Kinetics of Diabatic and Adiabatic Electron Exchange in Organic Systems Comparison of Theory and Experiment

Fine tuning of electron transfer and spin chemistry parameters in triarylamine-bridge-naphthalene diimide dyads by bridge substituents

The photoinduced charge separation and charge recombination in a set of four molecular dyads consisting of a triarylamine donor and a naphthalene diimide acceptor were investigated by time resolved transient absorption spectroscopy with fs and ns time resolution. In these dyads the donor and acceptor are bridged by a meta-conjugated diethynylbenzene bridge whose electronic nature was tuned by small electron donating (OMe, Me) or electron withdrawing (Cl, CN) substituents. While the formation of the transient charge separated states is complete within tens of ps, charge recombination is biphasic with a shorter component of several hundred ns and a longer component of several microseconds. This behaviour could be rationalized by assuming an equilibrium of singlet and triplet charge separated states. Magnetic field dependent measurements showed a strong influence on the biphasic decay kinetics and also a pronounced level crossing effect in the magnetic field affected reaction yield (MARY) spectra caused by a significant exchange coupling. An analysis of the observed kinetics using classical kinetic rate equations yields rate constants for charge separation and charge recombination as well as the exchange interaction splitting in the radical ion pair, all of them showing a delicate dependence on the bridge substituents.

Are the current theories of electron transfer applicable to reactions in ionic liquids? An ESR-study on the TCNE/TCNE−˙ couple

Electron transfer reactions in ionic liquids are profoundly affected by solvent properties. The activation barriers cannot be generally accounted for by Marcus' theory.

Investigation of solvent dynamic effects on the electron self-exchange in two thianthrene couples with large inner reorganization energies

The electron self-exchange of thianthrenes, which show large structural changes during the reaction, is strongly affected by a solvent dynamic effect controlled by the longitudinal relaxation time.

Influence of the medium's viscosity on the kinetics of hydrogen atom self-exchange for N-hydroxy phthalimide/piperidine-N-oxyl (NHPI/PINO˙) measured by CW-ESR spectroscopy

Rates of hydrogen atom self-exchange measured by CW-ESR line broadening depend linearly on the medium’s viscosity.

Electron transfer and proton-coupled electron transfer reactivity and self-exchange of synthetic [2Fe-2S] complexes: models for Rieske and mitoNEET clusters

This report describes the thermochemistry, proton-coupled electron transfer (PCET) reactions and self-exchange rate constants for a set of bis-benzimidazolate-ligated [2Fe–2S] clusters. These clusters serve as a model for the chemistry of biological Rieske and mitoNEET clusters. PCET from [Fe₂S₂(^Prbbim)(^PrbbimH)]^2– (4) and [Fe₂S₂(^Prbbim)(^PrbbimH₂)]^1– (5) to TEMPO occurs via concerted proton–electron transfer (CPET) mechanisms (^PrbbimH₂ = 4,4-bis-(benzimidazol-2-yl)heptane). Intermolecular electron transfer (ET) self-exchange between [Fe₂S₂(^Prbbim)₂]^2– (1) and [Fe₂S₂(^Prbbim)₂]^3– (2) occurs with a rate constant of (1.20 ± 0.06) × 10⁵ M^–1 s^–1 at 26 °C. A similar self-exchange rate constant is found for the related [2Fe–2S] cluster [Fe₂S₂(SArO)₂]^2–/3–, SArO^2– = thiosalicylate. These are roughly an order of magnitude slower than that reported for larger [4Fe–4S] clusters and 1 order of magnitude faster than that reported for N-ligated high-spin iron complexes. These results suggest that the rate of intermolecular ET to/from [Fe–S] clusters is modulated by cluster size. The measured PCET self-exchange rate constant for 1 and 4 at −30 °C is (3.8 ± 0.7) × 10⁴ M^–1 s^–1. Analysis of rate constants using the Marcus cross-relation suggests that this process likely occurs via a concerted proton–electron transfer (CPET) mechanism. The implications of these findings to biological systems are also discussed, including the conclusion that histidine-ligated [2Fe–2S] clusters should not have a strong bias to undergo concerted e^–/H⁺ transfers.

