Calculation Of Redox Potentials Research Articles

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

A density functional theory (DFT) protocol for the calculation of redox potentials of copper complexes is developed based on 13 model copper complexes. The redox potentials are calculated in terms of Gibbs free energy change of the redox reaction at the theory level of CAM-B3LYP/6-31+G(d,p)/SMD, with the overall Gibbs free energy change being partitioned into the Gibbs free energy change of the gas phase reaction and the Gibbs free energy change of solvation. In addition, the calculated Gibbs free energy change of solvation is corrected by a unified correction factor of -0.258 eV as the second-layer Gibbs free energy change of solvation and other interactions for each redox reaction. And an empirical Gibbs free energy change of solvation at -0.348 eV is applied to each water molecule if the number of inner-sphere water molecule changes during the redox reaction. Satisfactory agreements between the DFT calculated and experimental results are obtained, with a maximum absolute error at 0.197 V, a mean absolute error at 0.114 V and a standard deviation at 0.133 V. Finally, it is concluded that the accurate prediction of redox potentials is dependent on the accurate prediction of geometrical structures as well as on geometrical conservation during the redox reaction.

A High-Speed Screening Method by Combining a High-Throughput Method and a Machine-Learning Algorithm for Developing Novel Organic Electrolytes in Rechargeable Batteries

A high-speed screening method was established by combining a high-throughput quantum simulation (HT) with a machine learning algorithm (ML), which is named as MAssive Molecular Map BUilder (MAMMBU). For the applications to high-voltage rechargeable batteries, the MAMMBU was applied to screen organic electrolytes based on redox potential calculations. The HT-method consists of the automatic input generator from existing organic compound database, error correction, and job scheduler. In the ML-method, the computational results of redox potentials for organic compounds obtained from HT were used as training and test data for an artificial neural network. This MAMMBU was targeted for building redox potentials map based on whole organic compounds database, such as PubChem, and finding novel organic electrolytes with the new types of cores, substituents, and functional groups. This will be possible by remarkable reducing time to predict redox potentials from several hours for quantum calculations to several seconds for the ML-method in MAMMBU.

Why many semiempirical molecular orbital theories fail for liquid water and how to fix them.

Water is an extremely important liquid for chemistry and the search for more accurate force fields for liquid water continues unabated. Neglect of diatomic differential overlap (NDDO) molecular orbital methods provide and intriguing generalization of classical force fields in this regard because they can account both for bond breaking and electronic polarization of molecules. However, we show that most standard NDDO methods fail for water because they give an incorrect description of hydrogen bonding, water's key structural feature. Using force matching, we design a reparameterized NDDO model and find that it qualitatively reproduces the experimental radial distribution function of water, as well as various monomer, dimer, and bulk properties that PM6 does not. This suggests that the apparent limitations of NDDO models are primarily due to poor parameterization and not to the NDDO approximations themselves. Finally, we identify the physical parameters that most influence the condensed phase properties. These results help to elucidate the chemistry that a semiempirical molecular orbital picture of water must capture. We conclude that properly parameterized NDDO models could be useful for simulations that require electronically detailed explicit solvent, including the calculation of redox potentials and simulation of charge transfer and photochemistry.

A method to calculate redox potentials relative to the normal hydrogen electrode in nonaqueous solution by using density functional theory-based molecular dynamics.

We demonstrate the redox potential calculation relative to the normal hydrogen electrode (NHE) in nonaqueous solution using a density functional theory-based molecular dynamics (DFT-MD) simulation. The calculation of the NHE in nonaqueous solution consists of two processes: the first step is the equilibrated simulation for a proton in nonaqueous solution to determine the space for inserting a proton in solution, and the second step is the thermodynamic integration method to calculate the solvation energy of the proton in the nonaqueous solution. In this work, we apply the method for a cation and an anion, i.e., copper(ii)/copper(i) and iodine/iodide in acetonitrile solution, and show that the errors in the calculated redox potential from experiments are within 0.21 V.

Redox potentials and acidity constants from density functional theory based molecular dynamics.

