A model of the distance dependence of photoinduced donor-acceptor electron transfer in DNA is presented that includes the distance dependence of the solvent reorganization energy and free energy in the heterogeneous DNA environment. DNA is modeled as a low dielectric region that represents the base stack and two regions with more moderate dielectric properties that represent the DNA backbone. The DNA is surrounded by a high dielectric medium, which represents water. Model calculations show the importance of including the reorganization energy and the free energy change and illustrate the differences between the inhomogeneous model and homogeneous single dielectric constant calculations using standard Marcus theory. Calculations are performed for comparison to published experimental work (Science 1997, 277, 673; 1 J. Am. Chem. Soc. 1992, 114, 3656 2 ). Fits to one set of data 2 permit the previously reported distance dependence to be separated into an electronic contribution and solvent reorganization energy and free energy contributions. For the other set of data, 1 inclusion of the solvent reorganization energy and free energy distance dependences in the analysis of the overall distance dependent data suggest that the Marcus form of the distance dependent rate constant including the Marcus reorganization energy is not consistent with the data.
Experimental determinations of the dynamics of photoinduced electron transfer from rubrene to duroquinone in three solvents, dibutyl phthalate, diethyl sebacate, and cyclohexanone are presented. Measurements of the donor (rubrene) fluorescence decays were made with time-correlated single-photon counting. The data are analyzed using recent theoretical developments that include important features of the solvent, i.e., the effects of finite molecular volume on local solvent structure and on the mutual donor-acceptor diffusion rates. Inclusion of the liquid radial distribution function (rdf) in the theory accounts for the significant variation of the acceptor concentration near a donor. Because the concentration of acceptors near a donor is substantially greater than the average concentration used in a featureless continuum liquid model, incorporating the rdf is necessary to properly analyze experimental data. Hydrodynamic effects, which slow the rate of donoracceptor approach at short distance, are important and are also included in the theoretical analysis of the data. The data analysis depends on a reasonable model of the rdf. A hard-sphere liquid rdf is shown to be sufficiently accurate by comparing model electron-transfer calculations using a hard-sphere rdf and an rdf from neutronscattering experiments reported in the literature. A method is presented to obtain the hard-sphere parameters needed to calculate the rdf. The method uses a self-consistent determination of the hard-sphere radius and diffusion constant and the solvent self-diffusion constant calculated from the Spernol and Wirtz equation. The Marcus form of the distance-dependent transfer rate is used. For the highest viscosity solvent (dibutyl phthalate), a unique set of the Marcus transfer parameters is obtained. For lower viscosity solvents, the transfer parameters are less well defined, but information on the distance and time dependence of charge separation is still acquired. These experiments, combined with the theoretical analysis, yield the first realistic description of through-solvent photoinduced electron transfer.
Photoinduced electron transfer between N,N-dimethylaniline (DMA) and octadecylrhodamine B (ODRB) is studied on the surfaces of three alkyltrimethylammonium bromide micelles: dodecyl-(DTAB), tetradecyl-(TTAB), and hexadecyltrimethylammonium bromide (CTAB). The DMA and ODRB molecules are localized at the micelle surface. Time-resolved fluorescence and fluorescence yield data are presented and analyzed with the theoretical methods of ref 1. Lateral diffusion of the molecules over the micelle surfaces is included. Although the three micelles are structurally similar, pronounced differences in the electron-transfer kinetics are observed, with the overall amount of electron transfer increasing with alkyl chain length for the same DMA surface packing fraction. This result is attributed to differences in the solvent reorganization energy, possibly due to varying extents of water penetration into the headgroup regions of the three micelles. As the surfactant chain length increases, the solvent reorganization energy is reduced, resulting in faster electron transfer.
Photoinduced intermolecular electron transfer between Rhodamine 3B and N,N-dimethylaniline has been studied in a series of seven liquids: acetonitrile, ethanol, propylene glycol, and mixtures of ethanol, 2-butanol, ethylene glycol, propylene glycol, and glycerol. In each liquid, the donor and acceptors have different diffusion constants and experience distinct dielectric properties. Ps time-dependent fluorescence measurements and steady-state fluorescence yield measurements were made and analyzed using a detailed statistical mechanical theory that includes a distance-dependent Marcus rate constant, diffusion with the hydrodynamic effect, and solvent structure. All solvent-dependent parameters necessary for calculations were measured, including dielectric constants, diffusion constants, and redox potentials, leaving the electronic coupling unknown. Taking the distance-dependence of the coupling to be ϭ1 Å Ϫ1 , data were fit to a single parameter, the coupling matrix element at contact, J 0. The theory is able to reproduce both the functional form of the time-dependence and the concentration-dependence of the data in all seven liquids by fitting only J 0. Despite the substantial differences in the properties of the experimental systems studied, fits to the data are very good and the values for J 0 are very similar for all solvents.
