Computational Redox Potential Predictions: Applications to Inorganic and Organic Aqueous Complexes, and Complexes Adsorbed to Mineral Surfaces

Prediction of Redox Potentials for U, Np, Pu, and Am in Aqueous Solution

The redox properties of the actinides in aqueous solution are important for fuel production/reprocessing and understanding the environmental impact of nuclear waste. The redox potentials for U, Np, Pu, and Am in oxidation states from 0 up to VII (as appropriate) in aqueous solutions have been predicted at the density functional theory level with the B3LYP functional, Stuttgart small core pseudopotential basis sets for the actinides, and explicit (30H2O molecules)/implicit treatment of the aqueous solvent using the self-consistent reaction field COSMO and SMD approaches for the implicit solvation. The predictions of the structural parameters of clusters incorporating first and second solvation shells are consistent with the available experimental data. Our results are typically within 0.2 V of the available experimental data using two explicit solvation shells with an implicit solvent model. The use of the PW91 functional substantially improved the prediction of the Pu(VI/V) redox couple. The redox couples for An(VI/IV) and An(V/IV) which involve the addition of protons and removal of the actinyl oxygens led to slightly larger differences from an experiment. The An(IV/0) and An(III/0) couples were reliably predicted with our approach. Predictions of the unknown An(II/I) redox potentials were negative, consistent with expectations, and predictions for unknown An(VII/VI), An(III/II), and An(II/0) redox couples improve prior estimates.

Unraveling redox pathways of the disulfide bond in dimethyl disulfide: Ab initio modeling

CONTEXT

In cellular environments, the reduction of disulfide bonds is pivotal for protein folding and synthesis. However, the intricate enzymatic mechanisms governing this process remain poorly understood. This study addresses this gap by investigating a disulfide bridge reduction reaction, serving as a model for comprehending electron and proton transfer in biological systems. Six potential mechanisms for reducing the dimethyl disulfide (DMDS) bridge through electron and proton capture were explored. Thermodynamic and kinetic analyses elucidated the sequence of proton and electron addition. MD-PMM, a method that combines molecular dynamics simulations and quantum-chemical calculations, was employed to compute the redox potential of the mechanism. This research provides valuable insights into the mechanisms and redox potentials involved in disulfide bridge reduction within proteins, offering an understanding of phenomena that are challenging to explore experimentally.

METHODS

All calculations used the Gaussian 09 software package at the MP2/6-311 + g(d,p) theory level. Visualization of the molecular orbitals and electron densities was conducted using Gaussview6. Molecular dynamics simulations were performed using GROMACS with the CHARMM36 force field. The PyMM program (Python Program for QM/MM Simulations Based on the Perturbed Matrix Method) is used to apply the Perturbed Matrix Method to MD simulations.

Mechanism of the Visible-Light-Promoted C(sp3)-H Oxidation via Uranyl Photocatalysis

Uranyl cation, as an emerging photocatalyst, has been successfully applied to synthetic chemistry in recent years and displayed remarkable catalytic ability under visible light. However, the molecular-level reaction mechanisms of uranyl photocatalysis are unclear. Here, we explore the mechanism of the stepwise benzylic C-H oxygenation of typical alkyl-substituted aromatics (i.e., toluene, ethylbenzene, and cumene) via uranyl photocatalysis using theoretical and experimental methods. Theoretical calculation results show that the most favorable reaction path for uranyl photocatalytic oxidation is as follows: first, hydrogen atom transfer (HAT) from the benzyl position to form a carbon radical ([R•]), then oxygen addition ([R•] + O2 → [ROO•]), then radical-radical combination ([ROO•] + [R•] → [ROOR] → 2[RO•]), and eventually [RO•] reduction to produce alcohols, of which 2° alcohol would further be oxidized to ketones and 1° would be stepwise-oxygenated to acids. The results of the designed verification experiments and the capture of reactive intermediates were consistent with those of theoretical calculations and the previously reported research that the active benzylic C-H would be stepwise-oxygenated in the presence of uranyl. This work deepens our understanding of the HAT mechanism of uranyl photocatalysis and provides important theoretical support for the relevant application of uranyl photocatalysts in organic transformation.

