Calculation of Metallocene Ionization Potentials via Auxiliary Field Quantum Monte Carlo: Towards Benchmark Quantum Chemistry for Transition Metals


The accurate ab initio prediction of ionization energies is essential to understanding the electrochemistry of transition metal complexes in both materials science and biological applications. However, such predictions have been complicated by the scarcity of gas-phase experimental data, the relatively large size of the relevant molecules, and the presence of strong electron correlation effects. In this work, we apply all-electron phase-less auxiliary-field quantum Monte Carlo (ph-AFQMC) utilizing multi-determinant trial wavefunctions to six metallocene complexes to compare the computed adiabaticand vertical ionization energies to experimental results. We find the ph-AFQMC mean averaged errors (MAE) of 1.69±1.02 kcal/mol for the adiabatic energies and 2.85±1.13 kcal/mol for the vertical energies. This significantly outperforms density functional theory (DFT), which has MAE’s of 3.62 to 6.98 and 3.31 to 9.88 kcal/mol, as well as a localized coupled cluster approach (DLPNO-CCSD(T0) with moderate PNO cut-offs), which has MAEs of 4.96 and 6.08 kcal/mol, respectively. We also test the reliability of DLPNO-CCSD(T0) and DFT on acetylacetonate (acac) complexes for adiabatic energies measured in the same manner experimentally, and find higher MAE’s, ranging from 4.56 kcal/mol to 10.99 kcal/mol (with a different ordering) for DFT and 6.97 kcal/mol for DLPNO-CCSD(T0), indicating that none of these approaches can be considered benchmark methods, at least for these complexes. We thus demonstrate that ph-AFQMC should be able to handle metallocene redox chemistry with the advantage of systematically improvable results. By utilizing experimental solvation energies, we show that accurate reduction potentials in solution can be obtained.

Version notes

Changes in reference to DLPNO-CCSD(T) discussion and improved text and corrected typoes


Supplementary material

Supporting Information Metallocene Ionization Energies
Tabulated DLPNO-CCSD(T0), ph-AFQMC vertical and adiabatic energies in the TZ basis set, basis set extrapolation corrections for all methods, scaling factors for the CBS extrapolations, free energy corrections, active space information, CASSCF energies, NOON’s, ⟨S2⟩ values, metal spin density values, details on the convergence of ph-AFQMC with respect to active space, details on the DFT integration grids, stability calculations, how CBS extrapolations are done for DLPNO-CCSD(T0), a workflow in terms of how other calculations complement the ph-AFQMC calculations, alternate experimental values, additional methodology details for ph-AFQMC, details on how potentials are calculated in solution, details on the calculation of statistical measures to compare to experiment, explanation of CS algorithms, ionization energies including diffuse functions on certain atoms, results with dispersion, B3LYP M-Cp distances in the metallocenes, literature experimental homolytic bond dissociation energies for the metallocenes, tests of DLPNO-CCSD(T) PNO cut-off and(T) treatment, and reorganization energies with one center approximation off.
XYZ Coordinates
B3LYP-optimized coordinates for transition metal complexes.