Modified Born-Oppenheimer basis for nonadiabatic coupling: Application to the vibronic spectrum of HD

Nonadiabatic matrix elements, when computed using a Born-Oppenheimer (BO) basis, do not vanish asymptotically because the motion of the electrons with the nuclei at large internuclear separations is not taken into account. We apply a method suggested by Delos [Rev. Mod. Phys. 53, 287 (1981)] to include the effect of electron translation factors in a quantum-mechanical framework, thus correcting the BO basis to incorporate proper boundary conditions. We calculate the nonadiabatic matrix elements for H⁺₂ and its isotopic variants. We focus our calculations on HD⁺, for which experimental results exist, and calculate its vibronic spectrum. This is the first application of this method to calculate high precision spectroscopic information for molecular systems.