A Density Functional Theory Based Protocol to Compute the Redox Potential of Transition Metal Complex with the Correction of Pseudo-Counterion: General Theory and Applications

Density Functional Theory-Based Protocol to Calculate the Redox Potentials of First-row Transition Metal Complexes for Aqueous Redox Targeting Flow Batteries

Transition metal complexes are a promising class of redox mediators for targeting redox flow batteries due to the tunability of their electrochemical potentials. However, reliable time-efficient tools for the prediction of their reduction potentials are needed. In this work, we establish a suitable density functional theory protocol for their prediction using an initial experimental data set of aqueous iron complexes with bidentate ligands. The approach is then cross-validated using different complexes found in the redox-flow literature. We find that the solvation model affects the prediction accuracy more than the functional or basis set. The smallest errors are obtained using the COSMO-RS solvation model (mean average error (MAE)=0.24 V). With implicit solvation models, a general deviation from experimental results is observed. For a set of similar ligands, they can be corrected using simple linear regression (MAE=0.051 V for the initial set of iron complexes).

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.

Protocols for Understanding the Redox Behavior of Copper-Containing Systems

Suitability of single-reference density functional theory (DFT) methods for the calculation of redox potentials of copper-containing macrocycle complexes was confirmed by the use of T ₁ diagnostics along with a verification of negligible spin contamination or wave function instability. When examining the effect of improvement in the cc-pVnZ basis set series on calculated redox potentials, the results readily converged at the cc-pVTZ level. The all-electron Def2-TZVPP basis set is shown to be a suitable choice of a basis set for the calculation of redox potentials when utilizing a cc-pVTZ geometry. The best-performing model chemistries are determined to be the M06/polarizable continuum model (PCM); therefore, a scheme for redox potential calculations of copper macrocycles using either M06/cc-pVTZ with PCM solvation is proposed to reliably reproduce experimental trends.

Factor analysis of error in oxidation potential calculation: A machine learning study

The conductor-like polarizable continuum model (C-PCM), which is a low-cost solvation model, cannot treat characteristic interactions between the solvent and substructure(s) of the solute. Moreover, the error in a charged system is significant. Using machine learning, we clarified that the systematic error of the oxidation potential calculated by the G3B3/C-PCM was correlated with the molecular size of a solute. The G3B3/C-PCM overestimated the Gibbs oxidation energy by averaging 6.94 kcal/mol. According to the performance of related methods reported in previous studies, this error is mainly due to the solvation energy of the charged solute. Additionally, we succeeded in reducing the error to 2.27 kcal/mol (32%)-3.2 kcal/mol (40%) by correction based on the substructure information of the solute. To modify the C-PCM, effects that correlate with the molecular size of the solute in the charged system should be incorporated.

Visible-Light-Driven, Iridium-Catalyzed Hydrogen Atom Transfer: Mechanistic Studies, Identification of Intermediates, and Catalyst Improvements

The harvesting of visible light is a powerful strategy for the synthesis of weak chemical bonds involving hydrogen that are below the thermodynamic threshold for spontaneous H₂ evolution. Piano-stool iridium hydride complexes are effective for the blue-light-driven hydrogenation of organic substrates and contra-thermodynamic dearomative isomerization. In this work, a combination of spectroscopic measurements, isotopic labeling, structure-reactivity relationships, and computational studies has been used to explore the mechanism of these stoichiometric and catalytic reactions. Photophysical measurements on the iridium hydride catalysts demonstrated the generation of long-lived excited states with principally metal-to-ligand charge transfer (MLCT) character. Transient absorption spectroscopic studies with a representative substrate, anthracene revealed a diffusion-controlled dynamic quenching of the MLCT state. The triplet state of anthracene was detected immediately after the quenching events, suggesting that triplet-triplet energy transfer initiated the photocatalytic process. The key role of triplet anthracene on the post-energy transfer step was further demonstrated by employing photocatalytic hydrogenation with a triplet photosensitizer and a HAT agent, hydroquinone. DFT calculations support a concerted hydrogen atom transfer mechanism in lieu of stepwise electron/proton or proton/electron transfer pathways. Kinetic monitoring of the deactivation channel established an inverse kinetic isotope effect, supporting reversible C(sp²)-H reductive coupling followed by rate-limiting ligand dissociation. Mechanistic insights enabled design of a piano-stool iridium hydride catalyst with a rationally modified supporting ligand that exhibited improved photostability under blue light irradiation. The complex also provided improved catalytic performance toward photoinduced hydrogenation with H₂ and contra-thermodynamic isomerization.

