Molcas Forum

MaxParadiz

Member

Registered: 2019-09-01

Posts: 22

Why do we minimize the average energy of the states in SA-CASSCF?

I am to an extent aware of the practical reasoning behind using state-averaging to obtain a balanced and converged description of multiple orthogonal states. However, I am wondering what the implications of such an approach are. Is there a fundamental reason why we would expect the average energy to be minimized? The variational theorem promises that we should be able to minimize the energy of the ground state by combining the basis functions in just the right way - but as far as I am aware it makes no such promises about the average energy, or the energy of the excited states. Shouldn't a state-averaged procedure be biased towards minimizing the energy of the ground state, then?

I am thinking that perhaps the basis sets are more complete for describing the ground state than for the excited states, so the averaging procedure can help balance this shortcoming. But if the reality is that the average energy of the system we want to study is not minimized, this approach sets us up for failure. Do we state-average because it is the best practical option? Or do we know that this approach (likely) will give us the most correct description of the states?