Properties of r-centroids for equal-frequency harmonic oscillators

Basic properties of r-centroids are discussed in the model of harmonic oscillators with equal frequencies and different oscillation centers (r_e values). In this approximation, r-centroids are found to be given by a very simple formula. They are characteristic of each Δυ=constant sequence and change regularly from one sequence to the next. The corresponding change in r-centroid is inversely proportional to the distance between the oscillation centers. The important special case of two abutting levels is studied and it is found that the r-centroid of the two levels is their common turning point. The conditions under which r-centroids can be considered as mean internuclear distances are specified. Applications of these simple results to molecular vibronic interactions are discussed. It is shown that the r-centroid of degenerate perturbing vibronic levels is located at the crossing of the corresponding electronic potential curves, so that, contrary to transition moments, the variation of electronic perturbation parameters with the internuclear separation R cannot be accurately deduced from only experimental data.