Nuclear gradients from auxiliary-field quantum Monte Carlo and their application in geometry optimization and transition state search

TL;DR

This paper introduces a scalable method for calculating nuclear forces using auxiliary-field quantum Monte Carlo, enabling accurate geometry optimizations and transition state searches with machine learning assistance.

Contribution

The authors develop an automatic differentiation-based approach for nuclear gradients in AFQMC and demonstrate its application in geometry optimization and transition state identification.

Findings

Accurate nuclear gradients computed with AFQMC validated against finite differences.

ML models effectively learn noisy AFQMC data for geometry and reaction path calculations.

Transition state geometries and barriers closely match high-level coupled-cluster results.

Abstract

In this article, we present a method for computing accurate and scalable nuclear forces within the phaseless auxiliary-field quantum Monte Carlo (AFQMC) framework. Our approach leverages automatic differentiation of the energy functional to obtain nuclear gradients at a computational cost comparable to that of energy evaluation. The accuracy of the method is validated against finite difference calculations, showing excellent agreement. We then explore several machine learning (ML) strategies for learning noisy AFQMC data. These ML potentials are subsequently used to perform geometry optimizations and nudged elastic band (NEB) calculations, successfully identifying the transition state of the formamide-formimidic acid tautomerization. The resulting transition state geometry and barrier heights are in close agreement with coupled-cluster reference values. This work paves the way for highly accurate geometry optimization, molecular dynamics, or reaction path calculations.