Handbook of Solvents - George Wypych - ChemTech - Ventech!

11.1 Theoretical treatment of solvent effects 665
as an analog of equation [11.1.66] for the case of arbitrary cavity shape. The PCM-CI
method has been applied for the calculation of solvatochromic shifts in the spectrum
4-[(4’-hydroxyphenyl)azo]-N-methylpyridine in a variety of solvents. 48
An integral equation formalism (IEF) has been developed as particularly suitable for
the description of solvent effects on spectral transition energies within the PCM model. 49
The respective theoretical equations have been applied for the calculation of
solvatochromic shifts of several carbonyl-group containing molecules at the self-consistent
field (SCF), configuration interaction (CI) and multiconfiguration self-consistent (MC
SCF) field level of theory. The calculated spectral shifts accompanying the transfer of a
solvatochromic compound from the gas phase to water were comparable with the experimental
data. In Table 11.1.4, the results of calculations are presented for three carbonyl
compounds, formaldehyde, acetaldehyde and acetone.
Table 11.1.4. The calculated and experimental solvatochromic shifts (from the gas
phase to water) in the spectra of some carbonyl compounds (cm -1 ) 49
Compound ΔSCF CI(SDT) CAS SCF Exp.
Formaldehyde 1889 839 944 1700-1900 a
Acetaldehyde 1854 979 1049 1700-1900 a
Acetone 2273 1574 1259 1539-1889
a an estimate from other compounds
The advantage of the PCM method is in that it is applicable to the solute cavity of practically
any shape in the solution. However, it is not clear how precisely should the molecular
cavity be defined bearing in mind the classical (quasi-macroscopic) representation of the
solvent. It is difficult to perceive that the solvent, e.g., the water molecules, can produce the
electrical polarization corresponding to the statistically average distribution in the macroscopic
liquid at infinitely small regions on the cavity surface. However, it is conceivable
that larger chemical groups in the molecules may possess their own reaction field created by
their charge distribution and the reaction fields of other groups in the solute molecule. A
multi-cavity self-consistent reaction field (MCa SCRF) has been proposed 50 for the description
of rotationally flexible molecules in condensed dielectric media. It proceeds from the
observation that the interaction of the charge and higher electrical moments of a charge distribution
in a spherical cavity with the corresponding reaction fields localized in the center
of the cavity does not depend on the position of charge or (point) multipole centers in this
cavity. Therefore, it is possible to divide a rotationally flexible solute molecule or a hydrogen-bonded
molecular complex between two or more spherical cavities that embed the
rotationally separated fragments of the solute or solute and solvent molecules, respectively.
Assuming the classical Born-Kirkwood-Onsager charge density expansion (Eq. 11.1.27)
for each of these fragments, the total energy of the solute in a dielectric medium can be expressed
as a sum of terms that correspond to the energies arising from the interaction of the
partial charge and the electric moments of a given molecular fragment with the reaction
field of its own and the reaction fields of other fragments, as well as from the interaction between
the reaction fields of different fragments. The Hartree-Fock-type equations derived
from the variational functional for the total energy E can then be solved iteratively using the