Computing the energy of a water molecule using MultiDeterminants: A simple, efficient algorithm

TL;DR

This paper introduces an efficient, scalable algorithm for computing water molecule energies using multiSlater-Jastrow wave functions in Quantum Monte Carlo, improving computational speed and memory usage.

Contribution

The paper presents a simple, efficient, and parallelizable method for handling multiSlater-Jastrow wave functions in QMC, with favorable quadratic scaling.

Findings

Method is easy to implement and parallelize

Computational cost scales quadratically with particle number

Successfully computed water molecule ground state energy

Abstract

Quantum Monte Carlo (QMC) methods such as variational Monte Carlo and fixed node diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational ansatz in electronic structure, more sophisticated wave-functions are critical to ascertaining new physics. One such wave function is the multiSlater-Jastrow wave function which consists of a Jastrow function multiplied by the sum of Slater determinants. In this paper we describe a method for working with these wavefunctions in QMC codes that is easy to implement, efficient both in computational speed as well as memory, and easily parallelized. The computational cost scales quadratically with particle number making this scaling no worse than the single determinant case and linear with the total number of excitations. Additionally we implement this method and use it to compute the ground state energy of a water molecule.