where indices pq and μν denote the MO and AO, respectively. Elements of + )+ are the MOLCAO amplitudes of AO 3 in the MO 4 Φ and Ψ ! denote the electronic ground and n th excited state, respectively, and / 0 ,+ is the one-particle excitation operator. Application of the AO overlap matrix S to the transition density matrix in the AO basis can then be used to compute elements of the CT matrix 84 (Eq. 4.3):