Charge asymmetry and rovibrational excitations of HD⁺

ABSTRACT: Average values of the interparticle distances for rovibrationally excited HD⁺ are calculated using a method where the Born–Oppenheimer (BO) approximation is not assumed. The difference between the proton–electron and deuteron–electron distances is used to describe the charge asymmetry in the system. All-particle one-centre explicitly correlated Gaussian functions are used in the calculations of the HD⁺ rovibrational states. In this work, the non-BO method is extended to calculate the rovibrational states corresponding to the total rotational quantum number of two (N = 2). The algorithms for calculating the Hamiltonian and overlap matrix elements, and the matrix elements of the analytical energy gradient determined with respect to the exponential parameters of the Gaussians, are presented. The gradient is employed in the variational optimisation of the parameters, which is key in obtaining very accurate rovibrational energies in the calculations. The algorithm for calculating the average interparticle distances is also shown. The charge asymmetry of HD⁺ near the dissociation limit occurs, as expected, with the electron preferentially being near to the deuteron. The asymmetry for a particular vibrational level increases with rotational excitations. The rovibrational transition energies are also calculated and compared with available experimental data.