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

Hydrated transition metal ions are prototypical systems that can be used to model properties of transition metals in complex chemical environments. These seemingly simple systems present challenges for computational chemistry and are thus crucial in evaluations of quantum chemical methods for spin-state and redox energetics. In this work, we explore the applicability of the domain-based pair natural orbital implementation of coupled cluster (DLPNO-CC) theory to the calculation of ionization energies and redox potentials for hydrated ions of all first transition row (3d) metals in the 2+/3+ oxidation states, in connection with various solvation approaches. In terms of model definition, we investigate the construction of a minimally explicitly hydrated quantum cluster with a first and second hydration layer. We report on the convergence with respect to the coupled cluster expansion and the PNO space, as well as on the role of perturbative triple excitations. A recent implementation of the conductor-like polarizable continuum model (CPCM) for the DLPNO-CC approach is employed to determine self-consistent redox potentials at the coupled cluster level. Our results establish conditions for the convergence of DLPNO-CCSD(T) energetics and stress the absolute necessity to explicitly consider the second solvation sphere even when CPCM is used. The achievable accuracy for redox potentials of a practical DLPNO-based approach is, on average, 0.13 V. Furthermore, multilayer approaches that combine a higher-level DLPNO-CCSD(T) description of the first solvation sphere with a lower-level description of the second solvation layer are investigated. The present work establishes optimal and transferable methodological choices for employing DLPNO-based coupled cluster theory, the associated CPCM implementation, and cost-efficient multilayer derivatives of the approach for open-shell transition metal systems in complex environments.

Bridging the Experiment-Calculation Divide: Machine Learning Corrections to Redox Potential Calculations in Implicit and Explicit Solvent Models

Prediction of redox potentials is essential for catalysis and energy storage. Although density functional theory (DFT) calculations have enabled rapid redox potential predictions for numerous compounds, prominent errors persist compared to experimental measurements. In this work, we develop machine learning (ML) models to reduce the errors of redox potential calculations in both implicit and explicit solvent models. Training and testing of the ML correction models are based on the diverse ROP313 data set with experimental redox potentials measured for organic and organometallic compounds in a variety of solvents. For the implicit solvent approach, our ML models can reduce both the systematic bias and the number of outliers. ML corrected redox potentials also demonstrate less sensitivity to DFT functional choice. For the explicit solvent approach, we significantly reduce the computational costs by embedding the microsolvated cluster in implicit bulk solvent, obtaining converged redox potential results with a smaller solvation shell. This combined implicit-explicit solvent model, together with GPU-accelerated quantum chemistry methods, enabled rapid generation of a large data set of explicit-solvent-calculated redox potentials for 165 organic compounds, allowing detailed investigation of the error sources in explicit solvent redox potential calculations.

Impact of substituent nature in diformylpyridyl Schiff base on photophysical and electrochemical properties of ruthenium- and iron-based complexes

The effect of substituents on the optical properties, redox potential, and reorganization energy in a series of Ru and Fe based complexes was studied. All studied complexes respond to the requirements for a sensitizer as the main component of DSSC.

Theoretical Study on Redox Potential Control of Iron-Sulfur Cluster by Hydrogen Bonds: A Possibility of Redox Potential Programming

The effect of hydrogen bonds around the active site of Anabaena [2Fe-2S] ferredoxin (Fd) on a vertical ionization potential of the reduced state (IP(red)) is examined based on the density functional theory (DFT) calculations. The results indicate that a single hydrogen bond increases the relative stability of the reduced state, and shifts IP(red) to a reductive side by 0.31–0.33 eV, regardless of the attached sulfur atoms. In addition, the IP(red) value can be changed by the number of hydrogen bonds around the active site. The results also suggest that the redox potential of [2Fe-2S] Fd is controlled by the number of hydrogen bonds because IP(red) is considered to be a major factor in the redox potential. Furthermore, there is a possibility that the redox potentials of artificial iron-sulfur clusters can be finely controlled by the number of the hydrogen bonds attached to the sulfur atoms of the cluster.

Computational Discovery of Transition-metal Complexes: From High-throughput Screening to Machine Learning

Transition-metal complexes are attractive targets for the design of catalysts and functional materials. The behavior of the metal-organic bond, while very tunable for achieving target properties, is challenging to predict and necessitates searching a wide and complex space to identify needles in haystacks for target applications. This review will focus on the techniques that make high-throughput search of transition-metal chemical space feasible for the discovery of complexes with desirable properties. The review will cover the development, promise, and limitations of "traditional" computational chemistry (i.e., force field, semiempirical, and density functional theory methods) as it pertains to data generation for inorganic molecular discovery. The review will also discuss the opportunities and limitations in leveraging experimental data sources. We will focus on how advances in statistical modeling, artificial intelligence, multiobjective optimization, and automation accelerate discovery of lead compounds and design rules. The overall objective of this review is to showcase how bringing together advances from diverse areas of computational chemistry and computer science have enabled the rapid uncovering of structure-property relationships in transition-metal chemistry. We aim to highlight how unique considerations in motifs of metal-organic bonding (e.g., variable spin and oxidation state, and bonding strength/nature) set them and their discovery apart from more commonly considered organic molecules. We will also highlight how uncertainty and relative data scarcity in transition-metal chemistry motivate specific developments in machine learning representations, model training, and in computational chemistry. Finally, we will conclude with an outlook of areas of opportunity for the accelerated discovery of transition-metal complexes.

