Vibronic Coupling. III. Adiabatic Potentials and Vibronic Functions

General vibronic equations are given for the coupling of two electronic states in terms of their adiabatic potentials. It is shown that in addition to the adiabatic potentials it is necessary to know U(Q), a unitary transformation that depends on the vibrational coordinates Q. It is suggested that U(Q) be obtained from the ``crude adiabatic'' model. The appropriate U(Q) for the Renner and Jahn—Teller effects are given. A more extensive discussion is given of the pseudo Jahn—Teller effect described in previous papers of this series. Adiabatic potentials are given and it is shown how vibronic energy levels may be related to these potentials.