Handbook of Solvents - George Wypych - ChemTech - Ventech!

11.1 Theoretical treatment of solvent effects 647
the average distance between the surface of the solute and the solvent molecules will decrease
in the Franck-Condon excited state of the former that normally causes the enhanced
solute-solvent repulsion in that state. At the same time, the dispersion energy that stabilizes
the solute-solvent system will also increase in the absolute value, but to the opposite direction.
In consequence, both effects may cancel each other and the net effect will be close to
zero. For the polar solutes, both in the ground and in the excited state, the electrostatic solvation
energy is therefore often considered as the most important term in Eq. [11.1.4].
During the excitation or de-excitation of the molecule, the molecular electronic
wavefunction and the electron distribution may change significantly. In result, substantial
differences are expected in the electrostatic and dispersion solvation energies of the ground
and the excited state, respectively. In addition, the hydrogen bonding between the solute
and solvent molecules may be affected by the excitation of the solute molecule that will be
reflected as another contribution to the difference in the solvation energy of solute in the
ground and in the excited state, respectively. In the following, we proceed with the systematic
presentation of the theoretical methods developed for the description of the
solvatochromic effects on molecular electronic and vibrational spectra in condensed disordered
media (liquids, solutions, glasses etc.).
11.1.2 THEORETICAL TREATMENT OF SOLVENT CAVITY EFFECTS ON
ELECTRONIC-VIBRATIONAL SPECTRA OF MOLECULES
As described above, the change (increase) in the size of the molecule during the excitation
will result in increased van-der-Waals repulsion between the electron clouds of the
chromophoric solute and the solvent molecules. Alternatively, the size of the molecule is
expected to shrink as a result of the de-excitation of the molecule back to the ground state. In
such case, the repulsion between the solute and solvent molecules will be reduced correspondingly.
The respective energetic effect may be modeled as the difference in the cavity
formation energies for the solute molecule in two states. The dependence of the cavity formation
energy on the cavity size has been derived using several different model concepts.
The simplest approach is based on the concept of microscopic surface tension on the
boundary between the solute cavity and the solvent. Within this approach, the free energy of
cavity formation is assumed simply proportional to the surface of the solute cavity, SM: ΔGcav =σ SM
[11.1.5]
where σ is the surface tension of the solvent. This formula has been applied for the evaluation
of the free energy of transfer of electroneutral solutes between different solvents. 4 It has
been extended to account for the size of the solvent molecule as follows:
( )
ΔG = σS −RTln 1 −V
n
[11.1.6]
cav M s s
where V S is the intrinsic volume of a solvent molecule and n S is the number density of the
solvent. In order to account for the chemical individuality of constituent atoms, it has been
suggested to use different surface tension values σ i for different atomic types in the solute
molecule. 5 Thus,
ΔG = C +∑σ A
[11.1.7]
cav i i
i