Rate-equilibrium relationships in hydride transfer reactions: the role of intrinsic barriers

A literature survey on the kinetics of hydride abstractions from CH-groups by carbocations reveals a general phenomenon: Variation of the hydride acceptor affects the rates of hydride transfer to a considerably greater extent than an equal change of the thermodynamic driving force caused by variation of the hydride donor. The origin of this relationship was investigated by quantum chemical calculations on various levels of ab initio and DFT theory for the transfer of an allylic hydrogen from 1-mono- and 1,1-disubstituted propenes (XYC=CH-CH(3)) to the 3-position of 1-mono- and 1,1-disubstituted allyl cations (XYC=CH-CH(2)(+)). The discussion is based on the results of the MP2/6-31+G(d,p)//RHF/6-31+G(d,p) calculations. Electron-releasing substituents X and Y in the hydride donors increase the exothermicity of the reaction, while electron-releasing substituents in the hydride acceptors decrease exothermicity. In line with Hammond's postulate, increasing exothermicity shifts the transition states on the reaction coordinate toward reactants, as revealed by the geometry parameters and the charge distribution in the activated complexes. Independent of the location of the transition state on the reaction coordinate, a value of 0.72 is found for Hammond-Leffler's alpha = deltaDeltaG/deltaDelta(r)G degrees when the hydride acceptor is varied, while alpha = 0.28 when the hydride donor is varied. The value of alpha thus cannot be related with the position of the transition state. Investigation of the degenerate reactions XYC=CH-CH(3) + XYC=CH-CH(2)(+) indicates that the migrating hydrogen carries a partial positive charge in the transition state and that the intrinsic barriers increase with increasing electron-releasing abilities of X and Y. Substituent variation in the donor thus influences reaction enthalpy and intrinsic barriers in the opposite sense, while substituent variation in the acceptor affects both terms in the same sense, in accord with the experimental findings. Marcus theory is employed to treat these effects quantitatively.     

Bimolecular electron transfers that follow a Sandros-Boltzmann dependence on free energy

Rate constants (k) for exergonic and endergonic electron-transfer reactions of equilibrating radical cations (A(?+) + B ? A + B(?+)) in acetonitrile could be fit well by a simple Sandros-Boltzmann (SB) function of the reaction free energy (ΔG) having a plateau with a limiting rate constant k(lim) in the exergonic region, followed, near the thermoneutral point, by a steep drop in log k vs ΔG with a slope of 1/RT. Similar behavior was observed for another charge shift reaction, the electron-transfer quenching of excited pyrylium cations (P(+)*) by neutral donors (P(+)* + D → P(?) + D(?+)). In this case, SB dependence was observed when the logarithm of the quenching constant (log k(q)) was plotted vs ΔG + s, where the shift term, s, equals +0.08 eV and ΔG is the free energy change for the net reaction (E(redox) - E(excit)). The shift term is attributed to partial desolvation of the radical cation in the product encounter pair (P(?)/D(?+)), which raises its free energy relative to the free species. Remarkably, electron-transfer quenching of neutral reactants (A* + D → A(?-) + D(?+)) using excited cyanoaromatic acceptors and aromatic hydrocarbon donors was also found to follow an SB dependence of log k(q) on ΔG, with a positive s, +0.06 eV. This positive shift contrasts with the long-accepted prediction of a negative value, -0.06 eV, for the free energy of an A(?-)/D(?+) encounter pair relative to the free radical ions. That prediction incorporated only a Coulombic stabilization of the A(?-)/D(?+) encounter pair relative to the free radical ions. In contrast, the results presented here show that the positive value of s indicates a decrease in solvent stabilization of the A(?-)/D(?+) encounter pair, which outweighs Coulombic stabilization in acetonitrile. These quenching reactions are proposed to proceed via rapidly interconverting encounter pairs with an exciplex as intermediate, A*/D ? exciplex ? A(?-)/D(?+). Weak exciplex fluorescence was observed in each case. For several reactions in the endergonic region, rate constants for the reversible formation and decay of the exciplexes were determined using time-correlated single-photon counting. The quenching constants derived from the transient kinetics agreed well with those from the conventional Stern-Volmer plots. For excited-state electron-transfer processes, caution is required in correlating quenching constants vs reaction free energies when ΔG exceeds ～+0.1 eV. Beyond this point, additional exciplex deactivation pathways-fluorescence, intersystem crossing, and nonradiative decay-are likely to dominate, resulting in a change in mechanism.     

