Handbook of Solvents - George Wypych - ChemTech - Ventech!

646 Mati Karelson
Scheme 21 Scheme 22
All theoretical treatments of solvatochromic shifts proceed from modelling the
solvational interactions in the liquids and solutions. Theoretically, the interaction potential
between a solute molecule and the surrounding solvent molecules Φ is given by the following
integral
∞
∫
() ()
2
Φ= C ϕ R g R R dR
0
[11.1.3]
where ϕ (R) and g(R) are the pair interaction potential between the solute and the solvent
molecule and the solvent radial distribution function around the solute molecule, respectively,
and C is a constant depending on the density of the system. The integration in the last
formula is carried out over the distance between the solute and the solvent molecule, R. The
equation [11.1.3] is derived proceeding from the assumption that the intermolecular forces
in the condensed medium are additive. This assumption may be, however, violated because
of possible three- and many-body interactions between the molecules in the solution. For
most of the real systems, the application of Eq. [11.1.3] directly is rather impractical because
of the low precision of ϕ (R) and g(R), particularly in the case of many-atomic molecules.
Moreover, this equation will be strictly valid only for the solute-solvent systems in
thermodynamic equilibrium and thus not applicable for the Franck-Condon states. Thus, almost
all theoretical calculations of solvatochromic effects proceed from different physical
models describing the intermolecular interactions in liquids and solutions.
Traditionally, the solvation energy of a molecule E solv in a given solvent can be divided
into the following terms 3
Esolv = E cav + E disp + E elst + E H − bond
[11.1.4]
each of which corresponds to a certain type of intermolecular interaction in the condensed
media. Thus, E cav denotes the energy of the cavity formation for the solute in the solvent,
E disp is the dispersion energy and E elst the electrostatic energy of the interaction of the solute
with the surrounding solvent molecules. The term E H-bond accounts for the energy of the hydrogen
bond formation between the solute and solvent molecules. The value of each of the
above terms will change as a result of the Franck-Condon excitation of the solute molecule.
First, the size of the molecule increases, as a rule, during the excitation. However, as the excitation
process is practically instantaneous, the position and orientation of the solvent molecules
in the solvation sheath of the chromophoric solute will not change. This means that