Exothermic Electron Transfer Reactions Research Articles

Molecular-Orbital-Based Verification of Water Photo-Splitting on Pt-Loaded TiO2: Effective Formation of HOOH and Reduced Platinum Cluster as Precursors of O2 and H2

Sayama and Arakawa reported in 1997 that Pt-loaded nc-TiO2 catalyzes effective H2O photo-splitting occurring in aqueous sodium carbonate solutions (pH8~11.5). Sayama and Arakawa’s H2O photo-splitting is now verified by density-functional theory-based molecular modeling (DFT/MM), where Yamashita-Jono’s nc-TiO2 model of [HOTi9O18H], hydrated hydroxide anion model of [HO-&H2O] and platinum triangular pillar model of [Pt6] are employed. At first, hydroxyl anion of HO-&H2O is verified to undergo endothermic one-electron transfer oxidation, giving hydrogen peroxide of HOOH&(H2O)2 via formation of hydroxyl radical of HO.&H2O and its coupling. As for verification of electron-transfer reduction of Pt6 cluster for the H2O photo-splitting to H2, the van der Waals complex of [Pt6] with nonpolar H2O trimer model of [ts-(H2O)3] is molecular-modeled, and highly exothermic electron transfer reactions verify the effective H2 formation via formation of hydrogen radical on [Pt6]. As the model of Pt-loaded nc-TiO2 catalyst, van der Waals and Coulomb interaction-based complex of [HOTi9O18H] with [Pt6] and [HO-&H2O] is successfully molecular-modeled, and the molecular orbital energy structure rationalizes that the effective water-splitting catalysis should occur via effective electron transfer from HOMO of [HO-&H2O] to LUMO of [Pt6] when the catalyst is photo-energized. DFT/MM also verifies successive oxidation of HOOH to 3O2 and photo-regeneration of HOOH via radical anion of O2 .- that could be produced from 3O2 under UV irradiance of Sayama and Arakawa’s photocatalysis systems.

Examination of barriered and barrierless hydrogen atom abstraction reactions by organic radical cations: the cytosine radical cation

The radical cations of the nucleobases cytosine and adenine are easily generated in a dual cell Fourier transform ion cyclotron resonance mass spectrometer by using the technique of laser-induced acoustic desorption coupled with electron ionization. The cytosine radical cation is found to undergo facile hydrogen atom abstraction reactions with a variety of neutral reagents even when barrierless, exothermic electron transfer reactions are expected to dominate. In contrast, the adenine radical cation undergoes hydrogen atom abstraction only slowly in most of the cases studied. The ionic curve-crossing model is used to rationalize these results. Some of the thermodynamic and molecular properties of a radical cation that are favorable for efficient hydrogen atom abstraction are described in this article. Based on this analysis, dimethyl sulfoxide radical cation was predicted to abstract hydrogen atoms efficiently. Indeed, it was found to abstract hydrogen atoms at rates similar to cytosine radical cation. The transition from barriered to barrierless hydrogen atom abstraction that occurs as the ionization energy of the neutral hydrogen atom donor is lowered was used to “bracket” the recombination energy of cytosine radical cation at 8.9 ± 0.2 eV.

Investigations on nonradiative transitions in different environments using excited (or ground state) 1,2,3,4-tetrahydroquinoline (THQ) as donor and ground state (or excited) 9-fluorenone (9FL) or 2-nitro-9-fluorenone (2N9FL) as acceptors