Two local minima for structures of [4Fe-4S] clusters obtained with density functional theory methods

[4Fe-4S] clusters are essential cofactors in many proteins involved in biological redox-active processes. Density functional theory (DFT) methods are widely used to study these clusters. Previous investigations have indicated that there exist two local minima for these clusters in proteins. We perform a detailed study of these minima in five proteins and two oxidation states, using combined quantum mechanical and molecular mechanical (QM/MM) methods. We show that one local minimum (L state) has longer Fe-Fe distances than the other (S state), and that the L state is more stable for all cases studied. We also show that some DFT methods may only obtain the L state, while others may obtain both states. Our work provides new insights into the structural diversity and stability of [4Fe-4S] clusters in proteins, and highlights the importance of reliable DFT methods and geometry optimization. We recommend r2SCAN for optimizing [4Fe-4S] clusters in proteins, which gives the most accurate structures for the five proteins studied.

Modified quantum mechanical approach for the estimation of single-electron reduction potential of nitroaromatic compounds in aqueous medium

The midpoint single-electron reduction potential of nitroaromatic compounds in aqueous medium at pH 7.0 (potential of ArNO₂/ArNO₂·^- couple, E_m7) frequently determines their therapeutic and/or toxic properties. However, its estimation remains a complex problem. We propose a modified method of E_m7 estimation by quantum mechanical calculations, based on the use of the dielectric continuum model together with a certain number of H₂O molecules at the vicinity of nitro group. The optimal number of H₂O molecules corresponds to a minimal difference between the experimentally determined and calculated values of E_m7, and/or the most negative value of calculated E_m7. This enabled us to calculate the E_m7 values for a number of ArNO₂ (n = 19) with the average deviation of 0.027 V from the experimentally determined ones. Apart from nitrobenzene derivatives, the application of this approach for the representatives of nitropyridines, nitrofurans, nitrothiophenes, and nitrothiazoles was demonstrated. In this case, nitroimidazole derivatives are an exception, evidently due to a strong proton accepting properties of N3 atom of their free radicals.

A Systematic Study on the Redox Potentials of Phenazine-Derivatives in Aqueous Media: A Combined Computational and Experimental Work

Phenazines are an emerging class of organic compounds that have been recently utilized in aqueous redox flow batteries, a promising technology for large-scale energy storage. A virtual screening based on density functional theory calculations is used to investigate the redox potentials of around 100 phenazine derivatives in aqueous media containing various electron-donating or electron-withdrawing groups at different positions. The calculations identify the crucial positions that should be functionalized with multiple hydroxy groups to design new anolytes. The combined experimental-computational methodology reported herein guides the development of a new molecule with a record low reversible redox potential as a potential anolyte for aqueous redox flow batteries.

Common Reactivity and Properties of Heme Peroxidases: A DFT Study of Their Origin

Electronic structure calculations using the density-functional theory (DFT) have been performed to analyse the effect of water molecules and protonation on the heme group of peroxidases in different redox (ferric, ferrous, compounds I and II) and spin states. Shared geometries, spectroscopic properties at the Soret region, and the thermodynamics of peroxidases are discussed. B3LYP and M06-2X density functionals with different basis sets were employed on a common molecular model of the active site (Fe-centred porphine and proximal imidazole). Computed Gibbs free energies indicate that the corresponding aquo complexes are not thermodynamically stable, supporting the five-coordinate Fe(III) centre in native ferric peroxidases, with a water molecule located at a non-bonding distance. Protonation of the ferryl oxygen of compound II is discussed in terms of thermodynamics, Fe-O bond distances, and redox properties. It is demonstrated that this protonation is necessary to account for the experimental data, and computed Gibbs free energies reveal pK_a values of compound II about 8.5-9.0. Computation indicates that the general oxidative properties of peroxidase intermediates, as well as their reactivity towards water and protons and Soret bands, are mainly controlled by the iron porphyrin and its proximal histidine ligand.

