Diatomic molecules as perturbed Morse oscillators and the effect of the breakdown of the Born-Oppenheimer approximation.

Abstract

Values of the PMO parameters (including the velocity-dependent parameter) are obtained for the ground state of the three isotopic molecules H(, 2), HD and D(, 2) using two approaches. In the first approach, iteration computations are used to evaluate the different parameters from the experimentally derived Dunham coefficients. In the second approach, the PMO parameters are obtained by fitting the experimental energies directly in terms of the model parameters. The second approach is preferred to the first due to inaccuracies in the empirical Dunham coefficients.

The nonadiabatic corrections calculated using the present method for H(, 2) and D(, 2) are in agreement with those obtained using alternative methods. Moreover the present method proves very successful in predicting eigenvalues for HD which are in a very good agreement with the experimental ones.

The perturbed Morse oscillator is modified by adding a velocity-dependent term to allow for the nonadiabatic correction due to the breakdown of the Born-Oppenheimer approximation. A recurrence formula for this velocity-dependent term is derived. This formula is then used to derive--via a perturbation calculation--explicit expressions for the Dunham coefficients which include the nonadiabatic corrections.