Can Electrophilicity Act as a Measure of the Redox Potential of First-Row Transition Metal Ions?

Wandering through quantum-mechanochemistry: from concepts to reactivity and switches

Mechanochemistry has experienced a renaissance in recent years witnessing, at the molecular level, a remarkable interplay between theory and experiment. Molecular mechanochemistry has welcomed a broad spectrum of quantum-chemical methods to evaluate the influence of an external mechanical force on molecular properties. In this contribution, an overview is given on recent work on quantum mechanochemistry in the Brussels Quantum Chemistry group (ALGC). The effect of an external force was scrutinized both in fundamental topics, like reactivity descriptors in Conceptual DFT, and in applied topics, such as designing molecular force probes and tuning the stereoselectivity of certain types of reactions. In the conceptual part, a brief overview of the techniques introducing mechanical forces into a quantum-mechanical description of a molecule is followed by an introduction to conceptual DFT. The evolution of the electronic chemical potential (or electronegativity), chemical hardness and electrophilicity are investigated when a chemical bond in a series of diatomics is put under mechanical stress. Its counterpart, the influence of mechanical stress on bond angles, is analyzed by varying the strain present in alkyne triple bonds by applying a bending force, taking the strain promoted alkyne-azide coupling cycloaddition as an example. The increase of reactivity of the alkyne upon bending is probed by Fukui functions and the local softness. In the applied part, a new molecular force probe is presented based on an intramolecular 6π-electrocyclization in constrained polyenes operating under thermal conditions. A cyclic process is conceived where ring opening and closure are triggered by applying or removing an external pulling force. The efficiency of mechanical activation strongly depends on the magnitude of the applied force and the distance between the pulling points. The idea of pulling point distances as a tool to identify new mechanochemical processes is then tested in [28]hexaphyrins with an intricate equilibrium between Möbius aromatic and Hückel antiaromatic topologies. A mechanical force is shown to trigger the interconversion between the two topologies, using the distance matrix as a guide to select appropriate pulling points. In a final application, the Felkin-Anh model for the addition of nucleophiles to chiral carbonyls under the presence of an external mechanical force is scrutinized. By applying a force for restricting the conformational freedom of the chiral ketone, otherwise inaccessible reaction pathways are promoted on the force-modified potential energy surfaces resulting in a diastereoselectivity different from the force-free reaction.

External fields in conceptual density functional theory

The necessity of the recent incorporation of new external variables in the context of conceptual DFT (CDFT) is discussed based on the ever-increasing portfolio of experimental reaction conditions in the endeavor of experimentalists to synthesize new molecules with unprecedented properties. Electric and magnetic fields (ε and B), mechanical forces (F), and confinement are proposed as valuable new variables, extending conventional CDFT and its associated response functions. A finite field approach is used to calculate the evolution of both global and local descriptors in a selected series of atomic and molecular applications, and from it derive new response function involving, with one exception, the first derivative to the field considered. The electric field results, displaying, for example, a case of a field-induced enantioselectivity in the Fukui function, may be instrumental in the recent upsurge of chemistry in oriented external electric fields. The study of atomic electronegativity and hardness in magnetic fields displays a piecewise behavior, associated to configurational jumps upon increasing field strength and reveals an overall compression of their ranges for stronger fields, which may be guiding upon investigating chemistry in extremely high fields like in white dwarfs. The evolution of the electronegativity and hardness of diatomics under mechanical force can elegantly be traced back to differences in their equilibrium distance in the neutral, cationic, and anionic state. The well-known reduction of the polarizability under confinement can be seen as a fore-runner of the increasing hardness of atoms under pressure, presently under investigation. Periodicity showing up in a spontaneous way in the variety of properties is a leitmotiv in this study, as well as the interconnections/analogies between the different response functions.

Heterogeneity of ferrous iron-containing endolysosomes and effects of endolysosome iron on endolysosome numbers, sizes, and localization patterns

Endolysosomes are key regulators of iron metabolism and are central to iron trafficking and redox signaling. Iron homeostasis is linked to endolysosome acidity and inhibition of endolysosome acidity triggers iron dysregulation. Because of the physiological importance and pathological relevance of ferrous iron (Fe2+ ), we determined levels of Fe2+ specifically and quantitatively in endolysosomes as well as the effects of Fe2+ on endolysosome morphology, distribution patterns, and function. The fluorescence dye FeRhoNox-1 was specific for Fe2+ and localized to endolysosomes in U87MG astrocytoma cells and primary rat cortical neurons; in U87MG cells the endolysosome concentration of Fe2+ ([Fe2+ ]el ) was 50.4 μM in control cells, 73.6 μM in ferric ammonium citrate (FAC) treated cells, and 12.4 μM in cells treated with the iron chelator deferoxamine (DFO). Under control conditions, in primary rat cortical neurons, [Fe2+ ]el was 32.7 μM. Endolysosomes containing the highest levels of Fe2+ were located perinuclearly. Treatment of cells with FAC resulted in endolysosomes that were less acidic, increased in numbers and sizes, and located further from the nucleus; opposite effects were observed for treatments with DFO. Thus, FeRhoNox-1 is a useful probe for the study of endolysosome Fe2+ , and much more work is needed to understand better the physiological significance and pathological relevance of endolysosomes classified according to their heterogeneous iron content Cover Image for this issue: https://doi.org/10.1111/jnc.15396.

