Assessment of DFT functionals for a minimal nitrogenase [Fe(SH)(4)H](-) model employing state-of-the-art ab initio methods

We have designed a [Fe(SH)(4)H](-) model with the fifth proton binding either to Fe or S. We show that the energy difference between these two isomers (?E) is hard to estimate with quantum-mechanical (QM) methods. For example, different density functional theory (DFT) methods give increment Delta E estimates that vary by almost 140 kJ/mol, mainly depending on the amount of exact Hartree-Fock included (0%-54%). The model is so small that it can be treated by many high-level QM methods, including coupled-cluster (CC) and multiconfigurational perturbation theory approaches. With extrapolated CC series (up to fully connected coupled-cluster calculations with singles, doubles, and triples) and semistochastic heat-bath configuration interaction methods, we obtain results that seem to be converged to full configuration interaction results within 5 kJ/mol. Our best result for increment Delta E is 101 kJ/mol. With this reference, we show that M06 and B3LYP-D3 give the best results among 35 DFT methods tested for this system. Brueckner doubles coupled cluster with perturbaitve triples seems to be the most accurate coupled-cluster approach with approximate triples. CCSD(T) with Kohn-Sham orbitals gives results within 4-11 kJ/mol of the extrapolated CC results, depending on the DFT method. Single-reference CC calculations seem to be reasonably accurate (giving an error of similar to 5 kJ/mol compared to multireference methods), even if the D-1 diagnostic is quite high (0.25) for one of the two isomers. (c) 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

We designed a [Fe(SH)(4)H](-) model with the fifth proton binding to either Fe or S. The energy difference between these two isomers (?E) is difficult to estimate using quantum-mechanical methods. Different density functional theory methods give varying estimates for Delta E, ranging from 0%-54% of exact Hartree-Fock inclusion and differing by almost 140 kJ/mol. Using high-level quantum-mechanical methods, we obtained converged results for Delta E, with the best result being 101 kJ/mol. Among 35 tested DFT methods, M06 and B3LYP-D3 performed the best for this system.