Towards a Systematic Improvement of the Fixed-Node Approximation in Diffusion Monte Carlo for Solids -- A Case Study In Diamond

TL;DR

This paper introduces a systematic approach to improve the fixed-node approximation in diffusion Monte Carlo calculations for solids, using CIPSI-generated trial wavefunctions and a protocol for extrapolating to the thermodynamic limit, demonstrated on diamond.

Contribution

The paper presents a new method to generate systematically improvable trial wavefunctions for DMC in solids using CIPSI and a protocol for thermodynamic limit extrapolation.

Findings

CIPSI can produce trial wavefunctions with systematically improved nodes.

The proposed extrapolation protocol effectively approaches the thermodynamic limit.

Application to diamond demonstrates the method's potential for accurate solid-state calculations.

Abstract

While Diffusion Monte Carlo (DMC) is in principle an exact stochastic method for \textit{ab initio} electronic structure calculations, in practice the fermionic sign problem necessitates the use of the fixed-node approximation and trial wavefunctions with approximate nodes (or zeros) must be used. This approximation introduces a variational error in the energy that potentially can be tested and systematically improved. Here, we present a computational method that produces trial wavefunctions with systematically improvable nodes for DMC calculations of periodic solids. These trial wavefunctions are efficiently generated with the configuration interaction using a perturbative selection made iteratively (CIPSI) method. A simple protocol in which both exact and approximate results for finite supercells are used to extrapolate to the thermodynamic limit is introduced.