites are related to photon energies ($E_P$ values) in the spectrum of atomic hydrogen. An expression determined previously is used to relat...
分子轨道方法在有机反应机理中的应用%Application of Molecular Orbital Method to Organic Reaction Mechanisms
Institute of Scientific and Technical Information of China (English)
唐敏
2014-01-01
利用分子轨道理论直观解释了有机反应机理中所涉及到的立体化学、区域选择性以及对称性选择规律等有机化学中不易解释清楚的问题。相较于传统的“电子推动”方法，分子轨道方法更加直观，并能为有机反应机理的学习提供更深的理解。%The stereochemistry, regioselectivity and symmetry selectivity rules in organic reaction mechanisms, which are difficult to be explained clearly, are illustrated explicitly through molecular orbital theory. Compared to tra-ditional “electron pushing” method, molecular orbital method can give a visual interpretation and provide a better un-derstanding of organic reaction mechanisms.
Last Multipliers on Lie Algebroids
Indian Academy of Sciences (India)
Mircea Crasmareanu; Cristina-Elena Hreţcanu
2009-06-01
In this paper we extend the theory of last multipliers as solutions of the Liouville’s transport equation to Lie algebroids with their top exterior power as trivial line bundle (previously developed for vector fields and multivectors). We define the notion of exact section and the Liouville equation on Lie algebroids. The aim of the present work is to develop the theory of this extension from the tangent bundle algebroid to a general Lie algebroid (e.g. the set of sections with a prescribed last multiplier is still a Gerstenhaber subalgebra). We present some characterizations of this extension in terms of Witten and Marsden differentials.
McCourt, M.; Shibata, M.; McIver, J. W.; Rein, R.
1988-01-01
Recent discoveries have established the fact that RNA is capable of acting as an enzyme. In this study two different types of molecular orbital calculations, INDO and ab initio, were used in an attempt to assess the structural/functional role of the Mg2+ hydrated complex in ribozyme reactions. Preliminary studies indicate that the reaction is multistep and that the Mg2+ complex exerts a stabilizing effect on the intermediate or midpoint of the reaction.
Prabavathi, N; Senthil Nayaki, N; Venkatram Reddy, B
2015-02-05
Vibrational spectral analysis of the molecules 3,6-dichloro-4-methylpyridazine (DMP) and 3,6-dichloropyridazine-4-carboxylic acid (DPC) was carried out using FT-IR and FT-Raman spectroscopic techniques. The molecular structure and vibrational spectra of DMP and DPC were obtained by the density functional theory (DFT) method, using B3LYP functional, with 6-311++G(d,p) basis set. A detailed interpretation of the Infrared and Raman spectra of the two molecules were reported based on potential energy distribution (PED). The theoretically predicted FTIR and FT-Raman spectra of the titled molecules have been simulated and were compared with the experimental spectra. Determination of electric dipole moment (μ) and hyperpolarizability β0 helps to study the non-linear optical (NLO) behavior of DMP and DPC. Stability of the molecules arising from hyperconjugative interactions, charge delocalization have been analyzed using natural bond orbital (NBO) analysis. (13)C and (1)H NMR spectra were recorded and (13)C and (1)H NMR chemical shifts of the molecules were calculated using the gauge independent atomic orbital (GIAO) method. UV-visible spectrum of the compounds was also recorded in the region 200-1100 nm and electronic properties, HOMO (Highest Occupied Molecular Orbitals) and LUMO (Lowest Unoccupied Molecular Orbitals) energies were measured by time-dependent TD-DFT approach. Charge density distribution and site of chemical reactivity of the molecule have been studied by mapping electron density isosurface with molecular electrostatic potential (MESP). Copyright © 2014 Elsevier B.V. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Tachikawa, Masanori [Quantum Chemistry Division, Graduate School of NanoBioScience, Yokohama City University, 22-2 Seto, Kanazawa, Yokohama 236-0027 (Japan)
2015-12-31
To theoretically demonstrate the binding of a positron to small polarized molecules, we have calculated the vibrational averaged positron affinity (PA) values along the local vibrational contribution with the configuration interaction level of multi-component molecular orbital method. This method can take the electron-positron correlation contribution into account through single electronic - single positronic excitation configurations. The PA values are enhanced by including the local vibrational contribution from vertical PA values due to the anharmonicity of the potential.
Gravitating fluids with Lie symmetries
Msomi, A M; Maharaj, S D
2010-01-01
We analyse the underlying nonlinear partial differential equation which arises in the study of gravitating flat fluid plates of embedding class one. Our interest in this equation lies in discussing new solutions that can be found by means of Lie point symmetries. The method utilised reduces the partial differential equation to an ordinary differential equation according to the Lie symmetry admitted. We show that a class of solutions found previously can be characterised by a particular Lie generator. Several new families of solutions are found explicitly. In particular we find the relevant ordinary differential equation for all one-dimensional optimal subgroups; in several cases the ordinary differential equation can be solved in general. We are in a position to characterise particular solutions with a linear barotropic equation of state.
Historical Techniques of Lie Detection
Directory of Open Access Journals (Sweden)
Martina Vicianova
2015-08-01
Full Text Available Since time immemorial, lying has been a part of everyday life. For this reason, it has become a subject of interest in several disciplines, including psychology. The purpose of this article is to provide a general overview of the literature and thinking to date about the evolution of lie detection techniques. The first part explores ancient methods recorded circa 1000 B.C. (e.g., God’s judgment in Europe. The second part describes technical methods based on sciences such as phrenology, polygraph and graphology. This is followed by an outline of more modern-day approaches such as FACS (Facial Action Coding System, functional MRI, and Brain Fingerprinting. Finally, after the familiarization with the historical development of techniques for lie detection, we discuss the scope for new initiatives not only in the area of designing new methods, but also for the research into lie detection itself, such as its motives and regulatory issues related to deception.
Structure of Solvable Quadratic Lie Algebras
Institute of Scientific and Technical Information of China (English)
ZHU Lin-sheng
2005-01-01
@@ Killing form plays a key role in the theory of semisimple Lie algebras. It is natural to extend the study to Lie algebras with a nondegenerate symmetric invariant bilinear form. Such a Lie algebra is generally called a quadratic Lie algebra which occur naturally in physics[10,12,13]. Besides semisimple Lie algebras, interesting quadratic Lie algebras include the Kac-Moody algebras and the Extended Affine Lie algebras.
Lie bialgebras of generalized Witt type
Institute of Scientific and Technical Information of China (English)
SONG; Guang'ai; SU; Yucai
2006-01-01
In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are considered. It is proved that, for any Lie algebra W of generalized Witt type, all Lie bialgebras on W are the coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group H1(W, W (x) W) is trivial.
An evaluation on Real Semisimple Lie Algebras
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
@@ The theory of Lie groups and Lie algebras stem from that of continuous groups founded by Sophus Lie at the end of 19th century. From the beginning, the theory of Lie groups and Lie algebras has displayed great value in both theoretical researches and applications.
The History of the Molniya Orbit
Kettering Group
Arthur C. Clarke's name is often linked with the Geostationary orbit as a result of his 1945 paper in Wireless World. Less well-known is where the credit for discovering the Molniya orbit should lie. This paper presents the evidence uncovered to date concerning the original concept and provides some insight into the ways in which the orbit has subsequently been exploited.
Cohomology of Heisenberg Lie superalgebras
Bai, Wei; Liu, Wende
2017-02-01
Suppose the ground field to be algebraically closed and of characteristic different from 2 and 3. All Heisenberg Lie superalgebras consist of two super-versions of the Heisenberg Lie algebras, 𝔥2m,n and 𝔟𝔞n with m a non-negative integer and n a positive integer. The space of a "classical" Heisenberg Lie superalgebra 𝔥2m,n is the direct sum of a superspace with a non-degenerate anti-supersymmetric even bilinear form and a one-dimensional space of values of this form constituting the even center. The other super-analog of the Heisenberg Lie algebra, 𝔟𝔞n, is constructed by means of a non-degenerate anti-supersymmetric odd bilinear form with values in the one-dimensional odd center. In this paper, we study the cohomology of 𝔥2m,n and 𝔟𝔞n with coefficients in the trivial module by using the Hochschild-Serre spectral sequences relative to a suitable ideal. In the characteristic zero case, for any Heisenberg Lie superalgebra, we determine completely the Betti numbers and associative superalgebra structures for their cohomology. In the characteristic p > 3 case, we determine the associative superalgebra structure for the divided power cohomology of 𝔟𝔞n and we also make an attempt to determine the divided power cohomology of 𝔥2m,n by computing it in a low-dimensional case.
Langs, R
In this paper an attempt is made to conceptualize a basic dimension of various psychotherapeutic treatment modalities, especially psychoanalysis and psychoanalytically oriented psychotherapy. The central variable under consideration is the extent to which each endeavors to approach the truth within both patient and therapist as it exists dynamically in terms of their spiraling unconscious communicative interaction. That treatment modality which takes into account every possible dimension of such truths is termed truth therapy. Treatment modalities that make no attempt to arrive at these truths or that deliberately or inadvertently falsify their nature are termed lie or barrier therapies. Extensive consideration is given to truth therapy and the truth system on which it is based. The basis for the need for lie therapies is explored, and lie systems, which may arise from either patient or therapist, or both, are identified. A classification of common types of lie patients and lie therapists (and their main techniques) is offered. The implications of this delineation for our understanding of the dynamic therapies are discussed, and a number of new clinical issues arising from this perspective are addressed.
Finite dimensional quadratic Lie superalgebras
Jarvis, Peter; Yates, Luke
2010-01-01
We consider a special class of Z_2-graded, polynomial algebras of degree 2, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the generalised Jacobi relations in the context of the Koszul property, and give a proof of the PBW basis theorem. We give several concrete examples of quadratic Lie superalgebras for low dimensional cases, and discuss aspects of their structure constants for the `type I' class. Based on the factorisation of the enveloping algebra, we derive the Kac module construction for typical and atypical modules, and a related direct construction of irreducible modules due to Gould. We investigate the method for one specific case, the quadratic generalisation gl_2(n/1) of the Lie superalgebra sl(n/1). We formulate the general atypicality conditions at level 1, and present an analysis of zero-and one-step atypical modules for a certain family of Kac modules.
Indian Academy of Sciences (India)
Antonio J Calderón Martín
2009-04-01
We begin the study of arbitrary split Lie triple systems by focussing on those with a coherent 0-root space. We show that any such triple systems with a symmetric root system is of the form $T=\\mathcal{U}+\\sum_j I_j$ with $\\mathcal{U}$ a subspace of the 0-root space $T_0$ and any $I_j$ a well described ideal of , satisfying $[I_j,T,I_k]=0$ if $j≠ k$. Under certain conditions, it is shown that is the direct sum of the family of its minimal ideals, each one being a simple split Lie triple system, and the simplicity of is characterized. The key tool in this job is the notion of connection of roots in the framework of split Lie triple systems.
Loop Virasoro Lie conformal algebra
Energy Technology Data Exchange (ETDEWEB)
Wu, Henan, E-mail: wuhenanby@163.com; Chen, Qiufan; Yue, Xiaoqing [Department of Mathematics, Tongji University, Shanghai 200092 (China)
2014-01-15
The Lie conformal algebra of loop Virasoro algebra, denoted by CW, is introduced in this paper. Explicitly, CW is a Lie conformal algebra with C[∂]-basis (L{sub i} | i∈Z) and λ-brackets [L{sub i} {sub λ} L{sub j}] = (−∂−2λ)L{sub i+j}. Then conformal derivations of CW are determined. Finally, rank one conformal modules and Z-graded free intermediate series modules over CW are classified.
Ferenczy, György G
2013-04-05
The application of the local basis equation (Ferenczy and Adams, J. Chem. Phys. 2009, 130, 134108) in mixed quantum mechanics/molecular mechanics (QM/MM) and quantum mechanics/quantum mechanics (QM/QM) methods is investigated. This equation is suitable to derive local basis nonorthogonal orbitals that minimize the energy of the system and it exhibits good convergence properties in a self-consistent field solution. These features make the equation appropriate to be used in mixed QM/MM and QM/QM methods to optimize orbitals in the field of frozen localized orbitals connecting the subsystems. Calculations performed for several properties in divers systems show that the method is robust with various choices of the frozen orbitals and frontier atom properties. With appropriate basis set assignment, it gives results equivalent with those of a related approach [G. G. Ferenczy previous paper in this issue] using the Huzinaga equation. Thus, the local basis equation can be used in mixed QM/MM methods with small size quantum subsystems to calculate properties in good agreement with reference Hartree-Fock-Roothaan results. It is shown that bond charges are not necessary when the local basis equation is applied, although they are required for the self-consistent field solution of the Huzinaga equation based method. Conversely, the deformation of the wave-function near to the boundary is observed without bond charges and this has a significant effect on deprotonation energies but a less pronounced effect when the total charge of the system is conserved. The local basis equation can also be used to define a two layer quantum system with nonorthogonal localized orbitals surrounding the central delocalized quantum subsystem.
Ferenczy, György G
2013-04-05
Mixed quantum mechanics/quantum mechanics (QM/QM) and quantum mechanics/molecular mechanics (QM/MM) methods make computations feasible for extended chemical systems by separating them into subsystems that are treated at different level of sophistication. In many applications, the subsystems are covalently bound and the use of frozen localized orbitals at the boundary is a possible way to separate the subsystems and to ensure a sensible description of the electronic structure near to the boundary. A complication in these methods is that orthogonality between optimized and frozen orbitals has to be warranted and this is usually achieved by an explicit orthogonalization of the basis set to the frozen orbitals. An alternative to this approach is proposed by calculating the wave-function from the Huzinaga equation that guaranties orthogonality to the frozen orbitals without basis set orthogonalization. The theoretical background and the practical aspects of the application of the Huzinaga equation in mixed methods are discussed. Forces have been derived to perform geometry optimization with wave-functions from the Huzinaga equation. Various properties have been calculated by applying the Huzinaga equation for the central QM subsystem, representing the environment by point charges and using frozen strictly localized orbitals to connect the subsystems. It is shown that a two to three bond separation of the chemical or physical event from the frozen bonds allows a very good reproduction (typically around 1 kcal/mol) of standard Hartree-Fock-Roothaan results. The proposed scheme provides an appropriate framework for mixed QM/QM and QM/MM methods.
Cartan Connections and Lie Algebroids
Directory of Open Access Journals (Sweden)
Michael Crampin
2009-06-01
Full Text Available This paper is a study of the relationship between two constructions associated with Cartan geometries, both of which involve Lie algebroids: the Cartan algebroid, due to [Blaom A.D., Trans. Amer. Math. Soc. 358 (2006, 3651–3671], and tractor calculus [Cap A., Gover A.R., Trans. Amer. Math. Soc. 354 (2001, 1511–1548].
Cartan Connections and Lie Algebroids
Crampin, Michael
2009-01-01
This paper is a study of the relationship between two constructions associated with Cartan geometries, both of which involve Lie algebroids: the Cartan algebroid, due to [Blaom A.D., Trans. Amer. Math. Soc. 358 (2006), 3651-3671], and tractor calculus [Cap A., Gover A.R., Trans. Amer. Math. Soc. 354 (2001), 1511-1548].
String Topology for Lie Groups
DEFF Research Database (Denmark)
A. Hepworth, Richard
2010-01-01
In 1999 Chas and Sullivan showed that the homology of the free loop space of an oriented manifold admits the structure of a Batalin-Vilkovisky algebra. In this paper we give a direct description of this Batalin-Vilkovisky algebra in the case that the manifold is a compact Lie group G. Our answer ...
Danel, J-F; Kazandjian, L
2015-01-01
We test two isothermal-isobaric mixing rules, respectively based on excess-pressure and total-pressure equilibration, applied to the equation of state of a dense plasma. While the equation of state is generally known for pure species, that of arbitrary mixtures is not available so that the validation of accurate mixing rules, that implies resorting to first-principles simulations, is very useful. Here we consider the case of a plastic with composition C(2)H(3) and we implement two complementary ab initio approaches adapted to the dense plasma domain: quantum molecular dynamics, limited to low temperature by its computational cost, and orbital-free molecular dynamics, that can be implemented at high temperature. The temperature and density range considered is 1-10 eV and 0.6-10 g/cm(3) for quantum molecular dynamics, and 5-1000 eV and 1-10 g/cm(3) for orbital-free molecular dynamics. Simulations for the full C(2)H(3) mixture are the benchmark against which to assess the mixing rules, and both pressure and internal energy are compared. We find that the mixing rule based on excess-pressure equilibration is overall more accurate than that based on total-pressure equilibration; except for quantum molecular dynamics and a thermodynamic domain characterized by very low or negative excess pressures, it gives pressures which are generally within statistical error or within 1% of the exact ones. Besides, its superiority is amplified in the calculation of a principal Hugoniot.
Guseinov, I. I.
2005-01-01
Ozdogan (Int. J. Quantum Chem., 92 (2003) 419) published formulas for evaluating the multielectron multicenter molecular integrals over Slater-type orbitals (STOs). It is demonstrated that the formulas presented in this work are not original and they can easily be derived by means of a simple algebra from the relationship of our published papers (I.I.Guseinov, J.Mol.Struct.(Theochem), 417(1997)117; J.Mol.Struct.(Theochem), 593 (2002) 65; I.I.Guseinov,B.A.Mamedov,F.Oner,S.Huseyin, J.Mol.Struct...
Asada, Naoya; Fedorov, Dmitri G.; Kitaura, Kazuo; Nakanishi, Isao; Merz, Kenneth M.
2012-01-01
We propose an approach based on the overlapping multicenter ONIOM to evaluate intermolecular interaction energies in large systems and demonstrate its accuracy on several representative systems in the complete basis set limit at the MP2 and CCSD(T) level of theory. In the application to the intermolecular interaction energy between insulin dimer and 4′-hydroxyacetanilide at the MP2/CBS level, we use the fragment molecular orbital method for the calculation of the entire complex assigned to the lowest layer in three-layer ONIOM. The developed method is shown to be efficient and accurate in the evaluation of the protein-ligand interaction energies. PMID:23050059
Energy Technology Data Exchange (ETDEWEB)
Nakata, Hiroya, E-mail: nakata.h.ab@m.titech.ac.jp [Center for Biological Resources and Informatics, Tokyo Institute of Technology, B-62 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8501 (Japan); RIKEN, Research Cluster for Innovation, Nakamura Lab, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan); Fedorov, Dmitri G. [NRI, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568 (Japan); Yokojima, Satoshi [RIKEN, Research Cluster for Innovation, Nakamura Lab, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan); Tokyo University of Pharmacy and Life Sciences, 1423-1 Horinouchi, Hachioji-shi, Tokyo 192-0392 (Japan); Kitaura, Kazuo [Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501 (Japan); Sakurai, Minoru [Center for Biological Resources and Informatics, Tokyo Institute of Technology, B-62 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8501 (Japan); Nakamura, Shinichiro [RIKEN, Research Cluster for Innovation, Nakamura Lab, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan)
2014-04-14
We extended the fragment molecular orbital (FMO) method interfaced with density functional theory (DFT) into spin unrestricted formalism (UDFT) and developed energy gradients for the ground state and single point excited state energies based on time-dependent DFT. The accuracy of FMO is evaluated in comparison to the full calculations without fragmentation. Electronic excitations in solvated organic radicals and in the blue copper protein, plastocyanin (PDB code: 1BXV), are reported. The contributions of solvent molecules to the electronic excitations are analyzed in terms of the fragment polarization and quantum effects such as interfragment charge transfer.
Yamagishi, Kenji; Yamamoto, Keiko; Yamada, Sachiko; Tokiwa, Hiroaki
2006-03-01
Fragment molecular orbital-interfragment interaction energy calculations of the vitamin D receptor (VDR)/1α,25-dihydroxyvitamin D 3 complex were utilized to assign functions of key residues of the VDR. Only one residue forms a significant interaction with the corresponding hydroxy group of the ligand, although two residues are located around each hydroxy group. The degradation of binding affinity for derivatives upon removal of a hydroxy group is closely related to the trend in the strength of the hydrogen bonds. Type II hereditary rickets due to an Arg274 point mutation is caused by the lack of the strongest hydrogen bond.
Doi, Hideo; Okuwaki, Koji; Mochizuki, Yuji; Ozawa, Taku; Yasuoka, Kenji
2017-09-01
In dissipative particle dynamics (DPD) simulations, it is necessary to use the so-called χ parameter set that express the effective interactions between particles. Recently, we have developed a new scheme to evaluate the χ parameters in a non-empirical way through a series of fragment molecular orbital (FMO) calculations. As a challenging test, we have performed the DPD simulations using the FMO-based χ parameters for a mixture of 1-Palmitoyl-2-oleoyl phosphatidyl choline (POPC) and water. The structures of both membrane and vesicle were formed successfully. The calculated structural parameters of membrane were in good agreement with experimental results.
Electron-impact excitation of the low-lying electronic states of HCN
Chutjian, A.; Tanaka, H.; Srivastava, S. K.; Wicke, B. G.
1977-01-01
The first study of the low-energy electron-impact excitation of low-lying electronic transitions in the HCN molecule is reported. Measurements were made at incident electron energies of 11.6 and 21.6 eV in the energy-loss range of 3-10 eV, and at scattering angles of 20-130 deg. Inelastic scattering spectra were placed on the absolute cross-section scale by determining first the ratio of inelastic-to-elastic scattering cross sections, and then separately measuring the absolute elastic scattering cross section. Several new electronic transitions are observed which are intrinsically overlapped in the molecule itself. Assignments of these electronic transitions are suggested. These assignments are based on present spectroscopic and cross-sections measurements, high-energy electron scattering spectra, optical absorption spectra, and ab initio molecular orbital calculations.
The Demazure-Tits subgroup of a simple Lie group
Michel, L.; Patera, J.; Sharp, R. T.
1988-04-01
The Demazure-Tits subgroup of a simple Lie group G is the group of invariance of Clebsch-Gordan coefficients tables (assuming an appropriate choice of basis). The structure of the Demazure-Tits subgroups of An, Bn, Cn, Dn, and G2 is described. Orbits of the permutation action of the DT group in any irreducible finite-dimensional representation space of A2, C2, and G2 are decomposed into the sum of irreducible representations of the DT group.
Energy Technology Data Exchange (ETDEWEB)
Baldacchini, G.; Botti, S.; Grassano, U.M.; Luty, F.
1992-12-31
The spin-orbit parameter, spin-lattice relaxation time, and spin-mixing parameter of F/sub H/(OH/sup -/) and F/sub H/(CN/sup -/) centers in several alkali halides were studied with magnetic circular dichroism at about 2 K. A close comparison of the experimental results before and after optically induced association of the F center with the molecular ion was made. In crystals of NaCl structure, the negative spin-orbit parameter changes little between F and F/sub H/ centers in the same host. For CsCl and CsBr two values of spin-orbit parameter were derived for F/sub H/(CN/sup -/) centers with axes parallel or perpendicular to the magnetic field. In all studied systems, the spin-lattice relaxation time was already shorter before aggregation as compared with F centers in pure crystals, and became further shortened by the F/sub H/ center formation. The spin-mixing parameter decreased slightly for F/sub H/(OH/sup -/) as compared with F centers, while it increased drastically for F/sub H/(CN/sup -/) defects and reaches its maximum possible value, 0.5 in cesium halides. First attempts to interpret these magneto-optical results are presented in this paper.
Sato, Kota; Sugiyama, Yoko; Uchiyama, Akihiko; Iwabuchi, Susumu; Hirano, Tsuneo; Koinuma, Hideomi
1992-07-01
Successive hydrogen elimination reactions with low activation energies during the formation of a-Si:H by silane plasma chemical vapor deposition are proposed on the basis of an ab initio molecular-orbital method. The activation energy of the first step, the reaction of a dangling-bond site with an adjacent tetrahedrally coordinated silicon atom, was found to be 25.2 kcal/mol at 0 K when the zero-point vibrational energy was taken into account. The subsequent step was an exothermic process with a lower activation energy. The total process was thermodynamically much more favorable than the molecular processes by which a hydrogen atom or molecule is eliminated.
