Marcus Model Research Articles

Electron Transfer Modelling of Electrical Dark- and Photoconductivity of Redoxactive Ion Pairs

Abstract Ion pair charge-transfer (IPCT) complexes consisting of dianionic dithiolene metallates [ML2]2- M = Ni, Pd, Pt, Cu, Zn, and dicationic 4,4′- and 2,2′-bipyridinium derivatives (A2+) exhibit IPCT bands in the VIS-NIR region of the electronic absorption spectrum. When both components are planar, the solid state structure consists of mixed donor–acceptor stacks while that is not the case when one or both are non-planar. By proper selection of the two components the driving force of electron transfer (ΔG 12) from the dianion to the dication is varied from 0.7 to -0.1 eV. It is shown that the Hush relation between optical and thermal electron transfer is fulfilled for a number of thirty-two complexes. The reorganization energy is in the range of 60 kJ·mol−1 for the d8 complexes while it is almost two times larger for the d10 zinc compounds. The extent of charge delocalization is typical for outer-sphere complexes as indicated by the parameter α2 which is in the range of 10−4. Correspondingly, the interaction between the two redox states is rather weak as suggested by the values of 220-360 cm−1 calculated for the exchange matrix element. Free activation enthalpies ΔG∗ of electron transfer, as calculated within the Hush–Marcus model, amount from 0.15 to 0.73 eV. It is found that the electrical dark conductivity of these composite solids can be quantitatively predicted from ΔG∗ in the range from 10−10 to 10−3 ω−1 cm−1 in the case of complexes consisting of planar components (Class I) while in the presence of a nonplanar acceptor or copper as the central metal (Class II) no similar relation is observed. The electrical photoconductivity is wavelength dependent and exhibits a maximum in the region of the IPCT band. Laser excitation of the solids produces a transient photovoltage (Dember Voltage) with a half-life of about 20 milliseconds. The rcsults suggest that charge generation occurs by electron transfer and charge migration by a hopping mechanism. When a photoisomerizable olefinic acceptor is employed, the conductivity is ten times larger for the cis-isomer.

Electron transfer. 121. Oxidations by Rhodium‐Bound Superoxide

AbstractThe violet superoxo complex, [(H2O)4(OH)RhIII(O2)RhIII(OH)(H2O)4]3+, formed by treatment of (RhII)24+ with O2 in HClO4, is converted to a le− reduction product, the corresponding μ‐peroxo complex, by the reductants I−, IrCl63−, and the trinuclear aquamolybdenum(III) cation, (MoIII)3. Each reaction is first‐order in both redox partners, and the le− reduction by IrCl63− is followed by a much slower conversion to a peroxide‐free complex. Among the rapid reductions of the superoxo derivative examined here and in a previous study, only that by IrCl63− is accelerated by increases in acidity; the rate law for this reaction features both an acid‐independent and a [H+]‐proportional component, the latter stemming from partial conversion of the oxidant to its conjugate acid (pKA < −1.0). Rate laws for reductions by other metal‐center reagents generally exhibit inverse‐[H+] terms, reflecting deprotonation of the reductant. All reductions thus far observed involving this superoxo species appear to be outer‐sphere. Treatment of acid‐independent rate constants within the framework of the Marcus model, allows estimates of the self‐exchange rate, k11, for the (RhIII)2‐bound superoxo‐peroxo couple. Because values of k11 calculated from the several reductions span a range of 104.5, reductions of the superoxo complex cannot be taken to conform satisfactorily to the Marcus treatment, being in this respect comparable to the systems VO(OH)+/2+, Mn2+/3+, Eu2+/3+, and Ti(OH)2+/3+, each of which exhibits similar divergences. The wide range of calculated self‐exchange rates appears to invalidate an earlier suggestion that reduction of the superoxo complex by Fe2+ proceeds primarily through a bridged path. © 1994 John Wiley & Sons, Inc.