[Fe₂S₂(^Prbbim)(^PrbbimH_x)]^y- clusters have been generated in multiple redox and protonation states. Their PCET and ET thermochemistry and reactivity are described. The PCET self-exchange reaction occurs by concerted e⁻/H⁺ exchange, and the ET self-exchange barriers for different clusters are shown to scale with [Fe−S] cluster size. The implications of these results for the reactivity of biochemical imidazole-ligated clusters is discussed.

ESR-Investigations on the Dynamic Solvent Effects of Degenerate Electron Exchange Reactions. Part I: Cyanobenzenes

The rates of degenerate electron exchange (electron self-exchange) of various cyanobenzenes have been measured by EPR line broadening technique in nine different solvents at room temperature. The molecules studied comprise besides benzene-1,2-dicarbonitrile, benzene-1,4-dicarbonitrile and benzene-1,2,4,5-tetracarbonitrile, the two isomeric tricyanobenzenes, benzene-1,2,3-tricarbonitrile and benzene-1,2,4-tricarbonitrile, the anion radicals of which have not been characterized before.

The experimentally observed rates vary from 4.5 × 108 to 44.0 × 108 M−1 s−1 and show the pronounced dependence on the longitudinal relaxation times, τL, of the solvents. The solvent dynamical effect so manifested is confirmed with remarkable clarity using solvents spanning a wide range of τL-values, which comprise acetonitrile (0.2 ps) and o-dichlorobenzene (6.0 ps) at its extremes. The rate constants are compared with Marcus theory using the continuum model (CM) and the mean spherical approximation (MSA) for the outer sphere reorganization energies and Nelson’s method for the inner sphere reorganization energies. Furthermore, an estimation of the resonance splitting energies, V RP, is given based on the experimental rates.

On the Coherent Description of Diffusion-Influenced Fluorescence Quenching Experiments

The fluorescence quenching by electron transfer of a fluorophore, 2,5-bis(dimethylamino)-1,3-benzenedicarbonitrile, to 1,3-dimethyl-2-nitrobenzene, has been studied by means of time-resolved and steady-state experiments at different viscosities and up to large quencher concentrations. Differential Encounter Theory (DET) has been used to rationalize the results, in combination with electron transfer modelled by the Marcus theory. Additionally, the solvent structure and the hydrodynamic effect on the diffusion coefficient have been taken into account. Any simpler model failed to simultaneously fit all the results. The large number of quencher concentrations used is crucial to unambiguously extract the electron transfer parameters.

Continuum of outer- and inner-sphere mechanisms for organic electron transfer. Steric modulation of the precursor complex in paramagnetic (ion-radical) self-exchanges

Transient 1:1 precursor complexes for intermolecular self-exchange between various organic electron donors (D) and their paramagnetic cation radicals (D+*), as well as between different electron acceptors (A) paired with their anion radicals (A-*), are spectrally (UV-NIR) observed and structurally (X-ray) identified as the cofacial (pi-stacked) associates [D, D+*] and [A-*, A], respectively. Mulliken-Hush (two-state) analysis of their diagnostic intervalence bands affords the electronic coupling elements (HDA), which together with the Marcus reorganization energies (lambda) from the NIR spectral data are confirmed by molecular-orbital computations. The HDA values are found to be a sensitive function of the bulky substituents surrounding the redox centers. As a result, the steric modulation of the donor/acceptor separation (rDA) leads to distinctive electron-transfer rates between sterically hindered donors/acceptors and their more open (unsubstituted) parents. The latter is discussed in the context of a continuous series of outer- and inner-sphere mechanisms for organic electron-transfer processes in a manner originally formulated by Taube and co-workers for inorganic (coordination) donor/acceptor dyads-with conciliatory attention paid to traditional organic versus inorganic concepts.

