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S Wilson - One of the best experts on this subject based on the ideXlab platform.
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Alternatives to multireference methods for the Molecular Electronic Structure problem
International Journal of Quantum Chemistry, 2004Co-Authors: S WilsonAbstract:The development of robust many-body methods for the Molecular Electronic Structure problem with respect to multireference functions has attracted much attention over the past two decades. In recent years, multireference methods based on the Brillouin–Wigner expansion have been shown to overcome the intruder state problems which have plagued similar approaches based on the Rayleigh–Schrodinger series. However, there are some problems in Molecular Electronic Structure theory, which may be handled by means of multireference methods, but can be treated by methods that avoid the use of multireference functions. We consider two examples of alternatives to multireference methods for the Molecular Electronic Structure problem. The study of excited states having the same symmetry as the ground state or some lower lying excited state often involves the use of a multireference function. We describe an alternative procedure based on the generalized Rayleigh–Ritz variation principle. Gidopoulos, Glushkov, and Wilson have termed this the optimized trace method. The generalized Rayleigh–Ritz principle for the relativistic formulation of the Molecular Electronic Structure problem is briefly also considered. Molecular dissociative processes are frequently described by quantum chemical methods based on multireference functions. Single-reference Hartree–Fock methods usually provide a qualitatively incorrect description of such processes even in the simplest of molecules, H2. However, approximate single configuration wave functions constructed from nonorthogonal orbitals can often afford a useful approximation to bond-breaking processes. Each occupied nonorthogonal orbital is then an eigenfunction of a different Fock-like operator. Each of these Fock-like operators supports a spectrum of M single particle states, where M is the size of the basis set, and only the lowest of these is occupied. We briefly consider the relativistic formulation of the Molecular Electronic Structure problem based on approximations involving products of nonorthogonal functions within the Furry bound state interaction picture of quantum electrodynamics. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004
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On the use of many-body perturbation theory and quantum-electrodynamics in Molecular Electronic Structure theory☆
Journal of Molecular Structure-theochem, 2001Co-Authors: S WilsonAbstract:Abstract Many-body perturbation theory is firmly established in Molecular Electronic Structure studies both as a method of calculation in its own right and in underpinning other approaches to the electron correlation problem, such as coupled electron pair approximations and various cluster expansions. The central pillar of the many-body perturbation theory is the linked diagram theorem obtained by Goldstone using the method of Feynman graphs to enumerate the terms of the perturbation series. Feynman had introduced his graphs in his formulation of quantum electrodynamics. Goldstone restricted his analysis to the non-relativistic many-body problem, so that interactions were taken to be instantaneous and the effects of relativity were ignored. In recent years, the growing interest in the treatment of relativistic and quantum electrodynamic effects in atoms and molecules has necessitated the re-introduction of physics that has been known for over forty years. A key to this development for Molecular systems is a rigorous and robust implementation of the algebraic approximation for Dirac and Dirac-like equations. The algebraic approximation provides a representation of both the positive-energy and the negative-energy branches of the Dirac spectrum. Relativistic many-body perturbation theory, relativistic coupled pair approximations and relativistic coupled cluster theories can be formulated within the ‘no-virtual-pair’ approximation. Such formulations are restricted to the positive energy branch of the spectrum. However, the negative energy states make an essential contribution to the description of atomic and Molecular Electronic Structure. The investigation of this contribution is facilitated by proper implementation of the algebraic approximation using formulations which are amenable to systematic refinement.
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Practical Ab Initio Methods for Molecular Electronic Structure Studies. I. An Overview
Problem Solving in Computational Molecular Science, 1997Co-Authors: S WilsonAbstract:An overview of practical ab initio methods for Molecular Electronic Structure studies is given. A graphical interface, the UNICHEM computational chemistry package, is used to emphasize the various choices made in performing an Electronic Structure calculation and, in particular, to describe the way in which these choices affect both the utility of the results obtained and the tractability of the computation.
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Practical Ab Initio Methods for Molecular Electronic Structure Studies. IV. Relativistic Many-Body Perturbation Theory
Problem Solving in Computational Molecular Science, 1997Co-Authors: S WilsonAbstract:The generalization of the familiar non-relativistic diagrammatic many-body perturbation theory of atomic and Molecular Electronic Structure to the relativistic case is surveyed. It is noted that the treatment of relativistic and quantum electrodynamic effects in atoms and molecules requires the reintroduction of physics that was discarded in early studies of the many-body problem by Goldstone and others in which interactions were taken to be instantaneous and special relativity was ignored. Recent progress is described emphasizing three aspects: i) the representation of the positive and negative energy branches of the Dirac spectrum afforded by the algebraic approximation, and ii) the non-additivity of relativistic and correlation effects in calculations using the Dirac-Coulomb hamiltonian and the Dirac-Breit hamiltonian. Future directions of research are briefly described emphasizing particularly, i) improvements in the accuracy of matrix Dirac-Hartree-Fock-Breit calculations and in sum-over-states perturbative electron correlation calculations for molecules, and ii) the use of Bardeen-Cooper-Schrieffer reference models in calculations based on the diagrammatic many-body perturbation theory to afford a description of bond breaking processes.
