Excitation energies from diffusion Monte Carlo using selected Configuration Interaction nodes

TL;DR

This paper demonstrates that using selected configuration interaction nodes in diffusion Monte Carlo enables accurate excited-state energy calculations, with significant error cancellation between ground and excited states.

Contribution

It introduces a systematic, Jastrow-free QMC approach for excited states using sCI nodes, improving accuracy and efficiency in excitation energy computations.

Findings

Accurate excitation energies for water and formaldehyde achieved.

Error cancellation between ground and excited states is significant.

Method works with small basis sets and compact wave functions.

Abstract

Quantum Monte Carlo (QMC) is a stochastic method which has been particularly successful for ground-state electronic structure calculations but mostly unexplored for the computation of excited-state energies. Here, we show that, within a Jastrow-free QMC protocol relying on a deterministic and systematic construction of nodal surfaces using selected configuration interaction (sCI) expansions, one is able to obtain accurate excitation energies at the fixed-node diffusion Monte Carlo (FN-DMC) level. This evidences that the fixed-node errors in the ground and excited states obtained with sCI wave functions cancel out to a large extent. Our procedure is tested on two small organic molecules (water and formaldehyde) for which we report all-electron FN-DMC calculations. For both the singlet and triplet manifolds, accurate vertical excitation energies are obtained with relatively compact multideterminant expansions built with small (typically double-$\zeta$) basis sets.