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 pi -> pi* n -> pi*, and pi -> sigma* 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.