A theoretical study of the 21Ag←11Ag two-photon transition and its vibronic band in trans-stilbene

The two-photon spectrum of the 2(1)A(g)-->1(1)A(g) transition in trans-stilbene has been calculated at the complete active space self-consistent field (CASSCF) level of theory. Energies were obtained at the complete active space second-order perturbation (CASPT2) level of theory, while the geometries of both the initial and final states were optimized at the CASSCF level. The energy and the geometry optimizations were performed using an active space of 14 electrons in 14 active pi orbitals. The vibrational frequencies of both states and the two-photon transition (TPT) cross-section were calculated with a smaller active space where the two lowest pi orbitals were kept inactive. A newly implemented algorithm, in the quantum chemical package Molcas was used to determine the two-photon transition intensity. This method requires only the linear response of the CASSCF wavefunction. Furthermore, the vibronic structure of this TPT was studied. The Franck-Condon factors were obtained by calculating the overlap between the vibrational states involved, which were determined from the force fields of both the initial and final states, at the CASSCF level of theory. The results are in agreement with experiment.