The chemical mechanism by which nitrogenase enzymes catalyze the hydrogenation of N(2) (and other multiply bonded substrates) at the N(c)Fe(7)MoS(9)(homocitrate) active site (FeMo-co) is unknown, despite the accumulation of much data on enzyme reactivity and the influences of key amino acids surrounding FeMo-co. The mutual influences of H(2), substrates, and the inhibitor CO on reactivity are key experimental tests for postulated mechanisms. Fundamental to all aspects of mechanism is the accumulation of H atoms (from e(-) + H(+)) on FeMo-co, and the generation and influences of coordinated H(2). Here, I argue that the first introduction of H is via a water chain terminating at water 679 (PDB structure , Azotobacter vinelandii) to one of the mu(3)-S atoms (S3B) of FeMo-co. Next, using validated density functional calculations of a full chemical representation of FeMo-co and its connected residues (alpha-275(Cys), alpha-442(His)), I have characterized more than 80 possibilities for the coordination of up to three H atoms, and H(2), and H + H(2), on the S2A, Fe2, S2B, Fe6, S3B domain of FeMo-co, which is favored by recent targeted mutagenesis results. Included are calculated reaction profiles for movements of H atoms (between S and Fe, and between Fe and Fe), for the generation of Fe-H(2), for association and dissociation of Fe-H(2) at various reduction levels, and for H/H(2) exchange. This is new hydrogen chemistry on an unprecedented coordination frame, with some similarities to established hydrogen coordination chemistry, and with unexpected and unprecedented structures such as Fe(S)(3)(H(2))(2)(H) octahedral coordination. General principles for the hydrogen chemistry of FeMo-co include (1) the stereochemical mobility of H bound to mu(3)-S, (2) the differentiated endo- and exo- positions at Fe for coordination of H and/or H(2), and (3) coordinative allosteric influences in which structural and dynamic aspects of coordination at one Fe atom are affected by coordination at another Fe atom, and by H on S atoms. Evidence of end-differentiation in FeMo-co is described, providing a rationale for the occurrence of Mo. The reactivity results are discussed in the context of the Thorneley-Lowe scheme for nitrogenase reactions, and especially the scheme for the HD reaction (2H(+) + 2e(-) + D(2) --> 2HD), using a model containing an H-entry site and at least two coordinative sites on FeMo-co. I propose that S3B is the H-entry site, suggest details for the H(+) shuttle to S3B and subsequent movement of H atoms around FeMo-co preparatory to the binding and hydrogenation of N(2) and other substrates, and suggest how H could be transferred to an alkyne substrate. I propose that S2B (normally hydrogen bonded to alpha-195(His)) has a modulatory function and is not an H-entry site. Finally, the recent first experimental trapping of a hydrogenated intermediate with EPR and ENDOR characterization is discussed, leading to a consensual model for the intermediate.