  The high resolution rovibronic line list of MgH+ molecular cation are
presented in our work. The potential energy curves are calculated by the method
of multireference configuration interaction plus Davidson correction (MRCI+Q)
and spin-orbit coupling (SOC) effect. Spectroscopy constants are fitted and the
results are in good agreement with the experiment, ensuring the accuracy of the
electronic structure. On account of potential energy curves and transition
dipole moments, the Franck - Condon factors and Einstein coefficients of
transition are obtained. These calculations are used to obtain an accurate
partition functions and line list for the molecule. Using the data obtained
from the ab initio calculation, the absorption cross-sections under different
temperatures and pressures were simulated. Our work could provide some
theoretical insights into solar and cold planet spectrum.