CONSPECTUS: All-atom methods treat solute and solvent at the same level of electronic structure theory and statistical mechanics. All-atom computation of acidity constants (pKa) and redox potentials is still a challenge. In this Account, we review such a method combining density functional theory based molecular dynamics (DFTMD) and free energy perturbation (FEP) methods. The key computational tool is a FEP based method for reversible insertion of a proton or electron in a periodic DFTMD model system. The free energy of insertion (work function) is computed by thermodynamic integration of vertical energy gaps obtained from total energy differences. The problem of the loss of a physical reference for ionization energies under periodic boundary conditions is solved by comparing with the proton work function computed for the same supercell. The scheme acts as a computational hydrogen electrode, and the DFTMD redox energies can be directly compared with experimental redox potentials. Consistent with the closed shell nature of acid dissociation, pKa estimates computed using the proton insertion/removal scheme are found to be significantly more accurate than the redox potential calculations. This enables us to separate the DFT error from other sources of uncertainty such as finite system size and sampling errors. Drawing an analogy with charged defects in solids, we trace the error in redox potentials back to underestimation of the energy gap of the extended states of the solvent. Accordingly the improvement in the redox potential as calculated by hybrid functionals is explained as a consequence of the opening up of the bandgap by the Hartree-Fock exchange component in hybrids. Test calculations for a number of small inorganic and organic molecules show that the hybrid functional implementation of our method can reproduce acidity constants with an uncertainty of 1-2 pKa units (0.1 eV). The error for redox potentials is in the order of 0.2 V.

Calculations of pKa's and redox potentials of nucleobases with explicit waters and polarizable continuum solvation.

The SMD implicit solvation model augmented with one and four explicit water molecules was used to calculate pKa's and redox potentials of N-methyl-substituted nucleic acid bases guanine, adenine, cytosine, thymine, and uracil. Calculations were carried out with the B3LYP/6-31+G(d,p) level of theory. The same numbers of water molecules were hydrogen bonded to the neutral, protonated, and deprotonated nucleobases in their unoxidized and oxidized forms. The improvement in pKa1 involving neutrals and cations was modest. By contrast, the improvement in pKa2 involving neutrals and anions was quite significant, reducing the mean absolute error from 4.6 pKa units with no waters, to 2.6 with one water and 1.7 with four waters. For the oxidation of nucleobases, adding explicit waters did little to improve E(X(•),H(+)/XH), possibly because both species in the redox couple are neutral molecules at pH 7.

Reduction of U(VI) by Fe(II) during the Fe(II)-accelerated transformation of ferrihydrite.

X-ray absorption spectroscopy has been used to study the reduction of adsorbed U(VI) during the Fe(II)-accelerated transformation of ferrihydrite to goethite. The fate of U(VI) was examined across a variety of pH values and Fe(II) concentrations, with results suggesting that, in all cases, it was reduced over the course of the Fe(III) phase transformation to a U(V) species incorporated in goethite. A positive correlation between U(VI) reduction and ferrihydrite transformation rate constants implies that U(VI) reduction was driven by the production of goethite under the conditions used in these studies. This interpretation was supported by additional experimental evidence that demonstrated the (fast) reduction of U(VI) to U(V) by Fe(II) in the presence of goethite only. Theoretical redox potential calculations clearly indicate that the reduction of U(VI) by Fe(II) in the presence of goethite is thermodynamically favorable. In contrast, reduction of U(VI) by Fe(II) in the presence of ferrihydrite is largely thermodynamically unfavorable within the range of conditions examined in this study.

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

Applications of redox processes range over a number of scientific fields. This review article summarizes the theory behind the calculation of redox potentials in solution for species such as organic compounds, inorganic complexes, actinides, battery materials, and mineral surface-bound-species. Different computational approaches to predict and determine redox potentials of electron transitions are discussed along with their respective pros and cons for the prediction of redox potentials. Subsequently, recommendations are made for certain necessary computational settings required for accurate calculation of redox potentials. This article reviews the importance of computational parameters, such as basis sets, density functional theory (DFT) functionals, and relativistic approaches and the role that physicochemical processes play on the shift of redox potentials, such as hydration or spin orbit coupling, and will aid in finding suitable combinations of approaches for different chemical and geochemical applications. Identifying cost-effective and credible computational approaches is essential to benchmark redox potential calculations against experiments. Once a good theoretical approach is found to model the chemistry and thermodynamics of the redox and electron transfer process, this knowledge can be incorporated into models of more complex reaction mechanisms that include diffusion in the solute, surface diffusion, and dehydration, to name a few. This knowledge is important to fully understand the nature of redox processes be it a geochemical process that dictates natural redox reactions or one that is being used for the optimization of a chemical process in industry. In addition, it will help identify materials that will be useful to design catalytic redox agents, to come up with materials to be used for batteries and photovoltaic processes, and to identify new and improved remediation strategies in environmental engineering, for example the reduction of actinides and their subsequent immobilization. Highly under-investigated is the role of redox-active semiconducting mineral surfaces as catalysts for promoting natural redox processes. Such knowledge is crucial to derive process-oriented mechanisms, kinetics, and rate laws for inorganic and organic redox processes in nature. In addition, molecular-level details still need to be explored and understood to plan for safer disposal of hazardous materials. In light of this, we include new research on the effect of iron-sulfide mineral surfaces, such as pyrite and mackinawite, on the redox chemistry of actinyl aqua complexes in aqueous solution.

