Numerical Estimation of the Pseudo-Jahn–Teller Effect Using Nonadiabatic Coupling Integrals in Monocyclic and Bicyclic Conjugated Molecules

The pseudo-Jahn–Teller (pJT) effect in monocyclic and bicyclic conjugated molecules was investigated by using the state-averaged multiconfiguration self-consistent field (MCSCF) method, together with the 6-31G­(d,p) basis sets. Following the perturbation theory, the force constant along a normal mode Q is given by the sum of the classical force constant and the vibronic contribution (VC) resulting from the interaction of the ground state with excited states. The latter is given as the sum of individual contributions arising from vibronic interactions between the ground state and excited states. In the present work, each VC was calculated on the basis of nonadiabatic coupling (NAC) integrals. Furthermore, the classical force constant was estimated by taking advantage of the VC and the force constant obtained by vibrational analyses. For pentalene and heptalene, the present method seems to overestimate the VC in absolute value because of the small energy gap between the ground state and the lowest excited state. However, we are confident that the VC and the classical force constant for the other molecules are reasonable in magnitude in comparison with available literature information. Thus, it is proved that the present method is applicable and useful for numerical estimation of pJT effect.