Kishi, Ryohei; Fujii, Hiroaki; Kishimoto, Shingo; Murata, Yusuke; Ito, Soichi; Okuno, Katsuki; Shigeta, Yasuteru; Nakano, Masayoshi
2012-05-03
We develop novel calculation and analysis methods for the dynamic first hyperpolarizabilities β [the second-order nonlinear optical (NLO) properties at the molecular level] in the second-harmonic generation based on the quantum master equation method combined with the ab initio molecular orbital (MO) configuration interaction method. As examples, we have evaluated off-resonant dynamic β values of donor (NH(2))- and/or acceptor (NO(2))-substituted benzenes using these methods, which are shown to reproduce those by the conventional summation-over-states method well. The spatial contributions of electrons to the dynamic β of these systems are also analyzed using the dynamic β density and its partition into the MO contributions. The present results demonstrate the advantage of these methods in unraveling the mechanism of dynamic NLO properties and in building the structure-dynamic NLO property relationships of real molecules.
Semiclassical states on Lie algebras
Energy Technology Data Exchange (ETDEWEB)
Tsobanjan, Artur, E-mail: artur.tsobanjan@gmail.com [King’s College, 133 North River Street, Kingston, Pennsylvania 18702 (United States)
2015-03-15
The effective technique for analyzing representation-independent features of quantum systems based on the semiclassical approximation (developed elsewhere) has been successfully used in the context of the canonical (Weyl) algebra of the basic quantum observables. Here, we perform the important step of extending this effective technique to the quantization of a more general class of finite-dimensional Lie algebras. The case of a Lie algebra with a single central element (the Casimir element) is treated in detail by considering semiclassical states on the corresponding universal enveloping algebra. Restriction to an irreducible representation is performed by “effectively” fixing the Casimir condition, following the methods previously used for constrained quantum systems. We explicitly determine the conditions under which this restriction can be consistently performed alongside the semiclassical truncation.
... hemolytic streptococci may also cause orbital cellulitis. Orbital cellulitis infections in children may get worse very quickly and ... in the space around the eye. An orbital cellulitis infection can get worse very quickly. A person with ...
Symmetry via Lie algebra cohomology
Eastwood, Michael
2010-01-01
The Killing operator on a Riemannian manifold is a linear differential operator on vector fields whose kernel provides the infinitesimal Riemannian symmetries. The Killing operator is best understood in terms of its prolongation, which entails some simple tensor identities. These simple identities can be viewed as arising from the identification of certain Lie algebra cohomologies. The point is that this case provides a model for more complicated operators similarly concerned with symmetry.
Can Lies Be Detected Unconsciously?
Directory of Open Access Journals (Sweden)
David eShanks
2015-08-01
Full Text Available People are typically poor at telling apart truthful and deceptive statements. Based on the Unconscious Thought Theory, it has been suggested that poor lie detection arises from the intrinsic limitations of conscious thinking and can be improved by facilitating the contribution of unconscious thought. In support of this hypothesis, Reinhard, Greifeneder, and Scharmach (2013 observed improved lie detection among participants engaging in unconscious thought. The present study aimed to replicate this unconscious thought advantage using a similar experimental procedure but with an important improvement in a key control condition. Specifically, participants judged the truthfulness of 8 video recordings in three thinking modes: immediately after watching them or after a period of unconscious or conscious deliberation. Results from two experiments (combined N = 226 failed to reveal a significant difference in lie detection accuracy between the thinking modes, even after efforts were made to facilitate the occurrence of an unconscious thought advantage in Experiment 2. The results imply that the unconscious thought advantage in deception detection is not a robust phenomenon.
Gwaltney, Steven R; Rosokha, Sergiy V; Head-Gordon, Martin; Kochi, Jay K
2003-03-19
The highly disparate rates of aromatic nitrosation and nitration, despite the very similar (electrophilic) properties of the active species: NO(+) and NO(2)(+) in Chart 1, are quantitatively reconciled. First, the thorough mappings of the potential-energy surfaces by high level (ab initio) molecular-orbital methodologies involving extensive coupled-cluster CCSD(T)/6-31G optimizations establish the intervention of two reactive intermediates in nitration (Figure 8) but only one in nitrosation (Figure 7). Second, the same distinctive topologies involving double and single potential-energy minima (Figures 6 and 5) also emerge from the semiquantitative application of the Marcus-Hush theory to the transient spectral data. Such a striking convergence from quite different theoretical approaches indicates that the molecular-orbital and Marcus-Hush (potential-energy) surfaces are conceptually interchangeable. In the resultant charge-transfer mechanism, the bimolecular interactions of arene donors with both NO(+) and NO(2)(+) spontaneously lead (barrierless) to pi-complexes in which electron transfer is concurrent with complexation. Such a pi-complex in nitration is rapidly converted to the sigma-complex, whereas this Wheland adduct in nitrosation merely represents a high energy (transition-state) structure. Marcus-Hush analysis thus demonstrates how the strongly differentiated (arene) reactivities toward NO(+) and NO(2)(+) can actually be exploited in the quantitative development of a single coherent (electron-transfer) mechanism for both aromatic nitrosation and nitration.
Particle-like structure of Lie algebras
Vinogradov, A. M.
2017-07-01
If a Lie algebra structure 𝔤 on a vector space is the sum of a family of mutually compatible Lie algebra structures 𝔤i's, we say that 𝔤 is simply assembled from the 𝔤i's. Repeating this procedure with a number of Lie algebras, themselves simply assembled from the 𝔤i's, one obtains a Lie algebra assembled in two steps from 𝔤i's, and so on. We describe the process of modular disassembling of a Lie algebra into a unimodular and a non-unimodular part. We then study two inverse questions: which Lie algebras can be assembled from a given family of Lie algebras, and from which Lie algebras can a given Lie algebra be assembled. We develop some basic assembling and disassembling techniques that constitute the elements of a new approach to the general theory of Lie algebras. The main result of our theory is that any finite-dimensional Lie algebra over an algebraically closed field of characteristic zero or over R can be assembled in a finite number of steps from two elementary constituents, which we call dyons and triadons. Up to an abelian summand, a dyon is a Lie algebra structure isomorphic to the non-abelian 2-dimensional Lie algebra, while a triadon is isomorphic to the 3-dimensional Heisenberg Lie algebra. As an example, we describe constructions of classical Lie algebras from triadons.
What Lies Below a Martian Ice Cap
2008-01-01
for the north polar layered deposits. BU stands for basal unit, an ice-sand deposit that lies beneath parts of the north polar layered deposits. The Shallow Radar instrument was provided by the Italian Space Agency. Its operations are led by the University of Rome and its data are analyzed by a joint U.S.-Italian science team. JPL, a division of the California Institute of Technology, Pasadena, manages the Mars Reconnaissance Orbiter for the NASA Science Mission Directorate, Washington.
Huang, Y R; Knippenberg, S; Hajgató, B; François, J-P; Deng, J K; Deleuze, M S
2007-07-05
The main purpose of the present work is to predict from benchmark many-body quantum mechanical calculations the results of experimental studies of the valence electronic structure of dimethoxymethane employing electron momentum spectroscopy, and to establish once and for all the guidelines that should systematically be followed in order to reliably interpret the results of such experiments on conformationally versatile molecules. In a first step, accurate calculations of the energy differences between stationary points on the potential energy surface of this molecule are performed using Hartree-Fock (HF) theory and post-HF treatments of improving quality (MP2, MP3, CCSD, CCSD(T), along with basis sets of increasing size. This study focuses on the four conformers of this molecule, namely the trans-trans (TT), trans-gauche (TG), gauche-gauche (G+G+), and gauche-gauche (G+G-) structures, belonging to the C2v, C1, C2, and Cs symmetry point groups, respectively. A focal point analysis supplemented by suited extrapolations to the limit of asymptotically complete basis sets is carried out to determine how the conformational energy differences at 0 K approach the full CI limit. In a second step, statistical thermodynamics accounting for hindered rotations is used to calculate Gibbs free energy corrections to the above energy differences, and to evaluate the abundance of each conformer in the gas phase. It is found that, at room temperature, the G+G+ species accounts for 96% of the conformational mixture characterizing dimethoxymethane. In a third step, the valence one-electron and shake-up ionization spectrum of dimethoxymethane is analyzed according to calculations on the G+G+ conformer alone by means of one-particle Green's function [1p-GF] theory along with the benchmark third-order algebraic diagrammatic construction [ADC(3)] scheme. A complete breakdown of the orbital picture of ionization is noted at electron binding energies above 22 eV. A comparison with available
Local orbitals by minimizing powers of the orbital variance
DEFF Research Database (Denmark)
Jansik, Branislav; Høst, Stinne; Kristensen, Kasper;
2011-01-01
It is demonstrated that a set of local orthonormal Hartree–Fock (HF) molecular orbitals can be obtained for both the occupied and virtual orbital spaces by minimizing powers of the orbital variance using the trust-region algorithm. For a power exponent equal to one, the Boys localization function...... is obtained. For increasing power exponents, the penalty for delocalized orbitals is increased and smaller maximum orbital spreads are encountered. Calculations on superbenzene, C60, and a fragment of the titin protein show that for a power exponent equal to one, delocalized outlier orbitals may...
Filiform Lie algebras of order 3
Navarro, R. M.
2014-04-01
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, "Cohomologie des algèbres de Lie nilpotentes. Application à l'étude de la variété des algèbres de Lie nilpotentes," Bull. Soc. Math. France 98, 81-116 (1970)]. Also we give the dimension, using an adaptation of the {sl}(2,{C})-module Method, and a basis of such infinitesimal deformations in some generic cases.
Ultrafast Molecular Imaging by Laser Induced Electron Diffraction
Peters, Michel; Cornaggia, Christian; Saugout, Sébastien; Charron, Eric; Keller, Arne; Atabek, Osman
2010-01-01
We address the feasibility of imaging geometric and orbital structure of a polyatomic molecule on an attosecond time-scale using the Laser Induced Electron Diffraction, LIED, technique [T. Zuo \\textit{et al.}, Chem. Phys. Lett. \\textbf{259}, 313 (1996)]. We present numerical results obtained for the CO$_2$ molecule using a single active electron model. The molecular geometry (bond-lengths) is determined within 3% of accuracy from a diffraction pattern which also reflects the nodal properties of the initial molecular orbital. Robustness of the structure determination is discussed with respect to vibrational and rotational motions with a complete interpretation of the laser-induced mechanisms.
Transformation groups and Lie algebras
Ibragimov, Nail H
2013-01-01
This book is based on the extensive experience of teaching for mathematics, physics and engineering students in Russia, USA, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics. The methods of local Lie groups discussed in the book provide universal and effective method for solving nonlinear differential equations analytically. Introduction to approximate transformation groups also contained in the book helps to develop skills in constructing approximate solutions for differential equations with a small parameter.
Kauffmann, Jens; Zhang, Qizhou; Menten, Karl M; Goldsmith, Paul F; Lu, Xing; Guzmán, Andrés E; Schmiedeke, Anika
2016-01-01
We present the first systematic study of the density structure of clouds found in a complete sample covering all major molecular clouds in the Central Molecular Zone (CMZ; inner $\\sim{}200~\\rm{}pc$) of the Milky Way. This is made possible by using data from the Galactic Center Molecular Cloud Survey (GCMS), the first study resolving all major molecular clouds in the CMZ at interferometer angular resolution. We find that many CMZ molecular clouds have unusually shallow density gradients compared to regions elsewhere in the Milky Way. This is possibly a consequence of weak gravitational binding of the clouds. The resulting relative absence of dense gas on spatial scales $\\sim{}0.1~\\rm{}pc$ is probably one of the reasons why star formation (SF) in dense gas of the CMZ is suppressed by a factor $\\sim{}10$, compared to solar neighborhood clouds. Another factor suppressing star formation are the high SF density thresholds that likely result from the observed gas kinematics. Further, it is possible but not certain t...
Directory of Open Access Journals (Sweden)
Anatoliy Klimyk
2007-02-01
Full Text Available In the paper, properties of antisymmetric orbit functions are reviewed and further developed. Antisymmetric orbit functions on the Euclidean space $E_n$ are antisymmetrized exponential functions. Antisymmetrization is fulfilled by a Weyl group, corresponding to a Coxeter-Dynkin diagram. Properties of such functions are described. These functions are closely related to irreducible characters of a compact semisimple Lie group $G$ of rank $n$. Up to a sign, values of antisymmetric orbit functions are repeated on copies of the fundamental domain $F$ of the affine Weyl group (determined by the initial Weyl group in the entire Euclidean space $E_n$. Antisymmetric orbit functions are solutions of the corresponding Laplace equation in $E_n$, vanishing on the boundary of the fundamental domain $F$. Antisymmetric orbit functions determine a so-called antisymmetrized Fourier transform which is closely related to expansions of central functions in characters of irreducible representations of the group $G$. They also determine a transform on a finite set of points of $F$ (the discrete antisymmetric orbit function transform. Symmetric and antisymmetric multivariate exponential, sine and cosine discrete transforms are given.
Bauschlicher, C. W., Jr.; Silver, D. M.; Yarkony, D. R.
1980-01-01
The paper presents the multiconfiguration-self-consistent (MCSCF) and configuration state functions (CSF) for the low-lying electronic states of MgO. It was shown that simple description of these states was possible provided the 1 Sigma(+) states are individually optimized at the MCSCF level, noting that the 1(3 Sigma)(+) and 2(1 Sigma)(+) states which nominally result from the same electron occupation are separated energetically. The molecular orbitals obtained at this level of approximation should provide a useful starting point for extended configuration interaction calculations since they have been optimized for the particular states of interest.
Bauschlicher, C. W., Jr.; Silver, D. M.; Yarkony, D. R.
1980-01-01
The paper presents the multiconfiguration-self-consistent (MCSCF) and configuration state functions (CSF) for the low-lying electronic states of MgO. It was shown that simple description of these states was possible provided the 1 Sigma(+) states are individually optimized at the MCSCF level, noting that the 1(3 Sigma)(+) and 2(1 Sigma)(+) states which nominally result from the same electron occupation are separated energetically. The molecular orbitals obtained at this level of approximation should provide a useful starting point for extended configuration interaction calculations since they have been optimized for the particular states of interest.
Suresh, S; Gunasekaran, S; Srinivasan, S
2015-03-05
The solid phase FT-IR and FT-Raman spectra of 4-Hydroxy-2-methyl-N-(2-pyridinyl)-2H-1,2-benzothiazine-3-carboxamide-1,1-dioxide (Piroxicam) have been recorded in the region 4000-400 and 4000-100cm(-1) respectively. The molecular geometry, harmonic vibrational frequencies and bonding features of piroxicam in the ground state have been calculated by Hartree-Fock (HF) and density functional theory (DFT) methods using 6-311++G(d,p) basis set. The calculated harmonic vibrational frequencies are scaled and they are compared with experimental obtained by FT-IR and FT-Raman spectra. A detailed interpretation of the vibrational spectra of the title compound has been made on the basis of the calculated potential energy distribution (PED). The electronic properties, such as HOMO and LUMO energies, molecular electrostatic potential (MESP) are also performed. The linear polarizability (α) and the first order hyper polarizability (β) values of the title compound have been computed. The molecular stability arising from hyper conjugative interaction, charge delocalization has been analyzed using natural bond orbital (NBO) analysis.
Suresh, S.; Gunasekaran, S.; Srinivasan, S.
2015-03-01
The solid phase FT-IR and FT-Raman spectra of 4-Hydroxy-2-methyl-N-(2-pyridinyl)-2H-1,2-benzothiazine-3-carboxamide-1,1-dioxide (Piroxicam) have been recorded in the region 4000-400 and 4000-100 cm-1 respectively. The molecular geometry, harmonic vibrational frequencies and bonding features of piroxicam in the ground state have been calculated by Hartree-Fock (HF) and density functional theory (DFT) methods using 6-311++G(d,p) basis set. The calculated harmonic vibrational frequencies are scaled and they are compared with experimental obtained by FT-IR and FT-Raman spectra. A detailed interpretation of the vibrational spectra of the title compound has been made on the basis of the calculated potential energy distribution (PED). The electronic properties, such as HOMO and LUMO energies, molecular electrostatic potential (MESP) are also performed. The linear polarizability (α) and the first order hyper polarizability (β) values of the title compound have been computed. The molecular stability arising from hyper conjugative interaction, charge delocalization has been analyzed using natural bond orbital (NBO) analysis.
James, C.; Pettit, G. R.; Nielsen, O. F.; Jayakumar, V. S.; Joe, I. Hubert
2008-10-01
The NIR-FT Raman and FT-IR spectral studies of the novel antineoplastic and antiangiogenesis substance comprestatin A-4 prodrug (CA4P) were carried out. The equilibrium geometry, various bonding features and harmonic vibrational frequencies of CA4P have been investigated with the help of B3LYP density functional theory (DFT) method. The most preferred cis-configuration for its bioactivity has been demonstrated on the basis of torsional potential energy surface (PES) scan studies. Stability of the molecule arising from hyperconjugative interactions leading to its bioactivity, charge delocalization and mesomeric effects have been analyzed using natural bond orbital (NBO) analysis. Detailed assignments of the vibrational spectra have been made with the aid of theoretically predicted vibrational frequencies. The optimized geometry shows near-planarity of phenyl rings and perpendicular conformation of meta substituted methoxy group. The vibrational analysis confirms the differently acting ring modes, steric repulsion, π conjugation and back-donation.
Schipper, P. R. T.; Gritsenko, O. V.; van Gisbergen, S. J. A.; Baerends, E. J.
2000-01-01
An approximate Kohn-Sham exchange-correlation potential νxcSAOP is developed with the method of statistical averaging of (model) orbital potentials (SAOP) and is applied to the calculation of excitation energies as well as of static and frequency-dependent multipole polarizabilities and hyperpolarizabilities within time-dependent density functional theory (TDDFT). νxcSAOP provides high quality results for all calculated response properties and a substantial improvement upon the local density approximation (LDA) and the van Leeuwen-Baerends (LB) potentials for the prototype molecules CO, N2, CH2O, and C2H4. For the first three molecules and the lower excitations of the C2H4 the average error of the vertical excitation energies calculated with νxcSAOP approaches the benchmark accuracy of 0.1 eV for the electronic spectra.
Yamazaki, Masakazu; Oishi, Keiya; Nakazawa, Hiroyuki; Zhu, Chaoyuan; Takahashi, Masahiko
2015-03-13
We report a time-resolved (e, 2e) experiment on the deuterated acetone molecule in the S2 Rydberg state with a lifetime of 13.5 ps. The acetone S2 state was prepared by a 195 nm pump laser and probed with electron momentum spectroscopy using a 1.2 keV incident electron beam of 1 ps temporal width. In spite of the low data statistics as well as of the limited time resolution (±35 ps) due to velocity mismatch, the experimental results clearly demonstrate that electron momentum spectroscopy measurements of short-lived transient species are feasible, opening the door to time-resolved orbital imaging in momentum space.
A well-scaling natural orbital theory.
Gebauer, Ralph; Cohen, Morrel H; Car, Roberto
2016-11-15
We introduce an energy functional for ground-state electronic structure calculations. Its variables are the natural spin-orbitals of singlet many-body wave functions and their joint occupation probabilities deriving from controlled approximations to the two-particle density matrix that yield algebraic scaling in general, and Hartree-Fock scaling in its seniority-zero version. Results from the latter version for small molecular systems are compared with those of highly accurate quantum-chemical computations. The energies lie above full configuration interaction calculations, close to doubly occupied configuration interaction calculations. Their accuracy is considerably greater than that obtained from current density-functional theory approximations and from current functionals of the one-particle density matrix.
A well-scaling natural orbital theory
Gebauer, Ralph; Car, Roberto
2016-01-01
We introduce an energy functional for ground-state electronic structure calculations. Its variables are the natural spin-orbitals of singlet many-body wave functions and their joint occupation probabilities deriving from controlled approximations to the two-particle density matrix that yield algebraic scaling in general, and Hartree-Fock scaling in its seniority-zero version. Results from the latter version for small molecular systems are compared with those of highly accurate quantum-chemical computations. The energies lie above full configuration interaction calculations, close to doubly occupied configuration interaction calculations. Their accuracy is considerably greater than that obtained from current density-functional theory approximations and from current functionals of the one-particle density matrix.
Bultinck, Patrick; Van Neck, Dimitri; Acke, Guillaume; Ayers, Paul W
2012-02-21
The Fukui function is considered as the diagonal element of the Fukui matrix in position space, where the Fukui matrix is the derivative of the one particle density matrix (1DM) with respect to the number of electrons. Diagonalization of the Fukui matrix, expressed in an orthogonal orbital basis, explains why regions in space with negative Fukui functions exist. Using a test set of molecules, electron correlation is found to have a remarkable effect on the eigenvalues of the Fukui matrix. The Fukui matrices at the independent electron model level are mathematically proven to always have an eigenvalue equal to exactly unity while the rest of the eigenvalues possibly differ from zero but sum to zero. The loss of idempotency of the 1DM at correlated levels of theory causes the loss of these properties. The influence of electron correlation is examined in detail and the frontier molecular orbital concept is extended to correlated levels of theory by defining it as the eigenvector of the Fukui matrix with the largest eigenvalue. The effect of degeneracy on the Fukui matrix is examined in detail, revealing that this is another way by which the unity eigenvalue and perfect pairing of eigenvalues can disappear.
Sebastian, S.; Sylvestre, S.; Jayarajan, D.; Amalanathan, M.; Oudayakumar, K.; Gnanapoongothai, T.; Jayavarthanan, T.
2013-01-01
In this work, we report harmonic vibrational frequencies, molecular structure, NBO and HOMO, LUMO analysis of Umbelliferone also known as 7-hydroxycoumarin (7HC). The optimized geometric bond lengths and bond angles obtained by computation (monomer and dimmer) shows good agreement with experimental XRD data. Harmonic frequencies of 7HC were determined and analyzed by DFT utilizing 6-311+G(d,p) as basis set. The assignments of the vibrational spectra have been carried out with the help of Normal Coordinate Analysis (NCA) following the Scaled Quantum Mechanical Force Field Methodology (SQMFF). The change in electron density (ED) in the σ* and π* antibonding orbitals and stabilization energies E(2) have been calculated by Natural Bond Orbital (NBO) analysis to give clear evidence of stabilization originating in the hyperconjugation of hydrogen-bonded interaction. The energy and oscillator strength calculated by Time-Dependent Density Functional Theory (TD-DFT) complements with the experimental findings. The simulated spectra satisfactorily coincides with the experimental spectra. Microbial activity of studied compounds was tested against Staphylococcus aureus, Streptococcus pyogenes, Bacillus subtilis, Escherichia coli, Psuedomonas aeruginosa, Klebsiella pneumoniae, Proteus mirabilis, Shigella flexneri, Salmonella typhi and Enterococcus faecalis.
Directory of Open Access Journals (Sweden)
del Rio B. G.
2017-01-01
Full Text Available We report results of an orbital-free ab initio molecular dynamics (OF-AIMD study of the free liquid surface (FLS of Sn at 1000 K and 600 K. A key ingredient in the OF-AIMD method is the local pseudopotential describing the ions-valence electrons interaction. We have used a force-matching method to derive a local pseudopotential suitable to account for the variation of the forces from the bulk to the FLS. We obtain very good results for structural properties, such as the reflectivity, including the characteristic shoulder it presents in x-ray experiments. Moreover we have been able to study ab initio for the first time the evolution in some dynamical properties as we move from the central region, where the system behaves like the bulk liquid, to the FLS.
del Rio, B. G.; González, L. E.
2017-08-01
We report results of an orbital-free ab initio molecular dynamics (OF-AIMD) study of the free liquid surface (FLS) of Sn at 1000 K and 600 K. A key ingredient in the OF-AIMD method is the local pseudopotential describing the ions-valence electrons interaction. We have used a force-matching method to derive a local pseudopotential suitable to account for the variation of the forces from the bulk to the FLS. We obtain very good results for structural properties, such as the reflectivity, including the characteristic shoulder it presents in x-ray experiments. Moreover we have been able to study ab initio for the first time the evolution in some dynamical properties as we move from the central region, where the system behaves like the bulk liquid, to the FLS.
