The catalyzed electrochemical oxidation of ammonia to nitrogen (AOR) is an important fuel-cell half-reaction that underpins a future nitrogen-based energy economy. Our laboratory has reported spontaneous chemical and electrochemical oxidation of ammonia to dinitrogen via reaction of ammonia with the metal-metal bonded diruthenium complex Ru-2(chp)(4)OTf (chp(-) = 2-chloro-6-hydroxypyridinate, TfO- = trifluoromethanesulfonate). This complex facilitates electrocatalytic ammonia oxidation at mild applied potentials of -255 mV vs ferrocene, which is the [Ru-2(chp)(4)(NH3)](0/+) redox potential. We now report a comprehensive computational investigation of possible mechanisms for this reaction and electronic structure analysis of key intermediates therein. We extend this analysis to proposed second-generation electrocatalysts bearing structurally similar fhp and hmp (2-fluoro-6-hydroxypyridinate and 2-hydroxy-6-methylpyridinate, respectively) equatorial ligands, and we further expand this study from Ru-2 to analogous Os-2 cores. Predicted M-2(4+/5+) redox potentials, which we expect to correlate with experimental AOR overpotential, depend strongly on the identity of the metal center, and to a lesser degree on the nature of the equatorial supporting ligand. Os-2 complexes are easier to oxidize than analogous Ru-2 complexes by similar to 640 mV, on average. In contrast to mono-Ru catalysts, which oxidize ammonia via a rate-limiting activation of the strong N-H bond, we find lowest-energy reaction pathways for Ru-2 and Os-2 complexes that involve direct N-N bond formation onto electrophilic intermediates having terminal amido, imido, or nitrido groups. While transition state energies for Os-2 complexes are high, those for Ru-2 complexes are moderate and notably lower than those for mono-Ru complexes. We attribute these lower barriers to enhanced electrophilicity of the Ru-2 intermediates, which is a consequence of their metal-metal bonded structure. Os-2 intermediates are found to be, surprisingly, less electrophilic, and we suggest that Os-2 complexes may require access to oxidation states higher than Os-2(5+) in order to perform AOR at reasonable reaction rates.