By using steady state and time resolved spectroscopic techniques, investigations were made on the nature and mechanisms of different nonradiative processes involved within the excited donor (or acceptor) and ground state acceptor (or donor) in nonpolar n-heptane (NH), polar protic ethanol (EtOH), and polar aprotic acetonitrile (ACN) solvents at the ambient temperature as well as in EtOH rigid glassy matrix at 77 K. The bicyclic molecule 1,2,3,4-tetrahydroquinoline (THQ) was used as a donor (D) in the present investigation whereas 9-fluorenone (9FL) and 2-nitro-9-fluorenone (2N9FL) were chosen as electron acceptors (A). When the donor chromophore was excited in presence of an acceptor, highly exothermic electron transfer (ET) reactions seemed to occur from observed large negative driving energy (deltaG0) values, measured by electrochemical techniques, Förster's type energy transfer, static quenching, etc. An attempt was made to estimate separately the contributions of static and dynamic quenching modes in the overall quenching mechanism of donor fluorescence by using a model of modified Stern-Volmer (SV) relation. From this relation it seemingly indicated that the major contribution in quenching originated from the static mode. When excited acceptors react with the ground state donor THQ it is primarily ET reactions that seem to occur. Observations of the transient absorption spectra, by laser flash photolysis techniques, of contact ion-pairs of the present D-A systems along with the triplet absorption spectra of the monomeric acceptor (9FL and 2N9Fl) corroborate our views regarding the occurrence of photoinduced ET reactions within the present reacting systems. At 77 K the combined effect of Förster type energy transfer and static quenching seems to be responsible for observed lowering of donor fluorescence emission intensity in presence of acceptors (9FL or 2N9FL). However, the phosphorescence lifetime measurements reveal that the triplet donor might be involved in photoinduced ET reaction with the unexcited acceptor in rigid glassy matrix at 77 K and this possibly causes the reduction in the phosphorescence band intensity of the donor THQ in presence of the latter one. Key words: electron transfer, static quenching, fluorescence quenching, phosphorescence, energy transfer.

Investigations on the nature of non-radiative transitions from excited singlet and triplet states of dimethyl substituted phenols in the presence of acceptor 2-nitrofluorene at 77 K

Steady state emission measurements are combined with time-resolved experiments to examine the nature of the different non-radiative transitions from the photoexcited donors (D) (3,5-dimethylphenol, 35DMP; 2,6-dimethylphenol, 26DMP; 3,5-dimethylanisole, 35DMA; 2,5-dimethylanisole, 25DMA) in the presence of the acceptor (A) 2-nitrofluorene (2NF) in ethanol (EtOH) rigid glassy matrix at 77 K. At such low temperature observations of large negative driving energy (Δ G 0) values (−1.42 eV to −2.03 eV) for the systems of present excited singlet (S 1) donors and ground state 2NF are indicative of the occurrence of highly exothermic electron transfer (ET) reactions in the singlet state S 1 whereas relatively lower values of Δ G 0 (−0.17 eV to −0.70 eV) for the excited triplet (T 1) donors and the acceptor 2NF in the ground state suggest the involvement of moderately exothermic ET reactions within these D–A pairs. Following the Weller equation, the destabilization energy (Δ G 0 d) has been computed (to estimate the driving energy for ET reactions in solid solution) for the ion pair states of the present donor–acceptor molecules. However, the computed value of Δ G 0 d (∼0.26 eV) for the present D–A systems indicate that though, the driving energy decreases in magnitude does not reduce to a large extent on going from polar acetonitrile (ACN) liquid to EtOH glass. It seems in EtOH solid solution at 77 K dipole rotations of the solvent may not be fully eliminated unlike the situation observed by Wasielewski et al. in the case of less polar methyltetrahydrofuran glass environment. From the energy gap dependence of ET rates and the observed relationships between λ, nuclear re-organization energy parameter and Δ G 0, it is apparent that singlet (S 1) ET reactions might be occurring in the Marcus inverted region (MIR) while such reactions between triplet donors and ground state acceptor 2NF seem to proceed through the normal/intermediate region. From the observations of the large spectral overlapping between the donor emission and electronic absorption spectra of the acceptor coupled with the high values of T (99%), the theoretical transfer efficiency of non-radiative energy transfer of Förster's type, and R 0 (∼27 Å), Förster's critical energy transfer distance, it seemingly indicates that the combined effect of the concurrent processes of photoinduced ET and Förster's type energy transfer is primarily responsible for the observed fluorescence quenching of the present donors in the presence of the acceptor 2NF at 77 K. The same trend was observed at the ambient temperature as reported earlier. Moreover, steady state and time-resolved data reveal that triplet–triplet (T D 1→T A 1) energy transfer along with triplet state ET reactions might be responsible for the observed donor phosphorescence quenching phenomena. Reaction schemes describing the various possible pathways for the non-radiative depletion of the excited (singlet and triplet) states of the donors effected through the interactions with the quencher (electron acceptor) 2NF have been proposed from the observed experimental results.