Molecular and Electronic Structures of the Long-Bonded π-Dimers of Tetrathiafulvalene Cation-Radical in Intermolecular Electron Transfer and in (Solid-State) Conductivity

Tetrathiafulvalene (TTF) as the prototypical electron donor for solid-state (electronics) applications is converted to the unusual cation-radical salt, TTF+* CB- (where CB- is the non-coordinating closo-dodecamethylcarboranate), for crystallographic and spectral analyses. Near-IR studies establish the spontaneous self-association of TTF+* to form the diamagnetic [TTF+,TTF+] dication and to also undergo the equally rapid cross-association with its parent donor to form the mixed-valence [TTF+*,TTF] cation-radical. The latter, most importantly, represents the first (dyad) member of a series of p-doped tetrathiafulvalene (stacked) arrays, and the thorough scrutiny of its electronic structure with the aid of Mulliken-Hush (two-state) analysis of the diagnostic (intervalence) NIR band reveals Robin-Day Class II behavior. The theoretical consequences of the unique structure of the mixed-valence [TTF+*,TTF] dyad on (a) the electron-transfer mechanism for self-exchange, (b) the molecular-orbital analysis of the Marcus reorganization energy, and (c) the ab initio computation of the coupling element or transfer integral in p-doped (solid-state) arrays are discussed.

Electron Transfer in Supercritical Carbon Dioxide: Ultraexothermic Charge Recombination at the End of the “Inverted Region”

Charge-recombination rates in contact radical-ion pairs, formed between aromatic hydrocarbons and nitriles in supercritical CO(2) and heptane, decrease with the exothermicity of the reactions until they reach -70 kcal mol(-1), but from there on an increase is observed. The first decrease in rate is typical of the "inverted region" of electron-transfer reactions. The change to an increase in the rate for ultra-exothermic electron transfer indicates a new free-energy relationship. We show that the resulting "double-inverted region" is not due to a change in mechanism. It is an intrinsic property of electron-transfer reactions, and it is due to the increase of the reorganisation energy with the reaction exothermicity.

ESR-spectroscopy in ionic liquids: Dynamic linebroadening effects caused by electron-self exchange reactions within the methylviologene redox couple

Well-resolved ESR-spectra of the methylviologene radical cation (MV*+) are recorded in room-temperature liquid ions as solvents. The temperature dependences of the ESR-coupling constants are similar to those measured in classical organic solvents. Electron-self exchange rates are reported for the methylviologene redox couple (MV++/MV*+) in 1-butyl-3-methylimidazolium hexafluorophosphate (bmim+ PF6-), 1-butlyl-3-methylimidazolium fluoroborate (bmim+ BF4-) and 1-ethyl-3-imidazolium ethylsulfate (emim+ O3SOEt-) within a temperature range of 350 K < or = T < or = 460 K. The diffusion controlled rate constants observed vary between 8.2 x 10(7) M(-1) s(-1) and 1.2 x 10(9) M(-1) s(-1). From temperature-dependent measurements the activation energies obtained range from 27.4 kJ/mol in emim+ O3SOEt- to 42.1 kJ/mol in bmim+ PF6-, respectively.

Intermolecular Electron-Transfer Mechanisms via Quantitative Structures and Ion-Pair Equilibria for Self-Exchange of Anionic (Dinitrobenzenide) Donors

Definitive X-ray structures of "separated" versus "contact" ion pairs, together with their spectral (UV-NIR, ESR) characterizations, provide the quantitative basis for evaluating the complex equilibria and intrinsic (self-exchange) electron-transfer rates for the potassium salts of p-dinitrobenzene radical anion (DNB(-)). Three principal types of ion pairs, K(L)(+)DNB(-), are designated as Classes S, M, and C via the specific ligation of K(+) with different macrocyclic polyether ligands (L). For Class S, the self-exchange rate constant for the separated ion pair (SIP) is essentially the same as that of the "free" anion, and we conclude that dinitrobenzenide reactivity is unaffected when the interionic distance in the separated ion pair is r(SIP) > or =6 Angstroms. For Class M, the dynamic equilibrium between the contact ion pair (with r(CIP) = 2.7 Angstroms) and its separated ion pair is quantitatively evaluated, and the rather minor fraction of SIP is nonetheless the principal contributor to the overall electron-transfer kinetics. For Class C, the SIP rate is limited by the slow rate of CIP right arrow over left arrow SIP interconversion, and the self-exchange proceeds via the contact ion pair by default. Theoretically, the electron-transfer rate constant for the separated ion pair is well-accommodated by the Marcus/Sutin two-state formulation when the precursor in Scheme 2 is identified as the "separated" inner-sphere complex (IS(SIP)) of cofacial DNB(-)/DNB dyads. By contrast, the significantly slower rate of self-exchange via the contact ion pair requires an associative mechanism (Scheme 3) in which the electron-transfer rate is strongly governed by cationic mobility of K(L)(+) within the "contact" precursor complex (IS(CIP)) according to the kinetics in Scheme 4.

