An empirical spectroscopic model for eleven electronic states of VO

Previously-determined empirical energy levels are used to construct a rovibronic model for the $\mathrm{X}\,^4\Sigma^-$, $\mathrm{A}'\,^4\Phi$, $\mathrm{A}\,^4\Pi$, $\mathrm{B}\,^4\Pi$, $\mathrm{C}\,^4\Sigma^-$, $\mathrm{D}\,^4\Delta$, $\mathrm{1}\,^2\Delta$, $\mathrm{1}\,^2\Sigma^+$, $\mathrm{1}\,^2\Phi$, $\mathrm{1}\,^2\Pi$ and $\mathrm{2}\,^2\Pi$ electronic states of vanadium mononoxide. The spectrum of VO is characterized by many couplings and crossings between the states associated with these curves. The model is based on the use of potential energy curves, represented as extended Morse oscillators, and couplings (spin-orbit, spin-spin, angular momentum), represented by polynomials, which are tuned to the data plus an empirical allowance for spin-rotation couplings. The curves are used as input for the variational nuclear motion code \duo. For the $\mathrm{X}\,^4\Sigma^-$, $\mathrm{1}\,^2\Phi$ and $\mathrm{1}\,^2\Pi$ states the model reproduces the observed energy to significantly better than 0.1 $\mathrm{cm}^{-1}$. For the other states the standard deviations are between 0.25 and 1.5 $\mathrm{cm}^{-1}$. Further experimental data and consideration of hyperfine effects would probably be needed to significantly improve this situation.