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

Ankush Thakur, Renu Bala, H. S. Nataraj

TL;DR

The paper addresses how heavy XH+ molecular ions can serve as precise probes for fundamental-constant variations by delivering high-accuracy, four-component relativistic coupled-cluster calculations of their ground-state structure and vibrational properties. Using CBS-extrapolated Dirac-Coulomb energies and finite-field derivatives, the authors compute spectroscopic constants, dipole moments, polarizabilities, quadrupole moments, and vibrational lifetimes for CdH+, HgH+, and YbH+. They validate CdH+ and HgH+ against experimental data and provide robust theoretical predictions for YbH+, including detailed vibrational spectra and lifetimes that are valuable for ultracold spectroscopy and tests of μ variations. The work furnishes first-of-its-kind CBS-level polarizabilities and quadrupole moments for these ions and estimates an ~6% uncertainty, establishing a solid foundation for experiments aimed at probing fundamental physics and precision timekeeping.

Abstract

The present work reports the spectroscopic parameters and molecular properties for the ground electronic state, $^1Σ^+$, 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 Schrödinger 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.

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

TL;DR

The paper addresses how heavy XH+ molecular ions can serve as precise probes for fundamental-constant variations by delivering high-accuracy, four-component relativistic coupled-cluster calculations of their ground-state structure and vibrational properties. Using CBS-extrapolated Dirac-Coulomb energies and finite-field derivatives, the authors compute spectroscopic constants, dipole moments, polarizabilities, quadrupole moments, and vibrational lifetimes for CdH+, HgH+, and YbH+. They validate CdH+ and HgH+ against experimental data and provide robust theoretical predictions for YbH+, including detailed vibrational spectra and lifetimes that are valuable for ultracold spectroscopy and tests of μ variations. The work furnishes first-of-its-kind CBS-level polarizabilities and quadrupole moments for these ions and estimates an ~6% uncertainty, establishing a solid foundation for experiments aimed at probing fundamental physics and precision timekeeping.

Abstract

The present work reports the spectroscopic parameters and molecular properties for the ground electronic state, , 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 Schrödinger 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 ( = , = ) due to BBR-induced transitions are estimated to be \,s for CdH, \,s for HgH, and \,s for YbH. Additionally, the rotational energies within each vibrational state are also calculated in this work.

Paper Structure

This paper contains 7 sections, 10 equations, 8 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Theory and Calculational details
  3. Results and discussion
  4. Spectroscopic constants
  5. Molecular Properties
  6. Vibrational parameters
  7. Summary

Figures (8)

  • Figure 1: PECs of XH$^+$ molecular ions computed at CBS limit using CCSD and CCSD(T) levels of theory, with respect to the dissociation energy at the CCSD level.
  • Figure 2: CBS values of PDM as a function of internuclear distance for XH$^+$ molecular ions, computed at CCSD(T) level of theory.
  • Figure 3: CBS values of QM as a function of internuclear distance for XH$^+$ molecular ions, computed at CCSD(T) level of theory.
  • Figure 4: CBS values of parallel component of static dipole polarizability ($\alpha_\parallel$) as a function of internuclear distance for XH$^+$ molecular ions, computed at CCSD(T) level of theory.
  • Figure 5: The figure shows (a) energy spacings between adjacent vibrational levels and (b) vibrationally coupled rotational constants for XH$^+$ molecular ions at CCSD(T) level of theory.
  • ...and 3 more figures