Probing DNA photocleavage efficiencies of Ru(II) polypyridyl complexes: Theoretical calculation of redox potentials

Theoretical studies on DNA-photocleavage efficiencies of Ru(II) polypyridyl complexes 1–4 have been carried out using the density functional theory (DFT) method. First, the redox potentials of Ru(II) polypyridyl complex were computed using different functionals. Secondly, the redox potentials of complexes 1–4 in the excited state were accurately computed. Finally, the trend in DNA-photocleavage efficiencies (φ) of complexes 1–4, i.e., φ (4)>φ (3)>φ (2)>φ (1), were reasonably explained by the excited-state reduction potentials. In particular, the DNA-photocleavage efficiency of a new Ru(II) complex 4 was predicted.

On the photostationary state of the flavylium network of chemical reactions

Abstract Calculation of the quantum yields from the photostationary state, in the cases where the thermal back reaction competes efficiently with the photoproducts formation is described. The system can be mathematically treated as a single equilibrium involving two opposite reactions, one driven by light of constant intensity and the other due to the thermal back reaction. By analogy with excited state redox potential calculations, the photostationary state can be defined by a constant, which is function of the number of absorbed photons by the cis and trans forms, the respective reaction quantum yields, the light intensity, irradiated volume, as well the rates of the thermal forward and backward thermal reactions (in the absence of light). Application of this concept to the flavylium network of chemical reactions is presented. The model compound 4′,7-dihydroxyflavylium was used to test the model.

Redox Reaction Mechanisms with Non-Triiodide Mediators in Dye-Sensitized Solar Cells by Redox Potential Calculations

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Comparison of pure and hybrid DFT functionals for geometry optimization and calculation of redox potentials for iron nitrosyl complexes with “μ-SCN” bridging ligands

The geometry and electronic structure of neutral molecules and mono-anions of iron nitrosyl complexes with “µ-SCN” bridging ligands [(¼-SC7H4SN)Fe(NO)2]2 (I) and [(µ-SC2H3N4)Fe(NO)2]2 (II) were studied using the density functional theory: pure functionals BP86, OLYP, OPBE, TPSS, PW91 and hybrid functionals B3LYP, B1B95, B3PW91 along with 6-311++G**//6-31G*. For geometry optimization, the pure functionals are more appropriate than the hybrid functionals. For mono-anions, pure functionals favor the doublet over the quartet state by 8.0–13.9 kcal/ mol, whereas hybrid functionals yield quartet spin state of these anions to be more stable. The redox potentials of complexes I and II have been computed by DFT and compared with experimental results obtained from cyclic voltammetry method. The calculated redox potentials for I and II with pure functionals (especially BP86) are close to the experimental values, whereas those obtained by using hybrid functionals significantly deviate from the experiment.

Redox Reaction Mechanisms with Non-triiodide Mediators in Dye-Sensitized Solar Cells by Redox Potential Calculations.

We investigate reaction mechanisms of the redox mediators in dye-sensitized solar cells through systematic calculations of redox potentials of possible cobalt complexes and iodides in acetonitrile solution by use of the thermodynamic cycle method with continuum solvent model. The calculated redox potentials were in good agreement with the experimental values, although the experimentalists used different reference electrodes. The maximum open circuit voltage (VOC) of the mediators calculated in this work indicate that the I2(•-)/2I(-) and I2/I2(•-) as well as the net I2/2I(-) redox reactions can dominate at both photoanode and counter-electrode.