Sure, Rebecca; Brandenburg, Jan Gerit; Grimme, Stefan
2016-04-01
In quantum chemical computations the combination of Hartree-Fock or a density functional theory (DFT) approximation with relatively small atomic orbital basis sets of double-zeta quality is still widely used, for example, in the popular B3LYP/6-31G* approach. In this Review, we critically analyze the two main sources of error in such computations, that is, the basis set superposition error on the one hand and the missing London dispersion interactions on the other. We review various strategies to correct those errors and present exemplary calculations on mainly noncovalently bound systems of widely varying size. Energies and geometries of small dimers, large supramolecular complexes, and molecular crystals are covered. We conclude that it is not justified to rely on fortunate error compensation, as the main inconsistencies can be cured by modern correction schemes which clearly outperform the plain mean-field methods.
Hofto, Laura; Hofto, Meghan; Cross, Jessica; Cafiero, Mauricio
2007-09-01
Many diseases can be traced to point mutations in the DNA coding for specific enzymes. These point mutations result in the change of one amino acid residue in the enzyme. We have developed a model using simple molecular orbital calculations which can be used to quantitatively determine the change in interaction between the enzyme's active site and necessary ligands upon mutation. We have applied this model to three hydroxylase proteins: phenylalanine hydroxylase, tyrosine hydroxylase, and tryptophan hydroxylase, and we have obtained excellent correlation between our results and observed disease symptoms. Furthermore, we are able to use this agreement as a baseline to screen other mutations which may also cause onset of disease symptoms. Our focus is on systems where the binding is due largely to dispersion, which is much more difficult to model inexpensively than pure electrostatic interactions. Our calculations are run in parallel on a sixteen processor cluster of 64-bit Athlon processors.
Wang, Jianji; Wu, Yanping; Xuan, Xiaopeng; Wang, Hanqing
2002-08-01
FTIR spectra have been recorded and analyzed for solutions of lithium perchlorate in propylene carbonate (PC), diethyl carbonate (DEC), and PC + DEC mixtures. It has been shown that the carbonyl stretch bands for PC and DEC are very sensitive to the interaction between Li+ and the solvent molecules. They split with addition of LiClO4, indicating a strong interaction of Li+ with PC and DEC through the oxygen group of PC and both oxygen and ether oxygen atoms of DEC. In conjunction with molecular orbital calculation, the optimized geometries of solvation are given. In addition, solvent separated ion pairs and contact ion pairs were observed in LiClO4/DEC solutions, and no preferential solvation of Li+ in LiClO4/PC + DEC solutions were detected.
DERIVATIONS AND EXTENSIONS OF LIE COLOR ALGEBRA
Institute of Scientific and Technical Information of China (English)
Zhang Qingcheng; Zhang Yongzheng
2008-01-01
In this article, the authors obtain some results concerning derivations of fi-nitely generated Lie color algebras and discuss the relation between skew derivation space SkDer(L) and central extension H2(L, F) on some Lie color algebras. Meanwhile, they generalize the notion of double extension to quadratic Lie color algebras, a sufficient con-dition for a quadratic Lie color algebra to be a double extension and further properties are given.
Infinite-dimensional Hamiltonian Lie superalgebras
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The natural filtration of the infinite-dimensional Hamiltonian Lie superalgebra over a field of positive characteristic is proved to be invariant under automorphisms by characterizing ad-nilpotent elements.We are thereby able to obtain an intrinsic characterization of the Hamiltonian Lie superalgebra and establish a property of the automorphisms of the Lie superalgebra.
SOME RESULTS OF MODULAR LIE SUPERALGEBRAS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In the present article, the authors give some properties on subinvariant subalgebras of modular Lie superalgebras and obtain the derivation tower theorem of modular Lie superalgebras, which is analogous to the automorphism tower theorem of finite groups.Moreover, they announce and prove some results of modular complete Lie superalgebras.
Emergence of Lying in Very Young Children
Evans, Angela D.; Lee, Kang
2013-01-01
Lying is a pervasive human behavior. Evidence to date suggests that from the age of 42 months onward, children become increasingly capable of telling lies in various social situations. However, there is limited experimental evidence regarding whether very young children will tell lies spontaneously. The present study investigated the emergence of…
A Kind of Braided-Lie Structures
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
@@ We introduce a family of braidedLie algebras.They are Lie algebras in the unifying YetterDrinfeldLong module categoryJJMQQ where J and Q are Hopf algebras.We study their structure and the braidedLie structure of an algebra A in JJM QQ.
Probability on real Lie algebras
Franz, Uwe
2016-01-01
This monograph is a progressive introduction to non-commutativity in probability theory, summarizing and synthesizing recent results about classical and quantum stochastic processes on Lie algebras. In the early chapters, focus is placed on concrete examples of the links between algebraic relations and the moments of probability distributions. The subsequent chapters are more advanced and deal with Wigner densities for non-commutative couples of random variables, non-commutative stochastic processes with independent increments (quantum Lévy processes), and the quantum Malliavin calculus. This book will appeal to advanced undergraduate and graduate students interested in the relations between algebra, probability, and quantum theory. It also addresses a more advanced audience by covering other topics related to non-commutativity in stochastic calculus, Lévy processes, and the Malliavin calculus.
Patrick, E. L.; Earle, G. D.; Kasprzak, W. T.; Mahaffy, Paul R.
2008-01-01
From commercial origins as a molybdenum molecular beam nozzle, a ceramic nozzle of silicon carbide (SiC) was developed for space environment simulation. The nozzle is mechanically stable under extreme conditions of temperature and pressure. A heated, continuous, supersonically-expanded hydrogen beam with a 1% argon seed produced an argon beam component of nearly 4 km/s, with an argon flux exceeding 1x1014 /cm2.s. This nozzle was part of a molecular beam machine used in the Atmospheric Experiments Branch at NASA Goddard Space Flight Center to characterize the performance of the University of Texas at Dallas Ram Wind Sensor (RWS) aboard the Air Force Communications/Navigation Outage Forecasting System (C/NOFS) launched in the Spring of 2008.
Energy Technology Data Exchange (ETDEWEB)
Vavere, A.
1979-01-01
Rates of ammonia decomposition on (110), (100), and (111) single crystal faces of rhodium were measured at 580 to 725/sup 0/K and 10/sup -3/ to 500 x 10/sup -3/ torr. The decomposition rates were proportional to P/sub NH/sub 3//sup/1/2/ and P/sub NH/sub 3// at low and high hydrogen pressures, respectively. The H/sub 2/ kinetic order varied from 0 (low P/sub H/sub 2//) to -1.0 (high P/sub H/). The rate was independent of N/sub 2/ pressure. NH/sub 3/ decomposes about 1.5 times faster than ND/sub 3/ on the (110) and (111) faces. Rates on the (110) surface are over 10 times as rapid as on the (111). LEED, Auger, and flash desorption experiments indicated that boron was a significant surface poison and that the Rh(110) surface was essentially nitrogen-free. A rate expression is derived from a model involving surface species Rh/sub 2/NH, RhH, and RhN on a nearly bare RH surface. The rate limiting process involves the concurrent dehydrogenation of Rh/sub 2/NH and desorption of N/sub 2/. A decreasing NH/sub 3/ order (< 1/2) at high P/sub NH/sub 3// and low T is due to buildup of surface intermediates. The relative bonding energies of hydrogen and nitrogen chemisorbed at three sites on a W(111) surface were obtained via the extended Hueckel molecular orbital theory. The preferred site for both H and N chemisorption was determined as the TOP position, i.e., a single coordination site on top of a protruding W atom. The W(111) surface was simulated by truncated arrays of seven tungsten atoms. The basis set for the calculations included the tungsten valence orbitals plus the filled 5p orbitals needed for repulsion at small internuclear distances. N adsorption in the three-fold holes available on the W(111) lattices used disrupted the W--W bonds sufficiently to cause the overall bond energy to be less than for the single coordination site. The dissymmetry between the three-fold lattices and the four-fold W d orbitals may also be a contributing factor.
Orbital interactions in chemistry
Albright, Thomas A; Whangbo, Myung-Hwan
2013-01-01
Explains the underlying structure that unites all disciplines in chemistry Now in its second edition, this book explores organic, organometallic, inorganic, solid state, and materials chemistry, demonstrating how common molecular orbital situations arise throughout the whole chemical spectrum. The authors explore the relationships that enable readers to grasp the theory that underlies and connects traditional fields of study within chemistry, thereby providing a conceptual framework with which to think about chemical structure and reactivity problems. Orbital Interactions
Institute of Scientific and Technical Information of China (English)
张志坚; 邝代治; 张复兴; 蒋伍玖; 庾江喜; 朱小明
2014-01-01
A Manganese (II) coordination polymer [Mn(μ2-η2-bp3dc)(H2O)2]n (bp3dc = 2,20-bipyridine-3, 30-dicarboxylate) has been synthesized and characterized by elemental analyses, IR and X-ray diffraction. Crystal data for this complex:monoclinic system, space group C2/c , with a=1.1648(2) nm,b=0.80422(15) nm,c=1.2949(3) nm,β=100.117(10)°,V=1.1941 (4) nm3,Z=4,Dc=1.853 g/cm3,µ(MoKα)=1.138 cm-1, F(000)=676,R1=0.0317, wR2=0.0733 [I>2σ(I) observed reflections] and R1=0.0246 , wR2=0.0703 (all reflections). A total of 3893 reflections collected, 1390 were unique and 1354 observed [I>2σ(I)] ones were used in the succeeding refinement. The asymmetric unit of the title polymer, [Mn(μ2-η2-bp3dc)(H2O)2]n, consists of an Mn(II) ion, which lies on a twofold axis, one half of a 2,20-bipyridine-3,30-dicarboxylate dianion and acoordinated water molecule. The one-dimensional chains extend into two-dimensional sheets via O-H…O hydrogen-bonding interactions. The crystal packing of the two-dimensional sheets appears to be dominated by aromatic π-πinteractions. The molecular structure adopts a distorted octahedral geometry around the Mn(II) atom. In order to explore the bonding characteristics of the complex, the molecular orbitals were investigated systematically. The sum of the square of atomic orbital coefficient was used to represent the contribution of each type of atom to molecular orbital and normalized. The atoms of the complex were divided into six groups(C atoms, carboxyl O atoms, water molecule O atoms, Mn atoms, N atoms, H atoms), and quantum chemistry calculation of the compound was performed with Gaussian98W program at B3LYP/LANL2DZ level. The calculation covered 31 atoms, 222 basis functions, 593 primitive gaussians, 80 electrons. In general. the stability of the structural unit is closely related to the total energy of the system and the frontier orbital energy. As for this compound, the total molecular energy is 1127.5481531 a.u., the energies of HOMO and LUMO are
Lie Algebraic Treatment of Linear and Nonlinear Beam Dynamics
Energy Technology Data Exchange (ETDEWEB)
Alex J. Dragt; Filippo Neri; Govindan Rangarajan; David Douglas; Liam M. Healy; Robert D. Ryne
1988-12-01
The purpose of this paper is to present a summary of new methods, employing Lie algebraic tools, for characterizing beam dynamics in charged-particle optical systems. These methods are applicable to accelerator design, charged-particle beam transport, electron microscopes, and also light optics. The new methods represent the action of each separate element of a compound optical system, including all departures from paraxial optics, by a certain operator. The operators for the various elements can then be concatenated, following well-defined rules, to obtain a resultant operator that characterizes the entire system. This paper deals mostly with accelerator design and charged-particle beam transport. The application of Lie algebraic methods to light optics and electron microscopes is described elsewhere (1, see also 44). To keep its scope within reasonable bounds, they restrict their treatment of accelerator design and charged-particle beam transport primarily to the use of Lie algebraic methods for the description of particle orbits in terms of transfer maps. There are other Lie algebraic or related approaches to accelerator problems that the reader may find of interest (2). For a general discussion of linear and nonlinear problems in accelerator physics see (3).
Percino, María Judith; Cerón, Margarita; Rodríguez, Oscar; Soriano-Moro, Guillermo; Castro, María Eugenia; Chapela, Víctor M; Siegler, Maxime A; Pérez-Gutiérrez, Enrique
2016-03-28
We report single crystal X-ray diffraction (hereafter, SCXRD) analyses of derivatives featuring the electron-donor N-ethylcarbazole or the (4-diphenylamino)phenyl moieties associated with a -CN group attached to a double bond. The compounds are (2Z)-3-(4-(diphenylamino)-phenyl)-2-(pyridin-3-yl)prop-2-enenitrile (I), (2Z)-3-(4-(diphenylamino)phenyl)-2-(pyridin-4-yl)-prop-2-enenitrile (II) and (2Z)-3-(9-ethyl-9H-carbazol-3-yl)-2-(pyridin-2-yl)enenitrile (III). SCXRD analyses reveal that I and III crystallize in the monoclinic space groups P2/c with Z' = 2 and C2/c with Z' = 1, respectively. Compound II crystallized in the orthorhombic space group Pbcn with Z' = 1. The molecular packing analysis was conducted to examine the pyridine core effect, depending on the ortho, meta- and para-positions of the nitrogen atom, with respect to the optical properties and number of independent molecules (Z'). It is found that the double bond bearing a diphenylamino moiety introduced properties to exhibit a strong π-π-interaction in the solid state. The compounds were examined to evaluate the effects of solvent polarity, the role of the molecular structure, and the molecular interactions on their self-assembly behaviors. Compound I crystallized with a cell with two conformers, anti and syn, due to interaction with solvent. DFT calculations indicated the anti and syn structures of I are energetically stable (less than 1 eV). Also electrochemical and photophysical properties of the compounds were investigated, as well as the determination of optimization calculations in gas and different solvent (chloroform, cyclohexane, methanol, ethanol, tetrahydrofuran, dichloromethane and dimethyl sulfoxide) in the Gaussian09 program. The effect of solvent by PCM method was also investigated. The frontier HOMO and LUMO energies and gap energies are reported.
Directory of Open Access Journals (Sweden)
María Judith Percino
2016-03-01
Full Text Available We report single crystal X-ray diffraction (hereafter, SCXRD analyses of derivatives featuring the electron-donor N-ethylcarbazole or the (4-diphenylaminophenyl moieties associated with a -CN group attached to a double bond. The compounds are (2Z-3-(4-(diphenylamino-phenyl-2-(pyridin-3-ylprop-2-enenitrile (I, (2Z-3-(4-(diphenylaminophenyl-2-(pyridin-4-yl-prop-2-enenitrile (II and (2Z-3-(9-ethyl-9H-carbazol-3-yl-2-(pyridin-2-ylenenitrile (III. SCXRD analyses reveal that I and III crystallize in the monoclinic space groups P2/c with Z’ = 2 and C2/c with Z’ = 1, respectively. Compound II crystallized in the orthorhombic space group Pbcn with Z’ = 1. The molecular packing analysis was conducted to examine the pyridine core effect, depending on the ortho, meta- and para-positions of the nitrogen atom, with respect to the optical properties and number of independent molecules (Z’. It is found that the double bond bearing a diphenylamino moiety introduced properties to exhibit a strong π-π-interaction in the solid state. The compounds were examined to evaluate the effects of solvent polarity, the role of the molecular structure, and the molecular interactions on their self-assembly behaviors. Compound I crystallized with a cell with two conformers, anti and syn, due to interaction with solvent. DFT calculations indicated the anti and syn structures of I are energetically stable (less than 1 eV. Also electrochemical and photophysical properties of the compounds were investigated, as well as the determination of optimization calculations in gas and different solvent (chloroform, cyclohexane, methanol, ethanol, tetrahydrofuran, dichloromethane and dimethyl sulfoxide in the Gaussian09 program. The effect of solvent by PCM method was also investigated. The frontier HOMO and LUMO energies and gap energies are reported.
Lies and Deception: A Failed Reconciliation
DEFF Research Database (Denmark)
Broncano-Berrocal, Fernando
2013-01-01
The traditional view of lying says that lying is a matter of intending to deceive others by making statements that one believes to be false. Jennifer Lackey has recently defended the following version of the traditional view: A lies to B just in case (i) A states that p to B, (ii) A believes that...... is false and (iii) A intends to be deceptive to B in stating that p. I argue that, despite all the virtues that Lackey ascribes to her view, conditions (i), (ii) and (iii) are not sufficient for lying.......The traditional view of lying says that lying is a matter of intending to deceive others by making statements that one believes to be false. Jennifer Lackey has recently defended the following version of the traditional view: A lies to B just in case (i) A states that p to B, (ii) A believes that p...
Gayathri, R.; Arivazhagan, M.
2017-02-01
In this work, a joint experimental (FTIR and FT-Raman) and theoretical (DFT and ab-initio) study on the structure and the vibrations of Trans-3-(trans-4-imidazolyl) acrylic acid (TTIAA) are compared and analyzed. The assignment of each normal mode has been made using the observed and calculated frequencies. The optimized geometries, harmonic vibrational wavenumbers and intensities of vibrational bands of trans-3-(trans-4-imidazolyl) acrylic acid (TTIAA) have been carried out using the HF/B3LYP method using the standard 6311++G(d,p) basis set calculations in this investigation. The result describes the variation in electrostatic and transport properties for zero and various external applied field. The variation in MPA charges are small due to the application of EFs: however, in most cases it is found to be systematic and almost uniform. When the field increases from 0.00 to 0.02 VÅ-1, the hybridization of molecular levels broadens the DOS and decreases the HLG from 3.6609 to 1.2325 eV; the decrease of band gap at the high field indicates that this molecule exhibit considerable electrical conductivity. Fukui indices to determine the local reactive site for the molecular systems during electrophilic, nucleophilic, radical and dual descriptor attacks. The results clearly show the superiority of MPA scheme. This study may be useful to design new molecules with more electrical conductivity.
Zobač, Vladimír; Lewis, James P; Abad, Enrique; Mendieta-Moreno, Jesús I; Hapala, Prokop; Jelínek, Pavel; Ortega, José
2015-05-08
The computational simulation of photo-induced processes in large molecular systems is a very challenging problem. Firstly, to properly simulate photo-induced reactions the potential energy surfaces corresponding to excited states must be appropriately accessed; secondly, understanding the mechanisms of these processes requires the exploration of complex configurational spaces and the localization of conical intersections; finally, photo-induced reactions are probability events, that require the simulation of hundreds of trajectories to obtain the statistical information for the analysis of the reaction profiles. Here, we present a detailed description of our implementation of a molecular dynamics with electronic transitions algorithm within the local-orbital density functional theory code FIREBALL, suitable for the computational study of these problems. As an example of the application of this approach, we also report results on the [2 + 2] cycloaddition of ethylene with maleic anhydride and on the [2 + 2] photo-induced polymerization reaction of two C60 molecules. We identify different deactivation channels of the initial electron excitation, depending on the time of the electronic transition from LUMO to HOMO, and the character of the HOMO after the transition.
Saravanan, S; Balachandran, V; Vishwanathan, K
2014-04-24
The FT-IR and FT-Raman spectra of 4-tert-butyl-3-methoxy-2,6-dinitrotoluene (musk ambrette) have been recorded in the regions 4000-400 cm(-1) and 3500-100 cm(-1), respectively. The total energy calculations of musk ambrette were tried for the possible conformers. The molecular structure, geometry optimization, vibrational frequencies were obtained by the density functional theory (DFT) using B3LYP and LSDA method with 6-311G(d,p) basis set for the most stable conformer "C1". The complete assignments were performed on the basis of the potential energy distribution (PED) of the vibrational modes, calculated and the scaled values were compared with experimental FT-IR and FT-Raman spectra. The observed and the calculated frequencies are found to be in good agreement. The stability of the molecule arising from hyper conjugate interactions and the charge delocalization has been analyzed using bond orbital (NBO) analysis. The HOMO and LUMO energy gap reveals that the energy gap reflects the chemical activity of the molecule. The dipole moment (μ), polarizability (α), anisotropy polarizability (Δα) and first hyperpolarizability (βtot) of the molecule have been reported. The thermodynamic functions (heat capacity, entropy and enthalpy) were obtained for the range of temperature 100-1000 K. Information about the size, shape, charge density distribution and site of chemical reactivity of the molecule has been obtained by mapping electron density isosurface with molecular electrostatic potential (MEP).
[Psychopathological study of lie motif in schizophrenia].
Otsuka, Koichiro; Kato, Satoshi
2006-01-01
The theme of a statement is called "lie motif" by the authors when schizophrenic patients say "I have lied to anybody". We tried to analyse of the psychopathological characteristics and anthropological meanings of the lie motifs in schizophrenia, which has not been thematically examined until now, based on 4 cases, and contrasting with the lie motif (Lügenmotiv) in depression taken up by A. Kraus (1989). We classified the lie motifs in schizophrenia into the following two types: a) the past directive lie motif: the patients speak about their real lie regarding it as a 'petty fault' in their distant past with self-guilty feeling, b) the present directive lie motif: the patients say repeatedly 'I have lied' (about their present speech and behavior), retreating from their previous commitments. The observed false confessions of innocent fault by the patients seem to belong to the present directed lie motif. In comparison with the lie motif in depression, it is characteristic for the lie motif in schizophrenia that the patients feel themselves to already have been caught out by others before they confess the lie. The lie motif in schizophrenia seems to come into being through the attribution process of taking the others' blame on ones' own shoulders, which has been pointed out to be common in the guilt experience in schizophrenia. The others' blame on this occasion is due to "the others' gaze" in the experience of the initial self-centralization (i.e. non delusional self-referential experience) in the early stage of schizophrenia (S. Kato 1999). The others' gaze is supposed to bring about the feeling of amorphous self-revelation which could also be regarded as the guilt feeling without content, to the patients. When the guilt feeling is bound with a past concrete fault, the patients tell the past directive lie motif. On the other hand, when the patients cannot find a past fixed content, and feel their present actions as uncertain and experience them as lies, the
Lumbroso, H.; Liégeois, C.; Pappalardo, G. C.; Grassi, A.
From the ab initio molecular energies of the possible conformers and from a classical dipole moment analysis of 2-oxopyrrolidin-l-ylacetamide (μ = 4.02 D in dioxan at 30.0°C), the preferred conformation in solution of this novel nootropic agent has been determined. The exocyclic N-CH 2 bond is rotated in one sense by 90° and the exocyclic CH 2-C bond rotated in the same sense by 120° from the "planar" ( OO)- cis conformation. The structures of the two enantiomers in solution differ from that of the crystalline molecule.
Learning to lie: Effects of practice on the cognitive cost of lying
Directory of Open Access Journals (Sweden)
Bram eVan Bockstaele
2012-11-01
Full Text Available Cognitive theories on deception posit that lying requires more cognitive resources than telling the truth. In line with this idea, it has been demonstrated that deceptive responses are typically associated with increased response times and higher error rates compared to truthful responses. Although the cognitive cost of lying has been assumed to be resistant to practice, it has recently been shown that people who are trained to lie can reduce this cost. In the present study (n = 42, we further explored the effects of practice on one’s ability to lie by manipulating the proportions of lie and truth-trials in a Sheffield lie test across three phases: Baseline (50% lie, 50% truth, Training (frequent-lie group: 75% lie, 25% truth; control group: 50% lie, 50% truth; and frequent-truth group: 25% lie, 75% truth, and Test (50% lie, 50% truth. The results showed that lying became easier while participants were trained to lie more often and that lying became more difficult while participants were trained to tell the truth more often. Furthermore, these effects did carry over to the test phase, but only for the specific items that were used for the training manipulation. Hence, our study confirms that relatively little practice is enough to alter the cognitive cost of lying, although this effect does not persist over time for non-practiced items.
di Battista, Patrick
1997-01-01
Examines whether a lie's cognitive representation affects deceivers' ability to respond to probing. Shows that behavioral changes made in response to probing varied depending on whether the lie was a familiar lie or an unfamiliar lie but that none of these behaviors were related to judges' ratings of truthfulness. (SR)
Directory of Open Access Journals (Sweden)
A. Mallaiah
2017-02-01
Full Text Available The electronic transport properties of electrons in a molecules are observed by using Non equilibrium Green’s function(NEGF. We present a extremely through and careful computational approach well ordered method to do a framework analysis of donor (CH3 and acceptor (CN molecules connected between the Au(111 contacts, and also observed current progress through molecular devices depends on number of bonds or not. Such observations implementation through not possible by standard quantum chemistry soft wares. The results shows I-V characteristics, Transport spectrum and Transport analysis can effectively tune the molecules works like a conventional semi-conductor based diodes, these results invoke to design the logic gates and logic circuits.
