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

31 January 2022, Version 3
This content is a preprint and has not undergone peer review at the time of posting.


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 phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) utilizing multi-determinant trial wavefunctions to six metallocene complexes to compare the computed adiabatic and vertical ionization energies to experimental results. We find that ph-AFQMC yields 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. We also carry out density functional theory (DFT) calculations using a variety of functionals, which yields 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)), 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 much 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). Finally, by utilizing experimental solvation energies, we show that accurate reduction potentials in solution for the metallocene series can be obtained from the AFQMC gas phase results.


auxiliary field quantum Monte Carlo
electronic structure
transition metal complex
density functional theory
coupled cluster
ionization energy
acetylacetonate ligands

Supplementary materials

XYZ Coordinates
B3LYP-optimized coordinates for transition metal complexes.
Supporting Information
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, discussion of relativistic effects, and cc-pVTZ-pp calculations.


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