Electron transfer. 123. Competitive redox reactions involving a Cobalt(I) intermediate

he hypophosphito derivative of CoIII, (NH3)5CoO2PH2 2+, decomposes in basic media, yielding Co(II) quantitatively, along with a 1:1 mixture of hypophosphite and phosphite. Earlier studies point to a cobalt (I) intermediate, which rapidly reduces a second molecule of Co(III) reactant to Co(II). In the presence of an external cobalt (III) oxidant (Co3X), the latter competes with the hypophosphito complex for Co(I), lowering the yield of free hypophosphite. From the ratio of phosphorus products (P3/P1), evaluated by proton decoupled 31P NMR, the relative reactivities (kt/kc) of the external Co(III) “traps” and the hypophosphito complex may be determined. A log-log plot comparing values of kt/kc with rates for reductions of the same series of Co(III) oxidants with Ru(NH3)6 2+ (kRu values) is badly scattered with a slope of only 0.23, well below the value of unity stipulated by the Marcus model, indicating that an outer-sphere mechanism cannot operate for all of the Co(III)-Co(I) reactions and may not operate for any, except for that with Co(NH3)5(py)3+. Among the carboxylato-substituted oxidants, there are no rate enhancements by neighbouring pyridine, -SR,-OH, -CHO, or -SO3H functions, in contrast to the accelerations previously observed for reductions by Cr(II), Eu(II) and Ti(III), which are attributed to intermediacy of chelate-stabilized precursor complexes. It is suggested that the Co(III)-Co(I) reactions, which determine the ratio of phosphorus products, are much more rapid than the ligand substitution at the Co(I) center which must precede chelate formation, and that the latter therefore does not intervene significantly in the redox processes.

Marcus inverted region: nature of donor–acceptor pairs and free ion yields

The free ion yield (ΦR) resulting from the fluorescence quenching of 9,10-dicyanoanthracene (DCA) by various electron donors in acetonitrile has been studied using ns laser photoconductivity. The influence of the chemical nature of the doors is established in a general manner. For a given oxidation potential Eox(D/D+), the rate constant of geminate ion recombination, kbac, decreases significantly as the electronic delocalization of the donor increases. As a consequence multiple Marcus plots are observed in the inverted region. These plots show decreasing curvature when going from stilbenes to amines as donors. This ‘fan effect’ is tentatively explained by considering the detailed roles of the parameters V, λ and hν in the Marcus model.

Vibrational relaxation, dissociation, and dissociation incubation times in norbornene

Shock waves in norbornene (bicyclo [2,2,1] hept-2-ene, C7H10)–krypton mixtures have been examined with the laser-schlieren technique over the very wide range of conditions, 542–1480 K, and 34–416 Torr in 0.5%, 2%, and 4% C7H10. The experiments exhibit both vibrational relaxation (542–1480 K) and the retro-Diels–Alder dissociation, norbornene→1,3-cyclopentadiene+ethylene (869–1480 K). Over 869–1304 K, and for pressures below 140 Torr, both relaxation and dissociation are resolved. These experiments provide the first measurements of unimolecular incubation (induction) times for the dissociation of a large polyatomic molecule. The ratio ti/τ decreases from ∼5 to 2 in 900–1300 K. Vibrational relaxation is rapid, log10 Pτ (μs atm)=0.066−6.70/T1/3, with a weak inverse temperature dependence, but is completely consistent with series excitation through the lowest-frequency mode. Dissociation shows very strong unimolecular falloff. A Rice–Ramsperger–Kassel–Marcus (RRKM) model, parametrized to fit the observations (E0=44.2 kcal/mol, 〈ΔE〉down=280 cm−1), finds the reaction closer to the low pressure limit k0 than to k∞ for 1400 K and 100 Torr. Earlier work at low temperatures (<750 K) has Ea too low to extrapolate to the present results. Thus a significant increase in Ea∞ is indicated over 700–1000 K, suggesting a change in mechanism.

Reductive quenching of excited states of chromium(III)-polypyridyl complexes with alkyl aryl sulphides

The variation in the quenching rate constants,k q, of *Cr(NN) 3 3+ with the change in the structure of organic sulphides in deaerated acetonitrile solutions is explained with Marcus model. The retardation in k q values for sulphides with bulky alkyl groups in RSPh is accounted for in terms of change of electron transfer distance. The formation of oxidised products in aerated solutions is explained by the formation of singlet oxygen in the system.

Kinetic energy release distribution in C 6H + [rad]6 → C 6H + [rad]4 + H 2. Partitioning of the reverse critical energy

The kinetic energy release distribution (KERD) in the unimolecular H 2 elimination reaction of the benzene molecular ion, which proceeds with a significant reverse critical energy, has been obtained. The existing statistical theories have been found inadequate to explain the experimental data. A modified statistical model which is an extension of a Marcus model has been proposed and the calculated result has been in fair agreement with the experimental data. The reason for some deviations from experimental KERD in both high and low kinetic energy release has been discussed.