Ab Initio Evaluation of the Redox Potential of Cytochrome c

Various biochemical activities of metabolism and biosynthesis are fulfilled by redox processes with explicit electron exchange, which furnish redox enzymes with high chemical reactivity. However, theoretical investigation of a redox process, which simultaneously involves a complex electronic change at a redox metal center and conformational reorganization of the surrounding protein environment coupled to the electronic change, requires computationally conflicting approaches, highly accurate quantum chemical calculations, and long-time molecular dynamics (MD) simulations, limiting the physicochemical understanding of biological redox processes. Here, we theoretically examined a redox process of cytochrome c by means of a hybrid molecular simulation technique, which enables one to consistently treat the redox center at the ab initio quantum chemistry level of theory and the protein reorganization with long-time MD simulations on the microsecond timescale. The calculations successfully evaluated a large absolute redox potential, 4.34 eV, with errors of only 0.03 to 0.34 eV to the experimental ones without any problem-specific empirical parameters. Through the long-time MD sampling, large and nonlinear reorganization of the protein environment was unveiled and the molecular determinants for the redox potential were identified. The present ab initio approach significantly expands the applicability of theoretical investigation to biological redox systems with more electronically complicated redox centers such as polynuclear transition metal complexes.

Photochemical reduction of Cr(vi) compounds by amino acid Schiff base copper complexes with a hydroxyl group and titanium oxide composites in aqueous solutions

The photo-driven reduction reaction of Cr(vi) to Cr(iii) by Schiff base Cu(ii) complexes was studied in aqueous and methanol solutions. The Cr(vi) reduction ratio with the CuVDB–TiO₂ system reached 91%.

A Density Functional Theory-Based Scheme to Compute the Redox Potential of a Transition Metal Complex: Applications to Heme Compound

We estimated the redox potential of a model heme compound by using the combination of our density functionals with a computational scheme, which corrects the solvation energy to the normal solvent model. Among many density functionals, the LC-BOP12 functional gave the smallest mean absolute error of 0.16 V in the test molecular sets. The application of these methods revealed that the redox potential of a model heme can be controlled within 200 mV by changing the protonation state and even within 20 mV by the flipping of the ligand histidine. In addition, the redox potential depends on the inverse of the dielectric constant, which controls the surroundings. The computational results also imply that a system with a low dielectric constant avoids the charged molecule by controlling either the redox potential or the protonation system.

A computational scheme of pKa values based on the three-dimensional reference interaction site model self-consistent field theory coupled with the linear fitting correction scheme

A scheme for quantitatively computing the acid dissociation constant, pKa, of hydrated molecules is proposed. It is based on the three-dimensional reference interaction site model self-consistent field (3D-RISM-SCF) theory coupled with the linear fitting correction (LFC) scheme. In LFC/3D-RISM-SCF, pKa values of target molecules are evaluated using the Gibbs energy difference between the protonated and unprotonated states calculated by 3D-RISM-SCF and the parameters fitted by the LFC scheme to the experimental values of training set systems. The pKa values computed by LFC/3D-RISM-SCF show quantitative agreement with the experimental data.

Accurate Prediction of One-Electron Reduction Potentials in Aqueous Solution by Variable-Temperature H-Atom Addition/Abstraction Methodology

A robust and efficient theoretical approach for calculation of the reduction potentials of charged species in aqueous solution is presented. Within this approach, the reduction potential of a charged complex (with a charge |n| ≥ 2) is probed by means of the reduction potential of its neutralized (protonated/deprotonated) cognate, employing one or several H-atom addition/abstraction thermodynamic cycles. This includes a separation of one-electron reduction from protonation/deprotonation through the temperature dependence. The accuracy of the method has been assessed for the set of 15 transition-metal complexes that are considered as highly challenging systems for computational electrochemistry. Unlike the standard computational protocol(s), the presented approach yields results that are in excellent agreement with experimental electrochemical data. Last but not least, the applicability and limitations of the approach are thoroughly discussed.

A density functional theory protocol for the calculation of redox potentials of copper complexes

The calculated redox potentials of copper complexes agree nicely with their corresponding experimental redox potentials.

Inducing magnetic communication in caged dinuclear Co(ii) systems

Magnetic interactions were probed for a series of mono and tri atomic bridged dinuclear Co(ii) azacryptand complexes. Magneto-structural correlations were established usingab initiocalculations.

Computational electrochemistry: prediction of liquid-phase reduction potentials

This article reviews recent developments and applications in the area of computational electrochemistry. Our focus is on predicting the reduction potentials of electron transfer and other electrochemical reactions and half-reactions in both aqueous and nonaqueous solutions. Topics covered include various computational protocols that combine quantum mechanical electronic structure methods (such as density functional theory) with implicit-solvent models, explicit-solvent protocols that employ Monte Carlo or molecular dynamics simulations (for example, Car-Parrinello molecular dynamics using the grand canonical ensemble formalism), and the Marcus theory of electronic charge transfer. We also review computational approaches based on empirical relationships between molecular and electronic structure and electron transfer reactivity. The scope of the implicit-solvent protocols is emphasized, and the present status of the theory and future directions are outlined.