  We demonstrate that a broad class of excited state variational principles is
not size consistent. In light of this difficulty, we develop and test an
approach to excited state optimization that transforms between variational
principles in order to achieve state selectivity, size consistency, and
compatibility with quantum Monte Carlo. To complement our formal analysis, we
provide numerical examples that confirm these properties and demonstrate how
they contribute to a more black box approach to excited states in quantum Monte
Carlo.