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A universal basis set for high-precision Molecular Electronic Structure studies
Journal of Physics B: Atomic Molecular and Optical Physics, 1994Co-Authors: David Moncrieff, S WilsonAbstract:High-precision matrix Hartree-Fock calculations are reported for a series of five isoElectronic diatomic systems in their ground states. A universal even-tempered basis set of Gaussian-type functions is developed for the nitrogen molecule at its experimentally derived equilibrium nuclear separation and then used to parameterize the single-particle state functions in the matrix Hartree-Fock description of the neutral molecules CO and BF, and in the ions NO+ and CN- at their respective experimentally determined equilibrium geometries. The calculated energies are compared with the results of previously reported fully numerical calculations which were performed by using finite difference and/or finite element techniques and which are taken to define Hartree-Fock limit. Energies obtained using the universal even-tempered finite basis set expansion are well within what is usually regarded as 'chemical accuracy' of approximately 1 mHartree and are only in error by approximately 2.3, approximately 1.5, approximately 90, approximately 40 and approximately 140 mu Hartree for N2, CO, BF, NO+ and Cn-, respectively.
Dimitri N. Laikov - One of the best experts on this subject based on the ideXlab platform.
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Atomic effective potentials for starting Molecular Electronic Structure calculations.
Theoretical Chemistry Accounts, 2020Co-Authors: Dimitri N. Laikov, Ksenia R. BrilingAbstract:Atomic effective one-electron potentials in a compact analytic form in terms of a few Gaussian charge distributions are developed, for Hydrogen through Nobelium, for starting Molecular Electronic Structure calculations by a simple diagonalization. For each element, all terms but one are optimized in an isolated-atom Hartree--Fock calculation, and the last one is parametrized on a set of molecules. This one-parameter-per-atom model gives a good starting guess for typical molecules and may be of interest even on its own.
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Atomic basis functions for Molecular Electronic Structure calculations
Theoretical Chemistry Accounts, 2019Co-Authors: Dimitri N. LaikovAbstract:Electronic Structure methods for accurate calculation of Molecular properties have a high cost that grows steeply with the problem size; therefore, it is helpful to have the underlying atomic basis functions that are less in number but of higher quality. Following our earlier work (Laikov in Chem Phys Lett 416:116, 2005 . https://doi.org/10.1016/j.cplett.2005.09.046 ) where general correlation-consistent basis sets are defined, for any atom, as solutions of purely atomic functional minimization problems, and which are shown to work well for chemical bonding in molecules, we take a further step here and define a new kind of atomic polarization functionals, whose minimization yields additional sets of diffuse functions that help to calculate better Molecular electron affinities, polarizabilities, and interMolecular dispersion interactions. Analytical representations by generally contracted Gaussian functions of up to microhartree numerical accuracy grades are developed for atoms hydrogen through nobelium within the four-component Dirac–Coulomb theory and its scalar-relativistic approximation, and also for hydrogen through krypton in the nonrelativistic case. The convergence of correlation energy with the basis set size is studied, and complete-basis-set extrapolation formulas are developed.
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Additive atomic approximation for relativistic effects: a two-component Hamiltonian for Molecular Electronic Structure calculations
The Journal of chemical physics, 2019Co-Authors: Dimitri N. LaikovAbstract:An approximate relativistic two-component Hamiltonian for use in Molecular Electronic Structure calculations is derived in the form of a sum of fixed atom-centered kinetic and spin-orbit operators added to the non-relativistic Hamiltonian. Starting from the well-known zeroth-order regular approximation, further steps are taken to get rid of its nonlinearity in the potential, ending up with a simple formulation with easily computable integrals that can seamlessly work with any traditional Electronic Structure method. Molecular tests show a good accuracy of this approximation.
