Optimizing the energy with quantum Monte Carlo: A lower numerical scaling for Jastrow-Slater expansions

TL;DR

This paper introduces an improved quantum Monte Carlo formalism that significantly reduces the computational scaling for energy derivatives and property calculations using Jastrow-Slater wave functions, enabling efficient optimization of large molecular systems.

Contribution

The authors develop a new formalism that lowers the computational scaling of energy derivatives in quantum Monte Carlo from linear to constant per derivative and reduces overall optimization complexity.

Findings

Scaling for derivatives is reduced to O(N_e) per derivative.

Wave function and geometry optimization scale as O(N^3)+O(N N_e).

Efficient optimization demonstrated on large molecules like C60H62.

Abstract

We present an improved formalism for quantum Monte Carlo calculations of energy derivatives and properties (e.g. the interatomic forces), with a multideterminant Jastrow-Slater function. As a function of the number $N_e$ of Slater determinants, the numerical scaling of $O(N_e)$ per derivative we have recently reported is here lowered to $O(N_e)$ for the entire set of derivatives. As a function of the number of electrons $N$, the scaling to optimize the wave function and the geometry of a molecular system is lowered to $O(N^3)+O(N N_e)$, the same as computing the energy alone in the sampling process. The scaling is demonstrated on linear polyenes up to C$_{60}$H$_{62}$ and the efficiency of the method is illustrated with the structural optimization of butadiene and octatetraene with Jastrow-Slater wave functions comprising as many as 200000 determinants and 60000 parameters.