Handbook of Solvents - George Wypych - ChemTech - Ventech!

13.1 Solvent effects on chemical reactivity 767
extracted from band-shape analyses of absorption spectra were found to fall in the range 0.2
- 0.4 eV. Upon partitioning these values into internal vibrations and solvent degrees of freedom,
although this matter is still ambiguous, the contribution of the solvent could well be on
the order of 0.2 - 0.3 eV. 152-154 Unfortunately, all continuum theories predict zero solvent reorganization
energies for ET in nonpolar liquids.
It is evident that some new mechanisms of ET, alternatively to permanent dipoles’ reorientation,
are to be sought. It should be emphasized that the problem cannot be resolved
by treatments of fixed positions of the liquid molecules, as their electronic polarization follows
adiabatically the transferred electron and thus cannot induce electronic transitions. On
the other hand, the displacement of molecules with induced dipoles are capable of activating
ET. In real liquids, as we have stated above, the appreciable free volume enables the solvent
molecules to change their coordinates. As a result, variations in charge distribution in
the reactants concomitantly alter the packing of liquid molecules. This point is corroborated
by computer simulations. 155 Charging a solute in a Stockmayer fluid alters the inner coordination
number from 11.8 for the neutral entity to 9.5 for the positively charged state, with
the process accompanied by a compression of the solvation shell. It is therefore apparent
that solvent reorganization involves reorganization of liquid density, in addition to the
reorientational contribution. This concept has been introduced by Matyushov, 156 who dissected
the overall solvent reorganization energy E s into a dipole reorganization component
E p and a density reorganization component E d,
E s = E p + E d [13.1.28]
It should be mentioned that the two contributions can be completely separated because
they have different symmetries, i.e., there are no density/orientation cross terms in the perturbation
expansion involved in the calculations. The density component comprises three
mechanisms of ET activation: (i) translations of permanent dipoles, (ii) translations of dipoles
induced by the electric field of the donor-acceptor complex (or the chromophore), and
(iii) dispersion solute-solvent forces. On the other hand, it appears that in the orientational
part only the permanent dipoles (without inductions) are involved.
With this novel molecular treatment of ET in liquids the corundum of the temperature
dependence of the solvent reorganization energy is straightforwardly resolved. Dielectric
continuum theories predict an increase of E s with temperature paralleling the decrease in the
dielectric constants. In contrast, experimental results becoming available quite recently
show that E s decreases with temperature. Also curved Arrhenius plots eventually featuring a
maximum are being reported, in weakly polar 157 and nonpolar 158 solvents. The bell-shaped
temperature dependence in endergonic and moderately exergonic regions found for ET
quenching reactions in acetonitrile 159 was attributed to a complex reaction mechanism.
Analogously, the maximum in the Arrhenius coordinates, peculiar to the fluorescence of
exciplexes formed in the intramolecular 160 and bimolecular 161 pathways, is commonly attributed
to a temperature dependent competition of exciplex formation and deactivation
rates. A more reasonable explanation can be given in terms of the new theory as follows.
A maximum in the Arrhenius coordinates follows from the fact that the two terms in
eq. [13.1.28] depend differently on temperature. Density fluctuation around the reacting
pair is determined mainly by the entropy of repacking hard spheres representing the repulsive
part of the intermolecular interaction. Mathematically, the entropy of activation arises