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.
We investigated applications of the hierarchical equation of motion (HEOM) method to perform high order perturbation calculations of reduced quantum dynamics for a harmonic bath with arbitrary spectral densities. Three different schemes are used to decompose the bath spectral density into analytical forms that are suitable to the HEOM treatment: (1) The multiple Lorentzian mode model that can be obtained by numerically fitting the model spectral density. (2) The combined Debye and oscillatory Debye modes model that can be constructed by fitting the corresponding classical bath correlation function. (3) A new method that uses undamped harmonic oscillator modes explicitly in the HEOM formalism. Methods to extract system-bath correlations were investigated for the above bath decomposition schemes. We also show that HEOM in the undamped harmonic oscillator modes can give detailed information on the partial Wigner transform of the total density operator. Theoretical analysis and numerical simulations of the spin-Boson dynamics and the absorption line shape of molecular dimers show that the HEOM formalism for high order perturbations can serve as an important tool in studying the quantum dissipative dynamics in the intermediate coupling regime.
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