Modeling the Effects of Fermi Resonances in the CH Stretching Region of the Spectra for Polycyclic Aromatic Hydrocarbon Anions

Abstract

A strategy is developed for evaluating spectra of anions of polycyclic aromatic hydrocarbon (PAH) molecules. The high symmetry of these systems and the similarity of the frequencies of the CH wagging and ring distortion vibrations result in normal modes that are highly mixed in character. This results in extensive mixing among the nearly degenerate states with energies in the 2600 to 3200 cm–1 region of the spectrum. When we generate vibrational modes that resemble localized CH stretching, CH wagging, or ring distortion vibrations from linear combinations of the normal modes, we find that the 2:1 Fermi resonances that couple the states with two quanta of excitation in the CH wagging vibration and one quantum of excitation in the corresponding CH stretching vibration are an order of magnitude or more larger than all of the other terms that couple these nearly degenerate states. The Fermi resonance coupling terms are evaluated for polar and Cartesian representations of the displacements of the hydrogen atom in the plane of the molecule for the anions of anthracene, pyrene, perylene, and fluoranthene. We find the Fermi coupling constants to be nearly constant across all of the CH bonds in these four ions, with values of 125 and 62 cm–1 for the Cartesian and polar representations of the Hamiltonian, respectively. When the polar coordinate representation of the displacements of the hydrogen atoms is used, the leading contribution to the Fermi coupling constant can be traced to the kinetic term in the Hamiltonian that involves the momentum of the wagging vibration, where the leading contribution to the effective mass is the moment of inertia of the CH bond. Using a Fermi coupling constant of 62 cm–1, along with a transferable model for the anharmonicity of the states in this energy range with one or two quanta of excitation, we can reproduce the recently reported spectra of these anions.