Calculation of vibronic coupling constant and vibronic coupling density analysis

Vibronic coupling, electron–phonon interaction, constants of Jahn–Teller molecules, C5H5 and C5D5, are computed as matrix elements of the electronic operator of the vibronic coupling operator using the electronic wave functions calculated by generalized restricted Hartree–Fock (GRHF) and state-averaged complete active space self-consistent-field (CASSCF) methods. The calculated values of vibronic coupling constants for C5H5 and C5D5 agree well with the experimental values. Vibronic coupling density analysis can explain the isotope effect on the vibronic coupling from view of the electronic and vibrational structures. Changes of the vibrational modes as well as the frequencies upon the deuteration can affect the vibronic coupling. Vibronic density analysis provides a local picture of the coupling in a molecule, and it enables us to control the coupling. This could open a way to engineering of the vibronic coupling, vibronics.