Effect of Oriented Electric Fields on Biologically Relevant Iron-Sulfur Clusters: Tuning Redox Reactivity for Catalysis

Enzyme-based iron-sulfur clusters, exemplified in families such as hydrogenases, nitrogenases, and radical S-adenosylmethionine enzymes, feature in many essential biological processes. The functionality of biological iron-sulfur clusters extends beyond simple electron transfer, relying primarily on the redox activity of the clusters, with a remarkable diversity for different enzymes. The active-site structure and the electrostatic environment in which the cluster resides direct this redox reactivity. Oriented electric fields in enzymatic active sites can be significantly strong, and understanding the extent of their effect on iron-sulfur cluster reactivity can inform first steps toward rationally engineering their reactivity. An extensive systematic density functional theory-based screening approach using OPBE/TZP has afforded a simple electric field-effect representation. The results demonstrate that the orientation of an external electric field of strength 28.8 MV cm^-1 at the center of the cluster can have a significant effect on its relative stability in the order of 35 kJ mol^-1. This shows clear implications for the reactivity of iron-sulfur clusters in enzymes. The results also demonstrate that the orientation of the electric field can alter the most stable broken-symmetry state, which further has implications on the directionality of initiated electron-transfer reactions. These insights open the path for manipulating the enzymatic redox reactivity of iron-sulfur cluster-containing enzymes by rationally engineering oriented electric fields within the enzymes.

Temperature-Dependent Approach to Electronic Charge Transfer

A charge transfer model is developed within the framework of the grand canonical ensemble through the analysis of the behavior of the fractional charge as a function of the chemical potential of the bath when the temperature and the external chemical potential are kept fixed. Departing from the fact that, before the interaction between two species, each one has a zero fractional charge, one can identify two situations after the interaction occurs where the fractional charge of at least one of the species is different from zero, indicating that there has been charge transference. One of them corresponds to the case when one of the species is immersed in a bath conformed by the other one, while the other is related to the case in which both species are present in equal amounts (stoichiometric proportion). Correlations between the fractional charges and average energies, thus obtained with experimental equilibrium constants, kinetic rate constants, hydration constants, and bond enthalpies, indicate that, although at the experimental temperatures, they are very small quantities, they have chemically meaningful information. Additionally, in the stoichiometric case, one also finds a rather good correlation between the equalized chemical potential and the one obtained from experimental information for a test set of diatomic and triatomic molecules.

Implementing the mechanical force into the conceptual DFT framework: understanding and predicting molecular mechanochemical properties

Studying mechanochemical properties through the implementation of the mechanical force into the conceptual DFT framework (E = E[N,v,F_ext]).

Scrutinizing the substituent effect on Mo-based electrocatalysts for molecular hydrogen release through axial–equatorial decomposition: a DFT study

The effect of electron-donating and -withdrawing groups is studied in terms of axial and equatorial locations at the p-pyridine rings in the [(PY₅Me₂)MoO]²⁺ for the H₂ release in aqueous media. It opens a way to modify its kinetics and thermodynamics.

How Biochemical Environments Fine-Tune a Redox Process: From Theoretical Models to Practical Applications

In this study, we give a new physical insight into how enzymatic environments influence a redox process. This is particularly important in a biochemical context, in which oxidoreductase enzymes and low-molecular-weight cofactors create a microenvironment, fine-tuning their specific redox potential. We present a new theoretical model, quantitatively backed up by quantum chemically calculated data obtained for key biological sulfur-based model reactions involved in preserving the cellular redox homeostasis during oxidative stress. We show that environmental effects can be quantitatively predicted from the thermodynamic cycle linking ΔΔ G(OX/RED)_ref-ligand values to the differential interaction energy ΔΔ G_int of the reduced and oxidized species with the environment. Our obtained data can be linked to hydrogen-bond patterns found in protein active sites. The thermodynamic model is further understood in the framework of molecular orbital theory. The key insight of this work is that the intrinsic properties of neither a redox couple nor the interacting environment (e.g., ligand) are enough by themselves to uniquely predict reduction potentials. Instead, system-environment interactions need to be considered. This study is of general interest as redox processes are pivotal to empower, protect, or damage organisms. Our presented thermodynamic model allows a pragmatically evaluation on the expected influence of a particular environment on a redox process, necessary to fully understand how redox processes take place in living organisms.

