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

Abstract

Generating accurate ab initio ionization energies for transition metal complexes is an important step toward the accurate computational description of their electrocatalytic reactions. Benchmark-quality data is required for testing existing theoretical methods and 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) in the def2-SVP basis set. 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 wave function and the PBE0 density functional correlate well with our analysis of multiconfigurational wave functions. 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 density functional theory (DFT) functionals on the 3dTMV set.

Do Optimally Tuned Range-Separated Hybrid Functionals Require a Reparametrization of the Dispersion Correction? It Depends

“…As an empirical functional, ωB97M-D4 has many parameters that were tailored to a specific (default) ω value, which might hamper the applicability of optimal tuning (a discussion of this is provided in the Supporting Information). While any final conclusions regarding the robustness of ωB97M-D4 concerning variations in ω clearly require many further tests beyond NCIs, recent studies appear to confirm that optimal tuning of ωB97M-D4 and related functionals improves the performance for various properties. ,, Nevertheless, caution is generally advisable when functionals, empirical or not, are applied with nondefault parameters, as illustrated by the poor performance of LC-BLYP.…”

“…This global empirical parameter is typically obtained by fitting to appropriate thermochemistry and kinetics data sets like GMTKN55 or MGCDB84 . However, in certain situations, the performance in ground and excited-state calculations can be improved by a molecule-specific nonempirical optimal tuning of the range-separation parameter ω. − This also applies to empirical functionals, i.e., those parametrized against large databases, like ωB97M-D4 studied here. , Recent studies have demonstrated much-improved performance in combination with optimal tuning for ground and excited states. , Further considerations regarding the optimal tuning of empirical functionals can be found in the Supporting Information.…”

“…While any final conclusions regarding the robustness of ωB97M-D4 concerning variations in ω clearly require many further tests beyond NCIs, recent studies appear to confirm that optimal tuning of ωB97M-D4 and related functionals improves the performance for various properties. 16,17,20 Nevertheless, caution is generally advisable when functionals, empirical or not, are applied with nondefault parameters, as illustrated by the poor performance of LC-BLYP.…”

“…13−17 This also applies to empirical functionals, i.e., those parametrized against large databases, like ωB97M-D4 studied here. 18,19 Recent studies have demonstrated much-improved performance in combination with optimal tuning for ground 16 and excited states. 17,20 Further considerations regarding the optimal tuning of empirical functionals can be found in the Supporting Information.…”

Expanding the Design Space of Constraints in Auxiliary-Field Quantum Monte Carlo

“…The behavior of the phaseless bias is difficult to quantify, and thus, the vast majority of studies to date focus on benchmarking ph-AFQMC with different trials in order to devise strategies to obtain increasingly accurate benchmark results on difficult systems at minimal cost. Such approaches have been largely successful, with calculations using multireference trials performing well on many transition metal complexes for which single-reference methods such as coupled cluster (CC) can fail. − …”