Reorganization of immobilized horse and yeast cytochrome c induced by pH changes or nitric oxide binding

The redox properties of horse and yeast cytochrome c electrostatically immobilized on carboxylic acid-terminated self-assembled monolayers (SAMs) have been determined over a broad pH range (pH 3.5-8) in the absence and presence of nitric oxide. Below pH 6, both proteins exhibit comparable midpoint potentials, coverages, and electron-transfer rate constants, which suggests that they are adsorbed on the SAM in a similar fashion. Above pH 6, a sharp decrease in electron-transfer rate constants is observed for immobilized yeast cytochrome c, which is indicative of a change in the electron tunneling pathway between the heme and the electrode and hence suggests that the protein reorients on the surface. Such a decrease is not observed for horse cytochrome c and therefore must be related to the specific charge distribution on yeast cytochrome c. Apart from the charge distribution on the protein, the reorientation also seems to be related to the charge on the SAM surface. The presence of nitric oxide causes a decrease in electron-transfer rate constants of both yeast and horse cytochrome c at low pH. This is probably due to the fact that nitric oxide induces a conformational change of the protein and also changes the reorganization energy for electron transfer.     

A perturbation molecular orbital theory of gas-phase dissociative electron-transfer rates

Gasphase dissociative electron-transfer (ET) reactions are examined in the light of modern electron-transfer theory and a perturbation molecular orbital (PMO) model for ion-molecule collision rates. Two dissociative ET reactions reported by Knighton and Grimsrud—the reaction of azulene anion with dibromodifluoromethane and with carbon tetrachloride—happened in the inverted region of the relationship between reaction rate and free energy. Carbon-halogen vibration participation in dissociative ET reactions is demonstrated in two reaction series. Carbon-hydrogen stretch (3050 cm^?1) activation of electron transfer happened in the most exothermic reaction series: dissociative capture to form bromide from bromotrichloromethane The reasons for the failure of classical ion-molecule collision theory to give a quantitative account of reactive ion-molecule collision rates are presented in some detail. The fundamental failure is a result of a previously unappreciated change in the polarizability of a molecule when the orbitals on the molecule overlap with those on an adjacent ion. The molecular orbital-based collision model used here avoids the need to evaluate the changes in the polarizability tensor with overlap.     

"Abnormal" salt and solvent effects on anion/cation electron-transfer reactions: an interpretation based on Marcus-Hush treatment

Salt and solvent effects on the kinetics of the reactions [Fe(CN)6]3- + [Ru(NH3)5pz](2+) right arrow over left arrow [Fe(CN)6]4- + [Ru(NH3)5pz]3+ (pz = pyrazine) have been studied through T-jump measurements. The forward and reverse reactions show different behaviors: "abnormal" salt and solvent effects in the first case and normal effects in the second one. These facts imply an asymmetric behavior of anion/cation reactions depending on the charge of the oxidant. The results can be rationalized by using the Marcus-Hush treatment for electron-transfer reactions.     

Comparison of the self-exchange and interfacial charge-transfer rate constants for methyl- versus tert-butyl-substituted Os(III) polypyridyl complexes

