Harmonic oscillator model liquid water

Second, the composite hat-curved-harmonic oscillator model provides a good perspective for a spectroscopic investigation of ice I (more precisely, of ice Ih), which is formed at rather low pressure near the freezing point (0°C). The molecular structure of ice I evidently resembles the water structure. Correspondingly, well-known experimental data show a similarity of the FIR spectra (unlike the low-frequency spectra) recorded in liquid water and in ice Ih. This similarity suggests an idea that rotational mobility does not differ much in... 

Figure 41. The scheme pertaining to the composite hat-curved—harmonic oscillator model the contributions of various mechanisms of dielectric relaxation to broadband spectra arising in liquid water. Frequency v is given in cm-1.

Recently, detailed molecular pictures of the interfacial structure on the time and distance scales of the ion-crossing event, as well as of ion transfer dynamics, have been provided by Benjamin s molecular dynamics computer simulations [71, 75, 128, 136]. The system studied [71, 75, 136] included 343 water molecules and 108 1,2-dichloroethane molecules, which were separately equilibrated in two liquid slabs, and then brought into contact to form a box about 4 nm long and of cross-section 2.17 nmx2.17 nm. In a previous study [128], the dynamics of ion transfer were studied in a system including 256 polar and 256 nonpolar diatomic molecules. Solvent-solvent and ion-solvent interactions were described with standard potential functions, comprising coulombic and Lennard-Jones 6-12 pairwise potentials for electrostatic and nonbonded interactions, respectively. While in the first study [128] the intramolecular bond vibration of both polar and nonpolar solvent molecules was modeled as a harmonic oscillator, the next studies [71,75,136] used a more advanced model [137] for water and a four-atom model, with a united atom for each of two... 

Since the reduced spectrum x"( ) clearly shows the low-ftequency Raman modes, we introduced a simple model to analyze the spectral profile of x"(.v) for obtaining the quantitative information. The model is composed of two damped harmonic oscillator modes and one Debye type relaxation mode (liquid water) or one Cole-Cole type relaxation mode (aqueous solution). Cole-Cole type relaxation is usually adopted in analyzing the dielectric relaxation. The formula of Cole-Cole type relaxation is represented as ... 

In order to account for some of the differences in thermodynamic properties of H2O and D2O, theoretical studies have been applied. Swain and Bader first calculated the differences in heat content, entropy, and free energy by treating the librational motion of each water molecule as a three-dimensional isotopic harmonic oscillator. Van Hook demonstrated that the vapor pressure of H2O and D2O on liquid water and ice could be understood quantitatively within the framework of the theory of isotope effects in condensed systems. Nemethy and Scheraga showed that in a model based on the flickering cluster concept, the mean number of hydrogen bonds formed by each water molecule is about 5% larger in D2O than in H2O at 25 °C. 

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