Simple formalism for efficient derivatives and multi-determinant expansions in quantum Monte Carlo

TL;DR

This paper introduces a simple, efficient formalism for computing derivatives and local properties in quantum Monte Carlo, significantly improving computational performance for multi-determinant wave functions.

Contribution

It presents a new formalism that streamlines the calculation of derivatives and local properties in multi-determinant quantum Monte Carlo wave functions, enhancing efficiency.

Findings

Achieves computational efficiency comparable to algorithmic differentiation.

Extends computational gains to all local properties in large multi-determinant expansions.

Applicable to both all-electron and pseudopotential calculations.

Abstract

We present a simple and general formalism to compute efficiently the derivatives of a multi-determinant Jastrow-Slater wave function, the local energy, the interatomic forces, and similar quantities needed in quantum Monte Carlo. Through a straightforward manipulation of matrices evaluated on the occupied and virtual orbitals, we obtain an efficiency equivalent to algorithmic differentiation in the computation of the interatomic forces and the optimization of the orbital paramaters. Furthermore, for a large multi-determinant expansion, the significant computational gain recently reported for the calculation of the wave function is here improved and extended to all local properties in both all-electron and pseudopotential calculations.