Calculation of Electric Quadrupole Linestrengths for Diatomic Molecules: Application to the H2, CO, HF and O2 Molecules

TL;DR

This paper develops a unified variational approach for calculating electric quadrupole line strengths in diatomic molecules, validated against experimental data, and provides accurate line lists for molecules like CO, HF, and O2.

Contribution

It introduces a comprehensive method for computing electric quadrupole properties in diatomic molecules, including transformation relations and validated implementations within the ext{Duo} code.

Findings

Validated against experimental quadrupole intensities for H2.

Provided accurate quadrupole moment functions for CO, HF, and O2.

Generated infrared E2 line lists for CO and HF.

Abstract

We present a unified variational treatment of the electric quadrupole (E2) matrix elements, Einstein coefficients, and line strengths for general open-shell diatomic molecules in the general purpose diatomic code \Duo. Transformation relations between the Cartesian representation (typically used in electronic structure calculations) to the tensorial representation (required for spectroscopic applications) of the electric quadrupole moment components are derived. The implementation has been validated against accurate theoretical calculations and experimental measurements of quadrupole intensities of $^1\text{H}_2$ available in the literature. We also present accurate electronic structure calculations of the electric quadrupole moment functions for the $X^1\Sigma^+$ electronic states of $\text{CO}$ and $\text{HF}$ at the CCSD(T) and MRCI levels of theory, respectively, as well for the $a^1\Delta_g$ -- $b^1\Sigma_g^+$ quadrupole transition moment of $\text{O}_2$ with MRCI level of theory. Accurate infrared E2 line lists for $^{12}\text{C}^{16}\text{O}$ and $^1\text{H}^{19}\text{F}$ are provided. A demonstration of spectroscopic applications is presented by simulating E2 spectra for $^{12}\text{C}^{16}\text{O}$, $\text{H}^{19}\text{F}$ and $^{16}\text{O}_2$ (Noxon $a^1\Delta_g$ -- $b^1\Sigma_g^+$ band).