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

Creators: Vysotskiy, Victor P.; Torbjörnsson, Magne; Jiang, Hao; Larsson, Ernst D.; Cao, Lili; Ryde, Ulf; Zhai, Huanchen; Lee, Seunghoon; Chan, Garnet Kin-Lic¹

1. California Institute of Technology

Abstract

We have designed a [Fe(SH)₄H]⁻ 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 ∆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 ∆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 ∼5 kJ/mol compared to multireference methods), even if the D₁ diagnostic is quite high (0.25) for one of the two isomers.

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Acknowledgement

The computations were performed on computer resources provided by the Swedish National Infrastructure for Computing (SNIC) at Lunarc at Lund University (Aurora), NSC at Linköping University (Tetralith), and HPC2N at Umeå University (Kebnekaise), partially funded by the Swedish Research Council (Grant No. 2018-05973).

This investigation has been supported by grants from the Swedish research council (Project No. 2018-05003) and the China Scholarship Council. Work by Seunghoon Lee was supported by the US Department of Energy through the US DOE, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division, under Triad National Security, LLC ("Triad") Contract Grant No. 89233218CNA000001. Huanchen Zhai and Garnet Kin-Lic Chan acknowledge support from the US National Science Foundation via Award No. 2102505.

Contributions

The manuscript was written with the contributions of all authors. All authors have approved the final version of the manuscript. Victor Vysotskiy performed canonical CC and SHCI calculations, as well as some of the DFT calculations, and analyzed the results obtained. Hao Jiang and Ernst D. Larsson performed the CASSCF/CASPT2, NEVPT2, MRCI+Q, MRAQCC, and MC-PDFT calculations. Magne Torbjörnsson performed most of the DFT calculations. Huanchen Zhai and Seunghoon Lee performed KS-CCSD(T) and DMRG-CASCI calculations. Lili Cao and Ulf Ryde created the models studied in this work. Ulf Ryde and Garnet Chan are the principal investigators and have both contributed to the management of this project and the organization of collaborative work.

Victor P. Vysotskiy: Data curation (equal); Formal analysis (equal); Investigation (lead); Methodology (equal); Software (equal); Validation (equal); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). Magne Torbjörnsson: Investigation (equal). Hao Jiang: Investigation (equal). Ernst D. Larsson: Investigation (equal); Methodology (equal); Supervision (equal). Lili Cao: Investigation (equal). Ulf Ryde: Conceptualization (lead); Data curation (equal); Formal analysis (equal); Funding acquisition (lead); Investigation (equal); Project administration (lead); Resources (lead); Supervision (lead); Validation (equal); Writing – original draft (equal); Writing – review & editing (lead). Huanchen Zhai: Data curation (equal); Formal analysis (equal); Investigation (lead); Methodology (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). Seunghoon Lee: Investigation (equal). Garnet Kin-Lic Chan: Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal).

Data Availability

The data that support the findings of this study are available within the article and its supplementary material.

Conflict of Interest

The authors have no conflicts to disclose.

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