Regarding notation, we use H to denote a quantum operator and a bold symbol T to denote a matrix. For classical degrees of freedom, we denote each component of classical vectors with a superscript label as in R α . We let i, j, k, . . . denote the canonical occupied orbitals, a, b, c . . . denote the canonical virtual orbitals. Wavefunctions are indexed with capital Roman letters I, J, K . . . and will usually refer to the CIS excitation states.