Fluoresence quenching between strong π-electron donor-acceptors of carbazolocarbazole and tetranitrofluorenone leading to electron transfer

Singlet energies and fluorescence quantum yields of synthesized dihydrocarbazolocarbazole, 1, dimethylcarbazolocarbazole, 2, dibenzylcarbazolocarbazole, 3, were measured to be between 76.5−74.3kcal/mol and 0.07−0.02, respectively. A Stern-Volmer plot of fluorescence quenching of dihydrocarbazolocarbazole, 1, with 2,4,5,7-tetranitrofluorenone, 4, has given a rate constant of quenching of kq=7.4×1012M−1s−1. The free energies of the exothermic electron transfer reaction are calculated to be −33.6 kcal/mol for dihydrocarbazolocarbazole, 1, and −26.8 kcal/mol for dimethylcarbazolocarbazole, 2. High values for the rate of fluorescence quenching and the free energies are the evidence for an electron transfer process between these strong π-electron donor-acceptor complexed molecules.

Studies on quenching reactions in the excited electronic states of tetrahydronaphthols both at the ambient temperature as well as at 77 K

The present investigation was carried out at the ambient temperature as well as at 77 K both by steady-state and time-resolved luminescence techniques to reveal the mechanisms of non-radiative transitions of the lowest excited singlet (S 1) and triplet (T 1) states of tetrahydronaphthol donors 5,6,7,8-tetrahydro-1-naphthol (THN1OH) and 5,6,7,8-tetrahydro-2-naphthol (THN2OH) in presence of the electron acceptor 2-nitrofluorene (2NF) in solvents of different polarity. At room temperature large negative values of ΔG ° (~ −1.9 eV), Gibbs free energy for photo-induced electron transfer (ET) reaction, indicate highly exothermic ET reaction occurs within the present donor-acceptor systems possibly in the Marcus inverted region. At this temperature evidence of concurrent occurrence of Förster's-type singlet-singlet (S D 1→S A 1) energy transfer process is also found. In presence of the acceptor 2NF, the fluorescence of the donor molecule is strongly quenched and the large dynamic (as there is absence of ground-state complex) fluorescence quenching rate constant k q , of the order of 10 12 M −1s −1 is observed. This quenching has been ascribed mainly due to two concurrent processes: non-radiative energy transfer and ET. Radiative energy transfer is found to have negligible role. In 2NF, apart from the quenching in fluorescence spectra of the present donor molecules a longer wavelength band of broad nature was observed due to formation of contact charge transfer (CT) complex in non-polar solvent. In highly polar acetonitrile (ACN) this band was absent but instead another broad band at a far longer wavelength region due to formation of donor anion (confirmed from metallic sodium experiment and excitation spectra) was found. It was suggested that this anion was produced from its initially formed cationic species, resulted from ET reaction with 2NF. The reaction scheme showing this mechanism is given. At 77 K it seems the Förster mechanism of singlet-singlet energy transfer is still operative resulting the observed fluorescence quenching of the donor in presence of the acceptor 2NF. A reaction mechanism has been proposed for the observed lowering of donor phosphorescence intensity in presence of the acceptor. The possibility of the occurrence of photo-induced ET reaction between excited (T 1) donor and ground-state acceptor is hinted from time-resolved phosphorescence measurements and thermodynamic considerations.

