VIBRONIC COUPLING .6. VIBRONIC BORROWING IN CYCLIC POLYENES AND PORPHYRIN

Vibronic borrowing in closed-shell aromatics is investigated by means of the cyclic-polyene model with the r electrons treated according to simple Hiickel theory and the a electrons treated as outlined by LonguetHiggins and Salem. The basis set for the vibronic wavefunctions consists of single-product Born-Oppenheimer functions whose electronic factors are LCAO cyclic-polyene molecular orbitals. The coupling between these Born-Oppenheimer functions is treated by means of perturbation theory. The dependence of the vibronic coupling on the size of the aromatic is given. Intensities of the vibronic transitions in benzene, coronene, triphenylene, 18-annulene, and porphyrin are calculated. Porphyrin is approximated by a 16-membered cyclic polyene with 18 electrons, and the absorption spectra, fluorescence polarization, and Zeeman spectra are interpreted in terms of vibronic interactions. The Jahn-Teller distortion vanishes in these cases, a result shown to be a general phenomenon for one-electron terms in E states arising from two e electrons or holes.