Excited states in variational Monte Carlo using a penalty method

TL;DR

This paper introduces a variational Monte Carlo method for calculating excited states of electronic systems by enforcing orthogonality to lower states, demonstrated on benzene with promising accuracy.

Contribution

The paper presents a novel penalty-based variational Monte Carlo approach for excited states, enabling efficient and accurate calculations.

Findings

Achieved ~0.2 eV agreement with coupled cluster methods

Optimized ~10,000 parameters for 12 excited states of benzene

Method effectively enforces orthogonality to lower states

Abstract

The authors present a technique using variational Monte Carlo to solve for excited states of electronic systems. The technique is based on enforcing orthogonality to lower energy states, which results in a simple variational principle for the excited states. Energy optimization is then used to solve for the excited states. This technique is applied to the well-characterized benzene molecule, in which $\sim$10,000 parameters are optimized for the first 12 excited states. Agreement within approximately 0.2 eV is obtained with higher scaling coupled cluster methods; small disagreements with experiment are likely due to vibrational effects.