An Efficient Variational Principle for the Direct Optimization of Excited States

We present a variational principle that enables systematically improvable predictions for individual excited states through an efficient Monte Carlo evaluation. We demonstrate its compatibility with different ansatzes and with both real space and Fock space sampling and discuss its potential for use in the solid state. In numerical demonstrations for challenging molecular excitations, the method rivals or surpasses the accuracy of very high level methods using drastically more compact wave function approximations.