Benchmark Study of Redox Potential Calculations for Iron-Sulfur Clusters in Proteins

Redox potentials have been calculated for 12 different iron–sulfur sites of 6 different types with 1–4 iron ions. Structures were optimized with combined quantum mechanical and molecular mechanical (QM/MM) methods, and the redox potentials were calculated using the QM/MM energies, single-point QM methods in a continuum solvent or by QM/MM thermodynamic cycle perturbations. We show that the best results are obtained with a large QM system (∼300 atoms, but a smaller QM system, ∼150 atoms, can be used for the QM/MM geometry optimization) and a large value of the dielectric constant (80). For absolute redox potentials, the B3LYP density functional method gives better results than TPSS, and the results are improved with a larger basis set. However, for relative redox potentials, the opposite is true. The results are insensitive to the force field (charges of the surroundings) used for the QM/MM calculations or whether the protein and solvent outside the QM system are relaxed or kept fixed at the crystal structure. With the best approach for relative potentials, mean absolute and maximum deviations of 0.17 and 0.44 V, respectively, are obtained after removing a systematic error of −0.55 V. Such an approach can be used to identify the correct oxidation states involved in a certain redox reaction.

We have studied redox potentials of 12 iron−sulfur sites of 6 types with 1−4 iron ions. Structures were optimized with combined quantum mechanical and molecular mechanical (QM/MM) methods, and the redox potentials were calculated with QM/MM, QM calculations in a continuum solvent or by QM/MM thermodynamic cycle perturbations. The best results are obtained with the second approach using ∼300 atoms in the QM model and a large dielectric constant.

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.

Disproportionation of the Uranyl(V) Coordination Complexes in Aqueous Solution through Outer-Sphere Electron Transfer

Among the linear actinyl(VI/V) cations, the uranyl(V) species are particularly intriguing because they are unstable and exhibit a unique behavior to undergo H⁺ promoted disproportionation in aqueous solution and form stable uranyl(VI) and U(IV) complexes. This study uses density functional theory (DFT) combined with the conductor-like polarizable continuum model approach to investigate [UO₂]^2+/+ to [U^IVO₂] reduction free energies (RFEs) and explores the stability of uranyl(V) complexes in aqueous solution through computing disproportionation free energies (DFEs) for an outer-sphere electron transfer process. In addition to the aqua complex (U1), another three commonly encountered ligands such as chloride (U2), acetate (U3), and carbonate (U4) in aqueous environmental conditions are taken into account. For the U1 complex, the computed 1e^- (V/IV) and 2e^- (VI/IV) RFEs are in good agreement with experiments. The computed DFEs reveal that the presence of H⁺ is imperative for the disproportionation to take place. Although the presence of the alkali cations favors the disproportionation to some extent, they cannot fully make the reaction thermodynamically feasible. For the anionic complexes, the high negative charge does not allow for the formation of a cation-cation encounter complex due to Coulombic repulsion. Furthermore, an additional factor is the ligand exchange reaction which is also an energy-demanding step. Therefore, the current study examined the Kern-Orlemann mechanism and our results validate the mechanism based on DFT computed DFEs and propose that for the anionic complexes, an outer-sphere electron transfer is highly probable and our computed protonation free energies further support this claim.

Understanding the sorption behaviors of heavy metal ions in the interlayer and nanopore of montmorillonite: A molecular dynamics study

The molecular-scale adsorption mechanism of heavy metal ions in the interlayer and nanopore regions of montmorillonite (MMT) were investigated by molecular dynamics simulations. Three typical heavy metals (zinc, cadmium, and lead) were selected as the model ions, and two types of MMT (Arizona and Wyoming) were considered. The results showed that Cd²⁺ and Pb²⁺ can form both inner- and outer-sphere complexes on Wyoming MMT, while Zn²⁺ only formed outer-sphere complex due to the stronger hydration interaction of Zn²⁺ than Cd²⁺ and Pb²⁺. For Arizona MMT, all of the three ions only formed outer-sphere complexes on its interlayer and external basal surface in which the cations remained a fully hydrated state. The calculated diffusion coefficients of three cations in interlayer and nanopore indicated that their diffusion abilities were significantly impaired, implying that MMT adsorbents have a strong ability to fix and retard heavy metal ions. The derived results and mechanisms are instrumental to a profound understanding of the transport and retention of heavy metal elements in subsurface environments, and provide guidance for the management of heavy metal pollution.

