When searching the universe for chemical signatures astronomers need to know what they find. This is done usually via reference data. But to know that the correct assignment has been made accurate data must be available. This is where the need for high-accuracy rovibronic energy levels and transition calculations come into play. Not only can this information help with identification of molecules found in gas giants, stars, and exoplanet atmospheres in the not too distant future, but it can also help guide the search for new physics. Astrophysical molecular spectroscopy is an important method of searching for new physics. We can do this through probing the variation of the proton-to-electron mass ratio, μ, with existing constraints limiting variation to a fractional change of less than 10-17 year-1. Being able to more accurately measure the variation of the proton-to-electron mass ratio could revolutionise physics by allowing us to filter through the currently competing fundamental physics theories. To aid the improvement of existing measurements, we have systematically looked at rovibronic spectral transitions from several different diatomic molecules and identified transitions that might allow a very high sensitivity measurement, if observable. This was done using spectroscopic models for these diatomics, along with the program DUO to solve the nuclear motion Schrodinger equation to produce high accuracy lists of energy levels and transitions. I will explain the structure of these spectroscopic models and how they are built and utilised to simulate a small shift in the proton-to-electron mass ratio, to determine key transitions. I will demonstrate how some of these diatomics have a significant number of low-intensity, but high-sensitive transitions at higher temperatures (1000 K), arising from an accidental near-degeneracy between vibrational levels in the ground and excited vibronic states.