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.

Based on the second-order perturbation combining spin-orbit and nonadiabatic couplings, we derived an analytical formula for nonradiative decay rate between the triplet and singlet states by using the thermal vibration correlation function (TVCF) approach. Origin displacement, distortion, and Duschinsky rotation of the potential energy surfaces are taken into accounts within the multiple harmonic oscillator model. When coupled with first-principles calculation for the anthracene, the theoretical phosphorescence spectrum is in good agreement with the experiment. Furthermore, we found that the intersystem crossing from the first excited singlet state (S1) to the triplet states S1(Bu)→T2(Ag) is forbidden by direct spin-orbit coupling at the first-order perturbation but becomes allowed through combined spin-orbit and the nonadiabatic couplings at the second-order perturbation, and the rate is calculated to be 0.26 × 10(8) s(-1), in good agreement with the experiment. Such formalism is also applied to describe the phosphorescence quantum efficiency and the temperature dependent optical emission spectrum for fac-tris(2-phenylpyridine) iridium. We predict that the radiative decay rate is 6.36 × 10(5) s(-1), the nonradiative decay rate is 5.04 × 10(4) s(-1), and the phosphorescence quantum efficiency is found to be 92.7% from T1 to S0, which reproduce well the corresponding experimental measurements.