Physical versus non-physical effective nuclear masses for non-adiabatic corrections to molecular spectra

Two types of developments for very accurate non-adiabatic corrections to rovibrational molecular energy levels, one of a formal nature and the other of a heuristic nature, lead to fundamentally different approaches for effective nuclear masses. The former yields effective masses that have non-physical interpretation at some ranges of nuclear distances. The later uses physical masses obtained from electronic structure calculations. This paper contains a brief review of the subject and proposes procedures to improve and generalize the heuristic approach. Comparisons are made of the results obtained by the two approaches for the H ${}_2$ molecule, since no further calculations were found with the proper accuracy, but some issues involving the HeH ${}^{+}$ ion and the water molecule are discussed. The conclusion is that the heuristic approach has many advantages over the formal one, namely, equivalent accuracy and physically grounded qualitative interpretation. But, moreover, it seems to be presently the only method that allows non-adiabatic calculations for well isolated states of larger molecules.