  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.
