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Title: The reorganization energy of electron transfer in nonpolar solvents: Molecular level treatment of the solvent

Abstract

The intermolecular electron transfer in a solute pair consisting of pyrene and dimethylaniline is investigated in a nonpolar solvent, n-hexane. The earlier elaborated approach [M. Tachiya, J. Phys Chem. 97, 5911 (1993)] is used; this method provides a physically relevant background for separating inertial and inertialess polarization responses for both nonpolarizable and polarizable molecular level simulations. The molecular-dynamics technique was implemented for obtaining the equilibrium ensemble of solvent configurations. The nonpolar solvent, n-hexane, was treated in terms of OPLS-AA parametrization. Solute Lennard-Jones parameters were taken from the same parametrization. Solute charge distributions of the initial and final states were determined using ab initio level [HF/6-31G(d,p)] quantum-chemical calculations. Configuration analysis was performed explicitly taking into account the anisotropic polarizability of n-hexane. It is shown that the Gaussian law well describes calculated distribution functions of the solvent coordinate, therefore, the rate constant of the ET reaction can be characterized by the reorganization energy. Evaluated values of the reorganization energies are in a range of 0.03-0.11 eV and significant contribution (more then 40% of magnitude) comes from anisotropic polarizability. Investigation of the reorganization energy {lambda} dependence on the solute pair separation distance d revealed unexpected behavior. The dependence has a very sharp peakmore » at the distance d=7 A where solvent molecules are able to penetrate into the intermediate space between the solute pair. The reason for such behavior is clarified. This new effect has a purely molecular origin and cannot be described within conventional continuum solvent models.« less

Authors:
;  [1]
  1. National Institute of Advanced Industrial Science and Technology, AIST Central 5, Tsukuba, Ibaraki 305-8565 (Japan)
Publication Date:
OSTI Identifier:
20723270
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 123; Journal Issue: 22; Other Information: DOI: 10.1063/1.2131054; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ANISOTROPY; CHARGE DISTRIBUTION; CHARGE EXCHANGE; DISTRIBUTION FUNCTIONS; ELECTRON TRANSFER; HARTREE-FOCK METHOD; HEXANE; LENNARD-JONES POTENTIAL; MILLI EV RANGE; MOLECULAR DYNAMICS METHOD; POLARIZABILITY; PYRENE; REACTION KINETICS; SIMULATION; SOLUTES; SOLVENTS

