A general mathematical treatment of vibronic coupling of two electronic states in molecules and dimers is presented. The 2×2 matrix Hamiltonian which is derived is shown to reduce to two one-dimensional Hamiltonians provided a certain minimum amount of symmetry is present. Some general selection rules governing electronic transitions to these states from the ground state are obtained, showing that the spectral distribution in hot bands may differ considerably from that in normal bands when vibronic coupling occurs. A special model which considers the coupling to arise from a single mode of vibration is presented. Two limiting cases which can be treated approximately by perturbation theory are considered in detail. These are shown to give rise to a ``pseudo Jahn-Teller effect'' and to vibrational borrowing in the two different limits.

We consider a model dimer composed of units with one allowed excited state and one symmetric vibration. The vibrational mode has the same force constant in the ground and excited states, but the excited state is assumed to have its equilibrium position shifted by an amount measured by λ. The dimer possesses a symmetry operation that exchanges the units and has an exciton coupling ε. Spectra for various λ and ε values are derived by computer. It is shown that the absorption intensity of the two polarizations rigorously satisfies two theorems: the center of gravity is at ±ε for all λ; the bandwidth is | λ | for all ε.

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