Study of ground state electronic structure of XH$^+$ (X : Cd, Hg and Yb) molecular ions via coupled-cluster approach

Abstract

The present work reports the spectroscopic parameters and molecular properties for the ground electronic state, $^1\Sigma^+$, of CdH$^+$, HgH$^{+}$, and YbH$^{+}$ molecular ions. We have used the state-of-the-art relativistic coupled cluster method together with the relativistic core-valence triple- and quadruple zeta quality basis sets for the calculation of structural parameters. The computed results have been extrapolated to the complete basis set limit using a two-point polynomial fit. The reliability of the results has been confirmed by their remarkable agreement with existing experimental and theoretical values. Further, we have calculated the relevant vibrational parameters by solving the vibrational Schr\"odinger equation using the potential energy curve and the permanent dipole moment curve of the electronic ground state. Subsequently, the lifetimes of the vibrational states have been determined by calculating the spontaneous and black-body radiation (BBR) induced transition rates. At room temperature, the lifetimes of the lowest ro-vibrational state ($v$ = \(0\), $J$ = \(0\)) due to BBR-induced transitions are estimated to be \(98.48\)\,s for CdH$^+$, \(204.85\)\,s for HgH$^+$, and \(1250.28\)\,s for YbH$^+$. Additionally, the rotational energies within each vibrational state are also calculated in this work.