In this paper we present DFT studies of all the elementary steps in the synthesis of ammonia from gaseous hydrogen and nitrogen over a ruthenium crystal. The stability and configurations of intermediates in the ammonia synthesis over a Ru(0001) surface have been investigated, both over a flat surface and over a stepped surface. The calculations show that the step sites on the surface are much more reactive than the terrace sites. The DFT results are then used to study the mechanism of promotion by alkalies over the Ru(0001) and to determine the rate-determining step in the synthesis of ammonia over the Ru catalyst. (C) 2003 Elsevier Inc. All rights reserved.