A Method for the Variational Calculation of Hyperfine-Resolved Rovibronic Spectra of Diatomic Molecules

Abstract

An algorithm for the calculation of hyperfine structure and spectra of diatomic molecules based on the variational nuclear motion is presented. The hyperfine coupling terms considered are Fermi-contact, nuclear spin-electron spin dipole–dipole, nuclear spin–orbit, nuclear spin-rotation, and nuclear electric quadrupole interactions. Initial hyperfine-unresolved wave functions are obtained for a given set of potential energy curves and associated couplings by a variation solution of the nuclear-motion Schrödinger equation. Fully hyperfine-resolved parity-conserved rovibronic Hamiltonian matrices for a given final angular momentum, F , are constructed and then diagonalized to give hyperfine-resolved energies and wave functions. Electric transition dipole moment curves can then be used to generate a hyperfine-resolved line list by applying rigorous selection rules. The algorithm is implemented in Duo , which is a general program for calculating spectra of diatomic molecules. This approach is tested for NO and MgH, and the results are compared to experiment and shown to be consistent with those given by the well-used effective Hamiltonian code PGOPHER.

An empirical spectroscopic model for eleven electronic states of VO

“…The bottom panel shows the fitting residues. have started to address this issue by extending our nuclear motion program Duo to explicitly include hyperfine effects [46] within its variational model. We have also built a hyperfine-resolved spectroscopic model for the ground X 4 Σ − state of 51 V 16 O [2].…”

Full spectroscopic model and trihybrid experimental-perturbative-variational line list for CN

“…For the far IR observations, it is recommended that astronomers use line list data from Splatalogue (Remijan et al 2007), which combines both JPL (Pickett et al 1998) and CDMS (Endres et al 2016) data for NH in one convenient online interface. It should be noted that an extended version of Duo has just been released (Qu et al 2022) that does allow hyperfine-resolved line lists to be generated (although for only one nucleus with nuclear spin); this could be a future avenue for the improvement of NH data and could potentially allow a unified single source of spectroscopic data across the electromagnetic spectrum. Any improvements in the accuracy of the existing nonhyperfine-resolved line list should focus on more precise quantification of the parameters relevant to forbidden transitions in the visible spectral region.…”

Photodissociation and photoionization of molecules of astronomical interest

“…When multiple excited states of varying symmetries are present, there are several sources of angular momentum couplings that need to be considered, such as electronic spin, electron orbital momentum, and molecular rotational motion. Additionally, effects due to hyperfine structure caused by nuclear spin angular momentum and external fields, either electric or magnetic, must be accounted for Qu et al (2022) as well as some additional consideration in the case of open shell (radical) diatomics that include transition metal atoms (Tennyson et al 2016a). These multitudes of state interactions cause the BO approximation to break down and it becomes impossible treat each electronic state in isolation.…”