  This work presents the first steps to modelling synthetic rovibrational
spectra for all molecules of astrophysical interest using a new approach
implemented in the Prometheus code. The goal is to create a new comprehensive
source of first-principles molecular spectra, thus bridging the gap for missing
data to help drive future high-resolution studies. Our primary application
domain is for molecules identified as signatures of life in planetary
atmospheres (biosignatures), but our approach is general and can be applied to
other systems. In this work we evaluate the accuracy of our method by studying
four diatomic molecules H$_2$, O$_2$, N$_2$ and CO, all of which have
well-known spectra. Prometheus uses the Transition-Optimised Shifted Hermite
(TOSH) theory to account for anharmonicity for the fundamental $\nu=0
\rightarrow \nu=1$ band, along with thermal profile modeling for the rotational
transitions. To this end, we expand TOSH theory to enable the modeling of
rotational constants. We show that our simple model achieves results that are a
better approximation of the real spectra than those produced through a harmonic
approach. We compare our results with high-resolution HITRAN and ExoMol
spectral data. We find that modelling accuracy tends to diminish for
rovibrational transition away from the band origin, thus highlighting the need
for the theory to be further adapted.
