Pseudopotential for ground state hydrogen molecule with nonadiabatic corrections

Abstract

Nonadiabaticity cannot be entirely reduced to correcting a single potential energy surface. To still maintain this very simple and instructive concept, one can introduce coordinate-dependent corrections to the nuclear reduced mass. Recently, these R-dependent corrections, both vibrational and rotational, have been accurately determined for the hydrogen molecule in the ground electronic state. In this paper, using an inverse perturbational approach, an effective rotationless pseudopotential for the system was constructed, the vibrational levels of which exactly coincide with the experimental ones. The specifically rotational nonadiabatic effects can be taken into account by combining the R-dependent mass correction functions with specific state-dependent coordinate shifts of the rotationless potential. These characteristic parameters typically range from 0.0002 to 0.0003 Å, depending on the vibrational state (v) but being nearly independent of the rotational state (J). For example, shifting the rotationless potential by 0.0002125Å was found optimal for v = 0. Using this constant value, the zeroth vibrational levels for J = 0 to 11 can be determined with about 0.001 cm−1 accuracy, as has been shown by comparing with the available high-resolution experimental data.