A normal coordinate analysis based on the local structure of liquid water

Abstract

Recent far-infrared, Raman, hyper-Raman, and inelastic neutron scattering measurements in the frequency range of about 100 to 1000 cm −1 have provided data related to the intermolecular motions of liquid water. A normal coordinate analysis of a simple mathematical model is used to study the motions of a rigid water molecule hydrogen bonded to its four nearest neighbors. The potential energy function for this model contains essentially four adjustable parameters, independent of temperature. Three of the parameters represent the stretching and bending of the hydrogen bonds. The fourth parameter is a term representing the interaction of the electric dipole moment of the water molecule with the local electric field. This four parameter model reproduces the frequencies and assignments of Walrafen using two bending constants which differ by about five percent. The number of parameters may be reduced to three with only small changes in the calculated frequencies if the bending constants are set equal. Both the hydrogen bonds and the large electric dipole moment of the molecule play important roles in the anomalous behavior found in many of the physical properties of water. The broad absorption bands found in this frequency range are incorporated in the model by means of a distribution of 0-0 distances based on the X-ray diffraction experiments of Narten, Danford, and Levy. The hydrogen bond properties are represented by the empirical potential function of Lippincott and Schroeder. The far infrared intensity ratios were calculated using a generalization of a dipole moment function used by Phillips. The results lend support to the frequency assignments of Walrafen. They also may be used to explain the experimental far-infrared spectra of Draegert et al. in terms of bandwidth, isotopic substitution, and temperature dependence. In addition, far-infrared frequencies are calculated with this model for ice which agree well with the measured frequency peaks.