Holomorph of Lie color algebras%Lie color代数的全形
Institute of Scientific and Technical Information of China (English)
杨恒云
2007-01-01
给出Lie color代数全形的一些性质,证明Lie color代数L的全形有分解(H)(L)=L(+)Z(H)(L)(L)的充分必要条件是它是完备Lie color代数.%To the holomorph of Lie color algebras, some properties are studied. A Lie color algebra L is complete if and only if (H)(L) = L(+)Z(H)(L) (L).
Institute of Scientific and Technical Information of China (English)
2008-01-01
The calculations on the potential energy curves and spectroscopic constants of the ground and low-lying excited states of BrCl+,one of the important molecular ions in environment science,have been performed by using the multireference configuration interaction method at high level of theory in quantum chemistry.Through analyses of the effects of the spin-orbit coupling interaction on the elec-tronic structures and spectroscopic properties,the multiconfiguration characteristic of the X2Π ground state and low-lying excited states was established.The spin-orbit coupling splitting energy of the X2 Π ground state was calculated to be 1814 cm-1,close to the experimental value 2070 cm-1.The spin-orbit coupling splitting energy of the 2Π(Ⅱ) exited state was predicted to be 766 cm-1.The transition dipole moments and Frank-Condon factors of the 3/2(Ⅲ)-X3/2 and 1/2(Ⅲ)-1/2(I) transitions were estimated,and the radiative lifetimes of the two transitions were briefly discussed.
Institute of Scientific and Technical Information of China (English)
WANG MingWei; WANG BingWu; CHEN ZhiDa
2008-01-01
The calculations on the potential energy curves and spectroscopic constants of the ground and low-lying excited states of BrCl+, one of the important molecular ions in environment science, have been performed by using the multireference configuration interaction method at high level of theory in quantum chemistry. Through analyses of the effects of the spin-orbit coupling interaction on the electronic structures and spectroscopic properties, the multiconfiguration characteristic of the X2∏ ground state and low-lying excited states was established. The spin-orbit coupling splitting energy of the X2∏ ground state was calculated to be 1814 cm-1, close to the experimental value 2070 cm-1. The spin-orbit coupling splitting energy of the 2∏(Ⅱ) exited state was predicted to be 766 cm-1. The transition dipole moments and Frank-Condon factors of the 3/2(Ⅲ)-X3/2 and 1/2(Ⅲ)-1/2(Ⅰ) transitions were estimated, and the radiative lifetimes of the two transitions were briefly discussed.
Kurnyavko, O. L.; Shirokov, I. V.
2016-07-01
We offer a method for constructing invariants of the coadjoint representation of Lie groups that reduces this problem to known problems of linear algebra. This method is based on passing to symplectic coordinates on the coadjoint representation orbits, which play the role of local coordinates on those orbits. The corresponding transition functions are their parametric equations. Eliminating the symplectic coordinates from the transition functions, we can obtain the complete set of invariants. The proposed method allows solving the problem of constructing invariants of the coadjoint representation for Lie groups with an arbitrary dimension and structure.
Low lying charmonium states at the physical point
Mohler, Daniel; Kronfeld, Andreas S; Lee, Song-haeng; Levkova, Ludmila; Simone, J N
2014-01-01
We present results for the mass splittings of low-lying charmonium states from a calculation with Wilson clover valence quarks with the Fermilab interpretation on an asqtad sea. We use five lattice spacings and two values of the light sea quark mass to extrapolate our results to the physical point. Sources of systematic uncertainty in our calculation are discussed and we compare our results for the 1S hyperfine splitting, the 1P-1S splitting and the P-wave spin orbit and tensor splittings to experiment.
Quantum Lie theory a multilinear approach
Kharchenko, Vladislav
2015-01-01
This is an introduction to the mathematics behind the phrase “quantum Lie algebra”. The numerous attempts over the last 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary “quantum” Lie bracket have not been widely accepted. In this book, an alternative approach is developed that includes multivariable operations. Among the problems discussed are the following: a PBW-type theorem; quantum deformations of Kac--Moody algebras; generic and symmetric quantum Lie operations; the Nichols algebras; the Gurevich--Manin Lie algebras; and Shestakov--Umirbaev operations for the Lie theory of nonassociative products. Opening with an introduction for beginners and continuing as a textbook for graduate students in physics and mathematics, the book can also be used as a reference by more advanced readers. With the exception of the introductory chapter, the content of this monograph has not previously appeared in book form.
Generalized derivations of Lie triple systems
Directory of Open Access Journals (Sweden)
Zhou Jia
2016-01-01
Full Text Available In this paper, we present some basic properties concerning the derivation algebra Der (T, the quasiderivation algebra QDer (T and the generalized derivation algebra GDer (T of a Lie triple system T, with the relationship Der (T ⊆ QDer (T ⊆ GDer (T ⊆ End (T. Furthermore, we completely determine those Lie triple systems T with condition QDer (T = End (T. We also show that the quasiderivations of T can be embedded as derivations in a larger Lie triple system.
3-Leibniz bialgebras (3-Lie bialgebras)
2016-01-01
In this paper by use of cohomology complex of $3$-Leibniz algebras, the definitions of Leibniz bialgebras (and Lie bialgebras) are extended for the case of $3$-Leibniz algebras. Many theorems about Leibniz bialgebras are extended and proved for the case of $3$-Leibniz bialgebras ($3$-Lie bialgebras). Moreover a new theorem on the correspondence between $3$-Leibniz bialgebra and its associated Leibniz bialgebra is proved. $3$-Lie bialgebra as particular case of the $3$-Leibniz bialgebra is inv...
Killing Forms of Isotropic Lie Algebras
Malagon, Audrey
2010-01-01
This paper presents a method for computing the Killing form of an isotropic Lie algebra defined over an arbitrary field based on the Killing form of a subalgebra containing its anisotropic kernel. This approach allows for streamlined formulas for many Lie algebras of types E6 and E7 and yields a unified formula for all Lie algebras of inner type E6, including the anisotropic ones.
ALIED: A Theory of Lie Detection
Directory of Open Access Journals (Sweden)
Chris N. H. Street
2016-07-01
Full Text Available We are very inaccurate lie detectors, and tend to believe what others tell us is the truth more often than we ought to. In fact, studies on lie detection typically describe our tendency to believe others as an error in judgment. Although people may look like hopeless lie detectors, the Adaptive Lie Detector theory (ALIED claims that people are actually making smart, informed judgments. This article explores the ALIED theory and what it means for those wanting to spot a liar.
Computations in finite-dimensional Lie algebras
Directory of Open Access Journals (Sweden)
A. M. Cohen
1997-12-01
Full Text Available This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven Lie Algebra System, within the computer algebra package GAP. A first sketch of the package can be found in Cohen and de Graaf[1]. Since then, in a collaborative effort with G. Ivanyos, the authors have continued to develop algorithms which were implemented in ELIAS by the second author. These activities are part of a bigger project, called ACELA and financed by STW, the Dutch Technology Foundation, which aims at an interactive book on Lie algebras (cf. Cohen and Meertens [2]. This paper gives a global description of the main ways in which to present Lie algebras on a computer. We focus on the transition from a Lie algebra abstractly given by an array of structure constants to a Lie algebra presented as a subalgebra of the Lie algebra of n×n matrices. We describe an algorithm typical of the structure analysis of a finite-dimensional Lie algebra: finding a Levi subalgebra of a Lie algebra.
Engel Subalgebras of n-Lie Algebras
Institute of Scientific and Technical Information of China (English)
Donald W. BARNES
2008-01-01
Engel subalgebras of finite-dimensional n Lie algebras are shown to have similar properties to those of Lie algebras.Using these,it is shown that an n Lie algebra,all of whose maximal subalgebras are ideals,is nilpotent.A primitive 2-soluble n Lie algebra is shown to split over its minimal ideal, and all the complements to its minimal ideal are conjugate.A subalgebra is shown to be a Cartan subalgebra if and only if it is minimal Engel,provided that the field has su .ciently many elements. Cartan subalgebras are shown to have a property analogous to intravariance.
2004-01-01
This animation shows the location of the newly discovered planet-like object, dubbed 'Sedna,' in relation to the rest of the solar system. Starting at the inner solar system, which includes the orbits of Mercury, Venus, Earth, and Mars (all in yellow), the view pulls away through the asteroid belt and the orbits of the outer planets beyond (green). Pluto and the distant Kuiper Belt objects are seen next until finally Sedna comes into view. As the field widens the full orbit of Sedna can be seen along with its current location. Sedna is nearing its closest approach to the Sun; its 10,000 year orbit typically takes it to far greater distances. Moving past Sedna, what was previously thought to be the inner edge of the Oort cloud appears. The Oort cloud is a spherical distribution of cold, icy bodies lying at the limits of the Sun's gravitational pull. Sedna's presence suggests that this Oort cloud is much closer than scientists believed.
2004-01-01
This animation shows the location of the newly discovered planet-like object, dubbed 'Sedna,' in relation to the rest of the solar system. Starting at the inner solar system, which includes the orbits of Mercury, Venus, Earth, and Mars (all in yellow), the view pulls away through the asteroid belt and the orbits of the outer planets beyond (green). Pluto and the distant Kuiper Belt objects are seen next until finally Sedna comes into view. As the field widens the full orbit of Sedna can be seen along with its current location. Sedna is nearing its closest approach to the Sun; its 10,000 year orbit typically takes it to far greater distances. Moving past Sedna, what was previously thought to be the inner edge of the Oort cloud appears. The Oort cloud is a spherical distribution of cold, icy bodies lying at the limits of the Sun's gravitational pull. Sedna's presence suggests that this Oort cloud is much closer than scientists believed.
Goldfeld, Dahlia A; Bochevarov, Arteum D; Friesner, Richard A
2008-12-07
This paper is a logical continuation of the 22 parameter, localized orbital correction (LOC) methodology that we developed in previous papers [R. A. Friesner et al., J. Chem. Phys. 125, 124107 (2006); E. H. Knoll and R. A. Friesner, J. Phys. Chem. B 110, 18787 (2006).] This methodology allows one to redress systematic density functional theory (DFT) errors, rooted in DFT's inherent inability to accurately describe nondynamical correlation. Variants of the LOC scheme, in conjunction with B3LYP (denoted as B3LYP-LOC), were previously applied to enthalpies of formation, ionization potentials, and electron affinities and showed impressive reduction in the errors. In this paper, we demonstrate for the first time that the B3LYP-LOC scheme is robust across different basis sets [6-31G( *), 6-311++G(3df,3pd), cc-pVTZ, and aug-cc-pVTZ] and reaction types (atomization reactions and molecular reactions). For example, for a test set of 70 molecular reactions, the LOC scheme reduces their mean unsigned error from 4.7 kcal/mol [obtained with B3LYP/6-311++G(3df,3pd)] to 0.8 kcal/mol. We also verified whether the LOC methodology would be equally successful if applied to the promising M05-2X functional. We conclude that although M05-2X produces better reaction enthalpies than B3LYP, the LOC scheme does not combine nearly as successfully with M05-2X than with B3LYP. A brief analysis of another functional, M06-2X, reveals that it is more accurate than M05-2X but its combination with LOC still cannot compete in accuracy with B3LYP-LOC. Indeed, B3LYP-LOC remains the best method of computing reaction enthalpies.
Mirzaeva, Irina V; Mainichev, Dmitry A; Kozlova, Svetlana G
2016-03-24
(103)Rh NMR parameters and the bonding structure of three complexes of [Cp*RhX2]2, where X = Cl, Br, or I, have been studied with the help of natural bond orbitals (NBOs) and natural localized molecular orbitals (NLMOs). The complexes of [Cp*RhX2]2, where X = Cl, Br, or I, have similar bonding structures, with the major difference being in the degree of covalency of the Rh-X bonds. The decomposition of (103)Rh NMR shielding into diamagnetic, paramagnetic, and spin-orbit terms shows that normal halogen dependence (NHD) of the (103)Rh NMR shift is defined mostly by the paramagnetic term, with the spin-orbit term being significantly smaller. The decomposition of (103)Rh shielding into spin-free NBO and NLMO contributions shows that (103)Rh shielding is dominated by Rh d-orbital deshielding contributions. We explain the NHD of the (103)Rh NMR shift with the increase in the energies of the virtual antibonding Rh-X orbitals along the X = Cl, Br, and I series.
Dietrick, Scott M; Iyengar, Srinivasan S
2012-12-11
A method of analysis is introduced to probe the spectral features obtained from ab initio molecular dynamics simulations. Here, the instantaneous mass-weighted velocities are projected onto irreducible representations constructed from discrete time translation groups comprising operations that invoke the time-domain symmetries (or periodic phase space orbits) reflected in the spectra. The projected velocities are decomposed using singular value decomposition (SVD) to construct a set of "modes" pertaining to a given frequency domain. These modes now include all anharmonicities, as sampled during the dynamics simulations. In this approach, the underlying motions are probed in a manner invariant with respect to coordinate transformations, operations being performed along the time axis rather than coordinate axes, making the analysis independent of choice of reference frame. The method is used to probe the underlying motions responsible for the doublet at ∼1000 cm(-1) in the vibrational spectrum of the H5O2(+), Zundel cation. The associated analysis results are confirmed by projecting the Fourier transformed velocities onto the harmonic normal mode coordinates and a set of mass-weighted, symmetrized Jacobi coordinates. It is found that the two peaks of the doublet are described and differentiated by their respective contributions from the proton transfer, water-water stretch, and water wag coordinates, as these are defined. Temperature dependent effects are also briefly noted.
Tsuzuki, Seiji; Hayamizu, Kikuko; Seki, Shiro; Ohno, Yasutaka; Kobayashi, Yo; Miyashiro, Hajime
2008-08-14
Interactions of the lithium bis(trifluoromethylsulfonyl)amide (LiTFSA) complex with N, N-diethyl-N-methyl-N-(2-methoxyethyl) ammonium (DEME), 1-ethyl-3-methylimidazolium (EMIM) cations, neutral diethylether (DEE), and the DEMETFSA complex were studied by ab initio molecular orbital calculations. An interaction energy potential calculated for the DEME cation with the LiTFSA complex has a minimum when the Li atom has contact with the oxygen atom of DEME cation, while potentials for the EMIM cation with the LiTFSA complex are always repulsive. The MP2/6-311G**//HF/6-311G** level interaction energy calculated for the DEME cation with the LiTFSA complex was -18.4 kcal/mol. The interaction energy for the neutral DEE with the LiTFSA complex was larger (-21.1 kcal/mol). The interaction energy for the DEMETFSA complex with LiTFSA complex is greater (-23.2 kcal/mol). The electrostatic and induction interactions are the major source of the attraction in the two systems. The substantial attraction between the DEME cation and the LiTFSA complex suggests that the interaction between the Li cation and the oxygen atom of DEME cation plays important roles in determining the mobility of the Li cation in DEME-based room temperature ionic liquids.
Morikami, Kenji; Itezono, Yoshiko; Nishimoto, Masahiro; Ohta, Masateru
2014-01-01
Compounds with a medium-sized flexible ring often show atropisomerism that is caused by the high-energy barriers between long-lived conformers that can be isolated and often have different biological properties to each other. In this study, the frequency of the transition between the two stable conformers, aS and aR, of thienotriazolodiazepine compounds with flexible 7-membered rings was estimated computationally by Monte Carlo (MC) simulations and validated experimentally by NMR experiments. To estimate the energy barriers for transitions as precisely as possible, the potential energy (PE) surfaces used in the MC simulations were calculated by molecular orbital (MO) methods. To accomplish the MC simulations with the MO-based PE surfaces in a practical central processing unit (CPU) time, the MO-based PE of each conformer was pre-calculated and stored before the MC simulations, and then only referred to during the MC simulations. The activation energies for transitions calculated by the MC simulations agreed well with the experimental ΔG determined by the NMR experiments. The analysis of the transition trajectories of the MC simulations revealed that the transition occurred not only through the transition states, but also through many different transition paths. Our computational methods gave us quantitative estimates of atropisomerism of the thienotriazolodiazepine compounds in a practical period of time, and the method could be applicable for other slow-dynamics phenomena that cannot be investigated by other atomistic simulations.
Ducati, Lucas C; Marchenko, Alex; Autschbach, Jochen
2016-11-21
The influence of solvent (water) coordination and dynamics on the electronic structure and nuclear magnetic resonance (NMR) indirect spin-spin coupling (J-coupling) constants in a series of Tl-Pt bonded complexes is investigated using Kohn-Sham (KS) Car-Parrinello molecular dynamics (CPMD) and relativistic hybrid KS NMR calculations with and without coordination to water. Coordination of the Tl center by water molecules has a dramatic impact on (1)J(Tl-Pt) and other J-coupling constants. It is shown that a previous computational study of the same complexes using static optimized structures and nonhybrid functionals was correct about the important role of the solvent but obtained reasonable agreement with experimental NMR data because of a cancellation of substantial errors. For example, the CPMD trajectories show that on average the inner coordination shell of Tl is not saturated, as previously assumed, which leads to poor agreement with experiment when the J-coupling constants are averaged over the CPMD trajectories using NMR calculations with nonhybrid functionals. The combination of CPMD with hybrid KS NMR calculations provides a much more realistic computational model that reproduces the large magnitudes of (1)J(Tl-Pt) and the correct trends for other coupling constants. An analysis of (1)J(Tl-Pt) in terms of localized orbitals shows that the presence of coordinating water molecules increases the capacity for covalent interactions between Tl and Pt. There is pronounced multicenter bonding along the metal-metal axis of the complexes.
Aguado, A
2001-01-01
The melting-like transition in potasium clusters K_N, with N=20, 55, 92 and 142, is studied by using an orbital-free density-functional constant-energy molecular dynamics simulation method, and compared to previous theoretical results on the melting-like transition in sodium clusters of the same sizes. Melting in potasium and sodium clusters proceeds in a similar way: a surface melting stage develops upon heating before the homogeneous melting temperature is reached. Premelting effects are nevertheless more important and more easily established in potasium clusters, and the transition regions spread over temperature intervals which are wider than in the case of sodium. For all the sizes considered, the percentage melting temperature reduction when passing from Na to K clusters is substantially larger than in the bulk. Once those two materials have been compared for a number of different cluster sizes, we study the melting-like transition in Rb_55 and Cs_55 clusters and make a comparison with the melting behav...
Suresh, S.; Gunasekaran, S.; Srinivasan, S.
2014-11-01
The solid phase FT-IR and FT-Raman spectra of 2-hydroxybenzoic acid (salicylic acid) have been recorded in the region 4000-400 and 4000-100 cm-1 respectively. The optimized molecular geometry and fundamental vibrational frequencies are interpreted with the aid of structure optimizations and normal coordinate force field calculations based on density functional theory (DFT) method and a comparative study between Hartree Fork (HF) method at 6-311++G(d,p) level basis set. The calculated harmonic vibrational frequencies are scaled and they are compared with experimentally obtained FT-IR and FT-Raman spectra. A detailed interpretation of the vibrational spectra of this compound has been made on the basis of the calculated potential energy distribution (PED). The time dependent DFT method is employed to predict its absorption energy and oscillator strength. The linear polarizability (α) and the first order hyper polarizability (β) values of the investigated molecule have been computed. The electronic properties, such as HOMO and LUMO energies, molecular electrostatic potential (MEP) are also performed. Stability of the molecule arising from hyper conjugative interaction, charge delocalization has been analyzed using natural bond orbital (NBO) analysis.
Suresh, S; Gunasekaran, S; Srinivasan, S
2014-11-11
The solid phase FT-IR and FT-Raman spectra of 2-hydroxybenzoic acid (salicylic acid) have been recorded in the region 4000-400 and 4000-100 cm(-1) respectively. The optimized molecular geometry and fundamental vibrational frequencies are interpreted with the aid of structure optimizations and normal coordinate force field calculations based on density functional theory (DFT) method and a comparative study between Hartree Fork (HF) method at 6-311++G(d,p) level basis set. The calculated harmonic vibrational frequencies are scaled and they are compared with experimentally obtained FT-IR and FT-Raman spectra. A detailed interpretation of the vibrational spectra of this compound has been made on the basis of the calculated potential energy distribution (PED). The time dependent DFT method is employed to predict its absorption energy and oscillator strength. The linear polarizability (α) and the first order hyper polarizability (β) values of the investigated molecule have been computed. The electronic properties, such as HOMO and LUMO energies, molecular electrostatic potential (MEP) are also performed. Stability of the molecule arising from hyper conjugative interaction, charge delocalization has been analyzed using natural bond orbital (NBO) analysis. Published by Elsevier B.V.
The structure of complex Lie groups
Lee, Dong Hoon
2001-01-01
Complex Lie groups have often been used as auxiliaries in the study of real Lie groups in areas such as differential geometry and representation theory. To date, however, no book has fully explored and developed their structural aspects.The Structure of Complex Lie Groups addresses this need. Self-contained, it begins with general concepts introduced via an almost complex structure on a real Lie group. It then moves to the theory of representative functions of Lie groups- used as a primary tool in subsequent chapters-and discusses the extension problem of representations that is essential for studying the structure of complex Lie groups. This is followed by a discourse on complex analytic groups that carry the structure of affine algebraic groups compatible with their analytic group structure. The author then uses the results of his earlier discussions to determine the observability of subgroups of complex Lie groups.The differences between complex algebraic groups and complex Lie groups are sometimes subtle ...
Classification and identification of Lie algebras
Snobl, Libor
2014-01-01
The purpose of this book is to serve as a tool for researchers and practitioners who apply Lie algebras and Lie groups to solve problems arising in science and engineering. The authors address the problem of expressing a Lie algebra obtained in some arbitrary basis in a more suitable basis in which all essential features of the Lie algebra are directly visible. This includes algorithms accomplishing decomposition into a direct sum, identification of the radical and the Levi decomposition, and the computation of the nilradical and of the Casimir invariants. Examples are given for each algorithm. For low-dimensional Lie algebras this makes it possible to identify the given Lie algebra completely. The authors provide a representative list of all Lie algebras of dimension less or equal to 6 together with their important properties, including their Casimir invariants. The list is ordered in a way to make identification easy, using only basis independent properties of the Lie algebras. They also describe certain cl...
Testosterone Administration Reduces Lying in Men
Wibral, M.; Dohmen, T.J.; Klingmüller, Dietrich; Weber, Bernd; Falk, Armin
2012-01-01
Lying is a pervasive phenomenon with important social and economic implications. However, despite substantial interest in the prevalence and determinants of lying, little is known about its biological foundations. Here we study a potential hormonal influence, focusing on the steroid hormone
Lie Group Techniques for Neural Learning
2005-01-03
Lie group techniques for Neural Learning Edinburgh June 2004 Elena Celledoni SINTEF Applied Mathematics, IMF-NTNU Lie group techniques for Neural...ORGANIZATION NAME(S) AND ADDRESS(ES) SINTEF Applied Mathematics, IMF-NTNU 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND
The Killing Forms of Lie Triple Systems
Institute of Scientific and Technical Information of China (English)
ZHANG Zhi Xue; GAO Rui
2009-01-01
For Lie triple systems in the characteristic zero setting, we obtain by means of the Killing forms two criterions for semisimplicity and for solvability respectively, and then investigate the relationship among the Killing forms of a real Lie triple system To, the complexification T of To, and the realification of T.
Matrix Lie Algebras and Integrable Couplings
Institute of Scientific and Technical Information of China (English)
ZHANG Yu-Feng; GUO Fu-Kui
2006-01-01
Three kinds of higher-dimensional Lie algebras are given which can be used to directly construct integrable couplings of the soliton integrable systems. The relations between the Lie algebras are discussed. Finally, the integrable couplings and the Hamiltonian structure of Giachetti-Johnson hierarchy and a new integrable system are obtained, respectively.
Induced Modules of Restricted Lie Superalgebras
Institute of Scientific and Technical Information of China (English)
刘文德
2005-01-01
In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established.Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.
On Nambu-Lie 3-algebra representations
Sochichiu, Corneliu
2008-01-01
We propose a recipe to construct matrix representations of Nambu--Lie 3-algebras in terms of irreducible representations of underlying Lie algebra. The case of Euclidean four-dimensional 3-algebra is considered in details. We find that representations of this 3-algebra are not possible in terms of only Hermitian matrices in spite of its Euclidean nature.
