Vibronic Interactions in the Anions of Benzene and Substituted Benzenes

Abstract

The Jahn–Teller and pseudo-Jahn–Teller effects involving degenerate and nearly degenerate electronic levels, respectively, are investigated for the anions of benzene and substituted benzenes. Two different transformation methods are discussed. In each the total Hamiltonian for the degenerate case is expressed in second quantized form. In the first method, complex orbitals and coordinates are used and a conanical transformation is employed. The coupling term of the transformed Hamiltonian becomes a small perturbation and the use of a small number of zeroth-order states suffices to give accurate values of the vibronic energy lowering for the lowest state. In the second method, real orbitals and coordinates are used, a different transformation is performed, and second-order perturbation theory is used to calculate the vibronic energy lowering. In both methods, the energy is expressed as a function of a dimensionless coupling parameter. The second method is then applied to the nondegenerate cases. The two transformation methods are compared with each other and with previous calculations. The transformation methods are much simpler computationally and provide comparable accuracy.