The title reaction is an important step in the synthesis of ammonia over ruthenium-based catalysts, which have recently received increasing attention. The study presented here is fully theoretical and uses a reduced dimensionality approach to the surface reaction. A potential energy surface is first obtained by density functional calculations using a supercell approach. We have then calculated rate constants in the range of temperature 200-1000 K, which includes the temperature at which the ammonia production is usually performed. This has been done within the framework of variational transition- state theory in a reaction-path formulation, comparing different levels of theory and including quantum transmission and reflection effects by semiclassical methods. Calculated rates are fitted by the Arrhenius law. Finally, we have carried out an accurate investigation of the isotopic effect by replacing hydrogen with deuterium.