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

Nitrogenase is the only enzyme that can cleave the triple bond in N, making nitrogen available to organisms. The detailed mechanism of this enzyme is currently not known, and computational studies are complicated by the fact that different density functional theory (DFT) methods give very different energetic results for calculations involving nitrogenase models. Recently, we designed a [Fe(SH)H] model with the fifth proton binding either to Fe or S to mimic different possible protonation states of the nitrogenase active site. We showed that the energy difference between these two isomers (Δ) is hard to estimate with quantum-mechanical methods. Based on nonrelativistic single-reference coupled-cluster (CC) calculations, we estimated that the Δ is 101 kJ/mol. In this study, we demonstrate that scalar relativistic effects play an important role and significantly affect Δ. Our best revised single-reference CC estimates for Δ are 85-91 kJ/mol, including energy corrections to account for contributions beyond triples, core-valence correlation, and basis-set incompleteness error. Among coupled-cluster approaches with approximate triples, the canonical CCSD(T) exhibits the largest error for this problem. Complementary to CC, we also used phaseless auxiliary-field quantum Monte Carlo calculations (ph-AFQMC). We show that with a Hartree-Fock (HF) trial wave function, ph-AFQMC reproduces the CC results within 5 ± 1 kJ/mol. With multi-Slater-determinant (MSD) trials, the results are 82-84 ± 2 kJ/mol, indicating that multireference effects may be rather modest. Among the DFT methods tested, τ-HCTH, rSCAN with 10-13% HF exchange with and without dispersion, and O3LYP/O3LYP-D4, and B3LYP*/B3LYP*-D4 generally perform the best. The rSCAN12 (with 12% HF exchange) functional mimics both the best reference MSD ph-AFQMC and CC Δ results within 2 kJ/mol.