Charge asymmetry in rovibrationally excited HD⁺ determined using explicitly correlated all-particle Gaussian functions

Very accurate non-Born-Oppenheimer quantum-mechanical calculations are performed to determine the average values of the interparticle distances and the proton-deuteron density function for the rovibrationally excited HD⁺ ion. The states corresponding to excitations to all bound vibrational states (v = 0,., 22) and simultaneously excited to the first excited rotational state (N = 1) are considered. To describe each state up to 8000 explicitly correlated all-particle Gaussian functions are used. The nonlinear parameters of the Gaussians are variationally optimized using a procedure that employs the analytical energy gradient determined with respect to these parameters. The results show an increasing asymmetry in the electron distribution with the vibrational excitation as the electron density shifts towards deuteron and away from the proton.