Luminescent Cationic Group 4 Metallocene Complexes Stabilized by Pendant N-Donor Groups

Cationic group 4 metallocene complexes with pendant imine and pyridine donor groups were prepared as stable crystalline [B(C₆F₅)₄]^- salts either by protonation of the intramolecularly bound ketimide moiety in neutral complexes [(η⁵-C₅Me₅){η⁵-C₅H₄CMe₂CMe₂C(R)═N-κN}MCl] (M = Ti, Zr, Hf; R = t-Bu, Ph) by PhNMe₂H⁺[B(C₆F₅)₄]^- to give [(η⁵-C₅Me₅){η⁵-C₅H₄CMe₂CMe₂C(R)═NH-κN}MCl]⁺[B(C₆F₅)₄]^- or by chloride ligand abstraction from the complexes [(η⁵-C₅Me₅)(η⁵-C₅H₄CMe₂CH₂C₅H₄N)MCl₂] (M = Ti, Zr) by Li[B(C₆F₅)₄]·2.5Et₂O to give [(η⁵-C₅Me₅)(η⁵-C₅H₄CMe₂CH₂C₅H₄N-κN)MCl]⁺[B(C₆F₅)₄]^-. Solid state structures of the new compounds were established by X-ray diffraction analysis, and their electrochemical behavior was studied by cyclic voltammetry. The cationic complexes of Zr and Hf, compared to the corresponding neutral species, exhibited significantly enhanced luminescence predominantly from triplet ligand-to-metal (³LMCT) excited states with lifetimes up to 62 μs and quantum yields up to 58% in the solid state. DFT calculations were performed to explain the structural features and optical and electrochemical properties of the complexes.

Synthesis and Properties of Higher Nuclearity Polyazanes

Polyazanes (i.e., higher nuclearity homologues of hydrazines) with increasing numbers of bound nitrogen atoms (from 3 to 5), including the first pentazane ever described, were prepared by the addition of lower-order polyazanes to diazo reagents. A structure was obtained. It was shown that the polynitrogen chains adopt a helical conformation. DFT modeling shows that the arrangement persists in solution. Although the polyazanes are all reducing agents, they become less so as the number of nitrogens increases.

How the Ancillary Ligand X Drives the Redox Properties of Biscyclopentadienyl Pentavalent Uranium Cp2U(═N-Ar)X Complexes

Relativistic zero order regular approximation (ZORA) density functional theory computations, coupled with the conductor-like screening model for solvation effects, are used to investigate the redox properties of a series of biscyclopentadienyl pentavalent uranium(V) complexes Cp₂U(═N-Ar)X (Ar = 2,6-Me₂-C₆H₃; X = OTf, C₆F₅, SPh, C═CPh, NPh₂, Ph, Me, OPh, N(TMS)₂, N═CPh₂). Regarding the U^V/U^IV and U^VI/U^V couple systems, a linear correlation (R² ∼ 0.99) is obtained at the ZORA/BP86/TZP level, between the calculated ionization energies and the measured experimental E_1/2 half-wave oxidation potentials (U^VI/U^V) and between the electron affinities and the reduction potentials E_1/2 (U^V/U^IV). The study brings to light the importance of solvation effects that are needed in order to achieve a good agreement between the theory and experiment. Introducing spin-orbit coupling corrections slightly improves this agreement. Both the singly occupied molecular orbital and the lowest unoccupied molecular orbital of the neutral U^V complexes exhibit a majority 5f orbital character. The frontier molecular orbitals show a substantial ancillary ligand X σ and/or π character that drives the redox properties. Moreover, our investigations allow estimating the redox potentials of the X = Ph, X = C₆F₅, and N(TMS)₂ U^V complexes for which no experimental electrochemical data exist.

Mechanistic Insights into Co and Fe Quaterpyridine-Based CO2 Reduction Catalysts: Metal-Ligand Orbital Interaction as the Key Driving Force for Distinct Pathways

Both [Co^II(qpy)(H₂O)₂]²⁺ and [Fe^II(qpy)(H₂O)₂]²⁺ (with qpy = 2,2':6',2″:6'',2‴-quaterpyridine) are efficient homogeneous electrocatalysts and photoelectrocatalysts for the reduction of CO₂ to CO. The Co catalyst is more efficient in the electrochemical reduction, while the Fe catalyst is an excellent photoelectrocatalyst ( ACS Catal. 2018, 8, 3411-3417). This work uses density functional theory to shed light on the contrasting catalytic pathways. While both catalysts experience primarily ligand-based reductions, the second reduction in the Co catalyst is delocalized onto the metal via a metal-ligand bonding interaction, causing a spin transition and a distorted ligand framework. This orbital interaction explains the experimentally observed mild reduction potential and slow kinetics of the second reduction. The decreased hardness and doubly occupied d_z²-orbital facilitate a σ-bond with the CO₂-π* in an η¹-κC binding mode. CO₂ binding is only possible after two reductions resulting in an EEC mechanism (E = electron transfer, C = chemical reaction), and the second protonation is rate-limiting. In contrast, the Fe catalyst maintains a Lewis acidic metal center throughout the reduction process because the metal orbitals do not strongly mix with the qpy-π* orbitals. This allows binding of the activated CO₂ in an η²-binding mode. This interaction stabilizes the activated CO₂ via a π-type interaction of a Fe-t_2g orbital and the CO₂-π* and a dative bond of the oxygen lone pair. This facilitates CO₂ binding to a singly reduced catalyst resulting in an ECE mechanism. The barrier for CO₂ addition and the second protonation are higher than those for the Co catalyst and rate-limiting.

