The nonradiative transition rates from the single vibronic levels of the first singlet excited state to the ground state were estimated using a time-dependent method based on Fermi’s golden rule. In the present method, the initial wave packet is constructed with the use of the nonadiabatic coupling matrix elements calculated by ab initio molecular orbital method. The wave packet dynamics calculation is carried out using the reaction path Hamiltonian. The vibrational relaxation on the ground state surface is treated by introducing the effective Hamiltonian. The parameters required to construct these Hamiltonians were obtained with the complete active space self-consistent field wave function and the electronic matrix elements of nonadiabatic coupling between the ground and first singlet excited states were calculated with the state-averaged complete active space self-consistent field wave function analytically. The calculated rate constants were in good agreement with the experimental ones. It is found that vibrational relaxation in the ground electronic state is an important factor in obtaining the nonradiative transition rate constants.