A Failure of Continuum Theory: Temperature Dependence of the Solvent Reorganization Energy of Electron Transfer in Highly Polar Solvents

Abstract

The temperature dependence of the solvent reorganization energy for intramolecular electron transfer (ET) in acetonitrile is measured experimentally and calculated theoretically. The Stokes shifts for the charge transfer, optical transitions of (tetrahydro-4H-thiopyran-4-ylidene)propanedinitrile indicate that the solvent reorganization energy for ET decreases with temperature, whereas dielectric continuum theories of solvent reorganization predict an increase with temperature. A molecular alternative to the continuum description is proposed that models the solvent as a fluid of polarizable, dipolar hard spheres. Good agreement between the molecular theory and experiment is achieved for both the ET reorganization energy and equilibrium energy gap. The negative temperature slope of the solvent reorganization energy is understood in terms of its dissection into components arising from different solute−solvent interaction potentials and contributions from different solvent modes activating ET. In the first approach, we consider reorganization energy components from permanent and induced dipoles. In the second dissection, the orientational and density solvent fluctuations are considered. The analyses show that the molecular nature of the solvent, embodied in density fluctuations and associated translational motions of the solvent permanent dipoles, is the principal source of the negative temperature dependence of the solvent reorganization energy. This component is absent in the continuum picture. Its absence is the reason the continuum model fails to correctly predict the sign of the reorganization energy temperature dependence in polar solvents.