Theoretical determination of half-wave potentials for phenanthroline-, bipyridine-, acetylacetonate-, and glycinate-containing copper (II) complexes

We report a protocol for the evaluation of theoretical half-wave potential (E_1/2) using a set of 22 mixed chelate copper (II) complexes containing 1,10-phenanthroline and 2,2'-bipyridine derivatives as primary ligands, and acetylacetonate or glycinate as secondary ligands (formally from the Casiopeínas® family) for which accurate experimental values were determined in a 2/5 mixture of ethanol/water. We have calibrated the BP86, PBE, PBE0, B3LYP, M06-2X, and ω-B97XD functionals, using the Los Alamos LANL2DZ and Stuttgart-Köln SDDAll effective core potentials for the Cu and Fe atoms and the 6-311+G* basis set for the C, H, O, and N atoms. To address the solvent effects, we have saturated the first solvation shell with up to 9 water molecules for the explicit model and compared it with the Continuum Like-Polarizable Continuum Model (CPCM) implicit solvent scheme. We found that the PBE/LANL2DZ-6-311+G* protocol (with the CPCM implicit solvent scheme with an effective dielectric constant ε = 64.9121 for the 2/5 mixture of ethanol/water) yields the overall best performance. The theoretical values are compared with experimental data, three of which are reported here for the first time. We find good correlations between the theoretical and experimental E_1/2 values for the 2,2'-bipyridine derivatives (R² = 0.987, MAE = 86 mV) and 1,10-phenanthroline derivatives (R² = 0.802, MAE = 58.4 mV). The correlation trends have been explained in terms of the copper atom's ability to be reduced in the presence of the ligands. The Gibbs free energy differences at 298 K obtained for the redox reactions show that the more flexible secondary ligands (acetylacetonate) lead to larger entropic contributions which, as expected, increase the average MAE values as compared with the more rigid ligands (glycine). The present protocol yields lower MAEs as compared with previous approaches for similar mixed and flexible Cu(II) complexes.

Computational Insights on the Electrocatalytic Behavior of [Cp*Rh] Molecular Catalysts Immobilized on Graphene for Heterogeneous Hydrogen Evolution Reaction

The heterogeneous metal-based molecular electrocatalyst can typically exhibit attractive features compared to its homogeneous analogue including recoverability and durability. As such, it is necessary to evaluate the electrocatalytic behavior of heterogenized molecular catalysts of interest toward gaining insights concerning the retainability of such behaviors while benefiting from heterogenization. In this work, we examined computationally the electrochemical properties of nanographene-based heterogenized molecular complexes of Rhodium. We assessed, as well, the electrocatalytic behavior of the heterogenized molecular catalyst for hydrogen evolution reaction (HER). Two electrochemical pathways were examined, namely one- and two-electron electrochemical reduction pathways. Interestingly, it is computationally demonstrated that [Rh^III(Cp*)(phen)Cl]⁺-Gr can exhibit redox and electrocatalytic properties for HER that are comparable to its homogeneous analogue via a two-electron reduction pathway. On the other hand, the one-electron reduction pathway is notably found to be less favorable kinetically and thermodynamically. Furthermore, molecular insights are provided with respect to the HER employing molecular orbitals analyses and mechanistic aspects. Importantly, our findings may provide insights toward designing more efficient graphene-based molecular heterogeneous electrocatalysts for more efficient energy production.

