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Title: Fixed-node quantum Monte Carlo for molecules

Abstract

The ground-state energies of H/sub 2/, LiH, Li/sub 2/, and H/sub 2/O are calculated by a fixed-node quantum Monte Carlo method, which is presented in detail. For each molecule, relatively simple trial wave functions Psi/sub T/ are chosen. Each Psi/sub T/ consists of a single Slater determinant of molecular orbitals multiplied by a product of pair-correlation (Jastrow) functions. These wave functions are used as importance functions in a stochastic approach that solves the Schroedinger equation by treating it as a diffusion equation. In this approach, Psi/sub T/ serves as a ''guiding function'' for a random walk of the electrons through configuration space. In the fixed-node approximation used here, the diffusion process is confined to connected regions of space, bounded by the nodes (zeros) of Psi/sub T/. This approximation simplifies the treatment of Fermi statistics, since within each region an electronic probability amplitude is obtained which does not change sign. Within these approximate boundaries, however, the Fermi problem is solved exactly. The energy obtained by this procedure is shown to be an upper bound to the true energy. For the molecular systems treated, at least as much of the correlation energy is accounted for with the relatively simple Psi/sub T/'s usedmore » here as by the best configuration interaction calculations presently available.« less

Authors:
; ; ;
Publication Date:
Research Org.:
National Resource for Computation in Chemistry, Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720
OSTI Identifier:
6705530
Resource Type:
Journal Article
Journal Name:
J. Chem. Phys.; (United States)
Additional Journal Information:
Journal Volume: 77:11
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; HYDROGEN; ELECTRONIC STRUCTURE; LITHIUM; LITHIUM HYDRIDES; WATER; ENERGY; GROUND STATES; MOLECULES; MONTE CARLO METHOD; QUANTUM MECHANICS; WAVE FUNCTIONS; ALKALI METAL COMPOUNDS; ALKALI METALS; ELEMENTS; ENERGY LEVELS; FUNCTIONS; HYDRIDES; HYDROGEN COMPOUNDS; LITHIUM COMPOUNDS; MECHANICS; METALS; NONMETALS; OXYGEN COMPOUNDS; 640302* - Atomic, Molecular & Chemical Physics- Atomic & Molecular Properties & Theory

Citation Formats

Reynolds, P J, Ceperley, D M, Alder, B J, and Lester, Jr, W A. Fixed-node quantum Monte Carlo for molecules. United States: N. p., 1982. Web.
Reynolds, P J, Ceperley, D M, Alder, B J, & Lester, Jr, W A. Fixed-node quantum Monte Carlo for molecules. United States.
Reynolds, P J, Ceperley, D M, Alder, B J, and Lester, Jr, W A. 1982. "Fixed-node quantum Monte Carlo for molecules". United States.
@article{osti_6705530,
title = {Fixed-node quantum Monte Carlo for molecules},
author = {Reynolds, P J and Ceperley, D M and Alder, B J and Lester, Jr, W A},
abstractNote = {The ground-state energies of H/sub 2/, LiH, Li/sub 2/, and H/sub 2/O are calculated by a fixed-node quantum Monte Carlo method, which is presented in detail. For each molecule, relatively simple trial wave functions Psi/sub T/ are chosen. Each Psi/sub T/ consists of a single Slater determinant of molecular orbitals multiplied by a product of pair-correlation (Jastrow) functions. These wave functions are used as importance functions in a stochastic approach that solves the Schroedinger equation by treating it as a diffusion equation. In this approach, Psi/sub T/ serves as a ''guiding function'' for a random walk of the electrons through configuration space. In the fixed-node approximation used here, the diffusion process is confined to connected regions of space, bounded by the nodes (zeros) of Psi/sub T/. This approximation simplifies the treatment of Fermi statistics, since within each region an electronic probability amplitude is obtained which does not change sign. Within these approximate boundaries, however, the Fermi problem is solved exactly. The energy obtained by this procedure is shown to be an upper bound to the true energy. For the molecular systems treated, at least as much of the correlation energy is accounted for with the relatively simple Psi/sub T/'s used here as by the best configuration interaction calculations presently available.},
doi = {},
url = {https://www.osti.gov/biblio/6705530}, journal = {J. Chem. Phys.; (United States)},
number = ,
volume = 77:11,
place = {United States},
year = {Wed Dec 01 00:00:00 EST 1982},
month = {Wed Dec 01 00:00:00 EST 1982}
}