The hydrogenation reactions of nitrogen (NHn,(ads) + H-(ads) -> NHn+1,((ads)), n = 0, 1, 2) on metal surfaces are important elementary steps in the catalytic formation of ammonia We investigate the reaction dynamics of these hydrogenations on a Ru(0001) surface using transition state theory, including small curvature tunneling corrections. Potential energy surfaces are derived by density functional theory (RPBE) in two or three dimensions. Tunneling is shown to enhance rates significantly for the first two hydrogenation steps at low and ambient temperatures, doubling reaction rates even at temperatures of 400 K. However, tunneling plays no significant role at current synthesis temperatures. (c) 2006 Elsevier Inc. All rights reserved.