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 due to 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 due to the large size of the systems. In this work, we present a data set of 34 3d metal-containing complexes with gas-phase ligand-dissociation energies that have reported uncertainties of $\leq$ 2 kcal/mol. We perform all-electron phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) utilizing multi-determinant trial wavefunctions selected by a blackbox procedure. We compare the results with those from DFT with various functionals, and DLPNO-CCSD(T). We find MAE of 1.09 $\pm$ 0.28 kcal/mol for our best ph-AFQMC method, vs 2.89 kcal/mol for DLPNO-CCSD(T) and 1.57 - 3.87 kcal/mol for DFT. We find maximum errors of 2.96 $\pm$ 1.71 kcal/mol for our best ph-AFQMC method, vs 9.15 kcal/mol for DLPNO-CCSD(T) and 5.98 - 13.69 kcal/mol for DFT. The reasonable performance of several functionals is in stark contrast to the much poorer accuracy previously demonstrated for diatomics, suggesting a moderation in electron correlation due to ligand coordination. However, the unpredictably large errors for a small subset of cases with both DFT and DLPNO-CCSD(T) leave cause for concern, especially due to the unreliability of common multi-reference indicators. In contrast, the robust and, in principle, systematically improvable results of ph-AFQMC for these realistic complexes establish it as a useful tool for elucidating the electronic structure of transition metal-containing complexes and predicting their gas-phase properties.