Accurate redox potentials of mononuclear iron, manganese, and nickel model complexes*

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.

Density functional theory and CCSD(T) evaluation of ionization potentials, redox potentials, and bond energies related to zirconocene polymerization catalysts

Quantum-mechanical-based computational design of molecular catalysts requires accurate and fast electronic structure calculations to determine and predict properties of transition-metal complexes. For Zr-based molecular complexes related to polyethylene catalysis, previous evaluation of density functional theory (DFT) and wavefunction methods only examined oxides and halides or select reaction barrier heights. In this work, we evaluate the performance of DFT against experimental redox potentials and bond dissociation enthalpies (BDEs) for zirconocene complexes directly relevant to ethylene polymerization catalysis. We also examined the ability of DFT to compute the fourth atomic ionization potential of zirconium and the effect the basis set selection has on the ionization potential computed with CCSD(T). Generally, the atomic ionization potential and redox potentials are very well reproduced by DFT, but we discovered relatively large deviations of DFT-calculated BDEs compared to experiment. However, evaluation of BDEs with CCSD(T) suggests that experimental values should be revisited, and our CCSD(T) values should be taken as most accurate.

Density function theory calculation to study the oxidation potential of electron-donating compounds; affirming the oxidation mechanism by NICS calculations

The manuscript describes a method for understanding the correlation of structural features and first oxidation potentials [Formula: see text] of electron-donating compounds (EDCs) with tetrathiafulvalene (TTF), dithiadiazafulvalenes (DTDAF), and tetraazafulvalene (TAF) frameworks. The density functional theory (DFT) procedure at B3LYP (6-31 + g(d)) was used for geometric optimization, given the large dimensions of the molecules studied, and their high structural similarity. First of all, the correlation between the oxidation potential and the highest occupied molecular orbital (HOMO) energy level as an effective quantum chemical descriptor was examined. Then, nucleus-independent chemical shifts (NICSs) calculation was applied to affirm the oxidation mechanism and interpret the effect of replacing the sulfur atoms by nitrogen, on the oxidation process. Finally, a more comprehensive investigation of structural features that affect the oxidation potential, topological, geometrical, constitutional, as well as, electrostatic, charged partial surface area, quantum-chemical, molecular orbital, and thermodynamic descriptors was calculated. A predictive model was developed based on the genetic algorithm multivariate linear regression (GA-MLR). There was an outstanding agreement between the theoretical and the experimental values obtained for the first oxidation potentials of the test set (Q²_Ext = 0.981).

Dimerization of [FeIII(bpy)3]3+ in Aqueous Solutions: Elucidating a Mechanism Based on Historical Proposals, Electrochemical Data, and Computational Free Energy Analysis

Iron(II) tris-bipyridine, [Fe^II(bpy)₃]²⁺, is a historically significant organometallic coordination complex with attractive redox and photophysical properties. With respect to energy storage, it is a low-cost, high-redox potential complex and thus attractive for use as a catholyte in aqueous redox flow batteries. Despite these favorable characteristics, its oxidized Fe(III) form undergoes dimerization to form μ-O-[Fe^III(bpy)₂(H₂O)]₂⁴⁺, leading to a dramatic ∼0.7 V decrease during battery discharge. To date, the energetics and complete mechanism of this slow, sequential electrochemical-chemical (EC) process, which includes electron transfer, nucleophilic attack, ligand cleavage, μ-oxo bond formation, and spin state transition, have not been elucidated. Using cyclic voltammetry, redox flow battery data, and density functional theory calculations guided by previously proposed mechanisms, we modeled more than 100 complexes and performed more than 50 geometry scans to resolve the key steps dictating these complex chemical processes. Quantitative free energy surfaces are developed to model the mechanism of dimerization accounting for the spins and identities of any possible Fe(II), Fe(III), or Fe(IV) intermediates. Electrochemical reduction of the dimer regenerates [Fe^II(bpy)₃]²⁺ in an overall reversible process. Computational electrochemistry interrogates the influence of spin state, coordination environment, and molecular conformation at the electrode-electrolyte interface through a proposed stepwise dimer reduction process. Experimentally, we show that the considerable overpotential associated with this event can be catalytically mitigated with disparate materials, including platinum, copper hexacyanoferrate, and activated carbon. The findings are of fundamental and applied significance and could elevate [Fe^II(bpy)₃]²⁺ and its derivatives to play a vital role in the burgeoning renewable energy economy.