Uranyl-Bound Tetra-Dentate Non-Innocent Ligands: Prediction of Structure and Redox Behaviour Using Density Functional Theory

Computational methods have been applied to understand the reduction potentials of [UO₂ -salmnt-L] complexes (L=pyridine, DMSO, DMF and TPPO), and their redox behavior is compared with previous experiments in dichloromethane solution. Since the experimental results were inconclusive regarding the influence of the uranyl-bound tetra-dentate 'salmnt' ligand, here we will show that salmnt acts as a redox-active ligand and exhibits non-innocent behavior to interfere with the otherwise expected one-electron metal (U) reduction. We have employed two approaches to determine the uranyl (VI/V) reduction potentials, using a direct study of one-electron reduction processes and an estimation of the overall reduction using isodesmic reactions. Hybrid density functional theory (DFT) methods were combined with the Conductor-like Polarizable Continuum Model (CPCM) to account for solvation effects. The computationally predicted one-electron reduction potentials for the range of [UO₂ -salmnt-L] complexes are in excellent agreement with shoulder peaks (∼1.4 eV) observed in the cyclic voltammetry experiments and clearly correlate with ligand reduction. Highly conjugated pi-bonds stabilize the ligand based delocalized orbital relative to the localized U f-orbitals, and as a consequence, the ligand traps the incoming electron. A second reduction step results in metal U(VI) to U(V) reduction, in good agreement with the experimentally assigned uranyl (VI/V) reduction potentials.

The basis for reevaluating the reactivity of pyrite surfaces: spin states and crystal field d-orbital splitting energies of bulk, terrace, edge, and corner Fe(ii) ions

Pyrite, one of the most important minerals to catalyze redox reactions in nature and a bulk low-spin Fe mineral, needs to provide high-spin Fe on surfaces to moderate spin-forbidden transitions. Here, the spin state of pyrite is investigated using density functional theory (DFT) calculations on cluster and periodic models. The energies of clusters FexS2x (where x = 4, 8, 16, and 32) were calculated as a function of total spin and different up/down spin configurations. The undercoordinated Fe on surfaces, edges, and corners were found to provide intermediate and high-spin Fe necessary for catalysis. Generally, the lower the crystal field splitting energy (CFSE), Δ, for a particular Fe atom, the higher is the spin density. Pyrite bulk (3D) and surfaces (2D) (+ water to mimic aqueous systems) were examined. The calculated bulk band gap (0.95 eV) is in excellent agreement with previous reports. For the surface, a conducting state is predicted. The calculated CFSE for bulk Fe(ii) in pyrite (∼2.2 eV) agrees with previous CFT results; due to surface states, this CFSE decreases to ∼1 eV on terraces. This study highlights the importance of accurately describing the spin state of pyrite.

Unveiling the relative stability and proton binding of non-classical Wells-Dawson isomers of [(NaF6)W18O54(OH)2]7- and [(SbO6)W18O54(OH)2]9-: a DFT study

Density functional theory calculations combined with the energy and building-block decomposition analyses have been carried out to investigate the structures, stability orders, redox potentials and proton binding of the six Baker-Figgis isomers (α, β, γ, α*, β* and γ*) of [(SbO₆)W₁₈O₅₄(OH)₂]^9- {H₂SbW₁₈} and [(NaF₆)W₁₈O₅₄(OH)₂]^7- {H₂NaW₁₈} anions at the level of PBEsol-D3/TZP. Both bonding energy and Gibbs free energy analyses exhibit that the two non-classical Wells-Dawson (WD) species behave quite differently from each other. The pyroanimonate {H₂SbW₁₈}, with a stability order of γ* > β* > α > α* > β > γ, is a non-classical WD species, while the hexafluoride {H₂NaW₁₈} (α > β > γ > γ* > β* > α*) is a transition intermediate between classical and non-classical WD types, possessing both non-classical ([XW₁₈O₆₀(OH)₂]^n-, X = I, Te and W) and classical [Si₂W₁₈O₆₂]^8- properties. Energy decomposition analyses (EDA) reveal that spatial arrangement (E_host), host-guest fragment interaction energy (FIE), and structural distortion energy (DE) are three key factors governing the relative stability of isomers; among these, DE is always dominant, while FIE and E_host are subordinated but are still important. Building-block decomposition analyses (BDA) disclose that the octahedral {MO₆} units of the equatorial belt, particularly the staggered belt, are always more distorted than those of the two polar caps inside each structure. The theoretical redox potentials demonstrate that the oxidizing power increases with a trend of α < β < γ and α* < β* < γ* for both species, and the first redox potential is closely related to the energy level of the LUMO of each anion. Evaluation of the proton inclusion energies suggests that {H₂NaW₁₈} can only embed two protons, while {H₂SbW₁₈} may encapsulate four; the number of embedded protons is controlled by both the charge of the heteroatom X and the volume of the tetrahedral {O₄}/{OF₃} cavity.

