Density functional theory of nonlinear triplet response properties with applications to phosphorescence

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We present density functional response theory generalized to triplet excitations. A method based on an exponential parametrization of the spin-dependent density operator is derived for the evaluation of linear and quadratic response functions for spin-dependent perturbations. The developed methodology is applicable to commonly available functionals, also hybrid functionals including exchange–correlation functionals at the general gradient-approximation level and fractional exact Hartree–Fock exchange. Illustrative calculations are presented for singlet–triplet transition moments and phosphorescence lifetimes, providing numerical data on these quantities for the first time using time-dependent density functional theory.