A simple predictive model for planar vibrations of polycyclic benzenoid hydrocarbons

Abstract

A very simple force field model is designed to be applied as a predictive means to all kinds of planar benzenoid hydrocarbons to the infinite size without any modifications and extra knowledge except for topological connections of hexagonal rings. The model involves only eight potential parameters including CC, CH, CCC, and CCH stretchings, CC–CCC and CC–CCH bendings, and two constants for conjugation effects which are essential for the description of strongly correlated collective motions of CC bonds. The CC–CC interaction constants in the standard set of parameters were found to be in good agreement with those for benzene experimentally determined by Ozkabak and Goodman and those obtained from scaled quantum mechanical (SQM) calculations by Pulay et al. The standard set of force constants in the present model were shown to be almost completely transferable for the known planar vibrations of typical benzenoids. It is of note that in comparison with the SQM method the present model gives a small difference of ∼16 cm−1 in average for the calculated planar frequencies of benzene and naphthalene. Further applications to large benzenoids including perylene, benzo(g,h,i)perylene, coronene, ovalene, and tribenzo-(a,g,m)coronene demonstrated that the present model predicts not only planar frequencies in an accuracy of ∼20 cm−1 but also vibronic band intensities in good agreement with experiment.