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. 2022 Mar 8;18(3):1437-1457.
doi: 10.1021/acs.jctc.1c00753. Epub 2022 Feb 15.

Analysis of the Geometric and Electronic Structure of Spin-Coupled Iron-Sulfur Dimers with Broken-Symmetry DFT: Implications for FeMoco

Bardi Benediktsson  1 , Ragnar Bjornsson  1   2
Affiliations

Analysis of the Geometric and Electronic Structure of Spin-Coupled Iron-Sulfur Dimers with Broken-Symmetry DFT: Implications for FeMoco

Bardi Benediktsson et al. J Chem Theory Comput. .

Abstract

The open-shell electronic structure of iron-sulfur clusters presents considerable challenges to quantum chemistry, with the complex iron-molybdenum cofactor (FeMoco) of nitrogenase representing perhaps the ultimate challenge for either wavefunction or density functional theory. While broken-symmetry density functional theory has seen some success in describing the electronic structure of such cofactors, there is a large exchange-correlation functional dependence in calculations that is not fully understood. In this work, we present a geometric benchmarking test set, FeMoD11, of synthetic spin-coupled Fe-Fe and Mo-Fe dimers, with relevance to the molecular and electronic structure of the Mo-nitrogenase FeMo cofactor. The reference data consists of high-resolution crystal structures of metal dimer compounds in different oxidation states. Multiple density functionals are tested on their ability to reproduce the local geometry, specifically the Fe-Fe/Mo-Fe distance, for both antiferromagnetically coupled and ferromagnetically coupled dimers via the broken-symmetry approach. The metal-metal distance is revealed not only to be highly sensitive to the amount of exact exchange in the functional but also to the specific exchange and correlation functionals. For the antiferromagnetically coupled dimers, the calculated metal-metal distance correlates well with the covalency of the bridging metal-ligand bonds, as revealed via the corresponding orbital analysis, Hirshfeld S/Fe charges, and Fe-S Mayer bond order. Superexchange via bridging ligands is expected to be the dominant interaction in these dimers, and our results suggest that functionals that predict accurate Fe-Fe and Mo-Fe distances describe the overall metal-ligand covalency more accurately and in turn the superexchange of these systems. The best performing density functionals of the 16 tested for the FeMoD11 test set are revealed to be either the nonhybrid functionals r2SCAN and B97-D3 or hybrid functionals with 10-15% exact exchange: TPSSh and B3LYP*. These same four functionals are furthermore found to reproduce the high-resolution X-ray structure of FeMoco well according to quantum mechanics/molecular mechanics (QM/MM) calculations. Almost all nonhybrid functionals systematically underestimate Fe-Fe and Mo-Fe distances (with r2SCAN and B97-D3 being the sole exceptions), while hybrid functionals with >15% exact exchange (including range-separated hybrid functionals) overestimate them. The results overall suggest r2SCAN, B97-D3, TPSSh, and B3LYP* as accurate density functionals for describing the electronic structure of iron-sulfur clusters in general, including the complex FeMoco cluster of nitrogenase.

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Conflict of interest statement

The authors declare no competing financial interest.