Synthesis and Photoproperties of Silicon Phthalocyanines and Silicon Naphthalocyanines

AbstractSilicon phthalocyanines and silicon naphthalocyanines, which are two derivatives in the family of hematoporphyrin, have been synthesized to assess their potential as photosensitizers for photodynamic therapy. For these complexes the red shift of their Q‐band maximum absorption tends to depend on the nature of the axial substituent. The bimolecular rate coefficients for the interacting between photosensitizer, either SiNC or SiPC, and generated singlet molecular oxygen were determined from the time‐resolved emission spectrum of singlet oxygen at 1.27 μm. On the basis of these data the electron‐transfer quenching mechanism is discussed in relation to the Marcus model.

An integral equation approximation for the dynamics of reversible electron-transfer reactions

The solution to an integral equation [J. Zhu and J. C. Rasaiah, J. Chem. Phys. 96, 1435 (1992)] for the survival probabilities in the Sumi–Marcus model of reversible electron-transfer (ET) reactions, in which ligand vibrations and fluctuations in the solvent polarization play important roles, is obtained numerically using a simple computer program suitable for use on a PC. The solutions depend on the time correlation function Δ(t) of the reacting intermediates along the reaction coordinate which is shown to be equal to the time correlation function of the Born free energy of solvation of these intermediates even in discrete molecular solvents provided its response is linear. This enables Δ(t) to be determined accurately from time-delayed fluorescence Stokes shift experiments or from dynamical theories of ion solvation; it is usually an exponential (Debye solvent) function of time or a sum of such exponentials (non-Debye solvent). The solutions to the integral equation, which can be obtained numerically for any given Δ(t), are found to predict the electron-transfer dynamics successfully over a wide range of model parameters. They can also be approximated by single or multiexponential interpolation formulas in which the thermally equilibrated rate constants are modified by a factor which reflects the relative importance of ligand (or inner-sphere solvent) vibration and outer-sphere solvation dynamics. The use of an effective longitudinal relaxation time in calculations of ET rates in solution is shown to be a poor assumption in some solvents. The theory is compared with an experiment in the inversion region, and its extension to include high-frequency vibrational modes that lead to an increased ET rate in other experiments is discussed.

A Marcus-type model for steric and electronic effects of ligands in atom transfer reactions of metal carbonyl radicals

The rate constants for reaction of a series of Re(CO) 4L (LCO, PR 3, P(OR) 3) radicals with various atom or functional group donors in hexane at room temperature have been measured using laser flash photolysis. The data in each series have been analyzed in terms of the linear free energy relationship, In k= aE i+bS i+ c, where E irepresents a measure of the donor character of ligand L (the 13C chemical shift of the CO groups in LNi(CO) 3), and S i represents a measure of its steric requirement (the ligand repulsive energy parameter, E R). Expressing the atom or group transfer process in terms of the Marcus model for atom transfer, the variation in electron donor-acceptor character of L is related to variation in the overall free energy change in the atom transfer step, ΔG°′. The variation in ligand steric requirement is related to variation in the intrinsic barrier for the process, ΔG *(O). The model leads to a new prediction: for a group of related reaction sets, such as the atom transfer reactions of the Re(CO) 4L radicals, the ratio a/b decreases monotonically with increasing exergonic character. That is, the relative sensitivity of the rate to variation in the electronic character of the ligand as compared with variation in its steric character decreases as the reaction becomes more exergonic. The predicted behavior is in good agreement with the experimental results for the large body of atom and group transfer data presented.

ESTIMATING MARYLAND CRITICAL AREA ACVS IMPACT ON FUTURE NONPOINT POLLUTION ALONG THE RHODE RWER ESTUARY1

ABSTRACT: This paper presents the results of an investigation of the effects of the Maryland Critical Area Act on generation of non‐point source loads of phosphorus, nitrogen, and sediment to the Rhode River estuary. The Simple Method model, the Marcus and Kearney regression model, and the CREAMS model were used to estimate annual loads under: (1) present conditions, (2) maximum land use development allowable under the Act, and (3) two sets of future land use conditions that might occur if the Act were not in place. Results indicate that the Critical Area Act can reduce the present generation of nonpoint nutrient and sediment loadings 20–30 percent from the regulated area. These reductions can occur while preserving agricultural lands and allowing limited residential and urban development. The decrease in nutrient loadings is primarily dependent upon implementation and enforcement of agricultural best management practices (BMPs). The BMPs could reduce present agricultural nutrient loadings by 90 percent to a level comparable to loadings from residential areas. The estimated effectiveness of the Critical Area Act is even greater when compared to potential future nutrient loadings if development in the area remains unregulated. Unrestricted residential and urban development could increase nutrient loadings by 200 percent to 1000 percent as compared to controlled development under Critical Area Act guidelines. The Critical Area Act primarily prevents these future increases by severely limiting woodland cutting, with lesser results obtained by requiring urban BMPs.

