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

TL;DR

This study uses advanced relativistic coupled cluster methods to accurately compute the ground state electronic, vibrational, and rotational properties of CdH$^+$, HgH$^+$, and YbH$^+$ molecular ions, including lifetimes of vibrational states.

Contribution

It provides highly accurate spectroscopic parameters and vibrational lifetimes for these molecular ions using relativistic coupled cluster calculations and extrapolation techniques.

Findings

Lifetimes of the lowest vibrational states are 98.48s for CdH$^+$, 204.85s for HgH$^+$, and 1250.28s for YbH$^+$.

Computed structural parameters agree well with experimental and theoretical data.

Rotational energies within vibrational states are also calculated.

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.