Ab initio study on vibrational dipole moments of XH⁺ molecular ions: X = ²⁴Mg, ⁴⁰Ca, ⁶⁴Zn, ⁸⁸Sr, ¹¹⁴Cd, ¹³⁸Ba, ¹⁷⁴Yb and ²⁰²Hg

The vibrational matrix elements of electric dipole moments were theoretically estimated for the electronic ground state of XH⁺ molecular ions (X = ²⁴Mg, ⁴⁰Ca, ⁶⁴Zn, ⁸⁸Sr, ¹¹⁴Cd, ¹³⁸Ba, ¹⁷⁴Yb and ²⁰²Hg) using the complete active space second-order perturbation theory method. Because of the large rotational constant and zero X-nuclear spin, these molecules are advantageous to be localized to a single (ν, J, F) state, where ν, J, F are quantum numbers of the vibrational, rotational and hyperfine states, respectively. The information of the dipole moments is very useful to discuss the period to localize the molecular ion to the (ν, J, F) = (0, 0, 1/2) state and also the period to remain in this state, which is limited by the interaction with the black body radiation. The agreement of experimental and our theoretical spectroscopic constants ensures the accuracy of our results. Vibrational permanent and transition dipole moments were obtained with special care of accuracy in numerical integration. Spontaneous emission rates were calculated from the vibrational dipole moments and transition energies.