H₂ formation from the E₂-E₄ states of nitrogenase

Nitrogenase is the only enzyme that can cleave the strong triple bond in N₂, making nitrogen available for biological lifeforms. The active site is a MoFe₇S₉C cluster (the FeMo cluster) that binds eight electrons and protons during one catalytic cycle, giving rise to eight intermediate states E₀-E₇. It is experimentally known that N₂ binds to the E₄ state and that H₂ is a compulsory byproduct of the reaction. However, formation of H₂ is also an unproductive side reaction that should be avoided, especially in the early steps of the reaction mechanism (E₂ and E₃). Here, we study the formation of H₂ for various structural interpretations of the E₂-E₄ states using combined quantum mechanical and molecular mechanical (QM/MM) calculations and four different density-functional theory methods. We find large differences in the predictions of the different methods. B3LYP strongly favours protonation of the central carbide ion and H₂ cannot form from such structures. On the other hand, with TPSS, r²SCAN and TPSSh, H₂ formation is strongly exothermic for all structures and E and therefore need strict kinetic control to be avoided. For the E₂ state, the kinetic barriers for the low-energy structures are high enough to avoid H₂ formation. However, for both the E₃ and E₄ states, all three methods predict that the best structure has two hydride ions bridging the same pair of Fe ions (Fe2 and Fe6) and these two ions can combine to form H₂ with an activation barrier of only 29-57 kJ mol^-1, corresponding to rates of 7 × 10² to 5 × 10⁷ s^-1, i.e. much faster than the turnover rate of the enzyme (1-5 s^-1). We have also studied H-atom movements within the FeMo cluster, showing that the various protonation states can quite freely be interconverted (activation barriers of 12-69 kJ mol^-1).