Ionization Energies and Redox Potentials of Hydrated Transition Metal Ions: Evaluation of Domain-Based Local Pair Natural Orbital Coupled Cluster Approaches

Bridging the Coordination Chemistry of Small Compounds and Metalloproteins Using Machine Learning

Metalloproteins require metal ions as cofactors to catalyze specific reactions with remarkable efficiency and specificity. In various electron transfer reactions, metals in the active sites change their oxidation states to facilitate the biochemical reactions. Cryogenic electron microscopy, X-ray, and X-ray free electron laser (XFEL) crystallography are used to image metalloproteins to understand the reaction mechanisms. However, radiation damage in cryoEM and X-ray crystallography, and the challenge of generating homogeneous crystals and keeping the appropriate experimental conditions for all the crystals in XFEL crystallography, may alter the oxidation states. Here, we build machine learning models trained on a large data set from the Cambridge Crystallographic Data Center to evaluate the metal oxidation states. The models yield high accuracy scores (from 82% to 94%) for all metals in the small molecules. Then, they were used to predict the oxidation states of more than 30 000 metal clusters in metalloproteins with Fe, Mn, Co, and Cu in their active sites. We found that most of the metals exist in the lower oxidation states (Fe2+ 77%, Mn2+ 85%, Co2+ 65%, and Cu+ 64%), and these populations correlate with the standard reduction potentials of the metal ions. Furthermore, we found no clear correlation between these populations and the resolution of the structures, which suggests no significant dependence of these predictions on the resolution. Our models represent a valuable tool for evaluating the oxidation states of the metals in metalloproteins imaged with different techniques. The data files and the machine learning code are available in a public GitHub repository: https://github.com/mamin03/OxitationStatesMetalloprotein.git.

Modeling the Zigzag Curves of Transition Metal Ions' Charge Transition Levels in Crystals

Predicting the defect levels of transition metal (TM) dopants in the band gap of crystals is critical in determining the charge states of TM dopants and explaining their electronic and optical properties. By analyzing the calculated charge transition levels and the crystal-field strengths of all the 3d-TM ions in several insulators, we demonstrate that the variation trend of the 3d-TM dopants in a crystal is a scaling of the variation of 3d-electron binding energies (ionization potential) of the free TM ions corrected by adding the contribution of the 3d-orbital's crystal-field splitting. We therefore develop a model to predict the relative location of TM ions' defect levels in the band gap from the defect level and crystal-field splitting of a reference TM ion in the host of concern. The model is applied to predict the defect levels of the series of TM ions in β-Ga2O3 and ZnO, which have moderate to small band gaps, making some of the levels fall into the conduction or valence bands. These results show that the model may serve as a quick reference for related material design and optimization.

G0W0 Ionization Potentials of First-Row Transition Metal Aqua Ions

We report computations of the vertical ionization potentials within the GW approximation of the near-complete series of first-row transition metal (V-Cu) aqua ions in their most common oxidation states, i.e., V3+, Cr3+, Cr2+, Mn2+, Fe3+, Fe2+, Co2+, Ni2+, and Cu2+. The d-orbital occupancy of these systems spans a broad range from d2 to d9. All of the structures were first optimized at the density functional theory level using a large cluster of explicit water molecules that are embedded in a continuum solvation model. Vertical ionization potentials were computed with the one-shot G0W0 approach on a range of transition metal ion clusters (6, 18, 40, and 60 explicit water molecules), wherein the convergence with respect to the basis set size was evaluated using the systems with 40 water molecules. We assess the results using three different density functional approximations as starting points for the vertical ionization potential calculations, namely, G0W0@PBE, G0W0@PBE0, and G0W0@r2SCAN. While the predicted ground-state structures are similar to all three exchange-correlation functionals, the vertical ionization potentials were in closer agreement with experiment when using the G0W0@PBE0 and G0W0@r2SCAN approaches, with the r2SCAN-based calculations being significantly less expensive. Computed bond distances and vertical ionization potentials for all structures are in good agreement with available experimental data.

Benchmarks for transition metal spin-state energetics: why and how to employ experimental reference data?

Accurate prediction of energy differences between alternative spin states of transition metal complexes is essential in computational (bio)inorganic chemistry-for example, in characterization of spin crossover materials and in the theoretical modeling of open-shell reaction mechanisms-but it remains one of the most compelling problems for quantum chemistry methods. A part of this challenge is to obtain reliable reference data for benchmark studies, as even the highest-level applicable methods are known to give divergent results. This Perspective discusses two possible approaches to method benchmarking for spin-state energetics: using either theoretically computed or experiment-derived reference data. With the focus on the latter approach, an extensive general review is provided for the available experimental data of spin-state energetics and their interpretations in the context of benchmark studies, targeting the possibility of back-correcting the vibrational effects and the influence of solvents or crystalline environments. With a growing amount of experience, these effects can be now not only qualitatively understood, but also quantitatively modeled, providing the way to derive nearly chemically accurate estimates of the electronic spin-state gaps to be used as benchmarks and advancing our understanding of the phenomena related to spin states in condensed phases.

