General formalism of absorption and emission spectra, and of radiative and nonradiative decay rates are derived using a thermal vibration correlation function formalism for the transition between two adiabatic electronic states in polyatomic molecules. Displacements, distortions, and Duschinsky rotation of potential energy surfaces are included within the framework of a multidimensional harmonic oscillator model. The Herzberg-Teller (HT) effect is also taken into account. This formalism gives a reliable description of the Q(x) spectral band of free-base porphyrin with weakly electric dipole-allowed transitions. For the strongly dipole-allowed transitions, e.g., S(1) --> S(0) and S(0) --> S(1) of linear polyacenes, anthracene, tetracene, and pentacene, the HT effect is found to enhance the radiative decay rates by approximately 10% compared to those without the HT effect. For nonradiative transition processes, a general formalism is presented to extend the application scope of the internal conversion theory by going beyond the promoting-mode approximation. Numerical calculations for the nonradiative S(1) --> S(0) decay rate of azulene well explain the origin of the violation of Kasha's rule. When coupled with first-principles density functional theory (DFT) calculations, the present approach appears to be an effective tool to obtain a quantitative description and detailed understanding of spectra and photophysical processes in polyatomic molecules.

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.