If the harmonic oscillator approximation to the potential energy surfaces is adopted, then the calculations of S-T crossing rates are similar to the calculation of vibrationally-resolved absorption and fluorescence spectra. In the latter cases, SOC operator is replaced with the dipole operator μ, and S 0 and S 1 states are concerned. We have implemented these timedependent correlation function approaches to calculate the vibronic spectra including oneand two-photon absorption and emission and resonance Raman scattering spectra. A summary of our previous works on the vibronic spectra has been given in Ref. 41. Here we extend this time-dependent approach to calculate the S-T crossing rates.