Electronic States of Aromatic Hydrocarbons: The Franck-Condon Principle and Geometries in Excited States

Abstract

It is suggested that electronic transitions in aromatic hydrocarbons can profitably be characterized by a quantity R, where R² is the sum of the squares of the bond length changes accompanying the transition. R determines, via the Franck-Condon principle, the distribution of intensity within the vibrational envelope of a transition. In polycyclic aromatics, values of R can be extracted from solution spectra, if the intervals of about 1400 cm^-1 which commonly separate the vibrational peaks are interpreted as defining quasi-progressions in a skeletal bond displacement vibration. Values of R so determined are compared with values computed from bond orders in excited states, using the wave-functions of Pariser. Such comparisons are made for benzene, naphthalene, azulene, and anthracene. Agreement is good. The calculated bond orders are tabulated. In an Appendix, bond angles in aromatic rings are calculated on the assumption that the observed angles minimize the σ-bond strain energy. Angles are calculated for the ground states of naphthalene and anthracene, and for two excited states of naphthalene. The excited state geometries so deduced are depicted.