Speeding up the ab initio diffusion Monte Carlo by a smart lattice regularization

TL;DR

This paper presents a novel lattice regularization approach for diffusion Monte Carlo that significantly reduces computational costs for heavy atoms, enabling more efficient all-electron calculations with near-acceptable scaling.

Contribution

The authors introduce a lattice regularized DMC algorithm that adapts lattice spacing near nuclei and in valence regions, improving scalability for large atomic numbers.

Findings

Achieves near Z^5 scaling with atomic number

Enables faster and more efficient all-electron DMC calculations

Theoretically validated using the Thomas-Fermi model

Abstract

One of the most significant drawbacks of the all-electron ab initio diffusion Monte Carlo (DMC) is that its computational cost drastically increases with the atomic number ($Z$), which typically scales with $Z^{\sim 6}$. In this study, we introduce an algorithm based on a very efficient implementation of the Lattice Regularized Diffusion Monte Carlo (LRDMC), where the conventional time discretization is replaced by its lattice space counterpart. This scheme enables us to conveniently adopt a small lattice space in the vicinity of nuclei, and a large one in the valence region, by which a considerable speedup is achieved, especially for large atomic number $Z$. Indeed, the computational performances of our algorithm can be theoretically established by using the Thomas-Fermi model for heavy atoms, yielding an almost affordable scaling with the atomic number, i.e., $Z^{\sim 5}$. This opens the way for efficient and accurate all-electron ab initio DMC in electronic structure calculations.