Variational quantum Monte Carlo calculation of electronic and structural properties of crystals Page: 2 of 14
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systems), and electron excitation energies.^
In this paper, we discuss a recently developed variational quantum
Monte Carlo (QMC) pseudopotential approach^ to the problem of electron
correlations in solids. A trial wavefunction of the Jastrow-Slater
form with one- and two-body correlation terms is employed. The total
energy of the system is evaluated using the Metropolis sampling
techniques^ and the exact electron-electron interaction, thus allowing
the treatment of valence electron correlations going beyond standard
self-consistent field methods. A pseudopotential scheme which incor-
porates the effects of the core electrons in the ionic potential is
also employed. The use of pseudopotentials for the electron-ion inter-
action removes from the problem the large fluctuations of electron
energies in the core region and makes practical the present approach
for systems with heavier elements.
We have applied the method to calculate the cohesive and structural
properties of diamond, graphite, and Si and the ionization energy and
electron affinity of the atoms. The results are shown to be in excel-
lent agreement with experiment. In particular the cohesive energy is a
significant improvement over those obtained from the standard local
density functional calculations. Further, the calculations have
provided results on quantities such as the single-particle orbital
occupancy and electron pair correlation functions for real crystals.
2. Theoretical Method
2.1. Pseudopotential and Variational Quantum Monte Carlo Approach
The basic idea here is to obtain the ground-state wavefunction
using the variational principle and from it the other properties of the
crystal. The total energy of the system is evaluated using the exact
Hamiltonian with a trial many-electron wavefunction. If the trial
wavefunction is chosen with sufficient insight, we obtain not only an
upper bound for the energy, but an accurate estimate of its value and
the wavefunction itself. From the total energy as a function of the
atomic coordinates, one obtains as usual the binding energy and the
static structural properties of the solid. From the optimal wavefunc-
tion, a host of other quantities may also be calculated which include
the charge density, the single-particle density matrix, the pair corre-
lation function, and the quasiparticle excitation energies.
The variational quantum Monte Carlo approach was pioneered by
McMillan to study liquid He4 in 1965^ and later extended to Fermion
liquid systems by Ceperley, Chester and Kalos in the 1970's.8
Recently, the Green's function quantum Monte Carlo approach has been
applied successfully to the electron gas^ and to light molecules.^
However, the application of these methods to real crystals had not been
realizable until very recently.^ A number of conceptual and technical
problems have to be overcome. These include the proper treatment of
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Louie, S.G. Variational quantum Monte Carlo calculation of electronic and structural properties of crystals, article, September 1, 1989; [Berkeley,] California. (https://digital.library.unt.edu/ark:/67531/metadc1093861/m1/2/: accessed March 26, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.