In the regime where traditional approaches to electronic structure cannotafford to achieve accurate energy differences via exhaustive wave functionflexibility, rigorous approaches to balancing different states' accuraciesbecome desirable. As a direct measure of a wave function's accuracy, the energyvariance offers one route to achieving such a balance. Here, we develop andtest a variance matching approach for predicting excitation energies within thecontext of variational Monte Carlo and selective configuration interaction. Ina series of tests on small but difficult molecules, we demonstrate that theapproach it is effective at delivering accurate excitation energies when thewave function is far from the exhaustive flexibility limit. Results in C$_3$,where we combine this approach with variational Monte Carlo orbitaloptimization, are especially encouraging.
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