Analytical calculation of far infrared spectra of ice in terms of a molecular model

Abstract

Wideband far infrared (FIR) spectra of complex permittivity ε( ν) of ice are calculated in terms of a simple analytical theory based on the method of dipolar autocorrelation functions. The molecular model represents a revision of the model recently presented for liquid water in Adv. Chem. Phys. 127 (2003) 65. A composite two-fractional model is proposed. The model is characterised by three phenomenological potential wells corresponding to the three FIR bands observed in ice. The first fraction comprises dipoles reorienting in a rather narrow and deep hat-like well; these dipoles generate the librational band centred at the frequency ≈880 cm −1. The second fraction comprises elastically interacting particles; they generate two nearby bands placed around frequency 200 cm −1. For description of one of these bands the harmonic oscillator (HO) model is used, in which translational oscillations of two charged molecules along the H-bond are considered. The other band is produced by the H-bond stretch, which governs hindered rotation of a rigid dipole. Such a motion and its dielectric response are described in terms of a new cut parabolic (CP) model applicable for any vibration amplitude. The composite hat-HO–CP model results in a smooth ε( ν) ice spectrum, which does not resemble the noise-like spectra of ice met in the known literature. The proposed theory satisfactorily agrees with the experimental ice spectrum measured at −7 °C. The calculated longitudinal optic-transverse optic (LO–TO) splitting occurring at ≈250 cm −1 qualitatively agrees with the measured data.