Higher excited vibrational states of polyatomic molecules

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The overtone bands in the vibrational specturm of methane can be accounted for on the same footing as the fundamentals by use of a simple vibrational Hamiltonian and the application of conventional symmetry considerations and radiative selection rules. This approach gives a rough map of all stretch vibrational states up to ∼24 000 cm−1, by fitting the states of the appropriate symmetry to the observed overtone spectrum. All vibrational states are described in terms of anharmonic symmetrized internal coordinate (SIC) states which are very close to the eigenstates of the Hamiltonian. The one-quantum SIC states are identical to the normal modes while some multiquantum SICs present features analogous to the ’’local modes’’ conventionally used in the interpretation of overtone spectra. The discrete structure of the vibrational state–space obtained from this treatment is in conflict with the symmetryless quasicontinuous structure of state–space postulated to explain IR multiphoton absorption in polyatomic molecules. At the same time, it suggests that this process might take place mainly through an equidistant ladder of states, as is found in molecules with several identical bonds.