Differences in the self-exchange and interfacial electron-transfer rate constants have been evaluated for a relatively unhindered Os(III/II) redox system, osmium(III/II) tris(4,4'-di-methyl-2,2'-bipyridyl), [Os(Me2bpy)3]3+/2+, relative to those of a relatively hindered system, osmium(III/II) tris(4,4'-di-tert-butyl-2,2'-bipyridyl), [Os(t-Bu2bpy)3]3+/2+. In contrast to the predicted increase in rate constant by a factor of 2-3 due to the difference in reorganization energy of the two complexes, introduction of the tert-butyl functionality decreased the self-exchange rate constant, as measured by NMR line-broadening techniques, by a factor of approximately 50 as compared to that of the analogous methyl-substituted osmium complex. Steady-state current density versus potential measurements, in conjunction with differential capacitance versus potential measurements, were used to compare the interfacial electron-transfer rate constants at n-type ZnO electrodes of [Os(t-Bu2bpy)3]3+/2+ and [Os(Me2bpy)3]3+/2+. The interfacial electron-transfer rate constant for the reduction of [Os(t-Bu2bpy)3]3+ was 100 times smaller than that for [Os(Me2bpy)3]3+. The results indicate that the tert-butyl group can act as a spacer on an outer-sphere redox couple and significantly decrease the electronic coupling of the electron-transfer reaction in both self-exchange and interfacial electron-transfer processes.     

Evidence for inverted region behavior in proton transfer to carbanions

The diphenylmethane-diphenylmethyl anion acid/base couple in N,N-dimethylformamide is taken as an example for investigating the dynamics of proton transfer at carbon in a system where the acid is not activated by an electron-withdrawing group or by removal of an electron. The laser flash electron photoinjection technique is applied to the determination of the rate constant for the protonation of diphenylmethyl anion by an extended series of acids that offers a range of driving forces encompassing over 1.2 eV. The plot of the rate constant versus the pK(a) difference between diphenylmethane and the acids or of the activation free energy versus the standard free energy of the reaction exhibits clear "inverted region" behavior (by a factor of 80 in terms of rate constants). While such behaviors have been predicted and observed for outersphere electron-transfer reactions, previous evidence for proton-transfer reactions was scarce. Entropic factors, derived from an investigation of the temperature dependence of the experimental rate constants, are also discussed.     

Thermodynamic characteristics of the formation reactions of nickel(II) glycinates and the solvation of reagents in aqueous ethanol solutions

Enthalpies of complexation reactions between nickel(II) and the glycinate ion in mixtures of water with ethanol containing up to 0.5 mole fraction ethanol were obtained by the calorimetric titration method at 298 K. With increasing ethanol concentration exothermicity of complexation was found to increase slightly for the first coordination step. The results obtained were analyzed from the standpoint of solvation approach based on thermodynamic characteristics of all reagents. It was shown that the main cause of the increase in the exothermicity of complexation reactions is the weakening of ligand solvation with increasing ethanol concentration.     

Quantifying the electrostatic driving force behind SmI2 reductions

The equilibrium constant for the electron transfer between SmI2 and substituted benzophenones was determined. The electron transfer reactions are exothermic with DeltaG(eq) ranging from -5.1 to -1.6 kcal/mol. Redox potentials suggest that the electron transfer reactions should be endothermic by ca. 25 kcal/mol, contrary to the experimental observation. It is suggested that the change from endothermicity to exothermicity stems from the electrostatic attraction between the negatively charged radical anion and Sm(3+).     

Dependence of enthalpies of formation of the Cu<Superscript>2+</Superscript> complexes with glycinate ions on the composition of water—dimethylsulfoxide solvent

Enthalpies of the complexing reactions of copper (II) with glycinate ions in mixtures of water with dimethylsulfoxide (DMSO) containing up to 0.9 mole parts of organic component (298 K) were obtained using a titration calorimeter. It was established that upon an increase in the DMSO content, the exothermicity of complexing increases at the first and second steps of the coordination. The obtained results were analyzed from the viewpoint of the solvation approach, based on the thermodynamic characterization of all reagents. It was shown that the main origin of the increase in the exothermicity of the complexing reactions is a weakening of ligand solvation when the DMSO concentration increases.     

Photoinduced intermolecular electron transfer from dimethyl aniline to 7-amino coumarin dyes in the surface of beta-cyclodextrin

The photoinduced electron-transfer reaction between Coumarin dyes and N,N-dimethylaniline has been investigated using steady-state and Time-resolved fluorescence spectroscopy in the surface of beta-cyclodextrin in dimethyl formamide (DMF) solvent. The electron-transfer rate constant has been correlated with the free-energy change during the process. We have observed a diffusion-controlled ET process in pure DMF by showing a normal Marcus region. However, the picture is different in presence of cyclodextrin. Here the ET is retarded at higher free-energy region. This unusual feature in bimolecular electron-transfer reaction is assumed to be arising from the different binding possibility of the Coumarin molecules to the cyclodextrin moity.     

