Multideterminant Wave Functions in Quantum Monte Carlo

Abstract

Quantum Monte Carlo (QMC) methods have received considerable attention over past decades due to their great promise for providing a direct solution to the many-body Schrodinger equation in electronic systems. Thanks to their low scaling with the number of particles, QMC methods present a compelling competitive alternative for the accurate study of large molecular systems and solid state calculations. In spite of such promise, the method has not permeated the quantum chemistry community broadly, mainly because of the fixed-node error, which can be large and whose control is difficult. In this Perspective, we present a systematic application of large scale multideterminant expansions in QMC and report on its impressive performance with first row dimers and the 55 molecules of the G1 test set. We demonstrate the potential of this strategy for systematically reducing the fixed-node error in the wave function and for achieving chemical accuracy in energy predictions. When compared to traditional quantum chemistry methods like MP2, CCSD(T), and various DFT approximations, the QMC results show a marked improvement over all of them. In fact, only the explicitly correlated CCSD(T) method with a large basis set produces more accurate results. Further developments in trial wave functions and algorithmic improvements appear promising for rendering QMC as the benchmark standard in large electronic systems.

Influence of single particle orbital sets and configuration selection on multideterminant wavefunctions in quantum Monte Carlo

“…DMC benchmarks over the G2 test set of various trial wavefunctions based on multideterminant expansions have finally produced subchemical accuracy for atomization energies, and near chemical accuracy for total energies. 8,10 For first row atoms and dimers, MSD's are able to routinely recover at least 99% of correlation energies. 10,16,17 MSD's have also been shown to be able to accurately describe the dissociation of the C2 and N2 dimers.…”

A Blocked Linear Method for Optimizing Large Parameter Sets in Variational Monte Carlo

“…The LM will thus be efficient (i.e. polynomial cost) for ansatzes that support the efficient evaluation of the derivative ratios n|Ψ x / n|Ψ and n|H|Ψ x / n|Ψ , examples of which include MSJ expansions [11,12,18], the Jastrow antisymmetric geminal power [25][26][27] (JAGP), and amplitude determinant coupled cluster with pairwise doubles [13].…”

First Principles Methods: A Perspective from Quantum Monte Carlo

“…The interested reader is encouraged to look at the references for more information on Slater-Jastrow wavefunctions [12,16]. One can also go beyond the Slater-Jastrow form; other possible choices include multi-Slater determinant expansions [17], geminals [18], etc. VMC can be improved if we consider classes of trial wavefunctions Ψ T (R, α) parameterized by α = (α 1 , ..., α m ) free parameters.…”