Nonharmonic transverse vibration of the H-bonded molecules and the THz spectra in ice and water

Abstract A nonlinear equation of motion is found for the dimer comprising two charged H 2 O molecules. The THz dielectric response to nonharmonic vibration of a nonrigid dipole, forming the hydrogen bond (HB), is found in the direction transverse to this bond. An explicit expression is derived for the autocorrelator that governs the spectrum generated by transverse vibration (TV) of such a dipole. This expression is obtained by analytical solution of the truncated set of recurrence equations. The far infrared (FIR) spectra of ice at the temperature − 7 °C are calculated. The wideband, in the wavenumber (frequency) ν range 0…1000 cm − 1 , spectra are obtained for liquid water at room temperature and for supercooled water at − 5.6 °C. All spectra are represented in terms of the complex permittivity e ( ν ) and the absorption coefficient α ( ν ). The obtained analytical formula for e comprises the term e ⊥ pertinent to the studied TV mechanism with three additional terms Δ e q , Δ e μ , and e or arising, respectively, from: elastic harmonic vibration of charged molecules along the H-bond; elastic reorientation of HB permanent dipoles; and rather free libration of permanent dipoles in ‘defects’ of water/ice structure. The suggested TV-dielectric relaxation mechanism allows us: (a) to remove the THz ‘deficit’ of loss e ″ inherent in previous theoretical studies; (b) to explain the THz loss and absorption spectra in supercooled (SC) water; and (c) to describe, in agreement with the experiment, the low- and high-frequency tails of the two bands of ice H 2 O located in the range 10…300 cm − 1 . Specific THz dielectric properties of SC water are ascribed to association of water molecules, revealed in our study by transverse vibration of HB charged molecules.