Theories are presented for calculating the solvent reorganization energy and the free energy change which occur in photoinduced donor/acceptor electron transfer at the surface of micelles. The theories are based on the Marcus theory for spherical reactants in a dielectric continuum. The micelle is modeled with regions of differing dielectric properties, representing the micelle core, the headgroup region, and the surrounding water. The free energy change accompanying electron transfer can be calculated from redox measurements made in bulk liquids. The theories are applied to previously published photoinduced intermolecular electron-transfer data between octadecylrhodamine B (ODRB) and N,N-dimethylaniline (DMA) molecules.1 The ODRB and DMA molecules are located in the surface region of three different types of surfactant micelles: dodecyl-, tetradecyl-, and cetyl-trimethylammonium bromide (DTAB, TTAB, and CTAB, respectively). The data show an increased rate of electron transfer with increasing micelle radius. Application of the new theory to the electron-transfer data along with information provided by neutron scattering experiments show that the headgroup regions of the three micelles have different dielectric constants because water penetration into the headgroup regions decreases as the surfactant length increases.
The coupled processes of intermolecular photoinduced forward electron transfer and geminate recombination between donors (rubrene) and acceptors (duroquinone) are studied in two molecular liquids: dibutyl phthalate and diethyl sebacate. Time-correlated single-photon counting and fluorescence yield measurements give information about the depletion of the donor excited state due to forward transfer, while pump-probe experiments give direct information about the radical survival kinetics. A straightforward procedure is presented for removing contributions from excited-state-excited-state absorption to the pump-probe data. The data are analyzed with a previously presented model that includes solvent structure and hydrodynamic effects in a detailed theory of through-solvent electron transfer. Models that neglect these effects are incapable of describing the data. When a detailed description of solvent effects is included in the theory, agreement with the experimental results is obtained. Forward electron transfer is well-described with a classical Marcus form of the rate equation, though the precise values of the rate parameters depend on the details of the solvents' radial distribution function. The additional experimental results presented here permit a more accurate determination of the forward transfer parameters than those presented previously.1 The geminate recombination (back transfer) data are highly inverted and cannot be analyzed with a classical Marcus expression. Good fits are instead obtained with an exponential distance dependence model of the rate constant and also with a more detailed semiclassical treatment suggested by Jortner.2 Analysis of the pump-probe data, however, suggests that the geminate recombination cannot be described with a single solvent dielectric constant. Rather, a time-dependent dielectric constant is required to properly account for diffusion occurring in a time-varying Coulomb potential. A model using a longitudinal dielectric relaxation time is presented. Additionally, previously reported theoretical results 3 are rederived in a general form that permits important physical effects to be included more rigorously.
The problem of photoinduced donor-acceptor electron transfer in liquid solution is analyzed to obtain an understanding of the relationship between approximate treatments of the role of diffusion in electron transfer, that is, the Collins-Kimball approach, and a detailed analysis of the problem. It is shown why previous analyses of experimental data have yielded distance dependences of electron transfer that are much too long range. From an appropriate fitting of the nonstationary kinetics of donor fluorescence quenching by diffusionassisted electron transfer, the effective radii and the steady-state constants associated with electron transfer are found for a donor-acceptor system studied experimentally in seven solvents with different viscosities. The dependence of diffusion agrees with the one predicted theoretically for electron transfer having a distancedependent transfer rate initially taken to be exponential with distance. In the fast-diffusion limit, the dependence on the rate of diffusion is well approximated by the Collins-Kimball relationship, which permits the kinetic rate constant and the effective radius associated with diffusion-induced quenching to be extracted from the experimental data. The effective radius is then related to the electron transfer rate with arbitrary distance dependence. From this relationship, the tunnelling length for both exponential and Marcus-type rates is obtained from the data analysis, and it is demonstrated that the latter is almost twice as long as the former. For the Marcus transfer rate, it is found that the Marcus parameter β ) 1.2 Å -1 (β ) 2/tunnelling length), which is in accord with previous measurements on a variety of systems. The theoretical analysis presented here resolves the apparent discrepancies between early measurements of very long tunnelling lengths in liquid systems and physically reasonable values of β ≈ 1 Å -1 .
Photoinduced intermolecular (donor/acceptor) electron transfer is studied both experimentally and theoretically for donors and acceptors located in the headgroup region of micelles. Fluorescence up-conversion and fluorescence yield measurements were performed to characterize photoinduced electron transfer from N,Ndimethylaniline (DMA) and N,N-dimethyl-1-naphthylamine (DMNA) to octadecylrhodamine B (ODRB) in three types of aqueous micelle solutions: dodecyl-, tetradecyl-, and cetyltrimethylammonium bromide (DTAB, TTAB, and CTAB, respectively). The data were analyzed with a detailed theory that assumes a Marcus distance-dependent rate constant. Because DMA, DMNA, and ODRB reside in the headgroup region of the micelles, the theory includes diffusion of the molecules in this region of the micelles. The micelles are modeled as a spherical core of low dielectric constant surrounded by a spherical shell headgroup region with intermediate dielectric properties, which in turn is surrounded by water. An analytical theory, which accounts for geometrical and dielectric properties of the three-region micelle environment, is used to calculate the solvent reorganization energy and free energy of transfer. To fit the data, the three-region dielectric model is necessary, and the dielectric constant of the micelle headgroup region of each micelle can be approximately determined. In addition, including local structure is required to fit the data, yielding some information about molecular organization in the headgroup region.
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