Adiabatic Corrections in a Simple Model of Two Interacting Electronic-Potential Curves

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Abstract
Accurate numerical methods are applied to the vibronic problem resulting from two interacting intersecting harmonic curves. Two examples are considered, corresponding to either degenerate or nondegenerate electronic states. The energies are obtained with (a) the zeroth-order Born-Oppenheimer approximation; (b) the so-called adiabatic approximation, which includes the diagonal corrections to (a); (c) the full vibronic procedure. Several features in the correlation diagrams giving the energies as a function of the configuration-interaction matrix element are given an explanation. We also note that, in the model treated here, inclusion of the diagonal corrections does not always lead to an improvement of the energies.