Grid-based numerical Hartree-Fock solutions of polyatomic molecules

2007 ◽  
Vol 76 (4) ◽  
Author(s):  
Toru Shiozaki ◽  
So Hirata
Keyword(s):  
Polyatomic Molecules ◽  
Hartree Fock ◽  
Grid Based

Simplified Non-Empirical Unrestricted Hartree-Fock Approximation (SUHF) for the Calculation of Electronic Ground State Properties of Molecules with Closed and Open Valence Shells. I. Method

1993 ◽  
Vol 48 (7) ◽  
pp. 829-833
Author(s):  
Wolfhard Koch
Keyword(s):  
Electron Correlation ◽  
Ground State ◽  
Atomic Orbital ◽  
Closed Shell ◽  
Open Shell ◽  
Polyatomic Molecules ◽  
Correlation Effects ◽  
Hartree Fock ◽  
Electron Correlation Effects ◽  
Electronic Ground

Abstract Focusing on relative stabilities of electronic states with different spin multiplicities of polyatomic molecules, a simplified unrestricted Hartree-Fock (SUHF) procedure is described. Using different orbitals for different spins (DODS), electron correlation effects of both closed-shell and open-shell systems are expected to be taken into account in the simplest way. While working within a symmetrically orthogonalized (Löwdin) basis we make use of the NDDO approximation (neglect of diatomic differential overlap) concerning the evaluation of electron repulsion and nuclear attraction integrals. Originally, a locally orthogonalized all-electron atomic orbital set of Slater type is considered. The approximation method is completely non-empirical. Rotational invariance is fully retained.

EMS studies of larger molecules of chemical and biochemical interest

1996 ◽  
Vol 74 (11-12) ◽  
pp. 773-781 ◽  
Author(s):  
J. J. Neville ◽  
Y. Zheng ◽  
B. P. Hollebone ◽  
N. M. Cann ◽  
C. E. Brion ◽  
...  
Keyword(s):  
Density Functional ◽  
Polyatomic Molecules ◽  
Target Compound ◽  
Frontier Orbitals ◽  
Functional Theory ◽  
Electron Momentum ◽  
Hartree Fock ◽  
Electron Momentum Spectroscopy ◽  
Key Factor ◽  
Increased Sensitivity

The challenges involved in extending electron momentum spectroscopy (EMS) studies beyond small polyatomic molecules to more complicated systems are discussed. EMS results for the highest occupied (frontier) molecular orbitals of glycine (NH2CH2COOH) and dimethoxymethane ((CH3O)2CH2) demonstrate possible approaches to overcoming such challenges as closely spaced valence orbitals, low volatility, and the conformational mobility of the target compound. The increased sensitivity available from recently developed multichannel electron momentum spectrometers is a key factor in overcoming these challenges and making such EMS studies feasible. The utility of Kohn–Sham density functional theory (DFT) for EMS calculations on larger molecules such as glycine and dimethoxymethane using the recently formulated target Kohn–Sham approximation is also investigated as experimental momentum profiles are compared with theoretical momentum profiles generated via Kohn–Sham DFT and a range of Hartree–Fock calculations. The Kohn–Sham DFT calculations provide better agreement with experiment for the frontier orbitals of glycine and dimethoxymethane than even the near Hartree–Fock limit results.

scholarly journals Block Circulant and Toeplitz Structures in the Linearized Hartree–Fock Equation on Finite Lattices: Tensor Approach

2017 ◽  
Vol 17 (3) ◽  
pp. 431-455 ◽  
Author(s):  
Venera Khoromskaia ◽  
Boris N. Khoromskij
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Periodic Problem ◽  
Type Systems ◽  
Dirichlet Boundary Conditions ◽  
Low Rank ◽  
Periodic Case ◽  
System Matrix ◽  
Hartree Fock ◽  
Grid Based

AbstractThis paper introduces and analyzes the new grid-based tensor approach to approximate solutions of the elliptic eigenvalue problem for the 3D lattice-structured systems. We consider the linearized Hartree–Fock equation over a spatial{L_{1}\times L_{2}\times L_{3}}lattice for both periodic and non-periodic problem setting, discretized in the localized Gaussian-type orbitals basis. In the periodic case, the Galerkin system matrix obeys a three-level block-circulant structure that allows the FFT-based diagonalization, while for the finite extended systems in a box (Dirichlet boundary conditions) we arrive at the perturbed block-Toeplitz representation providing fast matrix-vector multiplication and low storage size. The proposed grid-based tensor techniques manifest the twofold benefits: (a) the entries of the Fock matrix are computed by 1D operations using low-rank tensors represented on a 3D grid, (b) in the periodic case the low-rank tensor structure in the diagonal blocks of the Fock matrix in the Fourier space reduces the conventional 3D FFT to the product of 1D FFTs. Lattice type systems in a box with Dirichlet boundary conditions are treated numerically by our previous tensor solver for single molecules, which makes possible calculations on rather large{L_{1}\times L_{2}\times L_{3}}lattices due to reduced numerical cost for 3D problems. The numerical simulations for both box-type and periodic{L\times 1\times 1}lattice chain in a 3D rectangular “tube” withLup to several hundred confirm the theoretical complexity bounds for the block-structured eigenvalue solvers in the limit of largeL.

The any particle molecular orbital grid-based Hartree-Fock (APMO-GBHF) approach

2018 ◽  
Vol 148 (8) ◽  
pp. 084113 ◽  
Author(s):  
Edwin Posada ◽  
Félix Moncada ◽  
Andrés Reyes
Keyword(s):  
Molecular Orbital ◽  
Hartree Fock ◽  
Grid Based
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