Predicting reduction potentials of 1,3,6-triphenyl fulvenes using molecular electrostatic potential analysis of substituent effects

The influence of mono- and multiple substituent effect on the reduction potential (E⁰ ) of 1,3,6-triphenyl fulvenes is investigated using B3LYP-SMD/6-311+G(d,p) level density functional theory. The molecular electrostatic potential (MESP) minimum at the fulvene π-system (V_min ) and the change in MESP at any of the fulvene carbon atoms (ΔV_C ) for both neutral and reduced forms are used as excellent measures of substituent effect from the para and meta positions of the 1,3 and 6-phenyl moieties. Substitution at 6-phenyl para position has led to significant change in E⁰ than any other positions. By applying the additivity rule of substituent effects, an equation in ΔV_C is derived to predict E⁰ for multiply substituted fulvenes. Further, E⁰ is predicted for a set of 2000 hexa-substituted fulvene derivatives where the substituents and their positions in the system are chosen in a random way. The calculated E⁰ agreed very well with the experimental E⁰ reported by Godman et al. Predicting E⁰ solely by substituent effect offers a simple and powerful way to select suitable combinations of substituents on fulvene system for light harvesting applications. © 2018 Wiley Periodicals, Inc.

Electronic effect of ligands vs. reduction potentials of Fischer carbene complexes of chromium: a molecular electrostatic potential analysis

Molecular electrostatic potential at the chromium centre (V_Cr) emerges as a powerful predictor of reduction potential (E⁰).

Assessment of the isodesmic method in the calculation of standard reduction potential of copper complexes

Molecular phenomena involving electron transfer and reduction/oxidation processes are of the utmost importance in chemistry. However, accurate computational calculations of standard reduction potentials (SRPs) for transition metal complexes are still challenging. For this reason, some computational strategies have been proposed in order to overcome the main limitations in SRP calculations for copper complexes. However, these strategies are limited to particular coordination spheres and do not represent a general methodology. In this work, we present standard reduction potential calculations for copper complexes in aqueous solution covering a wide range of coordination spheres. These calculations were performed using the M06-2X density functional, and by employing the direct and isodesmic approaches. Result analysis reveals that values obtained with the use of the isodesmic method are in better agreement with experimental values than those obtained from the direct method (mean unsigned error 0.39 V with the direct and 0.08 V with the isodesmic method). This approach provides values with errors comparable to the experimental uncertainty due to the proper cancellation of computational errors. These results strongly suggest the isodesmic approach as an adequate methodology for the calculation of SRPs for copper complexes with diverse coordination spheres. Graphical Abstract Comparison between direct and isodesmic methods in the calculation of standard reduction potentials for copper complexes using DFT methods.

Intermolecular hydrogen bonds between 1,4-benzoquinones and HF molecule: Synergetic effects, reduction potentials and electron affinities

Some biological activities of quinones can be attributed to the H-bonding ability of acceptor oxygen atoms. According to the results obtained from the quantum mechanical calculations performed on a wide variety of complexes between the 1,4-benzoquinone (BQ) derivatives and HF molecules, the interplay between H-bonds and individual H-bond interaction energies (E_HB) can be affected by the substituents placed on the six-membered ring of BQ. The total binding energies of complexes become more negative by the electron donating substituents (EDSs) while the changes are reversed by the electron withdrawing substituents (EWSs). The mutual interplay between the X-BQ⋯(HF)_n (n=1-3) interactions has been investigated using the geometrical parameters, synergetic energies (SE) and the E_HB values. Hydrogen bonding decreases the reduction potentials (E⁰_red) and increases the electron affinities (EA) of X-BQ derivatives. Linear relationships have been observed between the E⁰_red (and EA) values and the Hammett constants of substituents.

Redox trends in cyclometalated palladium(ii) complexes

Electrochemical and DFT studies on palladacycles revealed an increase in the metal–metal distance in the complexes leads to higher oxidation potentials.