Electron transfer reactions of tris(polypyridine)cobalt(iii) complexes, [Co(N–N)3]3+, with verdazyl radicals in acetonitrile solution

The kinetics and mechanisms of the reactions of 3-(4-X)-phenyl-1,5-diphenyl-verdazyl radicals where X = Cl, H, CH3 and CH3O with [Co(N-N)3]3+, N-N = 2,2'-bipyridyl (bpy), 1,10-phenanthroline (phen) and 4,7-dimethyl-1,10-phenanthroline (4,7-Me2phen), have been investigated in acetonitrile at 25 degrees C and ionic strength 0.05 mol dm(-3)(nC4H9)4NPF6 using stopped flow spectrophotometry. In all cases, transfer of one electron from the radical takes place resulting in the production of a Co(II) species and a verdazylium cation. The electron transfer occurs by an outer-sphere mechanism and the reactions appear to be consistent with Marcus theory. The self-exchange rate constants for the verdazyl-verdazylium cation have been estimated and are of the order of 3.4(+/-1.9) x 10(7) dm(3) mol(-1) s(-1). This rate constant is consistent with the fact that the reactions of [Ru(bpy)3]3+ with verdazyl radicals are too rapid to be investigated by stopped flow spectrophotometry.

Donor-acceptor (electronic) coupling in the precursor complex to organic electron transfer: intermolecular and intramolecular self-exchange between phenothiazine redox centers

Intermolecular electron transfer (ET) between the free phenothiazine donor (PH) and its cation radical (PH*+) proceeds via the [1:1] precursor complex (PH)(2)*+ which is transiently observed for the first time by its diagnostic (charge-resonance) absorption band in the near-IR region. Similar intervalence (optical) transitions are also observed in mixed-valence cation radicals with the generic representation: P(br)P*+, in which two phenothiazine redox centers are interlinked by p-phenylene, o-xylylene, and o-phenylene (br) bridges. Mulliken-Hush analysis of the intervalence (charge-resonance) bands afford reliable values of the electronic coupling element H(IV) based on the separation parameters for (P/P*+) centers estimated from some X-ray structures of the intermolecular (PH)(2)*+ and the intramolecular P(br)P*+ systems. The values of H(IV), together with the reorganization energies lambda derived from the intervalence transitions, yield activation barriers DeltaG(ET)() and first-order rate constants k(ET) for electron-transfer based on the Marcus-Hush (two-state) formalism. Such theoretically based values of the intrinsic barrier and ET rate constants agree with the experimental activation barrier (E(a)) and the self-exchange rate constant (k(SE)) independently determined by ESR line broadening measurements. This convergence validates the use of the two-state model to adequately evaluate the critical electronic coupling elements between (P/P*+) redox centers in both (a) intermolecular ET via the precursor complex and (b) intramolecular ET within bridged mixed-valence cation radicals. Important to intermolecular ET mechanism is the intervention of the strongly coupled precursor complex since it leads to electron-transfer rates of self-exchange that are 2 orders of magnitude faster (and activation barrier that is substantially lower) than otherwise predicted solely on the basis of Marcus reorganization energy.

Electron Self-Exchange Kinetics Determined by MARY Spectroscopy: Theory and Experiment

The electron self-exchange between a neutral molecule and its charged radical, which is part of a spin-correlated radical ion pair, gives rise to line width effects in the fluorescence-detected MARY (magnetic field effect on reaction yield) spectrum similar to those observed in EPR spectroscopy. An increasing self-exchange rate (i.e., a higher concentration of the neutral molecule) leads to broadening and subsequent narrowing of the spectrum. Along with a series of MARY spectra recorded for several systems (the fluorophores pyrene, pyrene-d(10) and N-methylcarbazole in combination with 1,2- and 1,4-dicyanobenzene) in various solvents, a theoretical model is developed that describes the spin evolution and the diffusive recombination of the radical pair under the influence of the external magnetic field and electron self-exchange, thereby allowing the simulation of MARY spectra of the systems investigated experimentally. The spin evolution of the radicals in the pair is calculated separately using spin correlation tensors, thereby allowing rigorous quantum mechanical calculations for real spin systems. It is shown that the combination of these simulations with high resolution, low noise experimental spectra makes the MARY technique a novel, quantitative method for the determination of self-exchange rate constants. In comparison to a simple analytical formula which estimates the self-exchange rate constant from the slope of the linear part of a line width vs concentration plot, the simulation method yields more reliable and accurate results. The correctness of the results obtained by the MARY method is proved by a comparison with corresponding data from the well-established EPR line broadening technique. With its less stringent restrictions on radical lifetime and stability, the MARY technique provides an alternative to the classical EPR method, in particular for systems involving short-lived and unstable radicals.

