Evaluation of Spin-Orbit Couplings with Linear-Response Time-Dependent Density Functional Methods

A new versatile code based on Python scripts was developed to calculate spin−orbit coupling (SOC) elements between singlet and triplet states. The code, named PySOC, is interfaced to third- party quantum chemistry packages, such as Gaussian 09 and DFTB+. SOCs are evaluated using linear-response (LR) methods based on time- dependent density functional theory (TDDFT), the Tamm-Dancoff approximation (TDA), and time-dependent density functional tight binding (TD-DFTB). The evaluation employs Casida-type wave functions and the Breit-Pauli (BP) spin−orbit Hamiltonian with an effective charge approximation. For validation purposes, SOCs calculated with PySOC are benchmarked for several organic molecules, with SOC values spanning several orders of magnitude. The computed SOCs show little variation with the basis set, but are sensitive to the chosen density functional. The benchmark results are in good agreement with reference data obtained using higher-level spin−orbit Hamiltonians and electronic structure methods, such as CASPT2 and DFT/MRCI. PySOC can be easily interfaced to other third-party codes and other methods yielding CI-type wave functions.