Citation Formats

Leontyev, I.V., and Tachiya, M.. The reorganization energy of electron transfer in nonpolar solvents: Molecular level treatment of the solvent. United States: N. p., 2005. Web. doi:10.1063/1.2131054.
Leontyev, I.V., & Tachiya, M.. The reorganization energy of electron transfer in nonpolar solvents: Molecular level treatment of the solvent. United States. doi:10.1063/1.2131054.
Leontyev, I.V., and Tachiya, M.. Thu . "The reorganization energy of electron transfer in nonpolar solvents: Molecular level treatment of the solvent". United States. doi:10.1063/1.2131054.
@article{osti_20723270,
title = {The reorganization energy of electron transfer in nonpolar solvents: Molecular level treatment of the solvent},
author = {Leontyev, I.V. and Tachiya, M.},
abstractNote = {The intermolecular electron transfer in a solute pair consisting of pyrene and dimethylaniline is investigated in a nonpolar solvent, n-hexane. The earlier elaborated approach [M. Tachiya, J. Phys Chem. 97, 5911 (1993)] is used; this method provides a physically relevant background for separating inertial and inertialess polarization responses for both nonpolarizable and polarizable molecular level simulations. The molecular-dynamics technique was implemented for obtaining the equilibrium ensemble of solvent configurations. The nonpolar solvent, n-hexane, was treated in terms of OPLS-AA parametrization. Solute Lennard-Jones parameters were taken from the same parametrization. Solute charge distributions of the initial and final states were determined using ab initio level [HF/6-31G(d,p)] quantum-chemical calculations. Configuration analysis was performed explicitly taking into account the anisotropic polarizability of n-hexane. It is shown that the Gaussian law well describes calculated distribution functions of the solvent coordinate, therefore, the rate constant of the ET reaction can be characterized by the reorganization energy. Evaluated values of the reorganization energies are in a range of 0.03-0.11 eV and significant contribution (more then 40% of magnitude) comes from anisotropic polarizability. Investigation of the reorganization energy {lambda} dependence on the solute pair separation distance d revealed unexpected behavior. The dependence has a very sharp peak at the distance d=7 A where solvent molecules are able to penetrate into the intermediate space between the solute pair. The reason for such behavior is clarified. This new effect has a purely molecular origin and cannot be described within conventional continuum solvent models.},
doi = {10.1063/1.2131054},
journal = {Journal of Chemical Physics},
number = 22,
volume = 123,
place = {United States},
year = {Thu Dec 08 00:00:00 EST 2005},
month = {Thu Dec 08 00:00:00 EST 2005}
}
  • The solvent contribution {lambda}{sub s} to the reorganization energy of electron transfer can be estimated from averages of the potential energy gaps between neutral-pair and ion-pair states over an ensemble of structures generated from molecular dynamics simulations. Invoking a Marcus-type two-sphere model for charge separation and recombination in an aqueous environment, we explored the effect of a polarizable force field and noted a strong reduction of {lambda}{sub s} (by {approx}45%) compared to the corresponding value obtained with a standard nonpolarizable force field. Both types of force fields yield {lambda}{sub s} values that in agreement with the Marcus theory, vary strictlymore » linearly with the inverse of the donor-acceptor distance; the corresponding slopes translate into appropriate effective optical dielectric constants, {epsilon}{sub {infinity}}{approx_equal}1.0{+-}0.2 for a nonpolarizable and {epsilon}{sub {infinity}}{approx_equal}1.7{+-}0.4 for a polarizable force field. The reduction in the solvent reorganization energy due to a polarizable force field translates into a scaling factor that is essentially independent of the donor-acceptor distance. The corresponding effective optical dielectric constant, {epsilon}{sub {infinity}}{approx_equal}1.80, is in excellent agreement with experiment for water.« less
  • Outer-shell electron-transfer reorganization energies, {lambda}{sub 0}, as evaluated from intervalence band maxima, E{sub op}, for bis(ferrocenyl)acetylene (BFA{sup +}), 1,4-bis(ferrocenyl)butadiyne (BFB{sup +}), and biferrocene (BF{sup +}) cations in 13 solvents are compared with the predictions of some contemporary models of solvent reorganization in order to ascertain the importance of noncontiuum, or solvent molecularity, factors to {lambda}{sub 0}. Measurements of E{sub op} were made in relatively polar media in solutions containing low concentrations (less than a few millimoles per liter) of PF{sub 6}{sup {minus}} so to minimize complications from ion pairing. While E{sub op} correlates roughly with {epsilon}{sub op}{sup {minus}1} - {epsilon}{submore » s}{sup {minus}1} ({epsilon}{sub op} and {epsilon}{sub s} are optical and static dielectric constants), the plots display considerable scatter; smaller slopes and larger intercepts are obtained than anticipated from such dielectric continuum treatments so that E{sub op} tends to be smaller than the two-sphere continuum estimates, E{sub op}(con). However, the relative E{sub op} values for all three biferrocenes are essentially independent of the solvent; E{sub op} for BFB{sup +} relative to BFA{sup +} is in good agreement with the predictions of the two-sphere model (but not ellipsoid models), although the E{sub op} values for BF{sup +} are larger than expected, most probably due to electron delocalization effects. Taking into account anticipated electronic state modulation effects (ref 38) on the potential energy well improves somewhat the overall match with the observed E{sup op} values but cannot account for the scatter in the E{sub op} - ({epsilon}{sup op}{sup {minus}1} - {epsilon}{sub s}{sup {minus}1}) plots. Comparisons are made with the recent mean spherical approximation (MSA) treatment of solvent reorganization (ref 10).« less
  • The temperature dependencies of the quenching rate constants (k{sub q}) and cage escape yields of the redox products ({eta}{sub ce}) from the electron-transfer reaction of {sup *}Ru(bpy){sub 3}{sup 2+} (bpy = 2,2`-bipyridine) with nine aromatic amines in deaerated 1:1 (v/v) CH{sub 3}CN/H{sub 2}O solutions have been determined. Values of {lambda}, the solvent reorganization energy for electron-transfer quenching and back electron transfer within the solvent cage, have been extracted from plots of log(k{sub q}T{sup 1/2}) vs 1/T and log(({eta}{sub ce}{sup -1}-1)T{sup 1/2}) vs 1/T, respectively. For the quenching process, {lambda} is not a constant value for the series of quenchers; inmore » general, higher values of {lambda} are exhibited by primary amines and lower values by tertiary amines. The structure and size of the quenchers and the nature of the ring substituents contribute to the value of {lambda}. For the back-electron-transfer reaction within the geminate redox pair formed in the quenching process, the more sterically hindered two-ring amines exhibit a higher value of {lambda} (1.1{+-}0.08 eV) than do the majority of the one-ring amines (0.82{+-}0.04 eV). A Marcus plot of log({eta}{sub ce}{sup -1} -1) vs {Delta}G{degree}{sub bt} shows a correlation within only the inverted region for systems with the same {lambda}. 46 refs., 5 figs., 1 tab.« less
  • The reorganization energy of electron transfer processes in ionic fluids is studied under the linear response approximation using a molecule Debye-Hueckel theory. Reorganization energies of some model reactants of electron transfer reactions in molten salts are obtained from molecular simulations and a molecule Debye-Hueckel approach. Good agreements between simulation results and the results from our theoretical calculations using the same model Hamiltonian are found. Applications of our theory to electron transfer reactions in room temperature ionic liquids further demonstrate that our theoretical approach presents a reliable and accurate methodology for the estimation of reorganization energies of electron transfer reactions inmore » ionic fluids.« less
  • Electron transfer near an electrode immersed in ionic fluids is studied using the linear response approximation, namely, mean value of the vertical energy gap can be used to evaluate the reorganization energy, and hence any linear response model that can treat Coulomb interactions successfully can be used for the reorganization energy calculation. Specifically, a molecular Debye-Hückel theory is used to calculate the reorganization energy of electron transfer reactions in an electric cell. Applications to electron transfer near an electrode in molten salts show that the reorganization energies from our molecular Debye-Hückel theory agree well with the results from MD simulations.