Charge asymmetry in pure vibrational states of the HD molecule

Very accurate variational calculations of all rotationless states (also called pure vibrational states) of the HD molecule have been performed within the framework that does not assume the Born-Oppenheimer (BO) approximation. The non-BO wave functions of the states describing the internal motion of the proton, the deuteron, and the two electrons were expanded in terms of one-center explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance. Up to 6000 functions were used for each state. Both linear and nonlinear parameters of the wave functions of all 18 states were optimized with a procedure that employs the analytical gradient of the energy with respect to the nonlinear parameters of the Gaussians. These wave functions were used to calculate expectation values of the interparticle distances and some other related quantities. The results allow elucidation of the charge asymmetry in HD as a function of the vibrational excitation.