Assessment of Interstate Spin-Orbit Couplings from Linear Response Amplitudes.

In this work, we report benchmark spin-orbit calculations for a representative set of electronic states including π → π*, n → π*, and π → σ* and Rydberg states of organic molecules. Auxiliary many-electron wave functions (AMEWs) have been generated from left and/or right eigenvectors of Casida's non-Hermitian time-dependent density functional theory (TDDFT) equation. The newly developed Spoiler program has been used to evaluate spin-orbit matrix elements (SOMEs) from full linear response TDDFT and TDDFT calculations in Tamm-Dancoff approximation (TDA) in conjunction with the well-known B3-LYP and PBE0 hybrid functionals. The data thus obtained have been benchmarked against SOMEs from multireference configuration interaction calculations recently performed in our group. It turns out that the TDDFT SOMEs are rather insensitive with regard to the choice of eigenvectors (left, right, or mixed) as long as the AMEWs are normalized. To avoid problematic excitation energies of low-lying triplet excited states, the use of the TDA is recommended. With regard to SOMEs, a slight preference is found for the PBE0 functional.

Time-dependent approach to spin-vibronic coupling: implementation and assessment.

In this work, we present the generalization of a time-dependent method for the calculation of intersystem crossing (ISC) rates in the Condon approximation. When ISC takes place between electronic states with the same orbital type, i.e., when the transition is forbidden according to the El-Sayed rules, it is necessary to go beyond the Condon approximation. Similar to the Herzberg-Teller expansion of the vibronic interaction, the electronic spin-orbit matrix elements are assumed to depend linearly on the nuclear coordinates. The ISC rate is then a sum of three contributions: a direct, mixed direct-vibronic, and vibronic term. The method, presented in this work, is based on the generating function formalism and the multi-mode harmonic oscillator approximation. In addition to the zero-temperature case, we implemented formulae for finite-temperature conditions assuming a Boltzmann population of vibrational levels in the initial state. Tests have been carried out for a variety of molecules for which literature data were available. We computed vibronic one-photon spectra of free-base porphyrin and free-base chlorin and calculated ISC rates for xanthone, thioxanthone, thionine, as well as free-base porphyrin and found excellent agreement with previous results. Quantitative rates for triplet formation in rhodamine A have been determined theoretically for the first time. We find the S1↝ T2 channel to be the major source of triplet rhodamine formation in the gas phase.