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.