Slow hydrogen atom self-exchange between Os(IV) anilide and Os(III) aniline complexes: relationships with electron and proton transfer self-exchange

Hydrogen atom, proton and electron transfer self-exchange and cross-reaction rates have been determined for reactions of Os(IV) and Os(III) aniline and anilide complexes. Addition of an H-atom to the Os(IV) anilide TpOs(NHPh)Cl(2) (Os(IV)NHPh) gives the Os(III) aniline complex TpOs(NH(2)Ph)Cl(2) (Os(III)NH(2)Ph) with a new 66 kcal mol(-1) N-H bond. Concerted transfer of H* between Os(IV)NHPh and Os(III)NH(2)Ph is remarkably slow in MeCN-d(3), with k(ex)(H*) = (3 +/- 2) x 10(-3) M(-1) s(-1) at 298 K. This hydrogen atom transfer (HAT) reaction could also be termed proton-coupled electron transfer (PCET). Related to this HAT process are two proton transfer (PT) and two electron transfer (ET) self-exchange reactions, for instance, the ET reactions Os(IV)NHPh + Os(III)NHPh(-) and Os(IV)NH(2)Ph(+) + Os(III)NH(2)Ph. All four of these PT and ET reactions are much faster (k = 10(3)-10(5) M(-1) s(-1)) than HAT self-exchange. This is the first system where all five relevant self-exchange rates related to an HAT or PCET reaction have been measured. The slowness of concerted transfer of H* between Os(IV)NHPh and Os(III)NH(2)Ph is suggested to result not from a large intrinsic barrier but rather from a large work term for formation of the precursor complex to H* transfer and/or from significantly nonadiabatic reaction dynamics. The energetics for precursor complex formation is related to the strength of the hydrogen bond between reactants. To probe this effect further, HAT cross-reactions have been performed with sterically hindered aniline/anilide complexes and nitroxyl radical species. Positioning steric bulk near the active site retards both H* and H(+) transfer. Net H* transfer is catalyzed by trace acids and bases in both self-exchange and cross reactions, by stepwise mechanisms utilizing the fast ET and PT reactions.

Intermolecular electron transfer reactivity determined from cross-rate studies

Electron-transfer cross-reactions between neutral molecules and their radical cations spanning a wide range of structural type and intrinsic reactivity have been analyzed using classical Marcus theory. The principal factor found to govern intrinsic reactivity is the inner-shell bond reorganization energy. The HOMO-LUMO overlap of alkyl groups on reacting molecules is generally sufficient to provide facile electron transfer; however, a significant steric effect on this overlap is observed for hydrazines with alkyl groups larger than methyl.

Dimerization of organic free radicals in solution. 1. Temperature dependent measurements

Dimerization enthalpies and equilibrium constants have been determined for the radical anion of 2,3-dichloro-5,6-dicyano-p-benzoquinone (DDQ), the radical cations of N,N,N',N'-tetramethyl-p-phenylenediamine, N,N-dimethyl-p-phenylenediamine, 2,3,5,6-tetramethyl-p-phenylenediamine, N,N,N',N'-tetraethyl-p-phenylenediamine, N,N-diethyl-p-phenylenediamine and N,N,N'-trimethyl-p-phenylenediamine. Neutral radicals investigated are 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) and galvinoxyl. Solvent used was acetone, EtOH/Et2O-mixture (2:1 volume), propionitrile/butyronitrile-mixture (1:1 M) and dichloromethane. Measured dimerization enthalpies deltaHdim vary from -72.1 to -16.6 k/mol.