A computational protocol for the calculation of the standard reduction potential of iron complexes: application to Fe2+/3+-Aβ model systems relevant to Alzheimer's disease

Iron complexes play a key role in several biological processes, and they are also related to the development of neurological disorders, such as Alzheimer's and Parkinson's diseases. One of the main properties involved in these processes is the standard reduction potential (SRP) of iron complexes. However, the calculation of this property is challenging, mainly due to problems in the electronic structure description, solvent effects and the thermodynamic cycles used for its calculation. In this work, we proposed a computational protocol for the calculation of SRPs of iron complexes by evaluating a wide range of density functionals for the electronic structure description, two implicit solvent models with varying radii and two thermodynamic cycles. Results show that the M06L density functional in combination with the SMD solvation model and the isodesmic method provides good results compared with SRP experimental values for a set of iron complexes. Finally, this protocol was applied to three Fe^2+/3+-Aβ model systems involved in the development of Alzheimer's disease and the obtained SRP values are in good agreement with those reported previously by means of MP2 calculations.

Iron complexes play a key role in the development of neurological disorders, such as Alzheimer's disease. We provide a computational protocol based on DFT for the calculation of standard reduction potentials of iron complexes relevant to Alzheimer's disease.

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.

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.

Copper(ii) thiosemicarbazone complexes induce marked ROS accumulation and promote nrf2-mediated antioxidant response in highly resistant breast cancer cells

A series of water-soluble sodium salts of 3-formyl-4-hydroxybenzenesulfonic acid thiosemicarbazones (or sodium 5-sulfonate-salicylaldehyde thiosemicarbazones) containing different substituents at the terminal nitrogen atom (H, Me, Et, Ph) and their copper(ii) complexes have been prepared and characterised by elemental analysis, spectroscopic techniques (IR, UV-vis, ¹H NMR), ESI mass spectrometry, X-ray crystallography and cyclic voltammetry. The proligands and their copper(ii) complexes exhibit moderate water solubility and good stability in aqueous environment, determined by investigating their proton dissociation and complex formation equilibria. The copper(ii) complexes showed moderate anticancer activity in established human cancer cell lines, while the proligands were devoid of cytotoxicity. The anticancer activity of the copper(ii) complexes correlates with their ability to induce ROS accumulation in cells, consistent with their redox potentials within the biological window, triggering the activation of antioxidation defense mechanisms in response to the ROS insult. These studies pave the way for the investigation of ROS-inducing copper(ii) complexes as prospective antiproliferative agents in cancer chemotherapy.

Terminal Electron-Proton Transfer Dynamics in the Quinone Reduction of Respiratory Complex I

Complex I functions as a redox-driven proton pump in aerobic respiratory chains. By reducing quinone (Q), complex I employs the free energy released in the process to thermodynamically drive proton pumping across its membrane domain. The initial Q reduction step plays a central role in activating the proton pumping machinery. In order to probe the energetics, dynamics, and molecular mechanism for the proton-coupled electron transfer process linked to the Q reduction, we employ here multiscale quantum and classical molecular simulations. We identify that both ubiquinone (UQ) and menaquinone (MQ) can form stacking and hydrogen-bonded interactions with the conserved Q-binding-site residue His-38 and that conformational changes between these binding modes modulate the Q redox potentials and the rate of electron transfer (eT) from the terminal N2 iron-sulfur center. We further observe that, while the transient formation of semiquinone is not proton-coupled, the second eT process couples to a semiconcerted proton uptake from conserved tyrosine (Tyr-87) and histidine (His-38) residues within the active site. Our calculations indicate that both UQ and MQ have low redox potentials around -260 and -230 mV, respectively, in the Q-binding site, respectively, suggesting that release of the Q toward the membrane is coupled to an energy transduction step that could thermodynamically drive proton pumping in complex I.

Theoretical investigation of low-valent uranium and transuranium complexes of a flexible small-cavity macrocycle: structural, formation reaction and redox properties

Size matching of a flexible macrocycle with low-valent actinide(III/IV) ions as well as their bonding determines different coordination modes.

Computing pK(A) values of hexa-aqua transition metal complexes

Aqueous pKA values for 15 hexa-aqua transition metal complexes were computed using a combination of quantum chemical and electrostatic methods. Two different structure models were considered optimizing the isolated complexes in vacuum or in presence of explicit solvent using a QM/MM approach. They yield very good agreement with experimentally measured pKA values with an overall root mean square deviation of about 1 pH unit, excluding a single but different outlier for each of the two structure models. These outliers are hexa-aqua Cr(III) for the vacuum and hexa-aqua Mn(III) for the QM/MM structure model. Reasons leading to the deviations of the outlier complexes are partially explained. Compared to previous approaches from the same lab the precision of the method was systematically improved as discussed in this study. The refined methods to obtain the appropriate geometries of the complexes, developed in this work, may allow also the computation of accurate pKA values for multicore transition metal complexes in different oxidation states.