Ionization Energies and Aqueous Redox Potentials of Organic Molecules: Comparison of DFT, Correlated ab Initio Theory and Pair Natural Orbital Approaches

The calculation of redox potentials involves large energetic terms arising from gas phase ionization energies, thermodynamic contributions, and solvation energies of the reduced and oxidized species. In this work we study the performance of a wide range of wave function and density functional theory methods for the prediction of ionization energies and aqueous one-electron oxidation potentials of a set of 19 organic molecules. Emphasis is placed on evaluating methods that employ the computationally efficient local pair natural orbital (LPNO) approach, as well as several implementations of coupled cluster theory and explicitly correlated F12 methods. The electronic energies are combined with implicit solvation models for the solvation energies. With the exception of MP2 and its variants, which suffer from enormous errors arising at least partially from the poor Hartree-Fock reference, ionization energies can be systematically predicted with average errors below 0.1 eV for most of the correlated wave function based methods studies here, provided basis set extrapolation is performed. LPNO methods are the most efficient way to achieve this type of accuracy. DFT methods show in general larger errors and suffer from inconsistent behavior. The only exception is the M06-2X functional which is found to be competitive with the best LPNO-based approaches for ionization energies. Importantly, the limiting factor for the calculation of accurate redox potentials is the solvation energy. The errors in the predicted solvation energies by all continuum solvation models tested in this work dominate the final computed reduction potential, resulting in average errors typically in excess of 0.3 V and hence obscuring the gains that arise from choosing a more accurate electronic structure method.

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.

Electronegativity and redox reactions

Using the maximum hardness principle, we show that the oxidation potential of a molecule increases as its electronegativity increases and also increases as its electronegativity in its oxidized state increases.

Acidity constants and redox potentials of uranyl ions in hydrothermal solutions

We report a first principles molecular dynamics (FPMD) study of the structures, acidity constants (pK_a) and redox potentials (E⁰) of uranyl (UO₂²⁺) from ambient conditions to 573 K.

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.

Electrochemical analyses of redox-active iron minerals: a review of nonmediated and mediated approaches

Redox-active minerals are ubiquitous in the environment and are involved in numerous electron transfer reactions that significantly affect biogeochemical processes and cycles as well as pollutant dynamics. As a consequence, research in different scientific disciplines is devoted to elucidating the redox properties and reactivities of minerals. This review focuses on the characterization of mineral redox properties using electrochemical approaches from an applied (bio)geochemical and environmental analytical chemistry perspective. Establishing redox equilibria between the minerals and working electrodes is a major challenge in electrochemical measurements, which we discuss in an overview of traditional electrochemical techniques. These issues can be overcome with mediated electrochemical analyses in which dissolved redox mediators are used to increase the rate of electron transfer and to facilitate redox equilibration between working electrodes and minerals in both amperometric and potentiometric measurements. Using experimental data on an iron-bearing clay mineral, we illustrate how mediated electrochemical analyses can be employed to derive important thermodynamic and kinetic data on electron transfer to and from structural iron. We summarize anticipated methodological advancements that will further contribute to advance an improved understanding of electron transfer to and from minerals in environmentally relevant redox processes.

DFT study of the active site of the XoxF-type natural, cerium-dependent methanol dehydrogenase enzyme

Rare-earth metal cations have recently been demonstrated to be essential co-factors for the growth of the methanotrophic bacterium Methylacidiphilum fumariolicum SolV. A crystal structure of the rare-earth-dependent methanol dehydrogenase (MDH) includes a cerium cation in the active site. Herein, the Ce-MDH active site has been analyzed through DFT calculations. The results show the stability of the Ce(III)-pyrroloquinoline quinone (PQQ) semiquinone configuration. Calculations on the active oxidized form of this complex indicate a 0.81 eV stabilization of the PQQ(0) LUMO at cerium versus calcium, supporting the observation that the cerium cation in the active site confers a competitive advantage to Methylacidiphilum fumariolicum SolV. Using reported aqueous electrochemical data, a semi-empirical correlation was established based on cerium(IV/III) redox potentials. The correlation allowed estimation of the cerium oxidation potential of +1.35 V versus saturated calomel electrode (SCE) in the active site. The results are expected to guide the design of functional model complexes and alcohol-oxidation catalysts based on lanthanide complexes of biologically relevant quinones.