A dielectric model for the solvent effect on the intensity of light absorption

Abstract

A new dielectric model is proposed for the solvent effect on the absorption intensity. The ratio of the apparent oscillator strength f″ of a solute molecule measured in a solution of refractive index n to the oscillator strength f of the solute molecule is given by f″/f=[s(n2−1)+1]2/n, where s is a ‘‘shape’’ parameter of the cavity in which the solute molecule is supposed to lie. The parameter s is identified with the depolarization factor of a dielectric in the same shape as the cavity, for the direction of the transition moment. The proposed linear relation between (nf″)1/2 and n2−1 is demonstrated for the π → π* transition of β-carotene and for the n→ π* transition of pyrazine. For the allowed π → π* transitions of long linear polyenes, the s value is approximately 0, leading to the relation f″/f=1/n. The proposed formula also reduces to the well-known Chako formula f″/f=(n2+2)2/(9n) for the spherical cavity whose s value is 1/3. The theory predicts that 1/n≤f″/f≤n3. It is shown that the proposed formulas are also derivable from Scholte’s expressions of the cavity field and the reaction field for ellipsoidal cavity.