The role of Duschinsky rotation in intersystem crossing: a case study of uracil

The intersystem crossing rate for the transition between the lowest excited singlet and triplet electronic states of uracil was studied by means of ab initio methods. The rate was evaluated using the time-dependent approach based on the correlation function and its two approximations: the second-order cumulant expansion and the short-time approximation. The normal modes of the singlet and triplet states are related by the Duschinsky transformation, i.e., by rotation and translation. It was found that for singlet–triplet adiabatic energy gaps below 6000 cm-1, the inclusion of the Duschinsky rotation is necessary for quantitative results. Above energy gaps of 6000 cm-1, the rates obtained with and without the Duschinsky rotation are similar. The cumulant expansion approximates well the correlation function. The short-time approximation, although crude, can be used as the first estimate of the rate.