Fermi resonance in solid CO2

Publisher Website
Google Scholar
Abstract
A theory of Fermi resonance in molecular crystals is described and applied to the ω1; 2ω2 Fermi resonance region of the CO2 crystal. It is shown by means of the Green functions method that bound states can originate out of the two-phonon manifold of ω2+ω2 vibrational states for sufficiently high values of the anharmonicity constant. Starting from the crystal harmonic Hamiltonian, Green functions for the excitations of interest are built. Introducing as anharmonic contribution to the Hamiltonian the intramolecular coupling between ω1 and 2ω2, renormalization of the ω2 density of states results. The profiles of the renormalized density of states are seen to change both with mechanical anharmonicity and the unperturbed ω1 frequency. Two cases of practical interest are discussed: in the first the ω1 state is immersed into the ω2+ω2 manifold while in the second ω1 is well separated from that. The intensity of the Raman spectrum is discussed in terms of a direct mechanism, i.e. scattering of light by ω2(k) and ω2(−k) phonons through second order terms of the polarizability tensor and an indirect mechanism, through the ω1 Raman active mode, and of interference between them. Using known gas phase values of anharmonicity constant and ω1, good agreement with experiment is found. The intensity and frequency of the bound states as well as the intensity, position and profile of the two-phonon continuum are well reproduced by the model.