Size Consistent Excited States via Algorithmic Transformations between Variational Principles

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 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.