Ionization energies of metallocenes: a coupled cluster study of cobaltocene

Chelate Complexes of 3d Transition Metal Ions─A Challenge for Electronic-Structure Methods?

Different electronic-structure methods were assessed for their ability to predict two important properties of the industrially relevant chelating agent nitrilotriacetic acid (NTA): its selectivity with respect to six different first-row transition metal ions and the spin-state energetics of its complex with Fe(III). The investigated methods encompassed density functional theory (DFT), the random phase approximation (RPA), coupled cluster (CC) theory, and the auxiliary-field quantum Monte Carlo (AFQMC) method, as well as the complete active space self-consistent field (CASSCF) method and the respective on-top methods: second-order N-electron valence state perturbation theory (NEVPT2) and multiconfiguration pair-density functional theory (MC-PDFT). Different strategies for selecting active spaces were explored, and the density matrix renormalization group (DMRG) approach was used to solve the largest active spaces. Despite somewhat ambiguous multi-reference diagnostics, most methods gave relatively good agreement with experimental data for the chemical reactions connected to the selectivity, which only involved transition-metal complexes in their high-spin state. CC methods yielded the highest accuracy followed by range-separated DFT and AFQMC. We discussed in detail that even higher accuracies can be obtained with NEVPT2, under the prerequisite that consistent active spaces along the entire chemical reaction can be selected, which was not the case for reactions involving Fe(III). A bigger challenge for electronic-structure methods was the prediction of the spin-state energetics, which additionally involved lower spin states that exhibited larger multi-reference diagnostics. Conceptually different, typically accurate methods ranging from CC theory via DMRG-NEVPT2 in combination with large active spaces to AFQMC agreed well that the high-spin state is energetically significantly favored over the other spin states. This was in contrast to most DFT functionals and RPA which yielded a smaller stabilization and some common DFT functionals and MC-PDFT even predicting the low-spin state to be energetically most favorable.

Approaching the Complete Basis Set Limit for Spin-State Energetics of Mononuclear First-Row Transition Metal Complexes

Convergence to the complete basis set (CBS) limit is analyzed for the problem of spin-state energetics in mononuclear first-row transition metal (TM) complexes by taking under scrutiny a benchmark set of 18 energy differences between spin states for 13 chemically diverse TM complexes. The performance of conventional CCSD(T) and explicitly correlated CCSD(T)-F12a/b calculations in approaching the CCSD(T)/CBS limits is systematically studied. An economic computational protocol is developed based on the CCSD-F12a approximation and (here proposed) modified scaling of the perturbative triples term (T#). This computational protocol recovers the relative spin-state energetics of the benchmark set in excellent agreement with the reference CCSD(T)/CBS limits (mean absolute deviation of 0.4, mean signed deviation of 0.2, and maximum deviation of 0.8 kcal/mol) and enables performing canonical CCSD(T) calculations for mononuclear TM complexes sized up to ca. 50 atoms, which is illustrated by application to heme-related metalloporphyrins. Furthermore, a good transferability of the basis set incompleteness error (BSIE) is demonstrated for spin-state energetics computed using CCSD(T) and other wave function methods (MP2, CASPT2, CASPT2/CC, NEVPT2, and MRCI + Q), which justifies efficient focal-point approximations and simplifies the construction of multimethod benchmark studies.

Effect of a single methyl substituent on the electronic structure of cobaltocene studied by computationally assisted MATI spectroscopy

Metallocenes represent archetypical organometallic compounds playing key roles in various fields of fundamental and applied chemistry. Many of their unique properties arise from low ionization energies (IE) which can be tuned by introducing substituents into the rings. Here we report the first mass-analyzed threshold ionization (MATI) spectrum of a methylmetallocene, (Cp')(Cp)Co (Cp' = η5-C5H4Me, Cp = η5-C5H5). The presence of a single Me group allows us to study the "pure" effect of methylation without the mutual influence of substituents. The MATI technique provides an extremely high accuracy in determining the adiabatic IE of (Cp')(Cp)Co which equals 5.2097(6) eV. The effect of a Me group on the IE of cobaltocene appears to be 36% stronger than that in bis(η6-benzene)chromium. The MATI spectrum of (Cp')(Cp)Co shows a rich vibronic structure from which vibrational frequencies of the free ion are determined. This information provides a solid basis for testing the quality of quantum chemical calculations. Various levels of the DFT and coupled cluster computations are used to describe the structural and electronic transformations accompanying the detachment of an elctron from (Cp')(Cp)Co. New aspects of the methyl substituent influence on the potential energy surfaces, as well as on the inhomogeneous changes in charge density and electrostatic potential caused by ionization, are discussed.

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 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.

MP2-Based Correction Scheme to Approach the Limit of a Complete Pair Natural Orbitals Space in DLPNO-CCSD(T) Calculations

The domain-based local pair natural orbital (PNO) coupled-cluster DLPNO-CCSD(T) method has been proven to provide accurate single-point energies at a fraction of the cost of canonical CCSD(T) calculations. However, the desired "chemical accuracy" can only be obtained with a large PNO space and extended basis set. We present a simple yet accurate and efficient correction scheme based on a perturbative approach. Here, in addition to DLPNO-CCSD(T) energy, one calculates DLPNO-MP2 correlation energy with the same settings as in the preceding coupled-cluster calculation. In the next step, the canonical MP2 correlation energy is obtained in the same orbital basis. This can be efficiently performed for essentially all molecule sizes accessible with the DLPNO-CCSD(T) method. By taking the difference between the canonical MP2 and DLPNO-MP2 energies, we obtain a correction term that can be added to the DLPNO-CCSD(T) correlation energy. This way, one can obtain the total correlation energy close to the limit of the complete PNO space (cPNO). The presented approach allows us to significantly increase the accuracy of the DLPNO-CCSD(T) method for both closed- and open-shell systems. The latter are known to be especially challenging for locally correlated methods. Unlike the previously developed PNO extrapolation procedure by Altun, Neese, and Bistoni ( J. Chem. Theory Comput. 2020, 16, 6142-6149), this strategy allows us to get the DLPNO-CCSD(T) correlation energy at the cPNO limit in a cost-efficient way, resulting in a minimal overall increase in calculation time as compared to the uncorrected method.