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.

Redox Potentials of Uranyl Ions in Macrocyclic Complexes: Quantifying the Role of Counter-Ions

Several uranyl ions strapped with Schiff-base ligands in the presence of redox-innocent metal ions are synthesized, and their reduction potentials are recently estimated. The change in Lewis acidity of the redox-innocent metal ions contributes to ∼60 mV/pK_a unit quantified which is intriguing. Upon increasing the Lewis acidity of metal ions, the number of triflate molecules found near the metal ions also increases whose contributions toward the redox potentials remain poorly understood and not quantified until now. Most importantly, to ease the computational burden, triflate anions are often neglected in quantum chemical models due to their larger size and weak coordination to metal ions. Herein, we have quantified and dissected the individual contributions that arise alone from Lewis acid metal ions and from triflate anions with electronic structure calculations. The triflate anion contributions are large, in particular, for divalent and trivalent anions that cannot be neglected. It was presumed to be innocent, but we here show that they can contribute more than 50% to the predicted redox potentials, suggesting that their vital role in the overall reduction processes cannot be neglected.

Redox Potentials with COSMO-RS: Systematic Benchmarking with Different Databases

Recent techniques of computational electrochemistry can yield redox potentials with accuracy as good as 0.1 V. Yet, many such methods are not universal, easy to use, or computationally efficient. Herein, we provide a systematic benchmarking of a relatively cheap and straightforward computational approach for fairly accurate computations of redox potentials. It is based on a combination of the conductor-like screening model for real solvents (COSMO-RS) and the density functional theory (DFT). The benchmarking is done with databases covering diverse redox systems, including transition-metal aquacomplexes and various organic and inorganic compounds. In addition, we also present our own test set aiming at maximum chemical diversity and maximum range of redox potential values. We assess the performance of the fairly efficient computational protocol combining the COSMO-RS with the BP86 DFT functional. This is done by calibrating it against different high-level state-of-the-art techniques, in particular, polarizable continuum model (PCM) connected to composite G3(MP2,CC)(+) method, domain-based pair natural orbital implementation of coupled cluster theory, or complete basis set CBS-QB3 method. We also elaborate on the absolute reduction potential value of standard hydrogen electrode to be used with COSMO-RS, and we propose the value of approx. 4.4 V. The COSMO-RS/BP86-D3(BJ) combination outperforms other methods on a wide range of redox systems. However, we show that its accuracy is based on a balanced error cancelation and, therefore, it cannot be further systematically improved. As a result, the proposed procedure represents a pragmatic choice for large-scale screening, yet it could be combined with more advanced methods for detailed studies.

Reconciling Local Coupled Cluster with Multireference Approaches for Transition Metal Spin-State Energetics

Spin-state energetics of transition metal complexes remain one of the most challenging targets for electronic structure methods. Among single-reference wave function approaches, local correlation approximations to coupled cluster theory, most notably the domain-based local pair natural orbital (DLPNO) approach, hold the promise of bringing the accuracy of coupled cluster theory with single, double, and perturbative triple excitations, CCSD(T), to molecular systems of realistic size with acceptable computational cost. However, recent studies on spin-state energetics of iron-containing systems raised doubts about the ability of the DLPNO approach to adequately and systematically approximate energetics obtained by the reference-quality complete active space second-order perturbation theory with coupled-cluster semicore correlation, CASPT2/CC. Here, we revisit this problem using a diverse set of iron complexes and examine several aspects of the application of the DLPNO approach. We show that DLPNO-CCSD(T) can accurately reproduce both CASPT2/CC and canonical CCSD(T) results if two basic principles are followed. These include the consistent use of the improved iterative (T₁) versus the semicanonical perturbative triple corrections and, most importantly, a simple two-point extrapolation to the PNO space limit. The latter practically eliminates errors arising from the default truncation of electron-pair correlation spaces and should be viewed as standard practice in applications of the method to transition metal spin-state energetics. Our results show that reference-quality results can be readily achieved with DLPNO-CCSD(T) if these principles are followed. This is important also in view of the applicability of the method to larger single-reference systems and multinuclear clusters, whose treatment of dynamic correlation would be challenging for multireference-based approaches.