# Excitation Variance Matching with Limited Configuration Interaction Expansions in Variational Monte Carlo

## TL;DR

This paper introduces a variance matching method within variational Monte Carlo to accurately predict excitation energies in challenging molecules, especially when wave function flexibility is limited.

## Contribution

It develops and tests a variance matching approach combining variational Monte Carlo and selective configuration interaction for better excitation energy predictions.

## Key findings

- Effective at predicting excitation energies with limited wave function flexibility
- Successful application to small difficult molecules like C3
- Enhanced accuracy when combined with orbital optimization

## Abstract

In the regime where traditional approaches to electronic structure cannot afford to achieve accurate energy differences via exhaustive wave function flexibility, rigorous approaches to balancing different states' accuracies become desirable. As a direct measure of a wave function's accuracy, the energy variance offers one route to achieving such a balance. Here, we develop and test a variance matching approach for predicting excitation energies within the context of variational Monte Carlo and selective configuration interaction. In a series of tests on small but difficult molecules, we demonstrate that the approach it is effective at delivering accurate excitation energies when the wave function is far from the exhaustive flexibility limit. Results in C$_3$, where we combine this approach with variational Monte Carlo orbital optimization, are especially encouraging.