Electron-transfer oxidation properties of DNA bases and DNA oligomers

Kinetics for the thermal and photoinduced electron-transfer oxidation of a series of DNA bases with various oxidants having the known one-electron reduction potentials (E(red)) in an aqueous solution at 298 K were examined, and the resulting electron-transfer rate constants (k(et)) were evaluated in light of the free energy relationship of electron transfer to determine the one-electron oxidation potentials (E(ox)) of DNA bases and the intrinsic barrier of the electron transfer. Although the E(ox) value of GMP at pH 7 is the lowest (1.07 V vs SCE) among the four DNA bases, the highest E(ox) value (CMP) is only 0.19 V higher than that of GMP. The selective oxidation of GMP in the thermal electron-transfer oxidation of GMP results from a significant decrease in the pH dependent oxidation potential due to the deprotonation of GMP*+. The one-electron reduced species of the photosensitizer produced by photoinduced electron transfer are observed as the transient absorption spectra when the free energy change of electron transfer is negative. The rate constants of electron-transfer oxidation of the guanine moieties in DNA oligomers with Fe(bpy)3(3+) and Ru(bpy)3(3+) were also determined using DNA oligomers containing different guanine (G) sequences from 1 to 10 G. The rate constants of electron-transfer oxidation of the guanine moieties in single- and double-stranded DNA oligomers with Fe(bpy)3(2+) and Ru(bpy)3(3+) are dependent on the number of sequential guanine molecules as well as on pH.     

Effect of the relaxation of high-frequency vibrational modes on the kinetics of charge separation and recombination

The processes of intramolecular electron transfer from the second excited electron state accompanied by superfast reverse transfer to the first excited state are studied. The kinetics of the populations of the first and second excited states, along with that the charge-separated states, is calculated within the generalized stochastic model, taking into account the reorganization of the medium and intramolecular high-frequency vibrations. It is shown that variations in the relaxation rate of the high-frequency vibrational modes can change the population of the quenching products by a factor of two to three. It is established that in the case of the weak exothermicity of the charge separation process, the population of the charge-separated states declines upon an increase in the vibrational relaxation rate, while the population of the first excited state increases; in the region of high exothermicity, these dependences change to ones that are opposite. To reveal the scales of these effects in real systems, the kinetics of the photo-induced processes in the zinc-porphyrin derivatives, including electron-acceptor imide groups covalently coupled with porphyrin rings, are calculated. It is shown that the results from calculating the kinetics of the population of the first and the second excited states agree well with the experimental data on the kinetics of the fluorescence of these states. The absolute values of the population of the charge-separated state and the first excited state are determined. The key role of the hot electron transitions that occur in parallel with the relaxation of the medium and intramolecular vibrations in the considered process is shown.     

Electron-transfer reactions through the associated interaction between cytochrome c and self-assembled monolayers of optically active cobalt(III) complexes: molecular recognition ability induced by the chirality of the cobalt(III) units

Self-assembled monolayers (SAMs) of optically active Co(III) complexes ((S)-2/(R)-2) that contain (S)- or (R)-phenylalanine derivatives as a molecular recognition site were constructed on Au electrodes ((S)-2-Au/(R)-2-Au). Molecular recognition characteristics induced by the S and R configurations were investigated by measurements of electron-transfer reactions with horse heart cytochrome c (cyt c). The electrochemical studies indicate that the maximum current of cyt c reduction is obtained when the Au electrode is modified by 2 with a moderate coverage of approximately 4.0 x 10(-11) mol cm(-2). Since the Au electrode is not densely packed with the Co(III) units at this concentration, we conclude that the penetrative association process between cyt c and the Co(III) unit plays an important role in this electron-transfer system. The differences in the electron-transfer rates of (S)-2-Au and (R)-2-Au increase with increasing scan rates, a result indicating that the chiral ligand has an influence on the rate of association of the complexes with cyt c. 3-Au has a mixed monolayer composed of 2 and hexanethiol and exhibits electron-transfer behavior comparable to 2-Au. The difference in the association rates of (S)-3-Au and (R)-3-Au is larger than that between (S)-2-Au and (R)-2-Au, which indicates that the molecular recognition ability of 3-Au has been enhanced by filling the gap between molecules of 2 with hexanethiols. The differences in the oxidation rates of cyt c(II) between (S)-2-Au and (R)-2-Au and between (S)-3-Au and (R)-3-Au were larger than the differences in the rates of the reduction of cyt c(III); this suggests that the size of the heme crevice varies according to the oxidation state of cyt c.     

