  The sodium monoxide radical (NaO) is observed in night glow in the Earth's
mesosphere and likely has astronomical importance. This study concerns the
optical transitions within the ground X $^2\Pi$ state and to the very low-lying
($T_{\textrm e}\approx 2000$ cm$^{-1}$) excited A $^2\Sigma^+$ state. A line
list consisting of rovibronic term values, allowed electric dipole transitions,
Einstein coefficients, and partition functions for varying temperature are
produced due to a variational solution of the coupled-channel Schr\"{o}dinger
equations using the program \Duo. MRCI \textit{ab initio} calculations
characterising the potential energy curves of the both states, spin-orbit and
$L$-uncoupling non-adiabatic matrix elements, as well as permanent and
transition dipole moments were integral in formation of the final
deperturbation model. \textit{Ab initio} potential energy curves are
represented in the analytical Extended-Morse-Oscillator form and refined, along
with the spin-orbit and $L$-uncoupling functions, by least-squares fitting to
the available spectroscopic data. The input experimental data consisted of pure
rotational transitions within the fine structure components of the X $^2\Pi$
state for $v''\in [0,3]$ vibrational levels as well as the rovibronic A
$^2\Sigma^+(v'=0) \leftarrow$ X $^2\Pi(v''=0)$ transitions, both with limited
coverage over rotational excitation. The lack of data detailing the vibrational
structure of the X and A states prompts a request for further experimental
study of higher excited levels which would provide a robust spectroscopic
model. The NaO NaOUCMe line list is available via www.exomol.com and the CDS
database.