Computations in finite-dimensional Lie algebras
Cohen, A.M.; Graaf, W.A. de; Rónyai, L.
2001-01-01
This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven Lie Algebra System), within the computer algebra package GAP. A first sketch of the packagecan be found in Cohen and de Graaf[1]. Since then, in a collaborative
Permutation Weights and Modular Poincare Polynomials for Affine Lie Algebras
Gungormez, M
2010-01-01
Poincare Polynomial of a Kac-Moody Lie algebra can be obtained by classifying the Weyl orbit $W(\\rho)$ of its Weyl vector $\\rho$. A remarkable fact for Affine Lie algebras is that the number of elements of $W(\\rho)$ is finite at each and every depth level though totally it has infinite number of elements. This allows us to look at $W(\\rho)$ as a manifold graded by depths of its elements and hence a new kind of Poincare Polynomial is defined. We give these polynomials for all Affine Kac-Moody Lie algebras, non-twisted or twisted. The remarkable fact is however that, on the contrary to the ones which are classically defined,these new kind of Poincare polynomials have modular properties, namely they all are expressed in the form of eta-quotients. When one recalls Weyl-Kac character formula for irreducible characters, it is natural to think that this modularity properties could be directly related with Kac-Peterson theorem which says affine characters have modular properties. Another point to emphasize is the rel...
Lie symmetries and 2D Material Physics
Belhaj, Adil
2014-01-01
Inspired from Lie symmetry classification, we establish a correspondence between rank two Lie symmetries and 2D material physics. The material unit cell is accordingly interpreted as the geometry of a root system. The hexagonal cells, appearing in graphene like models, are analyzed in some details and are found to be associated with A_2 and G_2 Lie symmetries. This approach can be applied to Lie supersymmetries associated with fermionic degrees of freedom. It has been suggested that these extended symmetries can offer a new way to deal with doping material geometries. Motivated by Lie symmetry applications in high energy physics, we speculate on a possible connection with (p,q) brane networks used in the string theory compactification on singular Calabi-Yau manifolds.
Characteristics of the Eysenck Personality Questionnaire Lie Scale and of Extreme Lie Scorers.
Loo, Robert
1980-01-01
Results of statistical analyses suggest that high lie-scorers respond honestly, and that the Lie Scale for the Eysenck Personality Inventory may reflect a personality dimension of interest rather than an extraneous and undesirable factor to be eliminated. (Author)
M2 to D2 and vice versa by 3-Lie and Lie bialgebra
Energy Technology Data Exchange (ETDEWEB)
Aali-Javanangrouh, M.; Rezaei-Aghdam, A. [Azarbaijan Shahid Madani University, Department of Physics, Faculty of Science, Tabriz (Iran, Islamic Republic of)
2016-11-15
Using the concept of a 3-Lie bialgebra, which has recently been defined in arXiv:1604.04475, we construct a Bagger-Lambert-Gustavson (BLG) model for the M2-brane on a Manin triple of a special 3-Lie bialgebra. Then by using the correspondence and the relation between those 3-Lie bialgebra with Lie bialgebra, we reduce this model to an N = (4,4) WZW model (D2-brane), such that its algebraic structure is a Lie bialgebra with one 2-cocycle. In this manner by using the correspondence of the 3-Lie bialgebra and Lie bialgebra (for this special 3-Lie algebra) one can construct the M2-brane from a D2-brane and vice versa. (orig.)
Masaoka, Shigeyuki; Mukawa, Yuichiro; Sakai, Ken
2010-07-07
Two new Ru(II)Pt(II) dimers, [Ru(bpy)(2)(mu-L2)PtCl(2)](2+) (5) and [Ru(bpy)(2)(mu-L3)PtCl(2)](2+) (6), were synthesized and characterized, and their electrochemical and spectroscopic properties together with their photo-hydrogen-evolving activities were evaluated (bpy = 2,2'-bypridine; L2 = 4'-[1,10]phenanthrolin-5-ylcarbamoyl)-[2,2']bipyridinyl-4-carboxylic acid ethyl ester; L3 = 4'-methyl-[2,2']bipyridinyl-4-carboxylic acid [1,10]phenanthrolin-5-ylamide). The structures of 5 and 6 are basically identical with that of the first active model of a photo-hydrogen-evolving molecular device developed in our group, [Ru(bpy)(2)(mu-L1)PtCl(2)](2+) (4) (L1 = 4'-([1,10]phenanthrolin-5-ylcarbamoyl)-[2,2']bipyridinyl-4-carboxylic acid), except for the difference in the substituent group at the 4-position of the bpy moiety bound to Pt(II) (-COOH for 4; -COOEt for 5; -CH(3) for 6). Electrochemical studies revealed that the first reduction potential of 5 (E(1/2) = -1.23 V) is nearly consistent with that of 4 (E(1/2) = -1.20 V) but is more positive than that of 6 (E(1/2) = -1.39 V), where the first reduction is associated with the reduction of the bpy moiety bound to Pt(II), consistent with a general tendency that the first reduction of bpy shows an anodic shift upon introduction of electron-withdrawing group. Density functional theory (DFT) calculations for 5 and 6 also show that the lowest unoccupied molecular orbital (LUMO) corresponds to the pi* orbital of the bpy moiety bound to Pt(II) for all the Ru(II)Pt(II) dimers, and the energy level of the LUMO of 6 is destabilized compared with those of 4 and 5, consistent with the results of the electrochemical studies. The photochemical hydrogen evolution from water driven by 4-6 in the presence a sacrificial electron donor (EDTA) was investigated. 5 was found to be active as an H(2)-evolving catalyst, while 6 shows no activity at all. However, 6 was found to drive photochemical H(2) evolution in the presence of both EDTA and
A-扩张Lie Rinehart代数%On the A-extended Lie Rinehart Algebras
Institute of Scientific and Technical Information of China (English)
陈酌; 祁玉海
2007-01-01
The purpose of this paper is to give a brief introduction to the category of Lie Rinehart algebras and introduces the concept of smooth manifolds associated with a unitary,commutative, associative algebra A. It especially shows that the A-extended algebra as well as the action algebra can be realized as the space of A-left invariant vector fields on a Lie group, analogous to the well known relationship of Lie algebras and Lie groups.
The Prevalence of Lying in America: Three Studies of Self-Reported Lies
Serota, Kim B.; Levine, Timothy R.; Boster, Franklin J.
2010-01-01
This study addresses the frequency and the distribution of reported lying in the adult population. A national survey asked 1,000 U.S. adults to report the number of lies told in a 24-hour period. Sixty percent of subjects report telling no lies at all, and almost half of all lies are told by only 5% of subjects; thus, prevalence varies widely and…
Homology of Lie algebra of supersymmetries and of super Poincare Lie algebra
Energy Technology Data Exchange (ETDEWEB)
Movshev, M.V. [Department of Mathematics, Stony Brook University, Stony Brook, NY 11794-3651 (United States); Schwarz, A., E-mail: schwarz@math.ucdavis.edu [Department of Mathematics, University of California, Davis, CA 95616 (United States); Xu, Renjun [Department of Physics, University of California, Davis, CA 95616 (United States)
2012-01-11
We study the homology and cohomology groups of super Lie algebras of supersymmetries and of super Poincare Lie algebras in various dimensions. We give complete answers for (non-extended) supersymmetry in all dimensions {<=}11. For dimensions D=10,11 we describe also the cohomology of reduction of supersymmetry Lie algebra to lower dimensions. Our methods can be applied to extended supersymmetry Lie algebras.
A Class of Solvable Lie Algebras and Their Hom-Lie Algebra Structures
Institute of Scientific and Technical Information of China (English)
LI Xiao-chao; LI Dong-ya; JIN Quan-qin
2014-01-01
The finite-dimensional indecomposable solvable Lie algebras s with Q2n+1 as their nilradical are studied and classified, it turns out that the dimension of s is dim Q2n+1+1. Then the Hom-Lie algebra structures on solvable Lie algebras s are calculated.
Introduction to the theory of Lie groups
Godement, Roger
2017-01-01
This textbook covers the general theory of Lie groups. By first considering the case of linear groups (following von Neumann's method) before proceeding to the general case, the reader is naturally introduced to Lie theory. Written by a master of the subject and influential member of the Bourbaki group, the French edition of this textbook has been used by several generations of students. This translation preserves the distinctive style and lively exposition of the original. Requiring only basics of topology and algebra, this book offers an engaging introduction to Lie groups for graduate students and a valuable resource for researchers.
Quasi-big\\`ebres de Lie et cohomologie d'alg\\`ebre de Lie
Bangoura, Momo
2010-01-01
Lie quasi-bialgebras are natural generalisations of Lie bialgebras introduced by Drinfeld. To any Lie quasi-bialgebra structure of finite-dimensional (G, \\mu, \\gamma ,\\phi ?), correspond one Lie algebra structure on D = G\\oplus G*, called the double of the given Lie quasi-bialgebra. We show that there exist on \\Lambda G, the exterior algebra of G, a D-module structure and we establish an isomorphism of D-modules between \\Lambda D and End(\\Lambda G), D acting on \\Lambda D by the adjoint action.
Induced Lie Algebras of a Six-Dimensional Matrix Lie Algebra
Institute of Scientific and Technical Information of China (English)
ZHANG Yu-Feng; LIU Jing
2008-01-01
By using a six-dimensional matrix Lie algebra [Y.F. Zhang and Y. Wang, Phys. Lett. A 360 (2006) 92], three induced Lie algebras are constructed. One of them is obtained by extending Lie bracket, the others are higher-dimensional complex Lie algebras constructed by using linear transformations. The equivalent Lie algebras of the later two with multi-component forms are obtained as well. As their applications, we derive an integrable coupling and quasi-Hamiltonian structure of the modified TC hierarchy of soliton equations.
Kalfaoğlu, Emel; Karabulut, Bünyamin
2016-09-01
Electron paramagnetic resonance (EPR) spectra of VO2+ ions in NaH2PO4·2H2O 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 VO2+ complexes. These are located in different chemical environment and each environment contains four magnetically inequivalent VO2+ sites. The crystal field around VO2+ 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.
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.
Directory of Open Access Journals (Sweden)
Vyacheslav F. Kirichuk
2013-11-01
Full Text Available The study aims the influence of THz radiation on 129.0 GHz of atmospheric oxygen on blood pressure (BP and pulse, hemodynamic parameters of orbital arteries during the irradiation of biological active points of application in healthy volunteers and in patients with involutional macular degeneration (IMD. It had been noticed a decrease of systolic and diastolic components of arterial pressure and pulse; a normalization of systolic velocity of bloodstream (SVB and of resistance index (RI in orbital arteries in patients with IMD. The result of the research is: 1 the method of THz influence of on molecular spectrum of emission and absorption of 129.0 GHz atmospheric oxygen is safe and does not cause any negative side effects on common state in healthy volunteers and in patients with IMD; 2 single of THz influence of molecular spectrum of emission and absorption of 129.0 GHz atmospheric oxygen caused a statistical important improvement in vascular system of eyeball.
Song, Lingchun; Mo, Yirong; Gao, Jiali
2009-01-01
An effective Hamiltonian mixed molecular orbital and valence bond (EH-MOVB) method is described to obtain an accurate potential energy surface for chemical reactions. Building upon previous results on the construction of diabatic and adiabatic potential surfaces using ab initio MOVB theory, we introduce a diabatic-coupling scaling factor to uniformly scale the ab initio off-diagonal matrix element H(12) such that the computed energy of reaction from the EH-MOVB method is in agreement with the target value. The scaling factor is very close to unity, resulting in minimal alteration of the potential energy surface of the original MOVB model. Furthermore, the relative energy between the reactant and product diabatic states in the EH-MOVB method can be improved to match the experimental energy of reaction. A key ingredient in the EH-MOVB theory is that the off-diagonal matrix elements are functions of all degrees of freedom of the system and the overlap matrix is explicitly evaluated. The EH-MOVB method has been applied to the nucleophilic substitution reaction between hydrosulfide and chloromethane to illustrate the methodology and the results were matched to reproduce the results from ab initio valence bond self-consistent valence bond (VBSCF) calculations. The diabatic coupling (the off-diagonal matrix element in the generalized secular equation) has small variations along the minimum energy reaction path in the EH-MOVB model, whereas it shows a maximum value at the transition state and has nearly zero values in the regions of the ion-dipole complexes from VBSCF calculations. The difference in the diabatic coupling stabilization is attributed to the large overlap integral in the computationally efficient MOVB method.
Nigam, Sandeep; Majumder, Chiranjib; Kulshreshtha, S. K.
2004-10-01
The geometric and electronic structures of Sin, Sin+, and AlSin-1 clusters (2⩽n⩽13) have been investigated using the ab initio molecular orbital theory under the density functional theory formalism. The hybrid exchange-correlation energy function (B3LYP) and a standard split-valence basis set with polarization functions [6-31G(d)] were employed for this purpose. Relative stabilities of these clusters have been analyzed based on their binding energies, second difference in energy (Δ 2E) and fragmentation behavior. The equilibrium geometry of the neutral and charged Sin clusters show similar structural growth. However, significant differences have been observed in the electronic structure leading to their different stability pattern. While for neutral clusters, the Si10 is magic, the extra stability of the Si11+ cluster over the Si10+ and Si12+ bears evidence for the magic behavior of the Si11+ cluster, which is in excellent agreement with the recent experimental observations. Similarly for AlSin-1 clusters, which is isoelectronic with Sin+ clusters show extra stability of the AlSi10 cluster suggesting the influence of the electronic structures for different stabilities between neutral and charged clusters. The ground state geometries of the AlSin-1 clusters show that the impurity Al atom prefers to substitute for the Si atom, that has the highest coordination number in the host Sin cluster. The fragmentation behavior of all these clusters show that while small clusters prefers to evaporate monomer, the larger ones dissociate into two stable clusters of smaller size.
Watanabe, Chiduru; Fukuzawa, Kaori; Okiyama, Yoshio; Tsukamoto, Takayuki; Kato, Akifumi; Tanaka, Shigenori; Mochizuki, Yuji; Nakano, Tatsuya
2013-04-01
We develop an inter-fragment interaction energy (IFIE) analysis based on the three- and four-body corrected fragment molecular orbital (FMO3 and FMO4) method to evaluate the interactions of functional group units in structure-based drug design context. The novel subdividing fragmentation method for a ligand (in units of their functional groups) and amino acid residues (in units of their main and side chains) enables us to understand the ligand-binding mechanism in more detail without sacrificing chemical accuracy of the total energy and IFIEs by using the FMO4 method. We perform FMO4 calculations with the second order Møller-Plesset perturbation theory for an estrogen receptor (ER) and the 17β-estradiol (EST) complex using the proposed fragmentation method and assess the interaction for each ligand-binding site by the FMO4-IFIE analysis. When the steroidal EST is divided into two functional units including "A ring" and "D ring", respectively, the FMO4-IFIE analysis reveals their binding affinity with surrounding fragments of the amino acid residues; the "A ring" of EST has polarization interaction with the main chain of Thr347 and two hydrogen bonds with the side chains of Glu353 and Arg394; the "D ring" of EST has a hydrogen bond with the side chain of His524. In particular, the CH/π interactions of the "A ring" of EST with the side chains of Leu387 and Phe404 are easily identified in cooperation with the CHPI program. The FMO4-IFIE analysis using our novel subdividing fragmentation method, which provides higher resolution than the conventional IFIE analysis in units of ligand and each amino acid reside in the framework of two-body approximation, is a useful tool for revealing ligand-binding mechanism and would be applicable to rational drug design such as structure-based drug design and fragment-based drug design.
... Goodlick TA, Kay MD, Glaser JS, Tse DT, Chang WJ. Orbital disease and neuro-ophthalmology. In: Tasman ... 423. Review Date 8/20/2016 Updated by: Franklin W. Lusby, MD, ophthalmologist, Lusby Vision Institute, La ...
Numerical integration of the restricted three-body problem with Lie series
Abouelmagd, Elbaz I.; Guirao, Juan L. G.; Mostafa, A.
2014-12-01
The aim of this work is to present some recurrence formulas for the equations of motion of an infinitesimal body in the planar restricted three-body problem which allow us to integrate numerically this problem via a Lie series approach. For doing this, the equations of motion of the problem are transformed to an origin at one of the libration points and the Lie operator and recurrence formulas for the terms of the Lie series are constructed. In addition, we provide an algorithm that allows us to find any number of Lie series terms and which gives successful calculations for the orbit of the infinitesimal body around one of the libration points. Furthermore, all our mathematical relations are performed under the effect of the zonal harmonic parameters of the bigger primary up to J 4. Finally, a numerical application of these results is given to the case of the Earth-Moon system.
DEFF Research Database (Denmark)
Yazdanfard, Younes; Heegard, Steffen; Fledelius, Hans C.
2001-01-01
Ophthalmology, penetrating orbital injury, orbital foreign body, ultrasound, computed tomography (CT), histology......Ophthalmology, penetrating orbital injury, orbital foreign body, ultrasound, computed tomography (CT), histology...
The Frattini Subalgebra of Restricted Lie Superalgebras
Institute of Scientific and Technical Information of China (English)
Liang Yun CHEN; Dao Ji MENG; Yong Zheng ZHANG
2006-01-01
In the present paper, we study the Frattini subalgebra of a restricted Lie superalgebra (L, [p]). We show first that if L = A1 (⊙) A2 (⊙) … (⊙) An, then φp (L) = φp (A1) + φp (A2) +… +φp (An),where each Ai is a p-ideal of L. We then obtain two results: F(L) = φ(L) = J(L) = L(1) if and only if L is nilpotent; Fp(L) and F(L) are nilpotent ideals of L if L is solvable. In addition, necessary and sufficient conditions are found for φp-free restricted Lie superalgebras. Finally, we discuss the relationships of E-p-restricted Lie superalgebras and E-restricted Lie superalgebras.
Linearization from Complex Lie Point Transformations
Directory of Open Access Journals (Sweden)
Sajid Ali
2014-01-01
Full Text Available Complex Lie point transformations are used to linearize a class of systems of second order ordinary differential equations (ODEs which have Lie algebras of maximum dimension d, with d≤4. We identify such a class by employing complex structure on the manifold that defines the geometry of differential equations. Furthermore we provide a geometrical construction of the procedure adopted that provides an analogue in R3 of the linearizability criteria in R2.
Lie Superalgebras arising from bosonic representation
Jing, Naihuan
2012-01-01
A 2-toroidal Lie superalgebra is constructed using bosonic fields and a ghost field. The superalgebra contains $osp(1|2n)^{(1)}$ as a distinguished subalgebra and behaves similarly to the toroidal Lie superalgebra of type $B(0, n)$. Furthermore this algebra is a central extension of the algebra $osp(1|2n)\\otimes \\mathbb C[s, s^{-1}, t,t^{-1}]$.
Noncommutative geometry with graded differential Lie algebras
Wulkenhaar, Raimar
1997-06-01
Starting with a Hilbert space endowed with a representation of a unitary Lie algebra and an action of a generalized Dirac operator, we develop a mathematical concept towards gauge field theories. This concept shares common features with the Connes-Lott prescription of noncommutative geometry, differs from that, however, by the implementation of unitary Lie algebras instead of associative * -algebras. The general scheme is presented in detail and is applied to functions ⊗ matrices.
Post-Lie algebras and factorization theorems
Ebrahimi-Fard, Kurusch; Mencattini, Igor; Munthe-Kaas, Hans
2017-09-01
In this note we further explore the properties of universal enveloping algebras associated to a post-Lie algebra. Emphasizing the role of the Magnus expansion, we analyze the properties of group like-elements belonging to (suitable completions of) those Hopf algebras. Of particular interest is the case of post-Lie algebras defined in terms of solutions of modified classical Yang-Baxter equations. In this setting we will study factorization properties of the aforementioned group-like elements.
Constructing semisimple subalgebras of semisimple Lie algebras
de Graaf, Willem A
2010-01-01
Algorithms are described that help with obtaining a classification of the semisimple subalgebras of a given semisimple Lie algebra, up to linear equivalence. The algorithms have been used to obtain classifications of the semisimple subalgebras of the simple Lie algebras of ranks <= 8. These have been made available as a database inside the SLA package of GAP4. The subalgebras in this database are explicitly given, as well as the inclusion relations among them.
Lie Admissible Non-Associative Algebras
Institute of Scientific and Technical Information of China (English)
H.Mohammad Ahmadi; Ki-Bong Nam; Jonathan Pakinathan
2005-01-01
A non-associative ring which contains a well-known associative ring or Lie ring is interesting. In this paper, a method to construct a Lie admissible non-associative ring is given; a class of simple non-associative algebras is obtained; all the derivations of the non-associative simple N0,0,1 algebra defined in this paper are determined; and finally, a solid algebra is defined.
Central extension of graded Lie algebras
Welte, Angelika
2010-01-01
In this thesis we describe the universal central extension of two important classes of so-called root-graded Lie algebras defined over a commutative associative unital ring $k.$ Root-graded Lie algebras are Lie algebras which are graded by the root lattice of a locally finite root system and contain enough $\\mathfrak{sl}_2$-triples to separate the homogeneous spaces of the grading. Examples include the infinite rank analogs of the simple finite-dimensional complex Lie algebras. \\\\ In the thesis we show that in general the universal central extension of a root-graded Lie algebra $L$ is not root-graded anymore, but that we can measure quite easily how far it is away from being so, using the notion of degenerate sums, introduced by van der Kallen. We then concentrate on root-graded Lie algebras which are graded by the root systems of type $A$ with rank at least 2 and of type $C$. For them one can use the theory of Jordan algebras.
A twisted generalization of Lie-Yamaguti algebras
Gaparayi, Donatien
2010-01-01
A twisted generalization of Lie-Yamaguti algebras, called Hom-Lie-Yamaguti algebras, is defined. Hom-Lie-Yamaguti algebras generalize Hom-Lie triple systems (and susequently ternary Hom-Nambu algebras) and Hom-Lie algebras in the same way as Lie-Yamaguti algebras generalize Lie triple systems and Lie algebras. It is shown that the category of Hom-Lie-Yamaguti algebras is closed under twisting by self-morphisms. Constructions of Hom-Lie-Yamaguti algebras from classical Lie-Yamaguti algebras and Malcev algebras are given. It is observed that, when the ternary operation of a Hom-Lie-Yamaguti algebra expresses through its binary one in a specific way, then such a Hom-Lie-Yamaguti algebra is a Hom-Malcev algebra.
Detecting true lies:police officers' ability to detect suspects' lies
Mann, Samantha; Vrij, Aldert; Bull, Ray
2004-01-01
Ninety-nine police officers, not identified in previous research as belonging to groups which are superior in lie detection, attempted to detect truths and lies told by suspects during their videotaped police interviews. Accuracy rates were higher than typically found in deception research and reached levels similar to those obtained by specialized lie detectors in previous research. Accuracy was positively correlated with perceived experience in interviewing suspects and with mentioning cues...
Ozdogan, Telhat
2006-01-01
In a recent publication (Telhat Ozdogan, Int. J. Quantum Chem., 92 (2003) 419), we presented a unified algorithm for the evaluation of multicenter multielectron integrals over Slater type orbitals with noninteger principal quantum numbers, using the one center expansion formula for Slater type orbitals with integer principal quantum numbers (E. Oztekin et. all., J. Mol. Struct. Theochem, 544 (2001) 69; I.I. Guseinov et all., Z. Struct. Khim., 23 (1987) 148 (in Russian)). Guseinov in his comme...
Orbital science's 'Bermuda Triangle'
Sherrill, Thomas J.
1991-02-01
The effects of a part of the inner Van Allen belt lying closest to the earth, known as the South Atlantic Anomaly (SAA) upon spacecraft including the Hubble Space Telescope (HST), are discussed. The area consists of positively charged ions and electrons from the Van Allen Belt which become trapped in the earth's dipole field. Contor maps representing the number of protons per square centimeter per second having energies greater than 10 million electron volts are presented. It is noted that the HST orbit causes it to spend about 15 percent of its time in the SAA, but that, unlike the experience with earlier spacecraft, the satellite's skin, internal structure, and normal electronic's packaging provides sufficient protection against eletrons, although some higher energy protons still get through. Various charged particle effects which can arise within scientific instruments including fluorescence, Cerenkov radiation, and induced radioactivity are described.