Reprint of PSII manganese cluster: protonation of W2, O5, O4 and His337 in the S1 state explored by combined quantum chemical and electrostatic energy computations

Photosystem II (PSII) is a membrane-bound protein complex that oxidizes water to produce energized protons, which are used to built up a proton gradient across the thylakoidal membrane in the leafs of plants. This light-driven reaction is catalyzed by withdrawing electrons from the Mn₄CaO₅-cluster (Mn-cluster) in four discrete oxidation steps [S₁-(S₄/S₀)] characterized in the Kok-cycle. In order to understand in detail the proton release events and the subsequent translocation of such energized protons, the protonation pattern of the Mn-cluster need to be elucidated. The new high-resolution PSII crystal structure from Umena, Kawakami, Shen, and Kamiya is an excellent basis to make progress in solving this problem. Following our previous work on oxidation and protonation states of the Mn-cluster, in this work, quantum chemical/electrostatic calculations were performed in order to estimate the pKa of different protons of relevant groups and atoms of the Mn-cluster such as W2, O4, O5 and His337. In broad agreement with previous experimental and theoretical work, our data suggest that W2 and His337 are likely to be in hydroxyl and neutral form, respectively, O5 and O4 to be unprotonated. This article is part of a special issue entitled: photosynthesis research for sustainability: keys to produce clean energy.

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.

PSII manganese cluster: protonation of W2, O5, O4 and His337 in the S1 state explored by combined quantum chemical and electrostatic energy computations

Photosystem II (PSII) is a membrane-bound protein complex that oxidizes water to produce energized protons, which are used to built up a proton gradient across the thylakoidal membrane in the leafs of plants. This light-driven reaction is catalyzed by withdrawing electrons from the Mn₄CaO₅-cluster (Mn-cluster) in four discrete oxidation steps [S₁-(S₄/S₀)] characterized in the Kok-cycle. In order to understand in detail the proton release events and the subsequent translocation of such energized protons, the protonation pattern of the Mn-cluster need to be elucidated. The new high-resolution PSII crystal structure from Umena, Kawakami, Shen, and Kamiya is an excellent basis to make progress in solving this problem. Following our previous work on oxidation and protonation states of the Mn-cluster, in this work, quantum chemical/electrostatic calculations were performed in order to estimate the pKa of different protons of relevant groups and atoms of the Mn-cluster such as W2, O4, O5 and His337. In broad agreement with previous experimental and theoretical work, our data suggest that W2 and His337 are likely to be in hydroxyl and neutral form, respectively, O5 and O4 to be unprotonated. This article is part of a Special Issue entitled: Photosynthesis Research for Sustainability: Keys to Produce Clean Energy.

Quantum mechanical methods for the investigation of metalloproteins and related bioinorganic compounds

It is well known that transition metal ions are often bound to proteins, conveying very specific functional properties. In fact, metalloproteins play crucial biological roles in the transport and activation of small molecules such as H2, O2, and N2, as well as in several other biochemical processes. However, even if the presence of transition metals in the active site of proteins allows a very rich biochemistry, the experimental disclosure of structure-activity relationships in metalloproteins is generally difficult exactly because of the presence of transition metals, which are intrinsically characterized by a very versatile and often elusive chemistry. For this reason, computational methods are becoming very popular tools in the characterization of metalloproteins. In particular, since computing power is becoming less and less expensive, due to the continuous technological development of CPUs, the computational tools suited to investigate metalloproteins are becoming more accessible and therefore more commonly used also in molecular biology and biochemistry laboratories. Here, we present the main procedures and computational methods based on quantum mechanics, which are commonly used to study the structural, electronic, and reactivity properties of metalloproteins and related bioinspired compounds, with a specific focus on the practical and technical aspects that must be generally tackled to properly study such biomolecular systems.

Cobalt-porphyrin catalyzed electrochemical reduction of carbon dioxide in water. 2. Mechanism from first principles

We apply first principles computational techniques to analyze the two-electron, multistep, electrochemical reduction of CO(2) to CO in water using cobalt porphyrin as a catalyst. Density functional theory calculations with hybrid functionals and dielectric continuum solvation are used to determine the steps at which electrons are added. This information is corroborated with ab initio molecular dynamics simulations in an explicit aqueous environment which reveal the critical role of water in stabilizing a key intermediate formed by CO(2) bound to cobalt. By use of potential of mean force calculations, the intermediate is found to spontaneously accept a proton to form a carboxylate acid group at pH < 9.0, and the subsequent cleavage of a C-OH bond to form CO is exothermic and associated with a small free energy barrier. These predictions suggest that the proposed reaction mechanism is viable if electron transfer to the catalyst is sufficiently fast. The variation in cobalt ion charge and spin states during bond breaking, DFT+U treatment of cobalt 3d orbitals, and the need for computing electrochemical potentials are emphasized.