Figures

Figure 1
Figure 1
Spin-coupled redox states exhibited by the [2Fe–2S] core as representative for the FeMoD11 test set. Orange indicates iron, yellow indicates sulfur, and purple is a terminal ligand.
Figure 2
Figure 2
FeMoD11 test set of spin-coupled Fe–Fe and Fe–Mo dimers. The local oxidation state of each Fe ion is indicated as well as the charge of the core structure, the total spin, and the total charge of the complex.
Figure 3
Figure 3
FeCSD5 test set of closed-shell Fe–Fe dimers. The local oxidation state of each Fe ion is indicated as well as the charge of the core structure, the total spin, and the total charge of the complex.
Figure 4
Figure 4
Mean deviations (MDs) of Fe–S bond lengths and Fe–Fe distance of complex 7 ([Fe2S2Cl4]2–) using ECP-basis combinations (LANL2 or SDD on Fe with 6-31G* on S and Cl) or all-electron basis sets, with and without a scalar relativistic ZORA or Douglas–Kroll–Hess (DKH) Hamiltonian. Deviations are relative to the largest all-electron relativistic ZORA-def2-QZVPP reference (r(Fe–Fe) = 2.690 Å and rave(Fe–S) = 2.202 Å). The TPSSh functional was used with a CPCM(ε = ∞) continuum model included in all calculations.
Figure 5
Figure 5
Top: mean deviation (MD) of M–Fe (M = Mo, Fe) distances for optimized structures of FeMoD11 and FeCSD5 with different functionals w.r.t. the X-ray structure distances. Bottom: the corresponding mean absolute deviation (MAD). All calculations use a ZORA scalar relativistic Hamiltonian, the relativistically recontracted ZORA-def2-TZVP basis set, a D3BJ (except D3 for M06 and M06-2X) dispersion correction, and CPCM(ε = ∞).
Figure 6
Figure 6
Top: mean deviations of Fe–Fe, Mo–Fe, Fe–S, and Mo–S distances from 244 QM-atom QM/MM calculations (deviations relative to the 1.0 Å crystal structure, PDB ID: 3U7Q(2)). Bottom: mean deviations of the Fe–Fe, Mo–Fe, Fe–S, and Mo–S distances in the FeMoD11 test set relative to each respective crystal structure. A plot of the corresponding mean absolute deviations is available in the Supporting Information (SI) as Figure S1.
Figure 7
Figure 7
Deviation (Å) in the metal–metal distance, ΔM–Fe, vs the mean deviation in the metal–bridging ligand bond length, ΔM–R, for (a) FeMoD11 and for (b) FeCSD5. For (a), M = Fe, Mo and R = C, O, S, whereas for (b), R = C, S. Linear fit parameters for (a) are y = 2.955x – 0.0585 with R2 = 0.958.
Figure 8
Figure 8
Mean deviation in the Fe–Fe distance (ΔFe–Fe) vs mean Fe–S distance (ΔFe–S) of optimized structures in comparison to the X-ray structures (for FeMoco, PDB: 3U7Q, and for 7, CSD: EAPFTM01) with the functionals tested. Linear fit parameters y = 1.954x – 0.003, R2 = 0.977 (FeMoco) and y = 3.085x – 0.0301, R2 = 0.9509 (for complex 7). FeMoco data come from a 244 QM atom QM/MM model (see the Computational Details section).
Figure 9
Figure 9
Effect of constraining Fe–S/Fe–Cl distances at the X-ray distances, r(Fe–S) = 2.201 and 2.198 Å, whereas r(Fe–Cl) = 2.244 and 2.256 Å) on the Fe–Fe distance for [Fe2S2Cl4]2– complex 7 with different functionals.
Figure 10
Figure 10
Correlation plots of the optimized Fe–Fe distance (y-axis) of 7 vs various parameters evaluated on the X-ray structure (x-axis): J-coupling, Fe–S Mayer bond order, Hirshfeld S charge, or Hirshfeld Fe charge. (a) J-coupling constant evaluated in cm–1 according to the Yamaguchi equation,, (b) the calculated Fe–S Mayer bond order, (c) average Hirshfeld charge on sulfides, and (d) average Hirshfeld charge on Fe. The red line indicates the X-ray Fe–Fe distance. Certain functionals are color-coded (the gray dot which the orange line crosses is ωB97X-D3BJ). Values are tabulated in Table S1.
Figure 11
Figure 11
Unrestricted corresponding orbitals (UCOs) of 7. The UCOs are derived from single-point calculations with each respective functional on the X-ray crystal structure geometry. S indicates the overlap between the α and β orbitals. A contour value of 0.05 was used for the orbital isosurfaces.
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