Predicting Phosphorescence Rates of Light Organic Molecules Using Time-Dependent Density Functional Theory and the Path Integral Approach to Dynamics

In this work, we present a general method for predicting phosphorescence rates and spectra for molecules using time-dependent density functional theory (TD-DFT) and a path integral approach for the dynamics that relies on the harmonic oscillator approximation for the nuclear movement. We first discuss the theory involved in including spin-orbit coupling (SOC) among singlet and triplet excited states and then how to compute the corrected transition dipole moments and phosphorescence rates. We investigate the dependence of these rates on some TD-DFT parameters, such as the nature of the functional, the number of roots, and the Tamm-Dancoff approximation. After that, we evaluate the effect of different SOC integral schemes and show that our best method is applicable to a large number of systems with different excited state characters.