THEORY OF SOLVENT EFFECTS ON THE VISIBLE ABSORPTION-SPECTRUM OF BETA-CAROTENE BY A LATTICE-FILLED CAVITY MODEL

The visible absorption spectra of all-trans-beta-carotene in 21 solvents reported by Myers and Birge are analyzed in terms of a cavity model for solvent effects on strongly allowed electronic transitions. The chromophore is treated as a classical point dipole oscillator at the center of a spherical cavity in a continuum having the optical dielectric constant of the solvent. A simple cubic lattice of polarizable points filling the cavity space outside a cylindrical region approximating the size of the beta-carotene molecule represents the local solvent structure. The theory reproduces the observed dependence of oscillator strength, absorption peak wavenumber, and root-mean-square band wavenumber on solvent polarizability. Hypothetical vapor spectra are calculated from the observed spectra in three solvents, using a relationship between the complex polarizabilities in solution and vapor phase for arbitrary band shapes. The predicted vapor spectra show a large change in band shape having diminished vibronic peaks, an rms wavenumber of 24 890 +/- 240 cm-1, and oscillator strength 3.63 +/- 0.04. Predicted shifts in band shape from one solvent to another, using the same theory, show distortions of vibrational structure that are not seen experimentally. It is concluded that the theory is satisfactory for predicting solvent effects on oscillator strength and wavenumber of absorption spectra of this type but that it contains an inherent artifact in the treatment of vibrational structure.