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

A variational model for the hyperfine resolved spectrum of VO in its ground electronic state

A variational model for the infra-red spectrum of VO is presented which aims to accurately predict the hyperfine structure within the VO $\mathrm{X}\,^4\Sigma^-$ electronic ground state.To give the correct electron spin splitting of the $\mathrm{X}\,^4\Sigma^-$ state,electron spin dipolar interaction within the ground state and the spin-orbit coupling between $\mathrm{X}\,^4\Sigma^-$ and two excited states, $\mathrm{A}\,^4\Pi$ and $\mathrm{1}\,^2\Sigma^+$, arecalculated \abinitio alongside hyperfine interaction terms.Four hyperfine coupling terms are explicitly considered:Fermi-contact interaction,electron spin-nuclear spin dipolar interaction,nuclear spin-rotation interaction andnuclear electric quadrupole interaction. These terms are included as part of a fullvariational solution of the nuclear-motion Schr\"odinger equation performed using program \textsc{Duo}, which is used to generate both hyperfine-resolved energy levels and spectra.To improve the accuracy of the model, \abinitio curves are subject to small shifts.The energy levels generated by this modelshow good agreement with the recently derived empirical term values.This and other comparisonsvalidate both our model and the recently developed hyperfine modules in \textsc{Duo}.