This work presents the first steps to modelling synthetic rovibrational spectra for all molecules of astrophysical interest using the new code Prometheus. 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 on molecules identified as signatures of life in planetary atmospheres (biosignatures). As a starting point, in this work we evaluate the accuracy of our method by studying the diatomics 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 $ u=0 rightarrow u=1$ band, along with thermal profile modeling for the rotational transitions. We present a novel new application of the TOSH theory with regards to rotational constants. Our results show that this method can achieve results that are a better approximation than the ones produced through the basic harmonic method. We discuss the current limitations of our method. In particular, we compare our results with high-resolution HITRAN 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.
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