Quantum Mechanical Calculations of Redox Potentials of the Metal Clusters in Nitrogenase

We have calculated redox potentials of the two metal clusters in Mo-nitrogenase with quantum mechanical (QM) calculations. We employ an approach calibrated for iron–sulfur clusters with 1–4 Fe ions, involving QM-cluster calculations in continuum solvent and large QM systems (400–500 atoms), based on structures from combined QM and molecular mechanics (QM/MM) geometry optimisations. Calculations on the P-cluster show that we can reproduce the experimental redox potentials within 0.33 V. This is similar to the accuracy obtained for the smaller clusters, although two of the redox reactions involve also proton transfer. The calculated P¹⁺/P^N redox potential is nearly the same independently of whether P¹⁺ is protonated or deprotonated, explaining why redox titrations do not show any pH dependence. For the FeMo cluster, the calculations clearly show that the formal oxidation state of the cluster in the resting E₀ state is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi>Mo</mi></mrow><mrow><mi>III</mi></mrow></msup><msubsup><mrow><mi>Fe</mi></mrow><mn>3</mn><mrow><mi>II</mi></mrow></msubsup><msubsup><mrow><mi>Fe</mi></mrow><mn>4</mn><mrow><mi>III</mi></mrow></msubsup></mrow></semantics></math></inline-formula> , in agreement with previous experimental studies and QM calculations. Moreover, the redox potentials of the first five E₀–E₄ states are nearly constant, as is expected if the electrons are delivered by the same site (the P-cluster). However, the redox potentials are insensitive to the formal oxidation states of the Fe ion (i.e., whether the added protons bind to sulfide or Fe ions). Finally, we show that the later (E₄–E₈) states of the reaction mechanism have redox potential that are more positive (i.e., more exothermic) than that of the E₀/E₁ couple.