Adiabatic Jacobi corrections on the vibrational energy levels of H2(+) isotopologues.

The effect of an adiabatic approximation, named adiabatic Jacobi correction (AJC) and introduced in J. Chem. Phys. 126, 024102 (2007), was investigated on the complete set of vibrational levels of H(2)(+) and its isotopologues, most importantly on the highest-lying vibrational states of HD(+). In order to perform clamped nuclei calculations employing finite nuclear masses a constrained Hamiltonian has been derived utilizing interparticle coordinates. The Born-Oppenheimer (BO) potential, the adiabatic potential obtained after taking into account the traditional diagonal Born-Oppenheimer correction (DBOC), as well as the AJC-corrected potential have been determined by an accurate fitting to computed energy values. These potentials were included in one-dimensional variational computations and yielded the complete set of energy levels for H(2)(+), D(2)(+), and HD(+). A detailed investigation of the potential and the complete set of vibrational energy levels show the merits and the deficiencies of the BO, DBOC, and AJC treatments. In particular, it is shown that the AJC corrections are systematically smaller and have a different distance dependence than the DBOC corrections. For a large part of the spectrum of H(2)(+) and its isotopologues the adiabatic correction to the vibrational energy levels is smaller than the nonadiabatic correction, the adiabatic DBOC correction has the highest overall accuracy for the prediction of vibrational energy levels, it is surpassed by the AJC correction only for the highest energy levels of HD(+), and thus the use of the AJC correction is clearly the best choice only for states close to the dissociation limit of nonsymmetric isotopologues.