Librational region

A similar but less forceful argument can be made with respect to interpretation of the librational region of the spectra of H20(as) and liquid H2O. 

Recently, there were many attempts of MD simulations for the vibrational dynamics of ice. In these calculations more realistic, either non-rigid or polarizable, potentials were used. One such calculation was made by Itoh et al [72] using the KKY potential [9] which has three separate pair-wise terms yoo(r), VoH(r), VnH(r) and an extra three-body term for H-O-H and H-0—H bending. These calculations produced the all the fundamental modes up to 450 meV (or 3622 cm" ). The resulting spectra show very similar features to results from the MCY and TIP4P potentials in the translational and librational regions (see Fig. 16 and 17). 

A. De Santis, R. Frattini, M. Sampoli, V. Mazzacurati, M. Nardone, and M. A. Ricci. Raman spectra of water in the translational and librational regions. I. Study of the depolarization ratios. Molec. Phys., 67 1199-1212 (1987). 

In Ih phase, the selection rules for D6h are violated due to the proton disorder. So the observed band shape represents mostly the phonon density of states (DOS). As shown in Fig.2 (b), observed Raman spectra in the librational region in Ih phase surprisingly agrees with results of the neutron scattering (IINS) and MD calculation. In XI phase, Raman spectra show mostly the first order scattering around the T -point but qualitative agreement with neutron and MD studies is also seen in XI phases. 

In phase I, there is rotational and translational disorder of H2O and species, i.e. a quasi-liquid state of the water layer, with considerable orientational disorder of phosphate tetrahedra. The spectroscopic manifestation of such a state is the presence of a structureless broad absorption in the OH stretching and HjO and HsO librational region, i.e. individual contributions of protonic species are smeared out while the distinction between HjO and is observed only in the OH bending region. In... 

The calculated spectra for the ice II (H2O and D2O) up to 120 meV are shown in Figure I. The energy positions of these calculated spectra (continuous lines) agree well with the measured neutron spectra (dotted data) though we note that the calculated intensities in the librational region are lower than the measured spectrum. In our calculations die resolution of instrument has not been cmisidered so the data is sharper... 

Fig. 7.2. The radial dependence of the anisotropic part of the intermolecular potential (a) variation of height of the librational barrier in any diametrical cross-section of the cage and its rectangular approximation (b) the corresponding rectangular approximation of F(r) separation between the region of libration and that of free rotation inside the cage.

Figure 4.8. Calculated value of the rms amplitude or local polar libration (<5e2> /2) that satisfies Eq. (4.60) or Eq. (4.61) versus the assumed equilibrium polar angle (e0). The solid lines are the solutions of Eq. (4.60) for the indicated values of the reduced linear dichroism (LDr). The dashed lines are the solutions of Eq. (4.61) for the indicated values of A when the local angulaT motion of the transition dipole is assumed to be isotropic. The dotted lines are the solutions of Eq. (4.61) for the indicated values of A when the local angular motion of the transition dipole is assumed to be purely polar. The intersection of pairs of curves defines the region allowed" by a particular pair of LDr and A values and a particular assumption about the degree of anisotropy of the local angular motion of the transition dipole. If the LDr lies between -0.92 and -1.02, as indicated by experiment, then for isotropic internal motion, e0 = 70.5°, and 1/2 = 0.122 (7°) fall in the allowed region.

Furthermore, we replace the pair of variables, g and /, for h = g +f and cos 0 = l/s/h. As is seen in Fig. 10a, the phase region of the librators can be represented as the total phase region without the region occupied by the hindered rotators. Taking it into account, we obtain in accord with (65) and (67)... 

Figure 27. Evolution of the phase regions occupied by the librators (XC) and by the precessors (HP) with the increase of the form factor / from 0.65 (a) to 0.85 (b). The angular width of the hat-curved potential well, p, is n/9, and the reduced well depth, u, is 5.9.

The phase regions occupied by the librators and precessors are depicted in Fig. 27 in coordinates h, l2 for the parameters u = 5.9, p = %/9. We take two values of the form factor/ 0.65 in (a) and 0.85 in (b). When/increases, the / and 2P areas extend to the larger h and l values. The values of Vmin are shown as functions of l in Fig. 21c. In this example (and in the calculations described in Section V.C) the potential well depth U0 is much greater than kBT, that is, u> 1. We see in Fig. 27 that for the J and 2P areas the boundary values for h are still greater than it. This property is used to simplify analytical expressions for the spectral functions. 

In Table IX we present the list of optical constant of ordinary (H20) water [42] at 27°C covering very wide range of frequencies (from 10 cm-1 until 1000 cm-1). For two other temperatures (1°C and 50°C) we present in Table X such constants recorded in Ref. 53 for a narrower region from 400 cm-1 to 820 cm-1. Both tables comprise the absorption maximum of the librational band, and the first one includes also the maximum in the R-band. For lower frequencies we can use the empirical formulas of Liebe et al. [17], They are represented in Section G.2.a. Note that the absorption coefficient a is determined by the imaginary component... 

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