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A new parametrizable model of Molecular Electronic Structure
The Journal of chemical physics, 2011Co-Authors: Dimitri N. LaikovAbstract:A new Electronic Structure model is developed in which the ground state energy of a Molecular system is given by a Hartree-Fock-like expression with parametrized one- and two-electron integrals over an extended (minimal + polarization) set of orthogonalized atom-centered basis functions, the variational equations being solved formally within the minimal basis but the effect of polarization functions being included in the spirit of second-order perturbation theory. It is designed to yield good dipole polarizabilities and improved interMolecular potentials with dispersion terms. The Molecular integrals include up to three-center one-electron and two-center two-electron terms, all in simple analytical forms. A method to extract the effective one-electron Hamiltonian of nonlocal-exchange Kohn-Sham theory from the coupled-cluster one-electron density matrix is designed and used to get its matrix representation in a molecule-intrinsic minimal basis as an input to the paramtrization procedure -- making a direct link to the correlated wavefunction theory. The model has been trained for 15 elements (H, Li--F, Na--Cl, 720 parameters) on a set of 5581 molecules (including ions, transition states, and weakly-bound complexes) whose first- and second-order properties were computed by the coupled-cluster theory as a reference, and a good agreement is seen. The model looks promising for the study of large Molecular systems, it is believed to be an important step forward from the traditional semiempirical models towards higher accuracy at nearly as low a computational cost.
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a new parametrizable model of Molecular Electronic Structure
Journal of Chemical Physics, 2011Co-Authors: Dimitri N. LaikovAbstract:A new Electronic Structure model is developed in which the ground state energy of a Molecular system is given by a Hartree-Fock-like expression with parametrized one- and two-electron integrals over an extended (minimal + polarization) set of orthogonalized atom-centered basis functions, the variational equations being solved formally within the minimal basis but the effect of polarization functions being included in the spirit of second-order perturbation theory. It is designed to yield good dipole polarizabilities and improved interMolecular potentials with dispersion terms. The Molecular integrals include up to three-center one-electron and two-center two-electron terms, all in simple analytical forms. A method to extract the effective one-electron Hamiltonian of nonlocal-exchange Kohn-Sham theory from the coupled-cluster one-electron density matrix is designed and used to get its matrix representation in a molecule-intrinsic minimal basis as an input to the parametrization procedure – making a direct ...
P. W. Langhoff - One of the best experts on this subject based on the ideXlab platform.
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Atomic Spectral Methods for Molecular Electronic Structure Calculations
Bulletin of the American Physical Society, 2006Co-Authors: Robert J. Hinde, Jerry A Boatz, P. W. LanghoffAbstract:Abstract : New theoretical methods are reported for ab initio calculations of the adiabatic (Born-Oppenheimer) Electronic wave functions and potential energy surfaces of molecules and other atomic aggregates. An outer product of complete seets of atomic eigenstates familiar from perturbation-theoretical treatments of long-range interactions is employed as a representational basis without prior enforcement of aggregate wave function antisymmetry. The nature and attributes of this atomic spectral-product basis are indicated, completeness proofs for representation of antisymmetric stated provided, convergence of Schrodinger eigenstates in the basis established, and strategies for computational implementation of the theory described.
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Atomic spectral methods for Molecular Electronic Structure calculations.
The Journal of chemical physics, 2004Co-Authors: P. W. Langhoff, Jerry A Boatz, Robert J. Hinde, J. A. SheehyAbstract:Theoretical methods are reported for ab initio calculations of the adiabatic (Born–Oppenheimer) Electronic wave functions and potential energy surfaces of molecules and other atomic aggregates. An outer product of complete sets of atomic eigenstates familiar from perturbation-theoretical treatments of long-range interactions is employed as a representational basis without prior enforcement of aggregate wave function antisymmetry. The nature and attributes of this atomic spectral-product basis are indicated, completeness proofs for representation of antisymmetric states provided, convergence of Schrodinger eigenstates in the basis established, and strategies for computational implemention of the theory described. A diabaticlike Hamiltonian matrix representative is obtained, which is additive in atomic-energy and pairwise-atomic interaction-energy matrices, providing a basis for Molecular calculations in terms of the (Coulombic) interactions of the atomic constituents. The spectral-product basis is shown to...
Israel E. Wachs - One of the best experts on this subject based on the ideXlab platform.
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Molecular/Electronic Structure–surface acidity relationships of model-supported tungsten oxide catalysts
Journal of Catalysis, 2007Co-Authors: Taejin Kim, Andrew Burrows, Christopher J. Kiely, Israel E. WachsAbstract:A series of model-supported WO3 catalysts were synthesized on preformed Al2O3, Nb2O5, TiO2, and ZrO2 supports by impregnation of aqueous ammonium metatungstate, (NH4)10W12O41⋅5H2O. The Molecular and Electronic Structures of the supported tungsten oxide phases were determined with in situ Raman and UV–vis spectroscopy, respectively. The supported tungsten oxide Structures are the same on all oxide supports as a function of tungsten oxide surface density (W/nm2). Below monolayer coverage ( 5 W/nm2), crystalline WO3 nanoparticles are present on top of the surface WOx monolayer. Above ∼10 W/nm2, bulk-like WO3 crystallites become dominant. The number of catalytic active sites and surface chemistry of the supported tungsten oxide phases were chemically probed with CH3OH dehydration to CH3OCH3. The specific oxide support was found to significantly affect the relative catalytic acidity of the surface WOx species (Al2O3 ≫ TiO2 > Nb2O5 > ZrO2) to that of the supported WO3 nanoparticles. Consequently, no general relationship exists between the Molecular/Electronic Structures or domain size and the specific catalytic acidity of the supported tungsten oxide phases present in the model-supported WO3 catalysts.
