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

Wideband far infrared (FIR) spectra of complex permittivity 3(n) 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 z880 cmK1. The second fraction comprises elastically interacting particles; they generate two nearby bands placed around frequency 200 cmK1. 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 3(n) 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 K7 8C. The calculated longitudinal optic-transverse optic (LO–TO) splitting occurring at z250 cmK1 qualitatively agrees with the measured data. q 2004 Elsevier B.V. All rights reserved.