1,3-Dipolar reactions involving corannulene: how does its rim and spoke addition vary?

[reaction: see text] Corannulene undergoes 1,3-dipolar reactions with the dipoles, diazomethane, nitrile oxide, and nitrone through its rim and spoke pi bonds; the rim addition yields "one possible" adduct whereas two "regioselective" adducts are formed by spoke addition. Mechanisms of these reactions have been investigated at the B3LYP/6-31G(d) level. Computations show that both rim and spoke additions prefer concerted pathways that lie 2-5 kcal/mol lower in energy than stepwise paths. Stepwise additions can take place in two ways and the activation energies of these two modes differ by 1-2 kcal/mol. A close inspection of the energy profiles reveals that rim addition is more favorable kinetically and thermodynamically than spoke addition in view of lower activation energy and higher exothermicity observed for rim addition. The rim bond of corannulene is more flexible for distortion and also has a stronger double bond (i.e. pi-character) than the spoke bond and this facilitates rim addition over spoke addition. Deformation energy analysis also confirms the above through higher deformation in corannulene from the spoke addition when compared to rim addition. In the spoke addition, regio1 reaction is kinetically more favored than regio2 reaction. Attempts to react corannulene in an endohedral fashion have led to the exohedral adduct. Computed activation energies suggest that corannulene acts as a deactivated dipolarophile compared to ethylene. Even more striking is the observation that rim and spoke double bonds in corannulene are part of the local aromatic system but it shows remarkable reactivity compared to benzene despite the loss of aromaticity during the reaction. This is well indicated by computed NICS values. Inclusion of acetonitrile as solvent through the PCM model increases the reaction rate and exothermicity.     

Measurement of the dependence of interfacial charge-transfer rate constants on the reorganization energy of redox species at n-ZnO/H2O interfaces

The interfacial energetic and kinetics behavior of n-ZnO/H2O contacts have been determined for a series of compounds, cobalt trisbipyridine (Co(bpy)3(3+/2+)), ruthenium pentaamine pyridine (Ru(NH3)5 py(3+/2+)), cobalt bis-1,4,7-trithiacyclononane (Co(TTCN)2(3+/2+)), and osmium bis-dimethyl bipyridine bis-imidazole (Os(Me2bpy)2(Im)2(3+/2+)), which have similar formal reduction potentials yet which have reorganization energies that span approximately 1 eV. Differential capacitance vs potential and current density vs potential measurements were used to measure the interfacial electron-transfer rate constants for this series of one-electron outer-sphere redox couples. Each interface displayed a first-order dependence on the concentration of redox acceptor species and a first-order dependence on the concentration of electrons in the conduction band at the semiconductor surface, in accord with expectations for the ideal model of a semiconductor/liquid contact. Rate constants varied from 1 x 10(-19) to 6 x 10(-17) cm4 s(-1). The interfacial electron-transfer rate constant decreased as the reorganization energy, lambda, of the acceptor species increased, and a plot of the logarithm of the electron-transfer rate constant vs (lambda + deltaG(o)')(2)/4lambda k(B)T (where deltaG(o)' is the driving force for interfacial charge transfer) was linear with a slope of approximately -1. The rate constant at optimal exoergicity was found to be approximately 5 x 10(-17) cm4 s(-1) for this system. These results show that interfacial electron-transfer rate constants at semiconductor electrodes are in good agreement with the predictions of a Marcus-type model of interfacial electron-transfer reactions.     

