The Journal of
Physical Chemistry
0 Copyright 1995 by the American Chemical Society
VOLUME 99, NUMBER 7, FEBRUARY 16,1995
LETTERS Experimental and Theoretical Estimations of the Solvent Independence of the Electronic Coupling Matrix Element for an Organic Homogeneous Electron Self-Exchange Reaction Giinter Grampp*ti Institut f i r Physikalische und Theoretische Chemie der Universitat Erlangen-Niimberg, Egerlandstrasse 3, 0-91058 Erlangen, Germany
Guntram Rauhut$ Institut jiir Organische Chemie der Universitat Erlangen-Niimberg, Henkestrasse 42, 0-91054 Erlangen, Germany Received: August 1, 1994; In Final Form: December 8, 1994@ The solvent dependence of the electronic coupling matrix element V within electron transfer theory has been investigated for the homogeneous electron self-exchange reaction of the 1 ,Cdiaminobenzene/l ,Cdiaminobenzene radical cation couple. Experimental results from both ESR line broadening effects and semi-empirical MO calculations within the framework of self-consistent reaction field theory show that V is solventindependent.
1. Introduction The nonadiabatic rate constant of a homogeneous electron self-exchange reaction in solution like eq 1
can be expressed by'.2
42
dynamically influenced reactions through the longitudinal relaxation time TL of the solvent. All theories predict that V is solvent-independent. The aim of this paper is to prove this prediction experimentally as well as theoretically. Equation 2 is valid for the assumption that the relevant highfrequency vibrations in the reactant state can be replaced by one averaged mode with a single frequency, vi . AGO,denotes the solvent contributionto the activation barrier and is expressed within the usually used continuum model by3
k,, = K A k V 2 N L - ' ( 1 6 ~ r A G ~ ~ R 7exp(-S) ')~"~ x
NLdenotes Avogadro's number. In all solvent electron transfer theories, the solvent influence is described by the solvent reorganization energy AGosor additionally by adiabatic solvent
* To whom correspondence
should be addressed. New address: Institut fur Physikalische und Theoretische Chemie, Technische Universitat Graz, Technikerstrasse 4iI, A-8010 Graz, Austria. Present address: Deptartment of Chemistry & Biochemistry University of Arkansas, Fayetteville, AR 72701. Abstract published in Advance ACS Absrructs, January 15, 1995.
*
@
0022-3654/95/2099-1815$09.00/01
is the solvent parameter and given by y = (l/n2-1/cs),where n and cs are the refractive index and the static dielectric constant of the solvent, respectively. g(r,d) is a geometric term and is normally expressed in a simple spherical approximation by g(r,d) = (l/r-l/d), r is the molecular radius of the reactants, assumed to be equal in both redox states, and d the center-to-center distance in the precursor complex. S denotes the electron-vibration coupling strength: S = 4AGiJhviN~. 0 1995 American Chemical Society
1816 J. Phys. Chem., Vol. 99, No. 7, 1995
Letters
TABLE 1: Experimental Rate Constants k,, and Outer-Sphere Reorganization Energies AGosfor the 1,4-Diaminobenzene Electron Self-Exchange" solvent n2 E$ ke,/lO*M-' s-' AGo&.l mol-' V,,$hT mol-' Vtheo(hr)/kJmol-' Vtheo(n2)kJmol-' DMSO 2.185 46.45 6.0f 0.5 8.1 0.60 0.83 0.58
'
DMF CH3N02 CH3CN nitrobenzene methanol ethanol acetone pyridine CHzClz CHC13
2.046 1.909 1.807 2.422 1.765 1.853 1.846 2.280 2.28 2.091
37.2 37.0 35.94 34.78 32.50 24.55 20.9 12.9 8.93 4.8
** *
4.4 0.2 3.6 0.1 3.2 0.2
8.5 9.2 9.8
0.78 0.84 0.89
-
-
-
-
-
-
-
-
-
-
26.43~ 2.0
5.0
0.81
-
