Evaluating Multiconfigurational Trials for Accurate Phaseless Auxiliary-Field Quantum Monte Carlo on 3d Transition Metal Complexes

In this study, we evaluate multiconfigurational trial wave function protocols for phaseless auxiliary field quantum Monte Carlo (ph-AFQMC) on transition metal containing systems. First, we benchmark vertical ionization potentials for 22 3<i>d</i> transition metal complexes against published high-accuracy ph-AFQMC values in a double-ζ basis set. We then compute the vertical ionization potential for a set of six metallocenes using our best-performing protocol, alongside ph-AFQMC using a configuration interaction singles and doubles (CISD) trial state. We also analyze the performance of canonical coupled-cluster theory with singles, doubles and perturbative triples (CCSD(T)), as well as its local approximation using domain-based local pair natural orbitals (DLPNO-CCSD(T1)) using different reference orbitals. To reach the complete-basis-set (CBS) limit, we examine several extrapolation schemes and report CBS-limit ph-AFQMC and CCSD(T) values alongside experimental results. We find that ph-AFQMC with the best-performing trial in a triple-ζ basis, followed by CBS correction from DLPNO-CCSD(T1) with unrestricted B3LYP reference orbitals, yields small deviations from experiment at modest cost. Using a CISD trial state in ph-AFQMC gives the closest agreement with experiment (errors <2 kcal/mol), albeit with lower scalability.