Intramolecular charge transfer and exciplex formation in anthracene bichromophoric compounds

A binary compound containing strong electron donor and acceptor groups, ( N,N-dimethylanilino)-CH 2-9-cyanothrace ne ( II), was synthesized, and its photophysical behaviour was studied. Intramolecular exciplex emission was observed in non-polar and moderately polar solvents, but not in polar solvents. Exciplex formation in non-polar and moderately polar solvents accounts for the exothermic electron transfer reaction and/or the efficient coupling of the amine lone pair with 9-cyanoanthracene π orbitals; in polar solvents, the molecular structure corresponds to a solvent-separated radical ion pair formed by intermolecular electron transfer, where the energy is dissipated via back electron transfer (BET) without fluorescence emission. A new, blue-shifted emission at 510 nm appears in the region of the local emission band for compound II at 77 K, which may originate from a ground state, charge transfer (CT) conformer. The dependence of exciplex formation on the solvent and temperature is discussed by comparison with the compound ( N,N-dimethylanilino)-CH 2-anthracene ( I), and a simplified energy diagram showing intramolecular charge transfer and exciplex formation in compounds I and II is described. energy diagram showing intramlecular charge transfer and exciplex formation in compounds I and II is described.

Analysis of fluorescence quenching in some antioxidants from non-linear Stern—Volmer plots

The fluorescence quenching of 6-hydroxy-1,4-dimethylcarbazole (HDC) and α-tocopherol or vitamin E (α-toc) by methylene bromide (CH 2Br 2) in n-butanol was investigated by both stationary and time-dependence measurements. Nonlinear Stern-Volmer behavior was observed in both cases at higher quencher concentrations for these highly exothermic electron transfer (ET) intermolecular reactions. Both static and dynamic quenching models can fit the experimental data, but only the finite sink approximation model was able to recover both the mutual diffusion coefficient and the distance-averaged ‘activation energy controlled’ rate constant ( K a). The two ET reactions investigated are diffusion-controlled (α-toc) ( K a ⪢ K d) and diffusion-influenced (HDC) ( k a $ ̄ k d ) respectively.

Steady state and time resolved spectroscopic studies of the photoinduced electron-transfer reactions between electron donor xylenol and acceptor tetracyanoquinodimethane in acetonitrile at room temperature

The present study was undertaken both by steady state and time correlated single photon counting techniques to reveal the nature of the electron transfer (ET) process within excited (or ground) xylenol donor and ground state (excited) well-known acceptor tetracyanoquinodimethane (TCNQ) in highly polar solvent acetonitrile (ACN) at 300 K. Observations of poor overlap between the emission of the donor and the electronic absorption spectra of the acceptor and the high negative value of Δ G, the driving energy (Gibbs free energy) when either donor or acceptor chromophore is excited seemingly indicate that the observed fluorescence quenching of the donor in presence of TCNQ is mainly due to highly exothermic electron transfer reactions and no significant energy transfer process is operative here. It is suggested that such highly exothermic ET reaction, which has been proposed to be of outersphere type, occurs at a long distance (⩾7 A ̊ ) between the fluorescer (donor) and the quencher (acceptor). Observations of slow electron transfer rate, k ET (∼10 7 s −1) and − ΔG > λ (nuclear reorganization energy parameter) suggest that the reaction might occur in the Marcus inverted region. It has been proposed that in an ACN fluid solution the transient geminate ion-pair complex formed by ET reaction is of loose structure and due to the rapid dissociation of this complex stable anionic species TCNQ - ion is formed in the excited state. This anion is observed to emit at nearly 432 nm region. It is suggested that in the Marcus inverted region as the reaction becomes more exothermic, the necessary reorganization energy λ also increases.

