The inversion of diatomic Born-Oppenheimer-breakdown corrections

The inversion of diatomic vibration-rotation data to give the r dependence of operators is considered. For the Born-Oppenheimer energy levels E_vJ and for the expectation values 〈vJ|X(r)|vJ〉 of an operator X(r), the inversion is unambiguous if the reduced mass is known, leading to the potential energy function V(r) and to X(r). The breakdown of the Born-Oppenheimer approximation is represented in terms of three functions Qⁱ(r), Rⁱ(r), and Sⁱ(r) for each atom i. The function Qⁱ(r) can be removed by a transformation that changes the other functions to and , which still have one degree of indeterminacy. The effects of this indeterminacy in fits to truncated Hamiltonians is considered for the extensive data for isotopomers of the LiH molecule. This discussion is relevant to a recent claim that the dipole moment and rotational g_J factor of LiH can be determined from a fit to field-free vibration-rotation spectra. The values obtained for these quantities are unreliable because they are strongly dependent on the constraints used in the Born-Oppenheimer-breakdown functions.