Normal Coordinate Analysis and Vibrational Spectra of Aromatic Carbon Nanostructures

Theoretical infrared absorption spectra of aromatic ring molecules having up to 102 carbon atoms and with various edge hydrogenations have been obtained using a classic mechanical model and a simplified valence force field. Force constants have been adapted from those available for smaller molecules. Spectral line intensities are calculated in a double harmonic approximation with effective atomic charges obtained using a Hückel tight-binding Hamiltonian. Vibrational modes of clusters of like aromatic ring molecules are obtained through introduction of an interlayer force constant. These modes are predicted to occur in the wavelength range between 80 and 400 μm. We explore the effect of dehydrogenation on these spectra as well as hydrogenation of terminal C atoms in either aromatic or aliphatic form. Many spectra exhibit a quasi-continuum between 6 and 9 μm that arises from the overlap of many vibrational modes in this region. With CH₂ edge groups, we find a new spectral feature near 16 μm and the aliphatic CH₂ symmetric stretch vibration is found to shift from 3.5 to 3.3 μm when these groups are present at terminal sites on aromatic carbon skeletons. The relevance of calculated spectra to those of astronomical sources is briefly discussed.