Investigation of excited state electron-transfer reactions. A search for other associative processes

Abstract The present investigations were carried out to reveal the nature of the photoinduced electron-transfer (ET) process within the electron donors 1,2,3,4-tetrahydroquinoline (THQ) and 1-methyl-1,2,3,4-tetrahydroquinoline (THMe), and widely used acceptor tetracyanoquinodimethane (TCNQ) in the highly polar solvent acetonitrile (ACN) at 300 K. Observations of considerable overlapping between the emission spectrum of the donor molecules studied in the present investigation and the electronic absorption spectrum of the acceptor TCNQ, coupled to a high negative value of Δ G [the energy gap between the locally excited (LE) and radical ion pair (RIP) states] when one of the chromophores is excited, indicate the possibility of concurrent occurrence of the two processes, e.g. energy and electron transfer. Surprisingly even when the donor chromophore is photoexcited, no spectral manifestation of energy transfer was observed, though both steady state and time resolved (in the time domain of nanosecond order) spectroscopic measurements strongly suggest the occurrence of a highly exothermic ET reaction within the present donor—acceptor systems. Furthermore such ET reactions have been suggested to occur between donor and acceptor separated by a large distance ( ∼ 7 A), and quenching of fluorescence emission of donor molecules is caused primarily due to outer sphere ET reactions with the acceptor. Measured electron transfer rates ( k ET ) were found to be of much lower value ( ∼ 10 7 s −1 ). It is demonstrated that loose structure of the transient geminate ion pair complex is formed due to the encounter between excited acceptor (or donor) and unexcited donor (or acceptor), and due to this structural property, a stable anionic species (TCNQ − ion) is produced due to the rapid dissociation (probably in the picosecond time domain) of this excited complex. It is hinted that synthesis of biochromophoric systems in which the present donor and acceptor chromophore would be linked by a polymethylene type (σ-type) spacer might be useful in building good photoconducting materials.

The effects of quantum modes on the energy gap law for electron- transfer reactions

The effects of quantum modes on the free energy relationship for electron-transfer reactions formulated by the ‘‘spin-boson’’ model are examined. The modified energy gap law for exothermic electron transfer reactions with quantum modes is derived in a simple analytical form, using the method of steepest descent to avoid the usual multiple convolution integrals.

Interference of reaction channels for highly exothermic electron transfer reactions

The interference of electronic transitions to different vibronic states of the product is considered. The restrictions on the additivity of their rates are established. The upper limit of the full rate is found for the case when interference is significant. It cannot exceed the maximum rate in the fastest channel.

Redox-linked proton translocation in cytochrome oxidase: the importance of gating electron flow. The effects of slip in a model transducer

In at least one component of the mitochondrial respiratory chain, cytochrome c oxidase, exothermic electron transfer reactions are used to drive vectorial proton transport against an electrochemical hydrogen ion gradient across the mitochondrial inner membrane. The role of the gating of electrons (the regulation of the rates of electron transfer into and out of the proton transport site) in this coupling between electron transfer and proton pumping has been explored. The approach involves the solution of the steady-state rate equations pertinent to proton pump models which include, to various degrees, the uncoupled (i.e., not linked to proton pumping) electron transfer processes which are likely to occur in any real electron transfer-driven proton pump. This analysis furnishes a quantitative framework for examining the effects of variations in proton binding site pKas and metal center reduction potentials, the relationship between energy conservation efficiency and turnover rate, the conditions for maximum power output or minimum heat production, and required efficiency of the gating of electrons. Some novel conclusions emerge from the analysis, including: An efficient electron transfer-driven proton pump need not exhibit a pH-dependent reduction potential; Very efficient gating of electrons is required for efficient electron transfer driven proton pumping, especially when a reasonable correlation of electron transfer rate and electron transfer exoergonicity is assumed; and A consideration of the importance and possible mechanisms of the gating of electrons suggests that efficient proton pumping by CuA in cytochrome oxidase could, in principle, take place with structural changes confined to the immediate vicinity of the copper ion, while proton pumping by Fea would probably require conformational coupling between the iron and more remote structures in the enzyme. The conclusions are discussed with reference to proton pumping by cytochrome c oxidase, and some possible implications for oxidative phosphorylation are noted.