Lie algebraic similarity transformed Hamiltonians for lattice model systems
Wahlen-Strothman, Jacob M.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Scuseria, Gustavo E.
2015-01-01
We present a class of Lie algebraic similarity transformations generated by exponentials of two-body on-site Hermitian operators whose Hausdorff series can be summed exactly without truncation. The correlators are defined over the entire lattice and include the Gutzwiller factor ni ↑ni ↓ , and two-site products of density (ni ↑+ni ↓) and spin (ni ↑-ni ↓) operators. The resulting non-Hermitian many-body Hamiltonian can be solved in a biorthogonal mean-field approach with polynomial computational cost. The proposed similarity transformation generates locally weighted orbital transformations of the reference determinant. Although the energy of the model is unbound, projective equations in the spirit of coupled cluster theory lead to well-defined solutions. The theory is tested on the one- and two-dimensional repulsive Hubbard model where it yields accurate results for small and medium sized interaction strengths.
Statistical properties of high-lying chaotic eigenstates
Li, B; Li, Baowen; Robnik, Marko
1995-01-01
We study the statistical properties of the high-lying chaotic eigenstates (200,000 and above) which are deep in the semiclassical regime. The system we are analyzing is the billiard system inside the region defined by the quadratic (complex) conformal map of the unit disk as introduced by Robnik (1983). We are using Heller's method of plane wave decomposition of the numerical eigenfunctions, and perform extensive statistical analysis with the following conclusions: (1) The local average probability density is in excellent agreement with the microcanonical assumption and all statistical properties are also in excellent agreement with the Gaussian random model; \\qquad (2) The autocorrelation function is found to be strongly direction dependent and only after averaging over all directions agrees well with Berry's (1977) prediction; \\qquad (3) Although the scars of unstable classical periodic orbits (in such ergodic regime) are expected to exist, so far we have not found any (around 200,000th state) but a scar-li...
Lee, Sung Keun; Stebbins, Jonathan F.
2006-08-01
Estimation of the framework connectivity and the atomic structure of depolymerized silicate melts and glasses (NBO/T > 0) remains a difficult question in high-temperature geochemistry relevant to magmatic processes and glass science. Here, we explore the extent of disorder and the nature of polymerization in binary Ca-silicate and ternary Ca-aluminosilicate glasses with varying NBO/T (from 0 to 2.67) using O-17 NMR at two different magnetic fields of 9.4 and 14.1 T in conjunction with quantum chemical calculations. Non-random distributions among framework cations (Si and Al) are demonstrated in the variation of relative populations of oxygen sites with NBO/T. The proportion of non-bridging oxygen (NBO, Ca-O-Si) in the binary and ternary aluminosilicate glasses increases with NBO/T. While the trend is consistent with predictions from composition, the detailed fractions apparently deviate from the predicted values, suggesting further complications in the nature of polymerization. The proportion of each bridging oxygen in the glasses also varies with NBO/T. The fractions of Al-O-Si and Al-O-Al increase with increasing polymerization as CaO is replaced with Al 2O 3, while that of Si-O-Si seems to decrease, implying that activity of silica may decrease from calcium silicate to polymerized aluminosilicates (X=constant). Quantum chemical molecular orbital calculations based on density functional theory show that a silicate chain with Al-NBO (Ca-O-Al) has an energy penalty (calculated cluster energy difference) of about 108 kJ/mol compared with the cluster with Ca-O-Si, consistent with preferential depolymerization of Si-networks, reported in an earlier O-17 NMR study [Allwardt, J., Lee, S.K., Stebbins, J.F., 2003. Bonding preferences of non-bridging oxygens in calcium aluminosilicate glass: Evidence from O-17 MAS and 3QMAS NMR on calcium aluminate glass. Am. Mineral.88, 949-954]. These prominent types of non-randomness in the distributions suggest significant chemical
Sati, Hisham
2015-01-01
We uncover higher algebraic structures on Noether currents and BPS charges. It is known that equivalence classes of conserved currents form a Lie algebra. We show that at least for target space symmetries of higher parameterized WZW-type sigma-models this naturally lifts to a Lie (p+1)-algebra structure on the Noether currents themselves. Applied to the Green-Schwarz-type action functionals for super p-brane sigma-models this yields super Lie (p+1)-algebra refinements of the traditional BPS brane charge extensions of supersymmetry algebras. We discuss this in the generality of higher differential geometry, where it applies also to branes with (higher) gauge fields on their worldvolume. Applied to the M5-brane sigma-model we recover and properly globalize the M-theory super Lie algebra extension of 11-dimensional superisometries by 2-brane and 5-brane charges. Passing beyond the infinitesimal Lie theory we find cohomological corrections to these charges in higher analogy to the familiar corrections for D-brane...
Directory of Open Access Journals (Sweden)
Andrés Reyes
2009-06-01
Full Text Available Con el fin optimizar las geometrías promedio de sistemas moleculares utilizando la teoría del orbital molecular nuclear y electrónico (OMNE, se dedujo la expresión para el cálculo del gradiente analítico de la energía a nivel de teoría Hartree-Fock, para cualquier tipo de especie cuántica. La implementación computacional se realizó dentro del paquete APMO (Any-Particle Molecular Orbital y con el fin de comprobar la correcta implementación del método se calcularon las moléculas modelo H2, HF y H2O, por medio de métodos numéricos y analíticos. El uso de derivadas analíticas dentro del formalismo OMNE permitirá el cálculo más eficiente de la estructura núcleo-electrónica de sistemas moleculares con el paquete APMO.
Lie algebras for time evolution with applications from chaos studies to spintronics
Wendler, Tim G.; Berrondo, Manuel; Beus, Ty; Sayer, Ryan T.; van Huele, Jean-Francois S.
2012-10-01
We illustrate the power of Lie algebras in computing the time evolution of quantum systems with time-dependent physical parameters. By factorizing the quantum mechanical time evolution operator and using the linear independence of the Lie algebra generators, we reduce the operator equations to systems of coupled ordinary differential equations of scalar functions applicable to a variety of dynamical systems. We use the results to explore the possibility of detecting chaos in quantum nonlinear oscillators based on criteria from classical chaos studies and to follow spin currents in time-dependent spin-orbit coupled media.
Riemannian manifolds as Lie-Rinehart algebras
Pessers, Victor; van der Veken, Joeri
2016-07-01
In this paper, we show how Lie-Rinehart algebras can be applied to unify and generalize the elementary theory of Riemannian geometry. We will first review some necessary theory on a.o. modules, bilinear forms and derivations. We will then translate some classical theory on Riemannian geometry to the setting of Rinehart spaces, a special kind of Lie-Rinehart algebras. Some generalized versions of classical results will be obtained, such as the existence of a unique Levi-Civita connection, inducing a Levi-Civita connection on a submanifold, and the construction of spaces with constant sectional curvature.
Jardino, Sergio
2010-01-01
We extend the concept of a generalized Lie 3-algebra, known to octonions $\\mathbb{O}$, to split-octonions $\\mathbb{SO}$. In order to do that, we introduce a notational device that unifies the two elements product of both of the algebras. We have also proved that $\\mathbb{SO}$ is a Malcev algebra and have recalculated known relations for the structure constants in terms of the introduced structure tensor. An application of the split Lie $3-$algebra to a Bagger and Lambert gauge theory is also discussed.
Integrability of Lie Systems Through Riccati Equations
Cariñena, José F.; de Lucas, Javier
Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides us with a unified geometrical viewpoint that allows us to analyse some previous works on the topic and explain new properties. Moreover, this new approach can be straightforwardly generalised to describe integrability conditions for any Lie system. Finally, we show the usefulness of our treatment in order to study the problem of the linearisability of Riccati equations.
Integrability of Lie systems through Riccati equations
Cariñena, José F
2010-01-01
Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides us with a unified geometrical viewpoint that allows us to analyse some previous works on the topic and explain new properties. Moreover, this new approach can be straightforwardly generalised to describe integrability conditions for any Lie system. Finally, we show the usefulness of our treatment in order to study the problem of the linearisability of Riccati equations.
Quiver Gauge theories from Lie Superalgebras
Belhaj, A
2012-01-01
We discuss quiver gauge models with matter fields based on Dynkin diagrams of Lie superalgebra structures. We focus on A(1,0) case and we find first that it can be related to intersecting complex cycles with genus $g$. Using toric geometry, A(1,0) quivers are analyzed in some details and it is shown that A(1,0) can be used to incorporate fundamental fields to a product of two unitary factor groups. We expect that this approach can be applied to other kinds of Lie superalgebras;
Spiders for rank 2 Lie algebras
Kuperberg, G
1996-01-01
A spider is an axiomatization of the representation theory of a group, quantum group, Lie algebra, or other group or group-like object. We define certain combinatorial spiders by generators and relations that are isomorphic to the representation theories of the three rank two simple Lie algebras, namely A2, B2, and G2. They generalize the widely-used Temperley-Lieb spider for A1. Among other things, they yield bases for invariant spaces which are probably related to Lusztig's canonical bases, and they are useful for computing quantities such as generalized 6j-symbols and quantum link invariants.
Lie algebra contractions and separation of variables
Vinternits, P; Pogosyan, G S; Sissakian, A N
2001-01-01
The concept of analytical Lie group contractions is introduced to relate the separation of variables in space of constant nonzero curvature to separation in Euclidean or pseudo-Euclidean spaces. The contraction parameter is introduced explicitly into the basis of the Lie algebra, the Laplace-Beltrami operator, the complete set of commuting operators, the coordinates themselves and into the solutions. This enables to obtain asymptotic formulae connecting special functions related to the groups O(n) and O(n,1) to those related to Euclidean and pseudo-Euclidean groups
Lie Point Symmetries of Differential-Difference Equations
Institute of Scientific and Technical Information of China (English)
DING Wei; TANG Xiao-Yan
2004-01-01
In this paper, the classical Lie group approach is extended to find some Lie point symmetries of differentialdifference equations. It reveals that the obtained Lie point symmetries can constitute a Kac-Moody-Virasoro algebra.
Generalized double extension and descriptions of qadratic Lie superalgebras
Bajo, I; Bordemann, M
2007-01-01
A Lie superalgebra endowed with a supersymmetric, even, non-degenerate, invariant bilinear form is called a quadratic Lie superalgebra. In this paper we give inductive descriptions of quadratic Lie superalgebras in terms of generalized double extensions.
The Lie Algebras in which Every Subspace s Its Subalgebra
Institute of Scientific and Technical Information of China (English)
WU MING-ZHONG
2009-01-01
In this paper, we study the Lie algebras in which every subspace is its subalgebra (denoted by HB Lie algebras). We get that a nonabelian Lie algebra is an HB Lie algebra if and only if it is isomorphic to g+Cidg, where g is an abelian Lie algebra. Moreover we show that the derivation algebra and the holomorph of a nonabelian HB Lie algebra are complete.
Lie, truth, lie: the role of task switching in a deception context.
Debey, Evelyne; Liefooghe, Baptist; De Houwer, Jan; Verschuere, Bruno
2015-05-01
A cornerstone of the task switching literature is the finding that task performance is typically slower and more error-prone when the task switches than when it repeats. So far, deception research has largely ignored that such cognitive switch costs should also emerge when switching between truth telling and lying, and may affect the cognitive cost of lying as reflected in higher prefrontal brain activity and slower and less accurate responding compared to truth telling. To get a grasp on the relative size of the switch costs associated with lying and truth telling, the current study had participants perform a reaction time-based deception task, in which they alternated between lying and telling the truth to yes/no questions that were related to activities performed in the lab (Experiment 1) or neutral autobiographical facts (Experiment 2). In both experiments, the error and reaction time switch costs were found to be equally large for switching from truth telling to lying and from lying to truth telling. This symmetry in switch costs can be explained from the hypothesis that lying requires a first step of truth telling, and demonstrates that task switching does not contribute to the cognitive cost of lying when the repetition/switch ratio is balanced. Theoretical and methodological implications are considered.
Lying in Business : Insights from Hannah Arendt’s ‘Lying in Politics’
Eenkhoorn, P.; Graafland, J.J.
2010-01-01
The famous political philosopher Hannah Arendt develops several arguments why truthfulness cannot be counted among the political virtues. This article shows that similar arguments apply to lying in business. Based on Hannah Arendt’s theory, we distinguish five reasons why lying is a structural tempt
Teaching the Truth about Lies to Psychology Students: The Speed Lying Task
Pearson, Matthew R.; Richardson, Thomas A.
2013-01-01
To teach the importance of deception in everyday social life, an in-class activity called the "Speed Lying Task" was given in an introductory social psychology class. In class, two major research findings were replicated: Individuals detected deception at levels no better than expected by chance and lie detection confidence was unrelated…
Lying in Business : Insights from Hannah Arendt’s ‘Lying in Politics’
Eenkhoorn, P.; Graafland, J.J.
2010-01-01
The famous political philosopher Hannah Arendt develops several arguments why truthfulness cannot be counted among the political virtues. This article shows that similar arguments apply to lying in business. Based on Hannah Arendt’s theory, we distinguish five reasons why lying is a structural tempt
Lying in Business : Insights from Hannah Arendt’s ‘Lying in Politics’
Eenkhoorn, P.; Graafland, J.J.
2010-01-01
The famous political philosopher Hannah Arendt develops several arguments why truthfulness cannot be counted among the political virtues. This article shows that similar arguments apply to lying in business. Based on Hannah Arendt’s theory, we distinguish five reasons why lying is a structural
Teaching the Truth about Lies to Psychology Students: The Speed Lying Task
Pearson, Matthew R.; Richardson, Thomas A.
2013-01-01
To teach the importance of deception in everyday social life, an in-class activity called the "Speed Lying Task" was given in an introductory social psychology class. In class, two major research findings were replicated: Individuals detected deception at levels no better than expected by chance and lie detection confidence was unrelated…
Why Do Lie-Catchers Fail? A Lens Model Meta-Analysis of Human Lie Judgments
Hartwig, Maria; Bond, Charles F., Jr.
2011-01-01
Decades of research has shown that people are poor at detecting lies. Two explanations for this finding have been proposed. First, it has been suggested that lie detection is inaccurate because people rely on invalid cues when judging deception. Second, it has been suggested that lack of valid cues to deception limits accuracy. A series of 4…
Hydrogenoid orbitals revisited: From Slater orbitals to Coulomb Sturmians
Indian Academy of Sciences (India)
Danilo Calderini; Simonetta Cavalli; Cecilia Coletti; Gaia Grossi; Vincenzo Qquilanti
2012-01-01
The simple connection between the Slater orbitals, venerable in quantum chemistry, and the Coulomb Sturmian orbitals, more recently employed in atomic and molecular physics, is pointed out explicitly in view of the renewed interest in both as basis sets in applied quantum mechanics. Research in Slater orbitals mainly concerns multicentre, many-body integrals, whereas that on Sturmians exploits their orthonormality and completeness with no need of continuum states. An account of recent progress is outlined, also with reference to relationships between the two basis sets, and with the momentum space and hyperspherical harmonics representations.
The Apsidal Precession for Low Earth Sun Synchronized Orbits
Directory of Open Access Journals (Sweden)
Shkelzen Cakaj
2015-09-01
Full Text Available By nodal regression and apsidal precession, the Earth flattering at satellite low Earth orbits (LEO is manifested. Nodal regression refers to the shift of the orbit’s line of nodes over time as Earth revolves around the Sun. Nodal regression is orbit feature utilized for circular orbits to be Sun synchronized. A sun¬-synchronized orbit lies in a plane that maintains a fixed angle with respect to the Earth-Sun direction. In the low Earth Sun synchronized circular orbits are suited the satellites that accomplish their photo imagery missions. Nodal regression depends on orbital altitude and orbital inclination angle. For the respective orbital altitudes the inclination window for the Sun synchronization to be attained is determined. The apsidal precession represents major axis shift, respectively the argument of perigee deviation. The apsidal precession simulation, for inclination window of sun synchronized orbital altitudes, is provided through this paper.
Hiding an Inconvenient Truth : Lies and Vagueness
Serra Garcia, M.; van Damme, E.E.C.; Potters, J.J.M.
2010-01-01
When truth conflicts with e¢ ciency, can verbal communication destroy efficiency? Or are lies or vagueness used to hide inconvenient truths? We consider a sequential 2-player public good game in which the leader has private information about the value of the public good. This value can be low, high,
Are 'Lying Compositions' Detrimental To Student Growth?
Institute of Scientific and Technical Information of China (English)
2010-01-01
@@ A greater number of primary school students are inventing stories and telling lies when they are supposed to be writing about personal experiences. The Chengdu Business Daily said, of 40 pupils in a grade-four class, 30 wrote about how they struggled with human traffickers or thieves, and 26 pupils admitted they made the stories up.
Lie Algebra of Noncommutative Inhomogeneous Hopf Algebra
Lagraa, M
1997-01-01
We construct the vector space dual to the space of right-invariant differential forms construct from a first order differential calculus on inhomogeneous quantum group. We show that this vector space is equipped with a structure of a Hopf algebra which closes on a noncommutative Lie algebra satisfying a Jacobi identity.
SAYD modules over Lie-Hopf algebras
Rangipour, B
2011-01-01
In this paper a general van Est type isomorphism is established. The isomorphism is between the Lie algebra cohomology of a bicrossed sum Lie algebra and the Hopf cyclic cohomology of its Hopf algebra. We first prove a one to one correspondence between stable-anti-Yetter-Drinfeld (SAYD) modules over the total Lie algebra and SAYD modules over the associated Hopf algebra. In contrast to the non-general case done in our previous work, here the van Est isomorphism is found at the first level of a natural spectral sequence, rather than at the level of complexes. It is proved that the Connes-Moscovici Hopf algebras do not admit any finite dimensional SAYD modules except the unique one-dimensional one found by Connes- Moscovici in 1998. This is done by extending our techniques to work with the infinite dimensional Lie algebra of formal vector fields. At the end, the one to one correspondence is applied to construct a highly nontrivial four dimensional SAYD module over the Schwarzian Hopf algebra. We then illustrate...
Happiness lies somewhere in your brain
Institute of Scientific and Technical Information of China (English)
梅寒
2007-01-01
<正> When I was a kid,I defined happinessas being able to afford anything that was de-sired and thus I came up with the conclusionthat happiness lies in the possession of mon-ey.Time turned me tall and smart,also,able
Lie algebras and linear differential equations.
Brockett, R. W.; Rahimi, A.
1972-01-01
Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.
On Split Lie Triple Systems II
Indian Academy of Sciences (India)
Antonio J Calderón Martín; M Forero Piulestán
2010-04-01
In [4] it is studied that the structure of split Lie triple systems with a coherent 0-root space, that is, satisfying $[T_0,T_0,T]=0$ and $[T_0,T_,T_0]≠ 0$ for any nonzero root and where $T_0$ denotes the 0-root space and $T_$ the -root space, by showing that any of such triple systems with a symmetric root system is of the form $T=\\mathcal{U}+\\sum_j I_j$ with $\\mathcal{U}$ a subspace of the 0-root space $T_0$ and any $I_j$ a well described ideal of , satisfying $[I_j,T,I_k]=0$ if $j≠ k$. It is also shown in [4] that under certain conditions, a split Lie triple system with a coherent 0-root space is the direct sum of the family of its minimal ideals, each one being a simple split Lie triple system, and the simplicity of is characterized. In the present paper we extend these results to arbitrary split Lie triple systems with no restrictions on their 0-root spaces.
SAYD Modules over Lie-Hopf Algebras
Rangipour, Bahram; Sütlü, Serkan
2012-11-01
In this paper a general van Est type isomorphism is proved. The isomorphism is between the Lie algebra cohomology of a bicrossed sum Lie algebra and the Hopf cyclic cohomology of its Hopf algebra. We first prove a one to one correspondence between stable-anti-Yetter-Drinfeld (SAYD) modules over the total Lie algebra and those modules over the associated Hopf algebra. In contrast to the non-general case done in our previous work, here the van Est isomorphism is proved at the first level of a natural spectral sequence, rather than at the level of complexes. It is proved that the Connes-Moscovici Hopf algebras do not admit any finite dimensional SAYD modules except the unique one-dimensional one found by Connes-Moscovici in 1998. This is done by extending our techniques to work with the infinite dimensional Lie algebra of formal vector fields. At the end, the one to one correspondence is applied to construct a highly nontrivial four dimensional SAYD module over the Schwarzian Hopf algebra. We then illustrate the whole theory on this example. Finally explicit representative cocycles of the cohomology classes for this example are calculated.
Datta, Dipayan; Kossmann, Simone; Neese, Frank
2016-09-01
The domain-based local pair-natural orbital coupled-cluster (DLPNO-CC) theory has recently emerged as an efficient and powerful quantum-chemical method for the calculation of energies of molecules comprised of several hundred atoms. It has been demonstrated that the DLPNO-CC approach attains the accuracy of a standard canonical coupled-cluster calculation to about 99.9% of the basis set correlation energy while realizing linear scaling of the computational cost with respect to system size. This is achieved by combining (a) localized occupied orbitals, (b) large virtual orbital correlation domains spanned by the projected atomic orbitals (PAOs), and (c) compaction of the virtual space through a truncated pair natural orbital (PNO) basis. In this paper, we report on the implementation of an analytic scheme for the calculation of the first derivatives of the DLPNO-CC energy for basis set independent perturbations within the singles and doubles approximation (DLPNO-CCSD) for closed-shell molecules. Perturbation-independent one-particle density matrices have been implemented in order to account for the response of the CC wave function to the external perturbation. Orbital-relaxation effects due to external perturbation are not taken into account in the current implementation. We investigate in detail the dependence of the computed first-order electrical properties (e.g., dipole moment) on the three major truncation parameters used in a DLPNO-CC calculation, namely, the natural orbital occupation number cutoff used for the construction of the PNOs, the weak electron-pair cutoff, and the domain size cutoff. No additional truncation parameter has been introduced for property calculation. We present benchmark calculations on dipole moments for a set of 10 molecules consisting of 20-40 atoms. We demonstrate that 98%-99% accuracy relative to the canonical CCSD results can be consistently achieved in these calculations. However, this comes with the price of tightening the
Geometric orbit datum and orbit covers
Institute of Scientific and Technical Information of China (English)
梁科; 侯自新
2001-01-01
Vogan conjectured that the parabolic induction of orbit data is independent of the choice of the parabolic subgroup. In this paper we first give the parabolic induction of orbit covers, whose relationship with geometric orbit datum is also induced. Hence we show a geometric interpretation of orbit data and finally prove the conjugation for geometric orbit datum using geometric method.
Jasmine, N Jeeva; Muthiah, P Thomas; Arunagiri, C; Subashini, A
2015-06-05
The FT-IR, FT-Raman, (1)H, (13)C NMR and UV-Visible spectral measurements of N'-hydroxy-pyrimidine-2-carboximidamide (HPCI) and complete analysis of the observed spectra have been proposed. DFT calculation has been performed and the structural parameters of the compound was determined from the optimized geometry with 6-311+G(d,p) basis set and giving energies, harmonic vibrational frequencies and force constants. The results of the optimized molecular structure are presented and compared with the experimental. The geometric parameters, harmonic vibrational frequencies and chemical shifts were compared with the experimental data of the molecule. The title compound, C5H6N4O, is approximately planar, with an angle of 11.04 (15)°. The crystal structure is also stabilized by intermolecular N-H⋯O, N-H⋯N, O-H⋯N, C-H⋯O hydrogen bond and offset π-π stacking interactions. The influences of hydroxy and carboximidamide groups on the skeletal modes and proton chemical shifts have been investigated. Moreover, we have not only simulated highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) but also determined the transition state and band gap. The kinetic, thermodynamic stability and chemical hardness of the molecule have been determined. Complete NBO analysis was also carried out to find out the intermolecular electronic interactions and their stabilization energy. The thermodynamic properties like entropies and their correlations with temperatures were also obtained from the harmonic frequencies of the optimized structure.
Lee, S.; Doyle, C. S.; Stebbins, J. F.
