Predicting Ligand-Dissociation Energies of 3d Coordination Complexes with Auxiliary-Field Quantum Monte Carlo

Transition-metal complexes are ubiquitous in biology and chemical catalysis, yet they remain difficult to accurately describe with ab initio methods because of the presence of a large degree of dynamic electron correlation, and, in some cases, strong static correlation which results from a manifold of low-lying states. Progress has been hindered by a scarcity of high-quality gas-phase experimental data, while exact ab initio predictions are usually computationally unaffordable because of the large size of the relevant complexes. In this work, we present a data set of 34 tetrahedral, square planar, and octahedral 3d metal-containing complexes with gas-phase ligand-dissociation energies that have reported uncertainties of ≤2 kcal/mol. We perform all-electron phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) calculations utilizing multideterminant trial wave functions selected by a black box procedure. We compare the results with those from the density functional theory (DFT) with the B3LYP, B97, M06, PBE0, ωB97X-V, and DSD-PBEP86/2013 functionals and a localized orbital variant of the coupled cluster theory with single, double, and perturbative triple excitations (DLPNO-CCSD(T)). We find mean averaged errors of 1.07 ± 0.27 kcal/mol for our most sophisticated ph-AFQMC approach versus 2.81 kcal/mol for DLPNO-CCSD(T) and 1.49-3.78 kcal/mol for DFT. We find maximum errors of 2.96 ± 1.71 kcal/mol for our best ph-AFQMC method versus 9.15 kcal/mol for DLPNO-CCSD(T) and 5.98-13.69 kcal/mol for DFT. The reasonable performance of a number of DFT functionals is in stark contrast to the much poorer accuracy previously demonstrated for diatomic species, suggesting a moderation in electron correlation because of ligand coordination in most cases. However, the unpredictably large errors for a small subset of cases with both DFT and DLPNO-CCSD(T) methods leave cause for concern, especially in light of the unreliability of common multireference indicators. In contrast, the robust and, in principle, systematically improvable results of ph-AFQMC for these realistic complexes establish the method as a useful tool for elucidating the electronic structure of transition-metal-containing complexes and predicting their gas-phase properties.