Optical and radiationless intramolecular electron transitions in nonpolar fluids: Relative effects of induction and dispersion interactions

A microscopic theory of intramolecular optical and radiationless electron transitions in nonpolar fluids is developed. The solute is modeled by a polarizable dipolar hard sphere, and the solvent by polarizable hard spheres. The effect of the induction and dispersion interactions to the spectral line shift and width are calculated as a perturbation expansion in the solute-solvent attractions. The relative contributions of both these effects depend significantly on the solute size. Only for large solutes the dispersions are found to dominate the first order energy shift, while inductions become important if the solute size is comparable to that of the solvent molecules. If the solute dipole moment increases with excitation the dispersion and induction components of the first order spectral shift add up leading to a redshift. In the converse case (dipole moment decreasing) the two components have opposite signs, and the shift may switch from red to blue. Furthermore, both components cause the solvent reorganization energy to decrease sharply with the solute size. However, dispersions are of minor importance relative to inductions, for the parameter values used in this study. The linear correlation of the first order line shift with the solvent dielectric function (ε_∞- 1)/(ε_∞+2) of the dielectric constant ε is traced back to a compensating effect of dispersions and inductions. The continuum theory is shown to overestimate the solvent response substantially. Both the solvent reorganization energy and the Stokes shift (the difference between absorption and fluorescence energies) are predicted to vary inversely with temperature. If not masked by intramolecular reorganization, this dependence can cause a maximum in the Arrhenius coordinates for electron transfer rates in the near-to-activationless region.