The Need, Benefits, and Demonstration of a Minimization Principle for Excited States

It is shown that the standard methods of computing excited states in truncated spaces must yield wave functions that, beyond truncation, are in principle veered away from the exact, and a remedy is demonstrated via a presented functional, F${}_n$, obeying a minimization principle for excited states. It is further demonstrated that near avoided crossings, between two MCSCF ‘flipped roots’ the wave function that leads to the excited state has the lowest F${}_n$.