2001-12-01
Aluminosilicate melts are one of the dominant components in upper mantle and crust. Essential to the thermodynamic and transport properties of these systems is the full understanding on the atomic arrangements and the extent of disorder. Recent quantification of the extent of disorder among 'framework cations' in silicate melts using NMR provided improved prospects on the atomic structure of the glasses and melt and their corresponding properties and allowed the degree of randomness to be evaluated in terms of the degree of Al-avoidance (Q) and degree of phase separations (P) (Lee and Stebbins, J. Phys. Chem. B 104, 4091; Lee and Stebbins, GCA in press). Quantitative estimation of the extent of disorder among 'charge-balancing cations' including Na in aluminosilicate glasses, however, has remained an unsolved problem and these cations have often been assumed to be randomly distributed. Here, we explore the intermediate range order around Na in charge-balanced aluminosilicate glasses using Na-23 NMR and Near-edge X-ray absorption fine structure (NEXAFS) with full multiple scattering (FMS) simulations combined with ab initio molecular orbital calculations. We also quantify the extent of disorder in charge balancing cations as a function of Na-O bond length (d(Na-O)) distribution with composition and present a structural model favoring ordered Na distributions. Peak position in Na-23 magic angle spinning (MAS) spectra of aluminosilicate glasses with varying R (Si/Al) at 14.1 T varies from -10.28 ppm (R = 0.7) to -19.98 ppm (R = 6). These results suggest that average d(Na-O) increases with increasing R, which is confirmed by Na-23 multiple quantum MAS spectra where the chemical shift moves toward lower frequency with increasing Si and shows the individual Gaussian components of Na-O distributions such as Na-(Al-O-Al), Na-(Si-O-Al) and Na-(Si-O-Si). Calculated d(Na-(Al-O-Al)) of 2.57 Å is shorter than d(Na-(Si-O-Si)) of 2.88 Å. Strong compositional dependence is
Orbit Classification of Qutrit via the Gram Matrix
Institute of Scientific and Technical Information of China (English)
B. A. Tay; Hishamuddin Zainuddin
2008-01-01
We classify the orbits generated by unitary transformation on the density matrices of the three-state quantum systems (qutrits) via the Gram matrix. The Gram matrix is a real symmetric matrix formed from the Hilbert-Schmidt scalar products of the vectors lying in the tangent space to the orbits. The rank of the Gram matrix determines the dimensions of the orbits, which fall into three classes for qutrits.
The low-lying rotational bands of the neutron-rich nucleus 172Tm
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The microscopic mechanism of four experimentally observed bands in 172Tm is investigated using the particle-number conserving method of the cranked shell model with monopole and quadrupole paring interactions.The experimental results,including the moments of inertia and angular momentum alignments of four bands in 172Tm are reproduced well by the particle-number conserving calculations.The ω variation of the occupation probability of each cranked orbital and the contribution to moment of inertia from each cranked orbital are analyzed.Other unobserved low-lying bands of 2-quansiparticles in 172Tm are predicted.
The low-lying rotational bands of the neutron-rich nucleus 172Tm
Institute of Scientific and Technical Information of China (English)
CHEN BaoRen; LI Tao; LIU ShuXin
2009-01-01
The microscopic mechanism of four experimentally observed bands in 172Tm is investigated using the particle-number conserving method of the cranked shell model with monopole and quadrupole paring interactions.The experimental results,including the momenta of inertia and angular momentum alignments of four bands in 172Tm are reproduced well by the particle-number conserving calculations.The ω variation of the occupation probability of each cranked orbital and the contribution to moment of inertia from each cranked orbital are analyzed.Other unobserved low-lying bands of 2-quansiparticles in 172Tm are predicted.
STS-31 Discovery, OV-103, rockets through low-lying clouds after KSC liftoff
1990-01-01
STS-31 Discovery, Orbiter Vehicle (OV) 103, rides above the firey glow of the solid rocket boosters (SRBs) and space shuttle main engines (SSMEs) and a long trail of exhaust as it heads toward Earth orbit. Kennedy Space Center (KSC) Launch Complex (LC) Pad 39B is covered in an exhaust cloud moments after the liftoff of OV-103 at 8:33:51.0492 am (Eastern Daylight Time (EDT)). The exhaust plume pierces the low-lying clouds as OV-103 soars into the clear skies above. A nearby waterway appears in the foreground.
Shell model description of low-lying states in Po and Rn isotopes
Higashiyama, Koji; Yoshinaga, Naotaka
2014-03-01
Nuclear structure of the Po and Rn isotopes is theoretically studied in terms of the spherical shell model with the monopole- and quadrupole-pairing plus quadrupole-quadrupole effective interaction. The experimental energy levels of low-lying states are well reproduced. The shell model results are examined in detail in a pair-truncated shell model. The analysis reveals the alignment of two protons in the 0h9/2 orbital at spin 8.
Shell model description of low-lying states in Po and Rn isotopes
Directory of Open Access Journals (Sweden)
Higashiyama Koji
2014-03-01
Full Text Available Nuclear structure of the Po and Rn isotopes is theoretically studied in terms of the spherical shell model with the monopole- and quadrupole-pairing plus quadrupole-quadrupole effective interaction. The experimental energy levels of low-lying states are well reproduced. The shell model results are examined in detail in a pair-truncated shell model. The analysis reveals the alignment of two protons in the 0h9/2 orbital at spin 8.
Dimension of the $c$-nilpotent multiplier of Lie algebras
Indian Academy of Sciences (India)
MEHDI ARASKHAN; MOHAMMAD REZA RISMANCHIAN
2016-08-01
The purpose of this paper is to derive some inequalities for dimension of the $c$-nilpotent multiplier of finite dimensional Lie algebras and their factor Lie algebras. We further obtain an inequality between dimensions of $c$-nilpotent multiplier of Lie algebra $L$ and tensor product of a central ideal by its abelianized factor Lie algebra
Legitimate lies : The relationship between omission, commission, and cheating
Pittarello, Andrea; Rubaltelli, Enrico; Motro, Daphna
2016-01-01
Across four experiments, we show that when people can serve their self-interest, they are more likely to refrain from reporting the truth ( lie of omission) than actively lie ( lie of commission). We developed a novel online "Heads or Tails" task in which participants can lie to win a monetary prize
Whittaker categories and strongly typical Whittaker modules for Lie superalgebras
Bagci, Irfan; Wiesner, Emilie
2012-01-01
Following analogous constructions for Lie algebras, we define Whittaker modules and Whittaker categories for finite-dimensional simple Lie superalgebras. Results include a decomposition of Whittaker categories for a Lie superalgebra according to the action of an appropriate sub-superalgebra; and, for basic classical Lie superalgebras of type I, a description of the strongly typical simple Whittaker modules.
A Local Characterization of Lie Homomorphisms of Nest Algebras
Institute of Scientific and Technical Information of China (English)
YANG Miao-xia; ZHANG Jian-hua
2014-01-01
In this paper, linear maps preserving Lie products at zero points on nest algebras are studied. It is proved that every linear map preserving Lie products at zero points on any finite nest algebra is a Lie homomorphism. As an application, the form of a linear bijection preserving Lie products at zero points between two finite nest algebras is obtained.
Lie symmetries for equations in conformal geometries
Hansraj, S; Msomi, A M; Govinder, K S
2005-01-01
We seek exact solutions to the Einstein field equations which arise when two spacetime geometries are conformally related. Whilst this is a simple method to generate new solutions to the field equations, very few such examples have been found in practice. We use the method of Lie analysis of differential equations to obtain new group invariant solutions to conformally related Petrov type D spacetimes. Four cases arise depending on the nature of the Lie symmetry generator. In three cases we are in a position to solve the master field equation in terms of elementary functions. In the fourth case special solutions in terms of Bessel functions are obtained. These solutions contain known models as special cases.
Geodesic models generated by Lie symmetries
Abebe, G Z; Govinder, K S
2014-01-01
We study the junction condition relating the pressure to the heat flux at the boundary of a shearing and expanding spherically symmetric radiating star when the fluid particles are travelling in geodesic motion. The Lie symmetry generators that leave the junction condition invariant are identified and the optimal system is generated. We use each element of the optimal system to transform the partial differential equation to an ordinary differential equation. New exact solutions, which are group invariant under the action of Lie point infinitesimal symmetries, are found. We obtain families of traveling wave solutions and self-similar solutions, amongst others. The gravitational potentials are given in terms of elementary functions, and the line elements can be given explicitly in all cases. We show that the Friedmann dust model is regained as a special case, and we can connect our results to earlier investigations.
Analytic factorization of Lie group representations
DEFF Research Database (Denmark)
Gimperlein, Heiko; Krötz, Bernhard; Lienau, Christoph
2012-01-01
For every moderate growth representation (p,E)(p,E) of a real Lie group G on a Fréchet space, we prove a factorization theorem of Dixmier–Malliavin type for the space of analytic vectors E¿E¿. There exists a natural algebra of superexponentially decreasing analytic functions A(G)A(G), such that E......¿=¿(A(G))E¿E¿=¿(A(G))E¿. As a corollary we obtain that E¿E¿ coincides with the space of analytic vectors for the Laplace–Beltrami operator on G.......For every moderate growth representation (p,E)(p,E) of a real Lie group G on a Fréchet space, we prove a factorization theorem of Dixmier–Malliavin type for the space of analytic vectors E¿E¿. There exists a natural algebra of superexponentially decreasing analytic functions A(G)A(G), such that E...
Constructions of Lie algebras and their modules
Seligman, George B
1988-01-01
This book deals with central simple Lie algebras over arbitrary fields of characteristic zero. It aims to give constructions of the algebras and their finite-dimensional modules in terms that are rational with respect to the given ground field. All isotropic algebras with non-reduced relative root systems are treated, along with classical anisotropic algebras. The latter are treated by what seems to be a novel device, namely by studying certain modules for isotropic classical algebras in which they are embedded. In this development, symmetric powers of central simple associative algebras, along with generalized even Clifford algebras of involutorial algebras, play central roles. Considerable attention is given to exceptional algebras. The pace is that of a rather expansive research monograph. The reader who has at hand a standard introductory text on Lie algebras, such as Jacobson or Humphreys, should be in a position to understand the results. More technical matters arise in some of the detailed arguments. T...
ON THE PRIMARY DECOMPOSITION THEOREM OF MODULAR LIE SUPERALGEBRAS
Institute of Scientific and Technical Information of China (English)
CHEN LIANGYUN; MENG DAOJI
2005-01-01
This gives some identities of associative Lie superalgebras and some properties of modular Lie superalgebras. Furthermore, the primry decomposition theorem of modular Lie superalgebras is shown. It is well known that the primary decomposition theorem of modular Lie algebras has played an important role in the classification of the finite-dimensional simple modular Lie algebras (see [5, 6]). Analogously, the primary decomposition theorem of modular Lie superalgebras may play an important role in the open classification of the finite dimensional simple modular Lie superalgebras.
Abstract Lie groups and locally compact topological groups
Directory of Open Access Journals (Sweden)
Jacek Lech
2004-05-01
Full Text Available We introduce a notion of abstract Lie group by means of the mapping which plays the role of the evolution operator. We show some basic properties of such groups very similar to the fundamentals of the infinite dimensional Lie theory. Next we give remarkable examples of abstract Lie groups which are not necessarily usual Lie groups. In particular, by making use of Yamabe theorem we prove that any locally compact topological group admits the structure of abstract Lie group and that the Lie algebra and the exponential mapping of it coincide with those determined by the Lie group structure.
Energy Technology Data Exchange (ETDEWEB)
Michelotti, L.
1995-01-01
The past fifteen years have witnessed a remarkable development of methods for analyzing single particle orbit dynamics in accelerators. Unlike their more classic counterparts, which act upon differential equations, these methods proceed by manipulating Poincare maps directly. This attribute makes them well matched for studying accelerators whose physics is most naturally modelled in terms of maps, an observation that has been championed most vigorously by Forest. In the following sections the author sketchs a little background, explains some of the physics underlying these techniques, and discusses the best computing strategy for implementing them in conjunction with modeling accelerators.
k-symplectic formalism on Lie algebroids
Energy Technology Data Exchange (ETDEWEB)
De Leon, M; De Diego, D Martin [Instituto de Ciencias Matematicas (CSIC-UAM-UC3M-UCM) C/Serrano 123, 28006 Madrid (Spain); Salgado, M; Vilarino, S [Departamento de XeometrIa e TopoloxIa, Facultade de Matematicas, Universidade de Santiago de Compostela, 15782-Santiago de Compostela (Spain)], E-mail: mdeleon@imaff.cfmac.csic.es, E-mail: d.martin@imaff.cfmac.csic.es, E-mail: modesto.salgado@usc.es, E-mail: silvia.vilarino@usc.es
2009-09-25
In this paper we introduce a geometric description of Lagrangian and Hamiltonian classical field theories on Lie algebroids in the framework of k-symplectic geometry. We discuss the relation between the Lagrangian and Hamiltonian descriptions through a convenient notion of Legendre transformation. The theory is a natural generalization of the standard one; in addition, other interesting examples are studied, in particular, systems with symmetry and Poisson-sigma models.
De Veaux, Richard D.; Hand, David J.
2005-01-01
As Huff’s landmark book made clear, lying with statistics can be accomplished in many ways. Distorting graphics, manipulating data or using biased samples are just a few of the tried and true methods. Failing to use the correct statistical procedure or failing to check the conditions for when the selected method is appropriate can distort results as well, whether the motives of the analyst are honorable or not. Even when the statistical procedure and motives are correct, bad data can produce ...
Lies, Incentives and Self-confidence
Maggian, Valeria
2013-01-01
The present thesis is composed by three chapters, each of them making contributions to three distinct topics in behavioral Economics. The chapters can thus be read independently from each other. The first chapter concerns an experimental analysis which aim is to examine the development of social preferences with respect to age and how they are related with lying behavior of children. The second chapter investigates the role of reciprocity in exacerbating inefficient and opportunistic behavior...
Spherical functions on affine Lie groups
Etingof, P; Kirillov, A A; Pavel Etingof; Igor Frenkel; Alexander Kirillov Jr
1994-01-01
We show that the space of holomorphic functions of a fixed degree on an affine Lie group which take values in a finite-dimensional representation of this group and are equivariant with respect to (twisted) conjugacy coin- cides with the space of conformal blocks of the Wess-Zumino-Witten conformal field theory on an elliptic curve with punctures, or, equivalently,with the space of states of the Chern-Simons topological field theory in genus 1. This provides a group-theoretic realization of the Segal modular functor for elliptic curves. We also show that the the radial part of the second order Laplace operator on an affine Lie group acting in the space of equivariant functions coincides with the operator defining the Knizhnik-Zamolodchikov connection on conformal blocks on elliptic curves, and its eigenfunctions coincide with the correlation functions of conformal blocks. At the critical value of the degree (minus the dual Coxeter number of the underlying simple Lie algebra) there exist higher order Laplace op...
... Eye Exams, Study Finds Additional Content Medical News Inflammation of the Orbit (Inflammatory Orbital Pseudotumor) By James ... Introduction to Eye Socket Disorders Cavernous Sinus Thrombosis Inflammation of the Orbit Orbital Cellulitis Preseptal Cellulitis Tumors ...
Guseinov, Israfil; Mamedov, Bahtiyar; Rzaeva, Afet
2002-04-01
The recurrence relations are established for the basic one-center Coulomb integrals over Slater-type orbitals (STOs). These formulae and the recurrence relations for basic overlap integrals are utilized for the calculation of multicenter electron-repulsion integrals. The calculations of multicenter electron-repulsion integrals are performed by the use of translation formulae for STOs obtained from the Lambda and Coulomb Sturmian exponential-type functions (ETFs). It is shown that these integrals show a faster convergence rate in the case of Coulomb Sturmian ETFs. The accuracy of the results is quite high for the quantum numbers of STOs and for the arbitrary values of internuclear distances and screening constants of atomic orbitals.
COMPLETE LIE ALGEBRAS WITH l-STEP NILPOTENT RADICALS
Institute of Scientific and Technical Information of China (English)
高永存; 孟道冀
2002-01-01
The authors first give a necessary and sufficient condition for some solvable Lie algebras with l-step nilpotent radicals to be complete, and then construct a new class of infinite dimensional complete Lie algebras by using the modules of simple Lie algebras. The quotient algebras of this new constructed Lie algebras are non-solvable complete Lie algebras with l-step nilpotent radicals.
Lie algebras with given properties of subalgebras and elements
Zusmanovich, Pasha
2011-01-01
Results about the following classes of finite-dimensional Lie algebras over a field of characteristic zero are presented: anisotropic (i.e., Lie algebras for which each adjoint operator is semisimple), regular (i.e., Lie algebras in which each nonzero element is regular in the sense of Bourbaki), minimal nonabelian (i.e., nonabelian Lie algebras all whose proper subalgebras are abelian), and algebras of depth 2 (i.e., Lie algebras all whose proper subalgebras are abelian or minimal nonabelian).
Classification of filiform Lie algebras of order 3
Navarro, Rosa María
2016-12-01
Lie algebras of order 3 constitute a generalization of Lie algebras and superalgebras. Throughout this paper the classification problem of filiform Lie algebras of order 3 is considered and therefore this work is a continuation papers seen in the literature. We approach this classification by extending Vergne's result for filiform Lie algebras and by considering algebras of order 3 of high nilindex. We find the expression of the law to which any elementary filiform Lie algebra of order 3 is isomorphic.
COADJOINT ORBITS FOR THE CENTRAL EXTENSION OF Diff+(S1) AND THEIR REPRESENTATIVES
Institute of Scientific and Technical Information of China (English)
Dai Jialing(戴佳玲); Doug Pickrell
2004-01-01
According to Kirillov's idea, the irreducible unitary representations of a Lie group G roughly correspond to the coadjoint orbits O. In the forward direction one applies the methods of geometric quantization to produce a representation, and in the reverse direction one computes a transform of the character of a representation, to obtain a coadjoint orbit. The method of orbits in the representations of Lie groups suggests the detailed study of coadjoint orbits of a Lie group G in the space g* dual to the Lie algebra g of G.In this paper, two primary goals are achieved: one is to completely classify the smooth coadjoint orbits of Virasoro group for nonzero central charge c; the other is to find representatives for coadjoint orbits. These questions have been considered previously by Segal,Kirillov, and Witten, but their results are not quite complete. To accomplish this, the authors start by describing the coadjoint action of D-the Lie group of all orientation preserving diffeomorphisms on the circle S1, and its central extension (~D), then the authors will give a complete classification of smooth coadjoint orbits. In fact, they can be parameterized by a subspace of conjugacy classes of PSU(1, 1). Finally, the authors will show how to find representatives of coadjoint orbits by analyzing the vector fields stabilizing the orbits, and describe the amazing connection between the characteristic (trace) of conjugacy classes of PSU(1, 1) and that of vector fields stabilizing orbits.
Lie color 代数的商代数%Algebras of quotients of Lie color algebras
Institute of Scientific and Technical Information of China (English)
裴凤; 周建华
2004-01-01
介绍了Lie color 代数的一些性质,如素性、半素性、非退化性等.给出了Lie color 代数的商代数以及弱商代数的概念,并把Lie color 代数的素性和半素性推广到它的商代数上.利用没有非零零化子的理想对Lie color 代数的商代数进行刻画,证明了:若L是Lie color 代数Q的子代数,则Q是L的商代数当且仅当Q理想吸收于L.通过具体构造证明了每一个半素Lie color 代数都有极大商代数,并给出这个极大商代数的等价刻画.
Seyed Hassan Mostafavi
2010-01-01
Preseptal and orbital cellulitis occur more commonly in children than adults. The history and physical examination are crucial in distinguishing between preseptal and orbital cellulitis. The orbital septum delineates the anterior eyelid soft tissues from the orbital soft tissue. Infections anterior to the orbital septum are classified as preseptal cellulitis and those posterior to the orbital septum are termed orbital cellulitis. "nRecognition of orbital involvement is important not only...
Energy Technology Data Exchange (ETDEWEB)
Lahmam-Bennani, A; Naja, A; Staicu Casagrande, E M; Okumus, N [Laboratoire des Collisions Atomiques et Moleculaires (LCAM), Universite Paris-Sud 11, Bat. 351, 91405 Orsay Cedex (France); Dal Cappello, C [Laboratoire de Physique Moleculaire et des Collisions, Institut de Physique, ICPMB (FR 2843), Universite Paul Verlaine-Metz, 1 rue Arago, 57078 Metz Cedex 3 (France); Charpentier, I [Laboratoire de Physique et Mecanique des Materiaux (UMR 7554), Universite Paul Verlaine-Metz, Ile du Saulcy, 57045 Metz Cedex 1 (France); Houamer, S [Laboratoire de Physique Quantique et Systemes Dynamiques, Universite Ferhat Abbas, Setif (Algeria)
2009-08-28
The triply differential cross section has been measured for electron-impact ionization of the outer valence 1t{sub 2} and the inner valence 2a{sub 1} orbitals of methane using the (e,2e) technique with coplanar asymmetric kinematics. The measurements are performed at scattered electron energy of 500 eV, ejected electron energy of 12, 37 and 74 eV and for scattering angle of the fast outgoing electron of 6 deg. This kinematics is characterized by a target ion recoil momentum ranging from moderate (0.25 au) to very large (3.2 au) values. The results are compared with theoretical cross sections calculated using the 1CW and the BBK models recently extended to molecules. The experimental cross sections exhibit a very large recoil scattering, especially for the inner 2a{sub 1} molecular orbital, which is not predicted by the theory. The differences between experiment and theory are attributed to the very strong scattering from the ion, not properly accounted for by theory. This indicates the need for further theoretical developments as well as experimental investigations in order to correctly model the process of molecular ionization.
Sheela, N R; Muthu, S; Sampathkrishnan, S
2014-01-01
The Fourier transform infrared (FTIR) and FT Raman (FTR) of 4-4'-(1H-1, 2, 4-triazol-1-yl methylene) dibenzonitrile (4-HTMDBN) have been recorded and analyzed. The equilibrium geometry harmonic vibrational frequencies have been investigated with the help of standard HF and DFT methods with 6-31G(d,p) as basis set. The assignments of the vibrational spectra have been carried out with the help of normal co-ordinate analysis (NCA) following the scaled quantum mechanical force field methodology (SQMFF). Theoretical simulations of the FTIR and FTR spectra of the title compound have been calculated. The (1)H and (13)C Nuclear Magnetic Resonance (NMR) chemical shifts of the molecule were calculated by the Gauge including atomic orbital (GIAO) method. The stability of the molecule has been analyzed using natural bond orbital (NBO) analysis. The linear polarizability (α) and the first order hyperpolarizability (β) values of the investigated molecule have been computed using HF/DFT/6-31G(d,p) methods on the finite field approach. UV-Vis spectrum of the compound is recorded and the electronic properties such as HOMO and LUMO energies, are performed. The directly calculated ionization potential (IP), electron affinity (EA), electronegativity (χ), electrophilicity index (ω), hardness (η) and chemical potential (ρ) are all correlated with the HOMO and LUMO energies with their molecular properties. Mulliken population analysis on atomic charges, molecular electrostatic potential maps (MEP) and thermodynamical properties of title compound at different temperature have been calculated.
Bhunia, Snehasis; Singh, Ajeet; Ojha, Animesh K
2017-03-01
Complexes of the dipeptide phenylalanine-phenylalanine (Phe-Phe) with divalent metal cations (Cu(2+), Zn(2+), Ca(2+) and Ba(2+)) were studied at the B3LYP and MP2 levels of theory with the basis sets 6-311++G(d,p) and 6-31 + G(d) in the gas phase. The relative energies of these complexes indicated that cation-π bidentate/tridentate conformations are more favourable than other conformations with uncoordinated rings. These findings were confirmed by the calculated values of thermodynamic parameters such as the Gibbs free energy. Natural bond orbital (NBO) analysis was carried out to explore the metal-ligand coordination in Phe-Phe-Cu(2+)/Zn(2+) complexes. Possible orbital transitions, types of orbitals and their occupancies were determined for a range of Phe-Phe-Cu(2+)/Zn(2+) complexes. The charge transfer involved in various orbital transitions was explored by considering the second-order perturbation energy. NBO analysis revealed that the change transfer is stronger when the metal cation uses both the 4s + 4p subshells rather than just its 4p subshell. We also performed molecular dynamics (MD) simulations to check the stability and consistency of the most favourable binding motifs of Cu(2+), Zn(2+), Ca(2+) and Ba(2+) with Phe-Phe over time. The structures of the Phe-Phe-Cu(2+)/Zn(2+)/Ca(2+)/Ba(2+) complexes obtained using MD simulation were found to be in good agreement with those obtained in the DFT-based calculations. Graphical Abstract Conformational search on encapsulation of divalent metal cations (Ca(2+), Zn(2+), Ca(2+), Ba(2+)) by the Phe-Phe dipeptide.
