where ω I is the same weight for state |I⟩ used in the underlying SA-CASSCF or SA-CASCI calculation. Generally, we take all weights to be equal (ω I = ω J ) such that γp q and γpr qs become partial traces of linear operators and therefore are independent of the basis-set representation of the model space and only dependent on the model space. In the case of a hybrid functional the final states come from a diagonalization of a weighted average of the L-PDFT Hamiltonian and electronic Hamiltonian