Handbook of Solvents - George Wypych - ChemTech - Ventech!

752 Roland Schmid
over the solute-solvent attractions. The reference system for the perturbation expansion is
chosen to be the HS liquid with the imbedded hard core of the solute. It should be noted for
clarity that ΔEdisp and ΔEdipolar are additive due to different symmetries: dispersion force is
non-directed (i.e., is a scalar quantity), and dipolar force is directed (i.e., is a vector). In
other words, the attractive intermolecular potential can be split into a radial and an angle-dependent
part. In modeling the solvent action on the optical excitation, the solute-solvent interactions
have to be dissected into electronic (inertialess) (dispersion, induction,
charge-transfer) and molecular (inertial) (molecular orientations, molecular packing)
modes. The idea is that the inertial modes are frozen on the time scale of the electronic transition.
This is the Franck-Condon principle with such types of transitions called vertical
transitions.
Thus the excited solute is to be considered as a Frank-Condon state, which is equilibrated
only to the electronic modes, whereas the inertial modes remain equilibrated to the
ground state. According to the frozen solvent configuration, the dipolar contribution is represented
as the sum of two terms corresponding to the two separate time scales of the solvent,
(i) the variation in the solvation potential due to the fast electronic degrees of freedom,
and (ii) the work needed to change the solute permanent dipole moment to the excited state
value in a frozen solvent field. The latter is calculated for accommodating the solute ground
state in the solvent given by orientations and local packing of the permanent solvent dipoles.
Finally, the solvent reorganization energy, which is the difference of the average solvent-solvent
interaction energy in going from the ground state to the excited state, is extracted
by treating the variation with temperature of the absorption energy. Unfortunately,
experimental thermochromic coefficients are available for a few solvents only.
The following results of the calculations are relevant. While the contributions of dispersions
and inductions are comparable in the π* scale, inductions are overshadowed in the
ET(30) values. Both effects reinforce each other in π*, producing the well-known red shift.
For the ET(30) scale, the effects due to dispersion and dipolar solvation have opposite signs
making the red shift for nonpolar solvents switch to the blue for polar solvents. Furthermore,
there is overall reasonable agreement between theory and experiment for both dyes,
as far as the nonpolar and select solvents are concerned, but there are also discrepant solvent
classes pointing to other kinds of solute-solvent interactions not accounted for in the model.
Thus, the predicted ET(30) values for protic solvents are uniformly too low, revealing a decrease
in H-bonding interactions of the excited state with lowered dipole moment.
Another intriguing observation is that the calculated π* values of the aromatic and
chlorinated solvents are throughout too high (in contrast to the ET(30) case). Clearly, these
deviations, reminiscent of the shape of the plots such as Figure 13.1.2, may not be explained
in terms of polarizability as traditionally done (see above), since this solvent property has
been adequately accommodated in the present model via the induction potential. Instead,
the theory/experiment discord may be rationalized
in either of two ways. One reason for the additional
solvating force can be sought in terms of solute-solvent
π overlap resulting in exciplex formation.
Charge-transfer (CT) interactions are increased between
the solvent and the more delocalized excited
state. 55 The alternative, and arguably more reason-
Figure 13.1.8
able, view considers the quadrupole moment which