Beyond the Born-Oppenheimer approximation with quantum Monte Carlo

TL;DR

This paper develops quantum Monte Carlo tools to study non-adiabatic effects in electron-ion systems, explicitly including quantum nuclei and electron-nucleus coupling, achieving highly accurate ground state energies.

Contribution

It introduces a novel wave function ansatz for electron-ion systems that incorporates both fixed and quantum ions, enabling non-adiabatic effect analysis with quantum Monte Carlo methods.

Findings

Accurately computed ground state energies for H₂, LiH, H₂O, and FHF⁻.

Wave function nodes explicitly depend on ion positions, capturing quantum nuclei effects.

Results show excellent agreement with experimental and theoretical data.

Abstract

In this work we develop tools that enable the study of non-adiabatic effects with variational and diffusion Monte Carlo methods. We introduce a highly accurate wave function ansatz for electron-ion systems that can involve a combination of both fixed and quantum ions. We explicitly calculate the ground state energies of H$_{2}$, LiH, H$_{2}$O and FHF$^{-}$ using fixed-node quantum Monte Carlo with wave function nodes that explicitly depend on the ion positions. The obtained energies implicitly include the effects arising from quantum nuclei and electron-nucleus coupling. We compare our results to the best theoretical and experimental results available and find excellent agreement.