Infrared measurements on wurzite GaN codoped with Mg and H reveal strong absorption at 3125 cm−1. Theorectical work provides strong evidence for the H being antibonding to N. We have performed an ab-initio study of Mg-H complexes in wurzite GaN, using the Local Density Approximation on a large H-terminated cluster MgHGa25N26H42. We have investigated the physical properties of three neutral configurations along the c direction. In all configurations Mg sits in a gallium substitutional site. H is then located in the Mg-N bond centre (BC), in the antibonding site on nitrogen side (ABN) or in the antibonding position on magnesium side (ABMg). We found the lowest total energy configuration is hydrogen in the antibonding on the nitrogen site. The stretch mode in this configuration is calculated at 3277 cm−1 which agrees with experiment and previous LDA calculations and we predict an unreported infra red active wag mode at 1311 cm−1. The experimental isotopic shift with D is well reproduced. The BC and ABMg configurations are 0.5 and 3.7 eV higher, producing local modes at 3645 and 2144 cm−1, respectively. No wag modes appear for the BC and ABMg configurations.