A time-dependent approach to the nonradiative decay of polyatomic molecule: S1 to S0 transition of H2CO

A time-dependent method to estimate a nonradiative transition rate was proposed and applied to the problem of decay of S1 to S0 state of formaldehyde. This approach is based upon the wave packet propagation with the reaction path Hamiltonian and the direct calculations of electronic matrix elements of nonadiabatic coupling using ab initio MO method. Since the auto-correlation function, operated with a Fourier transformation to obtain the rate constant, decays within a short time by introducing the effective Hamiltonian in time propagator, it is possible to estimate the rate constant by short time propagation of wave packet. The calculated nonradiative decay rates were in good agreement with the experimental ones.