Abedi-Fardad, J.; Rezaei-Aghdam, A.; Haghighatdoost, Gh.
2017-01-01
We classify all four-dimensional real Lie bialgebras of symplectic type and obtain the classical r-matrices for these Lie bialgebras and Poisson structures on all the associated four-dimensional Poisson-Lie groups. We obtain some new integrable models where a Poisson-Lie group plays the role of the phase space and its dual Lie group plays the role of the symmetry group of the system.
Murphy, Andrew; Haestad, Jace; Morgan, Thomas
2015-09-01
We report characteristics of closed classical orbits in an electric field in phase space produced in photoabsorption. Rydberg states of atomic and molecular hydrogen and helium are considered. The core potential used for the hydrogen molecule is an effective one electron one center core potential evaluated at the internuclear equilibrium distance. Poincare surfaces of section in phase space are generated by integrating the equations of motion in semiparabolic coordinates u = (r + z) 1 / 2 and v = (r - z) 1 / 2, and plotting the location in phase space (pv versus v) whenever u = 0, with the electric field in the z direction. Combination orbits produced by Rydberg electron core scattering are studied and the evolution in phase space of these combination orbits due to scattering from one closed orbit into another is investigated. Connections are made to measured laser photoabsorption experiments that excite Rydberg states (20 recurrence spectra. The phase space structures responsible for the spectra are identified.
Superintermolecular orbitals in the C$_{60}$/pentacene complex
G.P. Zhang; Gardner, A.; Latta, T.; Drake, K.; Bai, Y. H.
2016-01-01
We report a group of unusually big molecular orbitals in the C60/pentacene complex. Our first-principles density functional calculation shows that these orbitals are very delocalized and cover both C60 and pentacene, which we call superintermolecular orbitals or SIMOs. Their spatial extension can reach 1 nm or larger. Optically, SIMOs are dark. Different from ordinary unoccupied molecular orbitals, SIMOs have a very weak Coulomb and exchange interaction. Their energy levels are very similar t...
Borbolla-Pertierra, A M; Morales-Baños, D R; Martínez-Nava, L R; Garrido-Sánchez, G A; López-Hernández, C M; Velasco-Ramos, P
2017-02-01
The case is presented of a 46-year-old male with right eye proptosis and conjunctival hyperaemia, of 18 months onset. A well-defined intraconal mass was found in the computed tomography. In magnetic resonance this was hypo-intense on T1, enhanced with gadolinium and hyperintense on T2. Excisional biopsy was performed, which was reported as a well-differentiated liposarcoma in the histopathology study. Liposarcoma is a malignant adipose tissue tumour. It is very rare in the orbit, with 5 histological types, the most common being myxoid. The treatment of choice is wide surgical excision and may be accompanied with radiotherapy. As it is an infiltrative tumour, It has a high rate of recurrence. Copyright © 2016 Sociedad Española de Oftalmología. Publicado por Elsevier España, S.L.U. All rights reserved.
Directory of Open Access Journals (Sweden)
Masanori Tachikawa
2013-05-01
Full Text Available We have theoretically analyzed the nuclear quantum effect on the nuclear magnetic shieldings for the intramolecular hydrogen-bonded systems of σ-hydroxy acyl aromatic species using the gauge-including atomic orbital technique combined with our multi-component density functional theory. The effect of H/D quantum nature for geometry and nuclear magnetic shielding changes are analyzed. Our study clearly demonstrated that the geometrical changes of hydrogen-bonds induced by H/D isotope effect (called geometrical isotope effect: GIE is the dominant factor of deuterium isotope effect on 13C chemical shift.
Guseinov, I. I.
2005-01-01
In a recent paper Ozdogan (Z. Naturforsch, 59a(2004)743) published formulas for evaluating the two-center overlap and nuclear attraction integrals over integer and noninteger Slater type orbitals. The purpose of this article is to point out that the same formulas have previously been established by Guseinov et al. (J.Mol.Model.,8(2002)272) by using the same method. As we demonstrated in our Comment (Int.J.Quantum Chem., 91(2003)62), the expansion formula for the product of two normalized asso...
Almost-Riemannian Geometry on Lie Groups
Ayala, Victor; Jouan, Philippe
2015-01-01
A simple Almost-Riemmanian Structure on a Lie group G is defined by a linear vector field and dim(G)-1 left-invariant ones. We state results about the singular locus, the abnormal extremals and the desingularization of such ARS's, and these results are illustrated by examples on the 2D affine and the Heisenberg groups.These ARS's are extended in two ways to homogeneous spaces, and a necessary and sufficient condition for an ARS on a manifold to be equivalent to a general ARS on a homogeneous ...
The graded Lie algebra of general relativity
Reiterer, Michael
2014-01-01
We construct a graded Lie algebra in which a solution to the vacuum Einstein equations is any element of degree 1 whose bracket with itself is zero. Each solution generates a cochain complex, whose first cohomology is linearized gravity about that solution. We gauge-fix to get a smaller cochain complex with the same cohomologies (deformation retraction). The new complex is much smaller, it consists of the solution spaces of linear homogeneous wave equations (symmetric hyperbolic equations). The algorithm that produces these gauges and wave equations is both for linearized gravity and the full Einstein equations. The gauge groupoid is the groupoid of rank 2 complex vector bundles.
Fermionic realisations of simple Lie algebras
de Azcárraga, J A
2000-01-01
We study the representation ${\\cal D}$ of a simple compact Lie algebra $\\g$ of rank l constructed with the aid of the hermitian Dirac matrices of a (${\\rm dim} \\g$)-dimensional euclidean space. The irreducible representations of $\\g$ contained in ${\\cal D}$ are found by providing a general construction on suitable fermionic Fock spaces. We give full details not only for the simplest odd and even cases, namely su(2) and su(3), but also for the next (${dim} \\g$)-even case of su(5). Our results are far reaching: they apply to any $\\g$-invariant quantum mechanical system containing ${\\rm dim} \\g$ fermions. Another reason for undertaking this study is to examine the role of the $\\g$-invariant fermionic operators that naturally arise. These are given in terms of products of an odd number of gamma matrices, and include, besides a cubic operator, (l-1) fermionic scalars of higher order. The latter are constructed from the Lie algebra cohomology cocycles, and must be considered to be of theoretical significance simila...
Borsten, L; Ferrara, S; Marrani, A; Rubens, W
2012-01-01
We study both the "large" and "small" U-duality charge orbits of extremal black holes appearing in D = 5 and D = 4 Maxwell-Einstein supergravity theories with symmetric scalar manifolds. We exploit a formalism based on cubic Jordan algebras and their associated Freudenthal triple systems, in order to derive the minimal charge representatives, their stabilizers and the associated "moduli spaces". After recalling N = 8 maximal supergravity, we consider N = 2 and N = 4 theories coupled to an arbitrary number of vector multiplets, as well as N = 2 magic, STU, ST^2 and T^3 models. While the STU model may be considered as part of the general N = 2 sequence, albeit with an additional triality symmetry, the ST^2 and T^3 models demand a separate treatment, since their representative Jordan algebras are Euclidean or only admit non-zero elements of rank 3, respectively. Finally, we also consider minimally coupled N = 2, matter coupled N = 3, and "pure" N = 5 theories.
Configuration mixing in low-lying spectra of carbon hypernuclei
Xia, HaoJie; Mei, Hua; Yao, JiangMing
2017-10-01
We perform a coupled-channels study of the low-lying states in $^{13,15,17,19}_{~~~~~~~~~~~~~~~~~~~~~\\Lambda}$C with a covariant energy density functional based microscopic particle-core coupling model. The energy differences of $1/2^-$ and $3/2^-$ states in $^{13}_\\Lambda$C and $^{15}_\\Lambda$C are predicted to be 0.25 MeV and 0.34 MeV, respectively. We find that configuration mixings in the $1/2^-$ and $3/2^-$ states of $^{15}_\\Lambda$C are the weakest among those of $^{13,15,17,19}_{~~~~~~~~~~~~~~~~~~~~~\\Lambda}$C. It indicates that $^{15}_\\Lambda$C provides the best candidate among the carbon hypernuclei to study the spin-orbit splitting of $p_\\Lambda$ hyperon state.
On the low-lying states of CuO
Bagus, P. S.; Nelin, C. J.; Bauschlicher, C. W., Jr.
1984-01-01
Self consistent field and correlated wave functions have been computed for the ground and for several low-lying states of CuO. The ground state is X(2)PI and the lowest excited state, at approximately 8,000/cm above X(2)PI, is a previously unidentified 2-sigma(+) state. The separation of these states is compared to that for the similar states of KO and is analysed in terms of integrals between orbitals of the separated free ions. A classification of the states of the molecule based on states of Cu(+) and O(-) which leads to a division into manifolds of states arising from Cu(+) 3d(10) and Cu(+) 3d(9) 4s(1) is considered. It is predicted that the state of the 3d(9) 4s(1) manifold are 10,000 to 30,000/cm above the ground state and assign the observed A2-sigma(+) state at 16,500/cm to this manifold.
Uncertainty Principles on Two Step Nilpotent Lie Groups
Indian Academy of Sciences (India)
S K Ray
2001-08-01
We extend an uncertainty principle due to Cowling and Price to two step nilpotent Lie groups, which generalizes a classical theorem of Hardy. We also prove an analogue of Heisenberg inequality on two step nilpotent Lie groups.
Pants on fire: the electrophysiological signature of telling a lie.
Pfister, Roland; Foerster, Anna; Kunde, Wilfried
2014-01-01
Even though electroencephalography has played a prominent role for lie detection via personally relevant information, the electrophysiological signature of active lying is still elusive. We addressed this signature with two experiments in which participants helped a virtual police officer to locate a knife. Crucially, before this response, they announced whether they would lie or tell the truth about the knife's location. This design allowed us to study the signature of lie-telling in the absence of rare and personally significant oddball stimuli that are typically used for lie detection via electrophysiological markers, especially the P300 component. Our results indicate that active lying attenuated P300 amplitudes as well as N200 amplitudes for such non-oddball stimuli. These results support accounts that stress the high cognitive demand of lie-telling, including the need to suppress the truthful response and to generate a lie.
Institute of Scientific and Technical Information of China (English)
Nila; F.Moeloek
1993-01-01
Orbital anatomy, the clinical features of orbital tumors, the recent development of the diagnosis and management of orbital tumors were described. The incidence of orbital tumors in Dr. Cipto Mangunkusumo Hospital in the past years were introduced. The principle of management of orbital tumors and their prognosis were discussed.
Deleuze, M. S.; Knippenberg, S.
2006-09-01
The scope of the present work is to reconcile electron momentum spectroscopy with elementary thermodynamics, and refute conclusions drawn by Saha et al. in J. Chem. Phys. 123, 124315 (2005) regarding fingerprints of the gauche conformational isomer of 1,3-butadiene in electron momentum distributions that were experimentally inferred from gas phase (e,2e) measurements on this compound [M. J. Brunger et al., J. Chem. Phys. 108, 1859 (1998)]. Our analysis is based on thorough calculations of one-electron and shake-up ionization spectra employing one-particle Green's function theory along with the benchmark third-order algebraic diagrammatic construction [ADC(3)] scheme. Accurate spherically averaged electron momentum distributions are correspondingly computed from the related Dyson orbitals. The ionization spectra and Dyson orbital momentum distributions that were computed for the trans-conformer of 1,3-butadiene alone are amply sufficient to quantitatively unravel the shape of all available experimental (e,2e) electron momentum distributions. A comparison of theoretical ADC(3) spectra for the s-trans and gauche energy minima with inner- and outer-valence high-resolution photoelectron measurements employing a synchrotron radiation beam [D. M. P. Holland et al., J. Phys. B 29, 3091 (1996)] demonstrates that the gauche structure is incompatible with ionization experiments in high-vacuum conditions and at standard temperatures. On the other hand, outer-valence Green's function calculations on the s-trans energy minimum form and approaching basis set completeness provide highly quantitative insights, within ˜0.2eV accuracy, into the available experimental one-electron ionization energies. At last, analysis of the angular dependence of relative (e,2e) ionization intensities nicely confirms the presence of one rather intense π-2 π*+1 satellite at ˜13.1eV in the ionization spectrum of the s-trans conformer.
Muthu, S; Renuga, S
2014-01-24
FT-IR and FT-Raman spectra of 5-{1-hydroxy-2-[(propan-2-yl) amino] ethyl} benzene-1,3-diol (abbrevi- 54 ated as HPAEBD) were recorded in the region 4000-450 cm(-1) and 4000-100 cm(-1) respectively. The structure of the molecule was optimized and the structural characteristics were determined by density functional theory (B3LYP) and HF method with 6-31 G(d,p) as basis set. The theoretical wave numbers were scaled and compared with experimental FT-IR and FT-Raman spectra. A detailed interpretation of the vibrational spectra of this compound has been made on the basis of the calculated Potential energy distribution (PED). Stability of the molecule arising from hyperconjugation and charge delocalization is confirmed by the natural bond orbital analysis (NBO). The results show that electron density (ED) in the σ antibonding orbitals and E (2) energies confirm the occurrence of intra molecular charge transfer (ICT) within the molecule. The molecule orbital contributions were studied by using the total (TDOS), sum of α and β electron (αβDOS) density of States. Mulliken population analysis of atomic charges is also calculated. The calculated HOMO and LUMO energy gap shows that charge transfer occurs within the molecule. The electron density-based local reactivity descriptors such as Fukui functions were calculated to explain the chemical selectivity or reactivity site in this compound. On the basis of vibrational analyses, the thermodynamic properties of title compound at different temperatures have been calculated.
Twisted Hamiltonian Lie Algebras and Their Multiplicity-Free Representations
Institute of Scientific and Technical Information of China (English)
Ling CHEN
2011-01-01
We construct a class of new Lie algebras by generalizing the one-variable Lie algebras generated by the quadratic conformal algebras (or corresponding Hamiltonian operators) associated with Poisson algebras and a quasi-derivation found by Xu. These algebras can be viewed as certain twists of Xu's generalized Hamiltonian Lie algebras. The simplicity of these algebras is completely determined. Moreover, we construct a family of multiplicity-free representations of these Lie algebras and prove their irreducibility.
Lie symmetries and differential galois groups of linear equations
Oudshoorn, W.R.; Put, M. van der
2002-01-01
For a linear ordinary differential equation the Lie algebra of its infinitesimal Lie symmetries is compared with its differential Galois group. For this purpose an algebraic formulation of Lie symmetries is developed. It turns out that there is no direct relation between the two above objects. In co
33 CFR 401.92 - Wintering and lying-up.
2010-07-01
... 33 Navigation and Navigable Waters 3 2010-07-01 2010-07-01 false Wintering and lying-up. 401.92... OF TRANSPORTATION SEAWAY REGULATIONS AND RULES Regulations General § 401.92 Wintering and lying-up. No vessel shall winter within the Seaway or lie-up within the Seaway during the navigation...
Lie Pseudogroups à la Cartan from a Modern Perspective
Yudilevich, O.
2016-01-01
In 1904-05, the mathematician Élie Cartan published two pioneer papers in which he introduced a structure theory for Lie pseudogroups. Lie pseudogroups are mathematical objects that appear in both differential geometry and in the theory of differential equations as local symmetries of geometric stru
Graded Lie Algebra Generating of Parastatistical Algebraic Relations
Institute of Scientific and Technical Information of China (English)
JING Si-Cong; YANG Wei-Min; LI Ping
2001-01-01
A new kind of graded Lie algebra (We call it Z2,2 graded Lie algebra) is introduced as a framework for formulating parasupersymmetric theories. By choosing suitable Bose subspace of the Z2,2 graded Lie algebra and using relevant generalized Jacobi identities, we generate the whole algebraic structure of parastatistics.
Extremal projectors for contragredient Lie (super)symmetries (short review)
Tolstoy, V N
2010-01-01
A brief review of the extremal projectors for contragredient Lie (super)symmetries (finite-dimensional simple Lie algebras, basic classical Lie superalgebras, infinite-dimensional affine Kac-Moody algebras and superalgebras, as well as their quantum $q$-analogs) is given. Some bibliographic comments on the applications of extremal projectors are presented.
Focal sampling of cow lying behaviour for automated welfare assessment
Mattachini, G.; Riva, E.; Bisaglia, C.; Pompe, J.C.A.M.; Provolo, G.
2013-01-01
the objective of the current study was to determine the number of focal animals required to represent the daily lying behaviour of a herd of lactating dairy cows. the study was carried out at 3 commercial dairy farms. the lying time (h/d) and number of lying bouts (n/d) of 15 ± 3 focal dairy cows,
Universal representations of Lie algebras by coderivations
Petracci, Emanuela
2003-01-01
A class of representations of a Lie superalgebra (over a commutative superring) in its symmetric algebra is studied. As an application we get a direct and natural proof of a strong form of the Poincare'-Birkhoff-Witt theorem, extending this theorem to a class of nilpotent Lie superalgebras. Other applications are presented. Our results are new already for Lie algebras.
Lie symmetry algebra of one-dimensional nonconservative dynamical systems
Institute of Scientific and Technical Information of China (English)
Liu Cui-Mei; Wu Run-Heng; Fu Jing-Li
2007-01-01
Lie symmetry algebra of linear nonconservative dynamical systems is studied in this paper. By using 1-1 mapping,the Lie point and Lie contact symmetry algebras are obtained from two independent solutions of the one-dimensional linear equations of motion.
Central Extension for the Triangular Derivation Lie Algebra
Institute of Scientific and Technical Information of China (English)
Chunming LI; Ping XU
2012-01-01
In this paper,we study a class of subalgebras of the Lie algebra of vector fields on n-dimensional torus,which are called the Triangular derivation Lie algebra.We give the structure and the central extension of Triangular derivation Lie algebra.
Construction of Difference Equations Using Lie Groups
Energy Technology Data Exchange (ETDEWEB)
Axford, R.A.
1998-08-01
The theory of prolongations of the generators of groups of point transformations to the grid point values of dependent variables and grid spacings is developed and applied to the construction of group invariant numerical algorithms. The concepts of invariant difference operators and generalized discrete sources are introduced for the discretization of systems of inhomogeneous differential equations and shown to produce exact difference equations. Invariant numerical flux functions are constructed from the general solutions of first order partial differential equations that come out of the evaluation of the Lie derivatives of conservation forms of difference schemes. It is demonstrated that invariant numerical flux functions with invariant flux or slope limiters can be determined to yield high resolution difference schemes. The introduction of an invariant flux or slope limiter can be done so as not to break the symmetry properties of a numerical flux-function.
[Counter-acception or abort and lie].
Maruani, G
1979-09-01
In this very short but fiery and violent paper against abortion the author states that most women seeking abortion are actually lying to themselves, pretending they want something which, in reality, they do not want, i.e. an abortion. The laws regulating abortion in most countries are such that a woman is practically forbidden to make an independent decision, despite, or because of the number of counseling sessions and of meetings with doctors that she must go through. Radio, television, newspapers and magazines, friends and relatives, all contribute to make of abortion a run-of-the-mill operation, while it should be seen as scandal, and as the total negation of any maternal instinct.
Lie algebraic noncommuting structures from reparametrisation symmetry
Gangopadhyay, S
2007-01-01
We extend our earlier work of revealing both space-space and space-time noncommuting structures in various models in particle mechanics exhibiting reparametrisation symmetry. We show explicitly (in contrast to the earlier results in our paper \\cite{sg}) that for some special choices of the reparametrisation parameter $\\epsilon$, one can obtain space-space noncommuting structures which are Lie-algebraic in form even in the case of the relativistic free particle. The connection of these structures with the existing models in the literature is also briefly discussed. Further, there exists some values of $\\epsilon$ for which the noncommutativity in the space-space sector can be made to vanish. As a matter of internal consistency of our approach, we also study the angular momentum algebra in details.
On Quantum Lie Nilpotency of Order 2
Directory of Open Access Journals (Sweden)
E. A. Kireeva
2016-01-01
Full Text Available The paper investigates the free algebras of varieties of associative algebras modulo identities of quantum Lie nilpotency of order 1 and 2. Let q be an invertible element of the ground field K (or of its extension. The element[x,y]q = xy-qyxof the free associative algebra is called a quantum commutator. We consider the algebras modulo identities [x,y]q = 0 (1and [[x,y]q ,z]q = 0. (2It is natural to consider the aforementioned algebras as the quantum analogs of commutative algebras and algebras of Lie nilpotency of order 2. The free algebras of the varieties of associative algebras modulo the identity of Lie nilpotency of order 2, that is the identity[[x,y] ,z] =0,where [x,y]=xy-yx is a Lie commutator, are of great interest in the theory of algebras with polynomial identities, since it was proved by A.V.Grishin for algebras over fields of characteristic 2, and V.V.Shchigolev for algebras over fields of characteristic p>2, that these algebras contain non-finitely generated T-spaces.We prove in the paper that the algebras modulo identities (1 and (2 are nilpotent in the usual sense and calculate precisely the nilpotency order of these algebras. More precisely, we prove that the free algebra of the variety of associative algebras modulo identity (1 is nilpotent of order 2 if q ≠ ± 1, and nilpotent of order 3 if q = - 1 and the characteristic of K is not equal to 2. It is also proved that the free algebra of the variety of associative algebras modulo identity (2 is nilpotent of order 3 if q3 ≠ 1, q ≠ ± 1, nilpotent of order 4 if q3 = 1, q ≠ 1, and nilpotent of
Carter, Melvin Keith
2007-04-01
Cyclic voltammogram (CV) electrochemical measurements for pyrocatechol, resorcinol, hydroquinone, pyrogallol, and gallic acid in strong alkaline solution produced observable oxidation-reduction potentials for each hydroxy group present except for resorcinol. UV absorption spectra were also observed for the diluted solutions. Semi-empirical molecular orbital computations were conducted for these molecules of C2 v point group symmetry to determine the character and energies to aid interpretation of the experimental results. CV oxidation removed a π-electron by a radiationless π-π* transition followed by an electron shift from a negative oxygen to the positive aromatic π-system indicated by an observable σ-π* transition. Simple semi-empirical computations correlated with measured excited electronic states during electron transfer.
Sato, Kota; Honna, Hiroshi; Iwabuchi, Susumu; Hirano, Tsuneo; Koinuma, Hideomi
1994-07-01
Successive hydrogen-elimination reactions with low activation energies during the formation of a-Si:H by silane plasma chemical-vapor deposition proposed by us were studied by using a larger cluster model on the basis of an ab initio molecular-orbital method. The activation energy of the first step, the reaction of a dangling-bond site with an adjacent tetrahedrally coordinated silicon, was found to be 18.2 kcal/mol (0.79 eV) by employing a larger cluster model. The total process was also shown to be thermodynamically more favorable by using larger cluster models. Thus, the successive process is considered to play an important role in a-Si:H formation processes.
Detecting Children's Lies: Are Parents Accurate Judges of Their Own Children's Lies?
Talwar, Victoria; Renaud, Sarah-Jane; Conway, Lauryn
2015-01-01
The current study investigated whether parents are accurate judges of their own children's lie-telling behavior. Participants included 250 mother-child dyads. Children were between three and 11 years of age. A temptation resistance paradigm was used to elicit a minor transgressive behavior from the children involving peeking at a forbidden toy and…
Detecting Children's Lies: Are Parents Accurate Judges of Their Own Children's Lies?
Talwar, Victoria; Renaud, Sarah-Jane; Conway, Lauryn
2015-01-01
The current study investigated whether parents are accurate judges of their own children's lie-telling behavior. Participants included 250 mother-child dyads. Children were between three and 11 years of age. A temptation resistance paradigm was used to elicit a minor transgressive behavior from the children involving peeking at a forbidden toy and…