Nonharmonic vibrations

The three latter processes (b, c, d) are characteristic of the VIB state. In this state the lifetime xq of harmonic motion is about 0.07 ps. The lifetime t of a nonharmonic vibration is 0.2 ps for 7 and 0.06 ps for T7. In supercooled water, this vibration is accompanied by a noticeable association of water molecules. 

K for myoglobin (Parak et al., 1981). Thus, measurements of (x ) at temperatures below this value should show a much less steep temperature dependence than measurements above, if nonharmonic or collective motions (whose mean-square displacement is denoted (x )c) are a significant component of the total (x ). Figure 21 illustrates the expected behavior of (x )v, x, and their sum for a simple model system in which a small number of substates are separated by relatively large barriers. In practice, the relative contributions of simple harmonic vibrations and coUective modes will vary from residue to residue within a given protein. 

K. M. McDonald, W. R. Thorson, and J. H. Choi,/. Chem. Phys., 99,4611 (1993). Classical and Quantum Proton Vibration in a Nonharmonic Strongly Coupled System. 

The d mechanism concerns the same nonrigid 0+—H O- dipole performing a nonharmonic transverse vibration with respect to the equilibrium HB direction. 

Figure 3 Contributions e" to the loss factor of water at 27°C (a, c, e) and of ice at —7°C (b, d, f) due to longitudinal harmonic vibration of a nonrigid dipole (a, b) harmonic reorientation of a permanent dipole (c, d) and nonharmonic transverse vibration of a nonrigid dipole (e, f). Symbols T and V refer, respectively, to the T- and V-bands.

Thin lines in Figs. 5c-h and 6c-h refer to specific contributions due to nonharmonic reorientation of a permanent dipole in the hat potential (1), harmonic longitudinal vibration of HB nonrigid dipole (2), harmonic reorientation of a permanent HB dipole (3), and nonharmonic transverse vibration of a nonrigid HB dipole (4). 

Parameters of Nonharmonic Transverse Vibrations (j = 1,2,..., 7) (the Best Fit for the Dielectric Spectra Compare with Table VII)... 

In view of Fig. 12e we also remark that the contribution As s of nonharmonic transverse vibration to the static permittivity s increases with decrease of T, as does the contribution A q/f of harmonic vibration (see also Tables VI and VII). 

The model comprises the librational (LIB) and vibrational (VIB) fractions. A rigid permanent dipole, constituting the first (LIB) fraction, performs nonharmonic reorientation in the part of the structure formed by weak or torn hydrogen bonds (HB). This fraction stipulates the librational band of ice located at 800 cm-1. The second (VIB) fraction, constituted by two elastically vibrating oppositely charged HB molecules, describes T- and V-bands, located in... 

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