Gas-Phase reactions of NO 2− with nitrobenzenes and quinones. Electron transfer, clusters and formation of phenoxide and quinoxide negative ions. Use of NO 2 as a negative ion chemical ionization reagent

Negative-ion/molecule reactions in systems containing methane as the major gas (∼ 4 torr), with NO 2 and compounds A at mtorr pressures were studied in a pulsed electron, high pressure mass spectrometer. The compounds A were substituted nitrobenzenes and quinones. All these A compounds have positive electron affinities. Three types of reactions were observed and examined. (1) Electron transfer: A − + NO 2 = A + NO 2 −. The exothermic electron transfer reactions proceeded with ADO collision rates for exothermicities from 30 to ∼ 10 kcal mol −1. Lower exothermicities led to low collision yields. (2) Adduct formation: NO 2 − + A = NO 2 −·A. The equilibria for adduct formation were determined. Stable adducts are formed when A has hydrogens with partial protic character. The stability of the adducts NO 2 −·A increased with increase in the electron affinity of A, when A was a substituted nitrobenzene. Substituents that increase the electron affinity of nitrobenzene are electron-withdrawing groups which also increase the protic character of the hydrogens involved in bonding in NO 2 −·A. (3) Some of the compounds A were converted to phenoxy negative ions on reaction with NO 2 −. For example, para-dinitrobenzene leads to formation of the para-nitrophenoxide negative ion. The oxy-negative-ion-forming reaction can be isomer specific. The utility of reaction types (1)–(3) is examined from the standpoint of negative ion chemical ionization where the reagent gas is NO 2 in methane and the reagent ion is NO 2 −.

A semiconductor electrochemical approach to the kinetics of extremely exothermic electron transfer reactions

A semiconductor electrochemical approach to the kinetics of extremely exothermic electron transfer reactions

Theory of highly exothermic electron transfer reactions

The theory of highly exothermic homogeneous outer-sphere electron transfer reactions is discussed for transfers occurring over a range of distances. A finite rate of diffusion of reactants and their long-range force are treated by solving the diffusion equation numerically for the reactant pair distribution function. Steady-state solutions for the bimolecular rate constant are compared with experimental data as well as with our recent approximate analytic solution, which is found to agree in the present case. On the basis of short-time solutions, it is proposed that experiments which measure electron transfer rates at short times following the onset of reaction improve the possibility of observing the inverted effect in bimolecular systems. The chance of seeing it in linked systems (unimolecular reactions) is even greater. The relation between the prediction of an “inverted region” in the rate constant vs. ΔG° plot and the existence of a maximum in charge transfer spectral plots of intensity vs. absorption frequency is pointed out.

Exothermic rate restrictions on electron transfer in a rigid medium

Many highly exothermic (2–3 eV) electron transfer reactions are shown to be slower than moderately exothermic reactions by factors as large as 105. The decrease occurs in a regular way with increasing exothermicity, tending to confirm theoretical predictions of Franck–Condon restrictions on strongly exothermic electron transfer reactions. Deviations from the above trends occur if the reaction product, a molecular anion, has a low-lying electronic excited state into which the reaction may occur with more moderate vibrational exothermicity. Then greatly enhanced rates are found. The rates are enhanced to a lesser extent for acceptors likely to undergo configurational changes upon accepting an electron. These effects are found in measurements of rates of electron tunneling reactions between trapped electrons and 48 organic electron acceptors in rigid 2-methyltetrahydrofuran glass at 77 K. Electron tunneling rates were observed from 10−6 to 102 s. Measured tunneling distances were 15–40 Å. In most cases the observed kinetic decay curves are well simulated by a theory in which the only variable parameter is the effective Franck–Condon factor (F), which is a constant characteristic of the acceptor. For the various acceptors F ranges from 1 to 10−5, and scales the reaction rate at each distance. However in reactions of small vibration exothermicity, the Franck–Condon factors are expected to be very sensitive to small changes in reaction exothermicity caused by relaxations of trapped electrons, which deepen their trap depths with time and, possibly, a dispersion of trap depths. These effects cause F to change with time leading to changes in the shapes of the decay curves. The relationship between the shapes of the decay curves, Franck–Condon factors, and exothermicity allows a thorough and consistent semiquantitative interpretation of the present results and much of the earlier tunneling data on electron transfer reactions involving other solvents and solutes.

