The eigenfunctions of the Hamiltonian associated with
the oriented
vibrating HD+(2Σ+) ion are
calculated beyond the Born–Oppenheimer approximation in the
nuclear frame. This makes it possible to study the fully correlated
electron–nuclear dynamics of the HD+(2Σ+) after ionization of the HD(1Σ+) molecule. The dynamics is then characterized by the time-dependent
probability densities and flux densities of the individual particles,
i.e., deuteron, proton, and electron. The flux densities confirm that,
although the electric dipole moment changes over time, there is no
charge migration, as might be expected from the separation of energy
levels of the vibronic states. Instead, the variations of the electric
dipole moment over time are caused by small charge transfer and asymmetric
charge vibration. Fourier transforms of the time-dependent probability
and flux densities uncover the net asymmetric effective potential
acting on the electron.