Electronic structure of the high and low pressure polymorphs of MgSiN$_{2}$

We have performed density functional calculations on the group II-IV nitride MgSiN$_{2}$. At a pressure of about 20~GPa the ground state wurtzite derived MgSiN$_{2}$ structure (LP-MgSiN$_{2}$) transforms into a rock-salt derived structure (HP-MgSiN$_{2}$) in agreement with previous theoretical and experimental studies. Both phases are wide band gap semiconductors with indirect band gaps at equilibrium of 5.58 eV (LP-MgSiN$_{2}$) and 5.87 eV (HP-MgSiN$_{2}$), respectively. As the pressure increases, the band gaps become larger for both phases, however, the band gap in LP-MgSiN$_{2}$ increases faster than the gap in HP-MgSiN$_{2}$ and with a high enough pressure the band gap in LP-MgSiN$_{2}$ becomes larger than the band gap in HP-MgSiN$_{2}$.