Transients and specific rates of some reactions of the solvated electron with inorganic ions in liquid ammonia investigated by nanosecond pulse radiolysis at 23.degree.C

For ammoniacal solutions at 23/sup 0/C, the absorption spectrum of CuCl and the transient absorption spectra of Ni/sup +/, Zn/sup +/, Cd/sup +/, Hg, Tl, and Pb/sup +/ are given. For the solvent liquid ammonia at 23/sup 0/C and in units of M/sup -1/ s/sup -1/, the measured specific rates of reactions of e/sup -//sub am/ with inorganic solutes follow in parentheses after each solute: Cu/sup +/ (2.5 x 10/sup 8/), Hg/sup +/ (2.3 x 10/sup 11/), Tl/sup +/ (1.2 x 10/sup 12/), Fe/sup 2 +/ (1.2 x 10/sup 9/ at zero ionic strength), Co/sup 2 +/ (5.7 x 10/sup 11/), Ni/sup 2 +/ (1.1 x 10/sup 11/), Cu/sup 2 +/ (8.3 x 10/sup 11/), Zn/sup 2 +/ (1.3 x 10/sup 10/), Cd/sup 2 +/ (4.6 x 10/sup 11/), Hg/sup 2 +/ (3.2 x 10/sup 11/), Pb/sup 2 +/ (5.6 x 10/sup 11/), Al/sup 3 +/ (less than 6 x 10/sup 6/), Cr/sup 3 +/ (5.8 x 10/sup 10/), Fe/sup 3 +/ (4.9 x 10/sup 11/ at zero ionic strength), Co/sup 3 +/ (7.7 x 10/sup 11/), Ce/sup 3 +/ (3.1 x 10/sup 11/), Ce/sup 4 +/ (1.5 x 10/sup 11/), No/sub 3//sup -/ (1.2 x 10/sup 8/ at zeromore » ionic strength), ClO/sub 4//sup -/ (no reaction), I/sup -/ (no reaction). Only the reaction of e/sub am//sup -/ with Tl/sup +/ appears to be a diffusion-controlled reaction. For the solvent liquid ammonia at 25/sup 0/C, the standard free energy changes for the reactions of e/sub am//sup -/ with metal cations mentioned above have been computed. The activation-controlled specific rate increases and attains a plateau value with the increasing negative free energy of the reaction. This relationship is consistent with a quantum mechanical description of an exothermic electron transfer reaction, in which the theory is formulated by treating the reaction as the nonradiative decay of a ''supermolecule'' consisting of the electron donor, the electron acceptor, and the polar solvent.« less

The effect of intramolecular quantum modes on free energy relationships for electron transfer reactions

A general quantum mechanical description of exothermic electron transfer reactions is formulated by treating such reactions as the nonradiative decay of a ’’supermolecule’’ consisting of the electron donor, the electron acceptor, and the polar solvent. In particular, the role of the high-frequency intramolecular degrees of feedom on the free energy relationship for series of closely related reactions was investigated for various model systems involving displacement of potential energy surfaces, frequency shift, and anharmonicity effects. The free energy plots are generally found to pass through a maximum and to be asymmetric with a slower decrease in the transition probability with increasing energy of reaction. For high-frequency intramolecular modes this provides a rationalization of the experimental observation of ’’activationless’’ regions. Isotope effects are discussed as also are the oscillatory free energy relationships, predicted for low temperatures and high frequencies, and which are analogous to the vibrational structure in optical transitions.