Study of Proton Coupled Electron Transfer in a Biomimetic Dimanganese Water Oxidation Catalyst with Terminal Water Ligands

The oxomanganese complex [H(2)O(terpy)Mn(III)(μ-O)(2)Mn(IV)(terpy)H(2)O](3+) (1, terpy = 2,2':6-2″-terpyridine) is a biomimetic model of the oxygen evolving complex of photosystem II with terminal water ligands. When bound to TiO(2) surfaces, 1 is activated by primary oxidants (e.g., Ce(4+)(aq), or oxone in acetate buffers) to catalyze the oxidation of water yielding O(2) evolution [G. Li et al. Energy Environ. Sci. 2, 230-238 (2009)]. The activation is thought to involve oxidation of the inorganic core [Mn(III)(μ-O)(2)Mn(IV)](3+) to generate the [Mn(IV)(μ-O)(2)Mn(IV)](4+) state 1(ox) first and then the highly reactive Mn oxyl species Mn(IV)O(•) through proton coupled electron transfer (PCET). Here, we investigate the step 1 → 1(ox) as compared to the analogous conversion in an oxomanganese complex without terminal water ligands, the [(bpy)(2) Mn (III) (μ-O)(2) Mn (IV) (bpy)(2)](3+) complex (2, bpy = 2,2'-bipyridyl). We characterize the oxidation in terms of free energy calculations of redox potentials and pKa's as directly compared to cyclic voltammogram measurements. We find that the pKa's of terminal water ligands depend strongly on the oxidation states of the Mn centers, changing by ~13 pH units (i.e., from 14 to 1) during the III, IV→IV, IV transition. Furthermore, we find that the oxidation potential of 1 is strongly dependent on pH (in contrast to the pH-independent redox potential of 2) as well as by coordination of Lewis base moieties (e.g., carboxylate groups) that competitively bind to Mn by exchange with terminal water ligands. The reported analysis of ligand binding free energies, pKa's and redox potentials indicates that the III, IV→IV, IV oxidation of 1 in the presence of acetate (AcO(-)) involves the following PCET: [H(2)O(terpy)Mn(III)(μ-O)(2)Mn(IV)(terpy)AcO](2+) → [HO(terpy)Mn(IV)(μ-O)(2)Mn(IV)(terpy)AcO](2+) + H(+) + e(-).

Characterization of proton coupled electron transfer in a biomimetic oxomanganese complex: Evaluation of the DFT B3LYP level of theory

The capabilities and limitations of the Becke-3-Lee-Yang-Parr (B3LYP) density functional theory (DFT) for modeling proton coupled electron transfer (PCET) in the mixed-valence oxomanganese complex 1 [(bpy)(2)Mn(III)(mu-O)(2)Mn(IV)(bpy)(2)](3+) (bpy = 2,2'-bipyridyl) are analyzed. Complex 1 serves as a prototypical synthetic model for studies of redox processes analogous to those responsible for water oxidation in the oxygen-evolving complex (OEC) of photosystem II (PSII). DFT B3LYP free energy calculations of redox potentials and pKa's are obtained according to the thermodynamic cycle formalism applied in conjunction with a continuum solvation model. We find that the pKa's of the oxo-ligands depend strongly on the oxidation states of the complex, changing by approximately 10 pH units (i.e., from pH~2 to pH~12) upon III,IV-->III,III reduction of complex 1. These computational results are consistent with the experimental pKa's determined by solution magnetic susceptibility and near-IR spectroscopy as well as with the pH dependence of the redox potential reported by cyclic voltammogram measurements, suggesting that the III,IV-->III,III reduction of complex 1 is coupled to protonation of the di-mu-oxo bridge as follows: [(bpy)(2)Mn(III)(mu-O)(2) Mn(IV)(bpy)(2)](3+)+H(+)+e(-)-->[(bpy)(2)Mn(III)(mu-O)(mu-OH)Mn(III)(bpy)(2)](3+). It is thus natural to expect that analogous redox processes might strongly modulate the pKa's of oxo and hydroxo/water ligands in the OEC of PSII, leading to deprotonation of the OEC upon oxidation state transitions.