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

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.

Protonation of Homocitrate and the E1 State of Fe-Nitrogenase Studied by QM/MM Calculations

“…31 The former two were selected because they have been shown to give the best structures for nitrogenase models. 50 B3LYP gave the best results in two recent calibration studies on simple nitrogenase model systems with one or two Fe ions, 51,52 whereas TPSS has been used in most of our previous studies. 23,53,54 The calculations involved either the def2-SV(P) 30 basis set for all atoms or the def2-TZVP 30 basis set for the FeFe cluster (including the added proton), homocitrate, Cys-257 and His-423, and the def2-SV(P) basis set for other groups.…”

“…The former two were selected because they have been shown to give the best structures for nitrogenase models . B3LYP gave the best results in two recent calibration studies on simple nitrogenase model systems with one or two Fe ions, , whereas TPSS has been used in most of our previous studies. ,, The calculations involved either the def2-SV­(P) basis set for all atoms or the def2-TZVP basis set for the FeFe cluster (including the added proton), homocitrate, Cys-257 and His-423, and the def2-SV­(P) basis set for other groups. To enhance computational efficiency, Coulomb interactions were expanded in an auxiliary basis set by using the resolution-of-identity (RI) approximation. , Empirical dispersion corrections were applied using DFT-D4, as implemented in Turbomole.…”

Scalar Relativistic All-Electron and Pseudopotential Ab Initio Study of a Minimal Nitrogenase [Fe(SH)4H]− Model Employing Coupled-Cluster and Auxiliary-Field Quantum Monte Carlo Many-Body Methods

“…The coupled-cluster method with singles, doubles, and perturbative triples (CCSD(T)) is often referred to as the “gold standard” of computational chemistry because of its high accuracy and feasible computational scaling, O ( N 7 ), where N is the number of basis functions. For the present model using the nonrelativistic Dunning’s cc-pVDZ basis set, we recently showed that canonical CCSD(T) calculations with Hartree–Fock (HF) reference orbitals exhibit a rather large error for Δ E (>7 kJ/mol), while BCCD(T) provides an excellent accuracy (0.5 kJ/mol), compared to full CCSDT calculations . Furthermore, the BCCD(T) method consistently approaches CCSDT for both the total energy of the model structures and Δ E .…”

“…Our best estimate for Δ E was 101 kJ/mol. M06 and B3LYP were the two DFT functionals that came closest to this estimate . Meta-GGA and double hybrid DFT functionals were shown to underestimate and overestimate Δ E by at least 30 and 10 kJ/mol, respectively …”

Benchmarks for transition metal spin-state energetics: why and how to employ experimental reference data?

“…‡For typical problems of the nondynamic correlation, such as bond dissociation curves, it has been shown that the standard perturbative (T) correction performs worse than alternative, completely-renormalized (CR) corrections. 88 While there exist some (but still relatively few) applications of the CR methods to TM systems, 89–91 the standard (T) correction is still predominately used both in general-purpose thermochemistry protocols and in specific applications to the TM spin-state energetics problem. The present author once compared the results of standard CCSD(T) and completely renormalized CR-CC(2,3) methods for simplified heme models and found differences up to 2.5 kcal mol −1 in relative spin-state energies.…”