Thermodynamic and electron-transfer properties of copper(II/I) polyaminothiaether complexes

In electron-transfer reactions, the change in the oxidation states of the reactants is generally accompanied by structural changes, which influence the electron-transfer kinetics. Previous studies on the systems of Cu(II)/(I) complexes involving cyclic tetrathiaether ligands indicated that inversion of coordinated donor atoms is a major geometric change during the overall electron-transfer process. Complex formation and isomerization studies on complexes with the 1,4,8,11-tetraazacyclotetradecane ligand have demonstrated that a necessary condition for conformational change is deprotonation followed by inversion of coordinated N atoms. When one or more nitrogen donor atoms in a ligand are replaced with sulfur, there is a choice of N or S inversion. It has been hypothesized that donor atom inversion (N or S donors) is a major factor that can lead to conformationally limited electron-transfer kinetics of copper systems. In the current study, the thermodynamic properties, electron-transfer kinetics and conformational changes in copper(II)[1,4,8-trithia-11-azacyclotetradecane], copper(II)[1,8-dithia-4,11-diazacyclotetradecane] and copper(II)[1,11,-dithia-4,8-diazacyclotetradecane] were determined in order to determine the effect of inversion of coordinated N atoms on electron-transfer rates as a function of low concentrations of water in an aprotic solvent (acetonitrile). By using controlled amounts of water as a hydrogen ion acceptor, deprotonation of amine nitrogen and nitrogen donor inversion was followed by comparing self-exchange rate constants for reduction and oxidation of the copper complexes. Data on thermodynamic properties and electron-transfer kinetics are presented. Possible conformational changes and kinetic pathways for complexes with ligands having mixed N and S donor sets are presented.     

Thermodynamics of formation for the 18-crown-6-triglycine molecular complex in water-dimethylsulfoxide solvents

The effect of a water-dimethylsulfoxide (DMSO) solvent on the formation of a molecular complex of 18-crown-6 (18C6) with triglycine (diglycylglycine, 3Gly) is studied via calorimetric titration. It is found that switching from water to an H₂O-DMSO mixture with DMSO mole fraction of 0.30 is accompanied by a monotonic increase in the stability of [3Gly18C6] complex, from logK ^° = 1.10 to logK ^° = 2.44, and an increase in the exothermicity of the reaction of its formation, from ?5.9 to ?16.9 kJ/mol. It is shown that the [3Gly18C6] complex exhibits enthalpy stabilization with negative values of enthalpy and entropy over the investigated range of H₂O-DMSO solvents. Analysis of the reagents’ solvation characteristics reveals that the increase in the reaction’s exothermicity of transfer is due to differences in the solvation of [3Gly18C6] and 18C6 with a small solvation contribution from 3Gly. It is concluded that the change in the Gibbs energy of the reaction 3Gly_solv + 18C6_solv ? [3Gly18C6]_solv is due to differences in the change in the solvation state of the complex and the peptide (Δ_tr G ^°([3Gly18C6])-Δ_tr G ^°(3Gly)).     

Mechanism of scandium ion catalyzed Diels-Alder reaction of anthracenes with methyl vinyl ketone

Rates of Diels-Alder cycloadditions of anthracenes with methyl vinyl ketone (MVK) are accelerated significantly by the presence of scandium triflate [Sc(OTf)3]. Sc(OTf)3 also promotes photoinduced electron-transfer reactions from various electron donors to MVK significantly. Comparison of the promoting effect of Sc(OTf)3 in photoinduced electron-transfer reactions of MVK with the catalytic effect of Sc(OTf)3 in the Diels-Alder reaction of 9,10-dimethylanthracene with MVK has revealed that the MVK-Sc(OTf)3 complex is a reactive intermediate in both the Diels-Alder and photoinduced electron-transfer reactions. The observed second-order rate constants of the Sc(OTf)3-catalyzed Diels-Alder reactions of anthracenes with MVK are by far larger than those expected from the observed linear Gibbs energy relation for the Diels-Alder reactions of anthracenes with stronger electron acceptors than MVK, which are known to proceed via electron transfer. This indicates that the Sc(OTf)3-catalyzed Diels-Alder reactions of anthracenes with MVK does not proceed via an electron-transfer process from anthracences to the MVK-Sc(OTf)3 complex.