Slow time-resolved photodissociation ofp-iodotoluene ion

Using time-resolved photodissociation in the ion cyclotron resonance mass spectrometer, the dissociation of p-iodotoluene ion was time resolved at five wavelengths between 532 and 630 nm. This is the slowest dissociation which has been time resolved for ions of well defined internal energies, giving inverse time constants for fragment ion appearance ranging from 2×102 to 1.1×103 s−1. At the longer wavelengths, dissociation is in clear competition with infrared-radiative relaxation of the photoexcited ion, which is calculated by kinetic modeling of the observed curves to give an energy loss rate of 6.2 eV s−1 (50 000 cm−1 s−1). The dissociation kinetics of this ion are in complete accord with a Rice–Ramsberger–Kassel–Marcus (RRKM) model with E0 of 1.9 eV and ΔS1000 K of −4 eu. It is concluded from the high activation energy that the rate limiting step in the dissociation kinetics is a molecular rearrangement preceding dissociation.

Electron-transfer kinetics and ternary equilibria of the nitrogen dioxide(1+)/nitrogen dioxide/dinitrogen tetraoxide system by transient electrochemistry

The reversible redox potential is established for the NO{sub 2}{sup +}/NO{sub 2} couple by the cyclic voltammetric (CV) examination of the reduction of the nitronium ion as well as the microscopic reverse oxidation of nitrogen dioxide. The facile association of NO{sub 2} and dissociation of N{sub 2}O{sub 4} are specifically included in the electrode kinetics by the successful computer simulation of the cyclic voltammograms at relatively slow and fast CV scan rates. The kinetics of the N{sub 2}O{sub 4} dissociation (k{sub 1}) and NO{sub 2} association (k{sub 2}) are determined with the aid of single-step chronoamperometry by developing the theoretical working curves based on the CE(mono) mechanism in Scheme II. The strong dependence of the redox potential on the medium is associated with significant NO{sub 2}{sup +} coordination, as shown by the linear correlation with Gutmann's donor number of the solvent. The heterogeneous rate constant (k{sub s}) for electron transfer to NO{sub 2}{sup +} is found to be faster than k{sub s} for NO{sup +}, despite a significantly enhanced value of the intrinsic reorganization energy of NO{sub 2}{sup +} compared to NO{sup +} for outer-sphere electron transfer based on the Marcus model.

Unimolecular decomposition of methylsubstituted benzenes into benzyl radicals and hydrogen atoms

A homologous series of methylsubstituted benzenes and pyrazines are excited with an energy E by a short laser pulse following which, typically on a time scale of several hundred nanoseconds, hydrogen atoms are released from the methyl groups. The rate constants k(E) for the formation of the H or D atoms were determined from the time dependence of the laser-induced fluorescence (LIF) signals, and their velocity distributions were measured from the shapes of their LIF excitation curves. The velocity distributions were Maxwellian with translational temperatures remarkably close to the vibrational temperatures, typically 2000–3000 K, of the excited molecules assuming internal equilibration of the large energy E among the large number of internal modes. The logarithm of the rate constants obtained with 193 nm excitation plotted against 1/TV yields a straight line with an activation energy of 97 kcal/mol. A Rice–Ramsberger–Kassel–Marcus model invoking a transition state with several soft modes accounts very well for the rates of dissociation and for most but not all of the average kinetic energy of the released atoms.

The kinetic deuterium isotope effect of proton‐transfer reactions in solution. Comparison of the marcus and the quantum‐statistical mechanical models

AbstractThe free energy dependence of the kinetic deuterium isotope effect of proton‐transfer reactions in solution is usually analysed in terms of the Marcus model. By means of modern computer techniques, the more general quantumstatistical mechanical model is also amenable to routine application. The differnces in the basic assumptions of the two approaches concerning the kinetic isotope effect are discussed. Reaction series for which both the Brønsted relation and the free‐energy dependence of the kinetic isotope effect are available are analysed by means of the two models using one set of parameters for both free‐energy relations.

