Handbook of Solvents - George Wypych - ChemTech - Ventech!

680 Tai-ichi Shibuya
11.2 DIELECTRIC SOLVENT EFFECTS ON THE INTENSITY OF LIGHT
ABSORPTION AND THE RADIATIVE RATE CONSTANT
Tai-ichi Shibuya
Faculty of Textile Science and Technology
Shinshu University, Ueda, Japan
11.2.1 THE CHAKO FORMULA OR THE LORENTZ-LORENZ CORRECTION
The intensity of light absorption by a molecule is generally altered when the molecule is immersed
in a solvent or transferred from one solvent to another. The change may be small if
the solvents are inert and non-polar, but often a significant increase or decrease is observed.
The first attempt to correlate such effects with the nature of the solvent was made by Chako 1
in 1934. Chako’s formula reads as
f ′′
=
f
2 ( n + 2)
9n
2
[11.2.1]
where:
f oscillator strength of an absorption band of a molecule
f ′ apparent oscillator strength of the molecule in solution
n refractive index of the solution at the absorbing frequency
The apparent oscillator strength is proportional to the integrated intensity under the
molar absorption curve. To derive the formula, Chako followed the classical dispersion theory
with the Lorentz-Lorenz relation (also known as the Clausius-Mosotti relation), assuming
that the solute molecule is located at the center of the spherical cavity in the continuous
dielectric medium of the solvent. Hence, the factor derived by Chako is also called the Lorentz-Lorenz
correction. Similar derivation was also presented by Kort�m. 2 The same formula
was also derived by Polo and Wilson 3 from a viewpoint different from Chako.
Chako’s formula always predicts an increase of the absorption intensity with the refractive
index. This does not hold, for instance, for the allowed π→ π*electronic
transitions
of cyclohexadiene and cyclopentadiene, 4 and monomethyl substituted butadienes. 5
11.2.2 THE GENERALIZED LOCAL-FIELD FACTOR FOR THE ELLIPSOIDAL
CAVITY
A natural generalization of the Chako formula was made by generalizing the spherical cavity
to an ellipsoidal cavity. Such a generalization was shown by Shibuya 6 in 1983. The generalized
formula derived by him reads as
f′′
=
f
2 [ s( n − 1) + 1]
n
2
[11.2.2]
where:
s shape parameter which takes a value between 0 and 1
This parameter s is more generally known as the depolarization factor, whose values are
listed for special cases in general textbooks. 7 For the spherical cavity, s = 1/3 in any axis; for