Multiconfigurational quadratic response functions for singlet and triplet perturbations: The phosphorescence lifetime of formaldehyde

A formalism is presented for the calculation of quadratic response functions of multiconfigurational self-consistent field reference wave functions. The formalism is general in the sense that it applies equally well to singlet and triplet perturbations and it does not assume any permutational symmetry in the integrals of the perturbational operators. This formalism can be used to derive expressions for various properties related to singlet or triplet quadratic response functions and their residues. We focus on the spin-forbidden dipole transitions between singlet and triplet electronic states responsible for the long lifetime of phosphorescent states. The singlet–triplet transition moments are evaluated as the residues of quadratic response functions. Sample calculations are presented for the formaldehyde molecule.