First-principles method for calculating the rate constants of internal-conversion and intersystem-crossing transitions

A method for calculating the rate constants for internal-conversion (kIC) and intersystem-crossing (kISC) processes within the adiabatic and Franck-Condon (FC) approximations is proposed. The applicability of the method is demonstrated by calculation of kIC and kISC for a set of organic and organometallic compounds with experimentally known spectroscopic properties. The studied molecules were pyrromethene-567 dye, psoralene, hetero8circulenes, free-base porphyrin, naphthalene, and larger polyacenes. We also studied fac-Alq3 and fac-Ir(ppy)3, which are important molecules in organic light emitting diodes (OLEDs). The excitation energies were calculated at the multi-configuration quasi-degenerate second-order perturbation theory (XMC-QDPT2) level, which is found to yield excitation energies in good agreement with experimental data. Spin-orbit coupling matrix elements, non-adiabatic coupling matrix elements, Huang-Rhys factors, and vibrational energies were calculated at the time-dependent density functional theory (TDDFT) and complete active space self-consistent field (CASSCF) levels. The computed fluorescence quantum yields for the pyrromethene-567 dye, psoralene, hetero8circulenes, fac-Alq3 and fac-Ir(ppy)3 agree well with experimental data, whereas for the free-base porphyrin, naphthalene, and the polyacenes, the obtained quantum yields significantly differ from the experimental values, because the FC and adiabatic approximations are not accurate for these molecules.