Biological nitrogen fixation has been investigated beginning with the monoprotonated dinitrogen bound to the FeMo cofactor of nitrogenase up to the formation of the two ammonia molecules. The energy differences of the relevant intermediates, the reaction barriers, and potentially relevant side branches are presented. During the catalytic conversion, nitrogen bridges two Fe atoms of the central cage, replacing a sulfur bridge present before dinitrogen binds to the cofactor. A transformation from cis- to trans-diazene has been found. The strongly exothermic cleavage of the dinitrogen bond takes place, while the Fe atoms are bridged by a single nitrogen atom. The dissociation of the second ammonia from the cofactor is facilitated by the closing of the sulfur bridge following an intramolecular proton transfer. This closes the catalytic cycle.