Hat-curved-harmonic oscillator model

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... 

Fitted and Estimated Parameters of the Composite Hat-Curved-Harmonic Oscillator Model... 

A general picture of the dielectric spectra described in Section VI is confirmed here in main features, when a more advanced composite hat-curved-harmonic oscillator model was employed. Better agreement of theory with experimental data is obtained. Not less important is change of the conncepts underlying... 

The hat-curved-harmonic oscillator model, unlike other descriptions of the complex permittivity available now for us [17, 55, 56, 64], gives some insight into the mechanisms governing the experimental spectra. Namely, the estimated relaxation time of a nonrigid dipole (xovib 0.2 ps) is close to that determined in the course of very accurate experimental investigations and of their statistical treatment [17, 54-56]. The reduced parameters presented in Tables XIVA and XIVB and the form of the hat-curved potential well (determined by the parameters u, (3, f) do not show marked dependence on the temperature, while the spectra themselves vary with T in greater extent. We shall continue discussion of these results in Section X.A. 

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.

We conclude The submillimeter spectra calculated in terms of the harmonic oscillator model substantially differ from the spectra typical for the low-frequency Debye relaxation region. Such a fundamental difference of the spectra, calculated for water in microwave and submillimeter wavelength ranges, evidently reveals itself in the case of the composite hat-curved-harmonic oscillator model. 

Both hat-curved-harmonic oscillator and hat-curved-cosine-squared potential composite models considered in this section give excellent description of wideband spectra of water H20 and D20 in the range from 0 to 1000 cm-1. However, it appears that the physical picture of fast vibrations of the H-bonded molecules differ for these two approaches. In the first one, where... 

In Section V the reorientation mechanism (A) was investigated in terms of the only (hat curved) potential well. Correspondingly, the only stochastic process characterized by the Debye relaxation time rD was discussed there. This restriction has led to a poor description of the submillimeter (10-100 cm-1) spectrum of water, since it is the second stochastic process which determines the frequency dependence (v) in this frequency range. The specific vibration mechanism (B) is applied for investigation of the submillimetre and the far-infrared spectrum in water. Here we shall demonstrate that if the harmonic oscillator model is applied, the small isotope shift of the R-band could be interpreted as a result of a small difference of the masses of the water isotopes. 

So, the goal of this section is to set forward investigation of both (A) and (B) mechanisms in the frames of one treatment. In sections VII.A.2-VII.A.4 the hat-curved and harmonic oscillator models will be described with the details sufficient for understanding the employed method of calculations. The results of the latter will be described in Section VII.A.5 and will be discussed in Section VII.A.6. 

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