Solvent effect on the degree of (a)synchronicity in polar Diels-Alder reactions from the perspective of the reaction force constant analysis

In this work, we computationally evaluated the influence of six different molecular solvents, described as a polarizable continuum model at the M06-2X/6-31+G(d,p) level, on the activation barrier/reaction rate, overall energy change, TS geometry, and degree of (a)synchronicity of two concerted Diels-Alder cycloadditions of acrolein (R1) and its complex with Lewis acid acrolein···BH₃ (R2) to cyclopentadiene. In gas-phase, we found that both exothermicity and activation barrier are only reduced by about 2.0 kcal mol^-1, and the asynchronicity character of the mechanism is accentuated when BH₃ is included. An increment in the solvent's polarity lowers the activation energy of R1 by 1.3 kcal mol^-1, while for R2 the reaction rate is enhanced by more than 2000 times at room temperature (i.e., the activation energy decreases by 4.5 kcal mol^-1) if the highest polar media is employed. Therefore, a synergistic effect is achieved when both external agents, i.e., Lewis acid catalyst and polar solvent, are included together. This effect was ascribed to the ability of the solvent to favor the encounter between cyclopentadiene and acrolein···BH₃. This was validated by the asymmetry of the TS which becomes highly pronounced when either both or just BH₃ is considered or the solvent's polarity is increased. Finally, the reaction force constant κ(ξ) reveals that an increment in the solvent's polarity is able to turn a moderate asynchronous mechanism of the formation of the new C-C σ-bonds into a highly asynchronous one. Graphical abstract A synergistic effect is achieved when both external agents, i.e., Lewis acid catalyst and polar solvent, are included together: lowered energy barriers and increased asynchronicities.

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.

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.

Systematic selection of metalloporphyrin-based catalysts for oxygen reduction by modulation of the donor-acceptor intermolecular hardness

Incisive modulation of the intermolecular hardness between metalloporphyrins and O2 can lead to the identification of promising catalysts for oxygen reduction. The dependency of the electrocatalytic reduction of O2 by metalloporphyrins on the nature of the central metal yields a volcano-type curve, which is rationalized to be in accordance with the Sabatier principle by using an approximation of the electrophilicity of the complexes. By using electrochemical and UV/Vis data, the influence of a selection of meso-substituents on the change in the energy for the π→π* excitation of manganese porphyrins was evaluated allowing one to quantitatively correlate the influence of the various ligands on the electrocatalysis of O2 reduction by the complexes. A manganese porphyrin was identified that electrocatalyzes the reduction of oxygen at low overpotentials without generating hydrogen peroxide. The activity of the complex became remarkably enhanced upon its pyrolysis at 650 °C.

Electron capture by the thiyl radical and disulfide bond: ligand effects on the reduction potential

The effect of non-polar and polar ligands and of monovalent cations on the one-electron reduction potential of the thiyl radical and the disulfide bond was evaluated. The reduction potentials E° for the CH3S(.)-nL/CH3S(-)-nL and CH3SSCH3-L/CH3SSCH3(.-)-L redox couples were calculated at the B3LYP, M06-2X and MP2 levels of theory, with n=1, 2 and L=CH4, C2H4, H2O, CH3OH, NH3, CH3COOH, CH3CONH2, NH4(+), Na(+), K(+) and Li(+). Non-polar ligands decrease the E° value of the thiyl radical and disulfide bond, while neutral polar ligands favour electron uptake. Charged polar ligands and cations favour electron capture by the thiyl radical while disfavouring electron uptake by the disulfide bond. Thus, the same type of ligand can have a different effect on E° depending on the redox couple. Therefore, properties of an isolated ligand cannot uniquely determine E°. The ligand effects on E° are discussed in terms of the vertical electron affinity and reorganization energy, as well as molecular orbital theory. For a given redox couple, the ligand type influences the nature of the anion formed upon electron capture and the corresponding reorganization process towards the reduced geometry.

