Excited States In Variational Monte Carlo Using A Penalty Method

In this article, the authors present a technique using variational Monte Carlo to solve for excited states of electronic systems. This 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 similar to 10 000 parameters are optimized for the first 12 excited states. Agreement within similar to 0.2 eV is obtained with higher scaling coupled cluster methods; small disagreements with experiment are likely due to vibrational effects.