  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
$\mathrm{1}\,^2\Sigma^+$, are calculated ab initio alongside hyperfine
interaction 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 the
nuclear-motion Schr\"odinger equation performed using program DUO, which is
used to generate both hyperfine-resolved energy levels and spectra. To improve
the accuracy of the model, ab initio curves are subject to small shifts. The
energy levels generated by this model show good agreement with the recently
derived empirical term values. This and other comparisons validate both our
model and the recently developed hyperfine modules in DUO.