Rate dependence of electron transfer on donor-acceptor separation and on free enthalpy change. The tris(2,2'-bipyridine)ruthenium(2+)/viologen2+ system

By attachment of hydrocarbon chains of different lengths to the bipyridyl ligands in Ru(bpy)/sub 3//sup 2 +/ we have adjusted the donor-acceptor separation in the electron-transfer system Ru((C/sub n/H/sub 2n+1/)/sub 2/bpyl/sub 3//sup 2 +//methylviolgen. Two electron-transfer reactions with different ..delta..G are investigated in fluid solution: the quenching of the excited complexes by methylviologen (MV/sup 2 +/) which is exergonic with -0.4 eV and the thermal back electron transfer which is exergonic with -1.7 eV. We observe an exponential decrease of the quenching rate on distance. The back electron transfer is independent of donor-acceptor separation; electron transfer is found to take place at distances of 1.5 nm and more. The results are discussed in terms of a hypothesis on the interdependence of transfer distance and free enthalpy change and compared with current theories. In the framework of the simple classical Marcus model, the Marcus equation relating transfer rate and free enthalpy change is transposed into the Rehm-Weller equation by simple mathematical manipulations and the implications of this are discussed.

The Kinetic Deuterium Isotope Effect of Proton Transfer Reactions in Solution

The theoretical models for the treatment of the kinetic isotope effect of proton-transfer reactions (tunneling, Marcus and quantum-statistical mechanical model) are described. Scope and limits of these models are discussed with respect to intermolecular interaction, free energy relations, temperature, solvent and pressure dependence, and ultrafast protontransfer.

Interactions of several polycyclic aromatic hydrocarbons with DNA base molecules studied by absorption spectroscopy and fluorescence quenching

The interactions of several polycyclic aromatic hydrocarbons (PAHs) including benzo[ a]pyrene, benzo[ e]pyrene, benz[ a]anthracene, 7,12-dimethylbenz[ a]anthracene, 3-methylcholanthrene, dibenz[ a, c]anthracene and dibenz[ a, h]anthracene with selected deoxyribonucleic acid (DNA) bases, i.e. adenine, thymine, cytosine and 5-methylcytosine, and a nucleoside, guanosine, have been studied employing UV-visible absorption spectroscopy, fluorescence quenching and electrochemical measurements. The results indicate that PAHs interact with DNA bases by forming modernately strong 1:1 charge transfer (CT) complexes in their ground state. The fluorescence of PAHs was only quenched by 5-methylcytosine, quanosine and cytosine, and this was at lower than diffusion controlled rates in dimethyl sulfoxide. The fluorescence quenching rate constants showed a better inverse correlation with the solvent reorganization energies than with the free energies of activation calculated using the Marcus model of electron transfer.

LEED evaluation of three models of the Si{100} surface

A strong body of opinion has recently favoured the buckled dimer type of model for the Si{100} surface and we compare LEED calculations for two such models with experiment. The first model is that of Yin and Cohen which was proposed on the basis of minimization of the Hellman-Feynman forces using a self-consistent, local density, pseudopotential theory. The second model is that of Yang, Jona and Marcus which was found by varying structural parameters to obtain agreement with the LEED data. For comparison we also include the symmetric dimer model of Tong and Maldonado. Our calculations are fully dynamical and we treat the actual structures proposed without imposing any limitations to aid computation. We present visual comparisons of calculations and experimental data and also calculate the Pendry R factors. We find that the Yang, Jona and Marcus model is in best agreement with experiment, but the improvement over the other two models does not seem to be as great as one might expect if the structure were essentially correct. There is still some question therefore as to whether the model needs only minor modifications or significant changes.

Free‐energy correlation for catalysis of outer sphere electron‐transfer reactions by noncoordinated pyridine derivatives

AbstractRecent experimental data concerning the rate constants and their free energy of the outer sphere electron‐transfer reactions, as catalyzed by noncoordinated pyridine derivatives in aqueous solution, are examined for possible correlation. For the electron transfer reactions between V or Eu and the bipyridyl derivatives, such as N,N'‐dimethyl‐4,4′‐bipyridyl (paraquat) or diquat, the data are correlated quite well by the Marcus equation. The electron exchange rate constant, 5 × 107M−1·s−1, for an organic radical ion and its parent molecule obtained from semiquinones or their related compounds can be applied to these pyridine derivatives. However, in some cases such as electron transfer from paraquat or diquat cation radical to Co(en), positive departures from the Marcus model are observed. These positive departures are interpreted in terms of interaction between the molecular orbitals of electron donors and electron acceptors in the transition state.