Reduction of Systematic Uncertainty in DFT Redox Potentials of Transition-Metal Complexes

Reliable calculations of redox potentials could provide valuable insight into catalytic mechanisms of electrochemically active transition-metal complexes as well as guidelines for the design of new electrocatalysts. However, the correlation between theoretical and experimental data is often uncertain, since redox properties depend strongly on experimental conditions of electrochemical measurements, including the nature of the solvent, electrolyte, and working electrode. Here, we show that the use of internal references allows for quantitative theoretical predictions of redox potentials with standard deviations σ comparable to typical experimental errors of cyclic voltammetry measurements. Agreement for first-, second-, and third-row transition-metal complexes is demonstrated even at a rather modest level of density functional theory (σ = 64 mV for the UB3LYP/6-311G* level). This is shown for a series of benchmark redox couples, including ([MCp2]0/+ (Cp = η5-cyclopentadienyl), [MCp*2]0/+ (Cp* = η5-1,2,3,4,5-pentamethylcyclopentadienyl), [M(bpy)3]2+/3+ (bpy =2,2′-bipyridine), and [Ir(acac)3]0/+ (acac = acetylacetonate), with M = Fe, Co, Ni, Ru, Os, or Ir) in various nonaqueous solvents [acetonitrile (MeCN), dimethyl sulfoxide (DMSO), and dichloromethane (DCM)].

Computational Electrochemistry Study of 16 Isoindole-4,7-diones as Candidates for Organic Cathode Materials

Prediction of the redox behavior of electroactive molecules enables screening of a variety of compounds and can serve as a guideline in the search for organic molecules for use as cathode materials in, for example, Li ion batteries. In this study, we present a computational strategy, based on density functional theory, to calculate redox potentials and acid dissociation constants for a series of 16 isoindole-4,7-dione (IID) derivatives. The calculations take all possible electron and proton transfers into account, and the results were found to correlate very well with electrochemical and spectroscopic measurements. The possibility of polymerizing the IID derivatives was also assessed computationally, as polymerization serves as a straightforward route to immobilize the active material. Three of the considered IIDs (5,6-dicyano-2-methyl-isoindole-4,7-dione, 5,6-dihydroxy-2-methyl-isoindole-4,7-dione, and 2-methyl-5-(trifluoromethyl)-isoindole-4,7-dione) are predicted to be particularly interesting for maki...

DFT calculations for intermediate and active states of the diiron center with a tryptophan or tyrosine radical in Escherichia coli ribonucleotide reductase.

Class Ia ribonucleotide reductase subunit R2 contains a diiron active site. In this paper, active-site models for the intermediate X-Trp48(•+) and X-Tyr122(•), the active Fe(III)Fe(III)-Tyr122(•), and the met Fe(III)Fe(III) states of Escherichia coli R2 are studied, using broken-symmetry density functional theory incorporated with the conductor-like screening solvation model. Different structural isomers and different protonation states have been explored. Calculated geometric, energetic, Mössbauer, hyperfine, and redox properties are compared with available experimental data. Feasible detailed structures of these intermediate and active states are proposed. Asp84 and Trp48 are most likely the main contributing residues to the result that the transient Fe(IV)Fe(IV) state is not observed in wild-type class Ia E. coli R2. Asp84 is proposed to serve as a proton-transfer conduit between the diiron cluster and Tyr122 in both the tyrosine radical activation pathway and the first steps of the catalytic proton-coupled electron-transfer pathway. Proton-coupled and simple redox potential calculations show that the kinetic control of proton transfer to Tyr122(•) plays a critical role in preventing reduction from the active Fe(III)Fe(III)-Tyr122(•) state to the met state, which is potentially the reason why Tyr122(•) in the active state can be stable over a very long period.

First Principles Calculations of Atomic Nickel Redox Potentials and Dimerization Free Energies: A Study of Metal Nanoparticle Growth.

The redox potentials and dimerization free energies of transient transition metal cations in water shed light on the reactivity of species with unusual charge states and are particularly pertinent to understanding the mechanism and feasibility of radiolysis-assisted metal nanoparticle growth from salt solutions. A combination of quasi-chemical theory and ab initio molecular dynamics thermodynamic integration methods are applied to calculate these properties for nickel. The reduction potential for Ni(2+) (aq) is predicted to be between -1.05 to -1.28 V, which is substantially lower than previous estimates. This suggests that Ni(2+) reduction may possibly occur in the presence of organic radical anion electron scavengers and hydrogen atoms, not just hydrated electrons. In contrast, Ni(+) is found to be stable against disproportionation. The formation of dimers Ni2 and Ni2(+) from Ni and Ni(+) are predicted to be favorable in water.

Hybrid density functional calculations of redox potentials and formation energies of transition metal compounds

We compare the accuracy of conventional semilocal density functional theory (DFT), the DFT+U method, and the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional for structural parameters, redox react ...

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(-).

Calculation of Redox Potentials in Multi-Copper Oxidases: A Combined First Principles and Molecular Dynamics Study

not Available.