The effect of molecular reorientation on the lineshapes of degenerate vibrations in infra-red and Raman spectra of liquids

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Abstract
The reorientational lineshapes of perpendicular bands of a prolate symmetric top with Coriolis coupling are calculated using stochastic models to describe the molecular motion. The shape of each band (or component of a band), depends on the value of a constant, γ, for that band. This is related to the correlation time τ k of the angular momentum about the top axis and to the Coriolis coupling constant for the band. If τ k is sufficiently short the lineshape is lorentzian with width equal to the product of τ k and the second moment of the gas-phase spectrum. If γ is near unity the lineshapes depend on the model; the expected differences between a Gordon model with hard collisions and a Hubbard (or Langevin) model with soft collisions are shown. The theoretical properties of the transfer matrix describing the stochastic process are discussed.