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A variational model for the infra-red spectrum of VO is presented which aimsto accurately predict the hyperfine structure within the VO$\mathrm{X}\,^4\Sigma^-$ electronic ground state. To give the correct electronspin splitting of the $\mathrm{X}\,^4\Sigma^-$ state, electron spin dipolarinteraction within the ground state and the spin-orbit coupling between$\mathrm{X}\,^4\Sigma^-$ and two excited states, $\mathrm{A}\,^4\Pi$ and$\mathrm{1}\,^2\Sigma^+$, are calculated ab initio alongside hyperfineinteraction terms. Four hyperfine coupling terms are explicitly considered:Fermi-contact interaction, electron spin-nuclear spin dipolar interaction,nuclear spin-rotation interaction and nuclear electric quadrupole interaction.These terms are included as part of a full variational solution of thenuclear-motion Schr\"odinger equation performed using program DUO, which isused to generate both hyperfine-resolved energy levels and spectra. To improvethe accuracy of the model, ab initio curves are subject to small shifts. Theenergy levels generated by this model show good agreement with the recentlyderived empirical term values. This and other comparisons validate both ourmodel and the recently developed hyperfine modules in DUO.

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