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Molecular Electronic Structure surface acidity relationships of model supported tungsten oxide catalysts
Journal of Catalysis, 2007Co-Authors: Taejin Kim, Andrew Burrows, Christopher J. Kiely, Israel E. WachsAbstract:A series of model-supported WO3 catalysts were synthesized on preformed Al2O3, Nb2O5, TiO2, and ZrO2 supports by impregnation of aqueous ammonium metatungstate, (NH4)10W12O41⋅5H2O. The Molecular and Electronic Structures of the supported tungsten oxide phases were determined with in situ Raman and UV–vis spectroscopy, respectively. The supported tungsten oxide Structures are the same on all oxide supports as a function of tungsten oxide surface density (W/nm2). Below monolayer coverage ( 5 W/nm2), crystalline WO3 nanoparticles are present on top of the surface WOx monolayer. Above ∼10 W/nm2, bulk-like WO3 crystallites become dominant. The number of catalytic active sites and surface chemistry of the supported tungsten oxide phases were chemically probed with CH3OH dehydration to CH3OCH3. The specific oxide support was found to significantly affect the relative catalytic acidity of the surface WOx species (Al2O3 ≫ TiO2 > Nb2O5 > ZrO2) to that of the supported WO3 nanoparticles. Consequently, no general relationship exists between the Molecular/Electronic Structures or domain size and the specific catalytic acidity of the supported tungsten oxide phases present in the model-supported WO3 catalysts.
Jerry A Boatz - One of the best experts on this subject based on the ideXlab platform.
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Atomic Spectral Methods for Molecular Electronic Structure Calculations
Bulletin of the American Physical Society, 2006Co-Authors: Robert J. Hinde, Jerry A Boatz, P. W. LanghoffAbstract:Abstract : New theoretical methods are reported for ab initio calculations of the adiabatic (Born-Oppenheimer) Electronic wave functions and potential energy surfaces of molecules and other atomic aggregates. An outer product of complete seets of atomic eigenstates familiar from perturbation-theoretical treatments of long-range interactions is employed as a representational basis without prior enforcement of aggregate wave function antisymmetry. The nature and attributes of this atomic spectral-product basis are indicated, completeness proofs for representation of antisymmetric stated provided, convergence of Schrodinger eigenstates in the basis established, and strategies for computational implementation of the theory described.
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Atomic spectral methods for Molecular Electronic Structure calculations.
The Journal of chemical physics, 2004Co-Authors: P. W. Langhoff, Jerry A Boatz, Robert J. Hinde, J. A. SheehyAbstract:Theoretical methods are reported for ab initio calculations of the adiabatic (Born–Oppenheimer) Electronic wave functions and potential energy surfaces of molecules and other atomic aggregates. An outer product of complete sets of atomic eigenstates familiar from perturbation-theoretical treatments of long-range interactions is employed as a representational basis without prior enforcement of aggregate wave function antisymmetry. The nature and attributes of this atomic spectral-product basis are indicated, completeness proofs for representation of antisymmetric states provided, convergence of Schrodinger eigenstates in the basis established, and strategies for computational implemention of the theory described. A diabaticlike Hamiltonian matrix representative is obtained, which is additive in atomic-energy and pairwise-atomic interaction-energy matrices, providing a basis for Molecular calculations in terms of the (Coulombic) interactions of the atomic constituents. The spectral-product basis is shown to...
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general atomic and Molecular Electronic Structure system
Journal of Computational Chemistry, 1993Co-Authors: Michael W Schmidt, Kim K Baldridge, Jerry A Boatz, Steven T Elbert, Mark S Gordon, Jan H Jensen, Shiro Koseki, Nikita Matsunaga, Kiet A Nguyen, Shujun SuAbstract:A description of the ab initio quantum chemistry package GAMESS is presented. Chemical systems containing atoms through radon can be treated with wave functions ranging from the simplest closed-shell case up to a general MCSCF case, permitting calculations at the necessary level of sophistication. Emphasis is given to novel features of the program. The parallelization strategy used in the RHF, ROHF, UHF, and GVB sections of the program is described, and detailed speecup results are given. Parallel calculations can be run on ordinary workstations as well as dedicated parallel machines. © John Wiley & Sons, Inc.
