Influence of the protein and DFT method on the broken‐symmetry and spin states in nitrogenase

Abstract

The enzyme nitrogenase contains a complicated MoFe7CS9 cofactor with 35 possible broken‐symmetry (BS) states. We have studied how the energies of these states depend on the geometry, the surrounding protein, the DFT functional and the basis set, studying the resting state, a one‐electron reduced state and a protonated state. We find that the effect of the basis set is small, up to 11 kJ/mol. Likewise, the effect of the surrounding protein is restricted, up to 10 and 7 kJ/mol for the electrostatic and van der Waals energy terms. Single‐point energies calculated on a single geometry give a good correlation (R2 = 0.92‐0.98) to energies calculated after geometry optimization, but some BS states may be disfavored by up to 37 kJ/mol. A change from the pure TPSS functional to the hybrid B3LYP functional may change the relative energies by up to 58 kJ/mol and the correlation between the two results is only 0.57‐0.72. Both functionals agree that BS7 is the most stable BS state and that the ground spin state is the quartet for the resting state and the quintet for the reduced state. With the TPSS functional, the BS6 state is the second most stable state, always at least 21 kJ/mol less stable than the BS7 state. However, with the B3LYP functional, BS10 is the second most stable state and for the protonated state it comes close in energy. Based on these results, we suggest a procedure how to consider the 35 BS states in future investigations of the nitrogenase reaction mechanism.

Extremely large differences in DFT energies for nitrogenase models

“…7 The setup of the protein is identical to that of our previous studies. [29][30][31] The entire heterotetramer was included in the calculations and the DFT calculations were concentrated on the FeMo cluster in the C subunit. The P clusters and the FeMo cluster in subunit A were modelled by MM in the fully reduced and resting states, respectively.…”

“…All calculations employed the def2-SV(P) basis set, 39 because previous studies have shown that increasing the basis set to def2-TZVPD changes the relative energies by less than 16 kJ mol À1 . 29,31 The calculations were sped up by expanding the Coulomb interactions in an auxiliary basis set, the resolution-of-identity approximation. 59,60 Empirical dispersion corrections were included with the DFT-D3 approach 61 and Becke-Johnson damping, 62 using parameters optimised for each DFT method, as implemented in Turbomole for all functionals except M06, M06-L, M06-2X and M06-HF (for which no parameters are available because the methods should include dispersion effects by parameterisation).…”

“…3,13 These spin states were used in all calculations. The electronic structure of all QM calculations was obtained with the broken-symmetry (BS) approach: 18 for each model, we used the best of the 35 possible BS states 31 found in our previous study. 29 These states are specified in Table 1, which also give further description of the various models (which atoms are protonated and the number of bonds within the cluster).…”

Survey of the Geometric and Electronic Structures of the Key Hydrogenated Forms of FeMo-co, the Active Site of the Enzyme Nitrogenase: Principles of the Mechanistically Significant Coordination Chemistry

“…This is equivalent to the broken symmetry (BS) electronic state description [67,68], based on the up/down character of spins on each Fe atom. With the assumption of C3 symmetry for FeMo-co there are 10 BS states, but with the actual C1 symmetry there are 35 BS possibilities [58], and this is the number of possible spinsets for the hydrogenated forms of FeMo-co. There are four stable conformations for an H atom bound to S3B, shown in Scheme 1 panel D. In each of these S3B has pyramidal three-fold coordination, because one of the S3B-Fe interactions is elongated (usually to more than 2.7 Å).…”

“…With eight transition metals, the electronic structure of FeMo-co is complex. Each net spin (S) state possesses 35 electronic states [58,64], as do the various hydrogenated forms [51]. Therefore, descriptions of the possibilities for hydrogenated FeMo-co are essentially maps of geometry, electronic state, and relative energy.…”