The thermodynamics of thiol sulfenylation

Protein sulfenic acids are essential cysteine oxidations in cellular signaling pathways. The thermodynamics that drive protein sulfenylation are not entirely clear. Experimentally, sulfenic acid reduction potentials are hard to measure, because of their highly reactive nature. We designed a calculation method, the reduction potentials from electronic energies (REE) method, to give for the first time insight into the thermodynamic aspects of protein sulfenylation. The REE method is based on the correlation between reaction path-independent reaction energies and free energies of a series of analogous reactions. For human peroxiredoxin (Tpx-B), an antioxidant enzyme that forms a sulfenic acid on one of its active-site cysteines during reactive oxygen scavenging, we found that the reduction potential depends on the composition of the active site and on the protonation state of the cysteine. Interaction with polar residues directs the RSO(-)/RS(-) reduction to a lower potential than the RSOH/RSH reduction. A conserved arginine that thermodynamically favors the sulfenylation reaction might be a good candidate to favor the reaction kinetics. The REE method is not limited to thiol sulfenylation, but can be broadly applied to understand protein redox biology in general.

Solution-phase electronegativity scale: insight into the chemical behaviors of metal ions in solution

By incorporating the solvent effect into the Born effective radius, we have proposed an electronegativity scale of metal ions in aqueous solution with the most common oxidation states and hydration coordination numbers in terms of the effective ionic electrostatic potential. It is found that the metal ions in aqueous solution are poorer electron acceptors compared to those in the gas phase. This solution-phase electronegativity scale shows its efficiency in predicting some important properties of metal ions in aqueous solution such as the aqueous acidities of the metal ions, the stability constants of metal complexes, and the solubility product constants of the metal hydroxides. We have elaborated that the standard reduction potential and the solution-phase electronegativity are two different quantities for describing the processes of metal ions in aqueous solution to soak up electrons with different final states. This work provides a new insight into the chemical behaviors of the metal ions in aqueous solution, indicating a potential application of this electronegativity scale to the design of solution reactions.

Solution reaction design: electroaccepting and electrodonating powers of ions in solution

By considering a first-order variation in electroaccepting and electrodonating powers, ω±, induced by a change from gas to aqueous solution phase, the solvent effect on ω± for charged ions is examined. The expression of electroaccepting and electrodonating powers in the solution phase, ω±s, is obtained through establishing the quantitative relationship between the change of the ω± due to the solvation and the hydration free energy. It is shown that cations are poorer electron acceptors and anions are poorer electron donors in solution compared to those in gas phase. We have proven that the scaled aqueous electroaccepting power, ω+s, of cations can act as a good descriptor of the reduction reaction, which is expected to be applied in the design of solution reactions.

Regaining the Woodward–Hoffmann rules for chelotropic reactions via conceptual DFT

In our continuous effort to retrieve the Woodward–Hoffmann rules from conceptual density functional theory (DFT), we have examined the last type of pericyclic reactions, i.e., chelotropic reactions. Both the initial hardness response and the dual descriptor have been investigated to predict the allowed and forbidden character for the addition of SO2 to butadiene (4n system) and 1,3,5-hexatriene (4n + 2 system). It is shown that with both electronic descriptors, the conrotatory/disrotatory mode for the linear and nonlinear mechanisms are retrieved based on a density-only approach, free from consideration of orbital and (or) wave function symmetry. The dual descriptor moreover reveals that stabilizing interactions are presented only for the linear path, which can be considered as an overall favourable mechanism for a chelotropic reaction.

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.

Enzymatic catalysis: the emerging role of conceptual density functional theory

Experimentalists and quantum chemists are living in a different world. A wealth of theoretical enzymology-related publications is hardly known by experimentalists, and vice versa. Our aim is to bring both worlds together and to show the powerful possibilities of a multidisciplinary approach to study subtle details of complicated enzymatic processes to a broad readership. MD simulations and QM/MM approaches often focus on the calculation of reaction paths based on activation energies, which is a time-consuming task. A valuable alternative is the reactivity descriptors founded in conceptual DFT like softness, electrophilicity, and the Fukui function, which describe the kinetic aspects of a reaction in terms of the response to perturbations in N and/or upsilon(r), typical for a chemical reaction, of the reagents in the ground state. As such, the relative energies at the beginning of the reaction predict a sequence of activation energies only based on the properties of the reactants (Figure 5 ). In 2003, Geerlings et al. published a key review giving a detailed description of the principles and concepts of conceptual DFT and highlighting its success to study generalized acid/base reactions including addition, substitution, and elimination reactions. Since the time that this review appeared, conceptual DFT has proven its strength in literally hundreds of papers with application to organic and inorganic reactions. Its role in unravelling enzymatic reaction mechanisms, in handling experimentally difficult accessible biochemical problems, and in the interpretation of biochemical experimental observations is emerging and very promising.

Density functional theory for transition metals and transition metal chemistry

We introduce density functional theory and review recent progress in its application to transition metal chemistry. Topics covered include local, meta, hybrid, hybrid meta, and range-separated functionals, band theory, software, validation tests, and applications to spin states, magnetic exchange coupling, spectra, structure, reactivity, and catalysis, including molecules, clusters, nanoparticles, surfaces, and solids.