Toward Benchmark-quality Ab Initio Predictions for 3d Transition Metal Electrocatalysts - A Comparison of CCSD(T) and ph-AFQMC

Generating accurate ab initio ionization energies for transition metal complexes is an important step towards the accurate computational description of their electrocatalytic reactions. Benchmark-quality data is required for testing existing theoretical methods and for developing new ones but is complicated to obtain for many transition metal compounds due to the potential presence of both strong dynamical and static electron correlation. In this regime, it is questionable whether the so-called gold standard, coupled cluster with singles, doubles, and perturbative triples (CCSD(T)), provides the desired level of accuracy -- roughly 1-3 kcal/mol. In this work, we compiled a test set of 28 3d metal-containing molecules relevant to homogeneous electrocatalysis (termed 3dTMV) and computed their vertical ionization energies (ionization potentials) with CCSD(T) and phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC). A substantial effort has been made to converge away the phaseless bias in the ph-AFQMC reference values. We assess a wide variety of multireference diagnostics, and find that spin-symmetry breaking of the CCSD wavefunction and in the PBE0 density functional correlate well with our analysis of multiconfigurational wavefunctions. We propose quantitative criteria based on symmetry breaking to delineate correlation regimes inside of which appropriately-performed CCSD(T) can produce mean absolute deviations from the ph-AFQMC reference values of roughly 2 kcal/mol or less, and outside of which CCSD(T) is expected to fail. We also present a preliminary assessment of DFT functionals on the 3dTMV set.