Magnesium monofluoride is a polar molecule amenable to laser cooling which has caused renewed interest in its spectroscopy.
In this work we consider the case of three low-lying electronic excitations, namely $\rm X \, {}^{2}\Sigma \to A \, {}^{2}\Pi, \ \to B \, {}^{2}\Sigma, \ \to C \,{}^{2}\Sigma$,
using well developed quantum chemistry approaches, i.e., without reference to the spin-orbit splitting of the $\rm A \, {}^{2}\Pi$ states.
Accurate experimental data for these transitions have been available for over 50 years. Here we explore the linear response method at the level of CC2 theory, as well as
equation of motion methods at the level of CCSD and CC3, using two families of basis sets.
Excellent agreement is obtained for the first three transitions when using the correlation-consistent basis sets and extrapolation to the complete basis limit within EOM-CC3 (at a relative precision of $10^{-4}$), and qualitative agreement for the other two methods.
The purpose of this paper is to serve as a guide in how to approach the accurate calculation of excitations in polar diatomic molecules.