Stretch parameter

In stead, the electrostatic con tribn tion conies from definin g a set of bond dipole moments associated woth polar bonds. These bond moments are defined in the m m psir.LxL(dbf) file along with the bond stretching parameters and are given in units of Debyes. The cen ter of th e dipole Is defined to be th e m Idpoint of the bond an d two dipoles p. and pj. separated by Rjj. as shown beltnv ... 

Figure 13. Left Optical delay as a function of the stretching parameter. Right Transmission close to too % upper curve and contrasts as function of the generated delay. Low contrast corresponds to a fringes packet spreading.

Here,/Qj ax( ) is a generalized Debye-Waller factor giving account for the decay of the correlations at faster times. In the framework of the MCT it is also called non-ergodicity factor. The characteristic timescale r (T) is the structural relaxation time and (3 is the stretching parameter (0[Pg.73]

The data were fitted to a stretched exponential function (Eq. 4.9) setting the stretching parameter to its dielectric value. The solid lines included in Fig. 6.3 display the resulting curves. These fits lead to the Q-dependent characteristic relaxation times TKww(Q)> hich are converted to average relaxation times by Eq. 5.25 (see Fig. 6.4). 

However, deviations from the parabolic profile become progressively important as the length of the polymers N or the grafting density pa decreases. In a systematic derivation of the mean-field theory for Gaussian brushes [52] it was shown that the mean-field theory is characterized by a single parameter, namely the stretching parameter fi. In the limit p oo, the difference between the classical approximation and the mean-field theory vanishes, and one obtains the parabolic density profile. For finite /3 the full mean-field the-... 

Fig. 5 Left Mean-field results for the rescaled averaged polymer paths which end at a certain distance Ze from the wall for (S = I, 10, 100 (from top to bottom), corresponding to stretching values of y = 1.1, 1.9, 5.6 (as defined in Eq. 18). The thick solid line shows the unconstrained mean path obtained by averaging over all end-point positions. Note that the end-point stretching is small but finite for all finite stretching parameters p. Right End-point distributions...

The energy factored force field for carbonyls contains interaction parameters as well as stretching parameters. Such parameters are invariably required to be positive, for CO groups attached to the same metal, by the experimental finding that symmetric combinations of the individual CO vibrations occur at higher frequencies than similar antisymmetric combinations. 

In fact, it is always possible to fix the averaged CO stretching parameter, provided only all the frequencies are known and assigned the correct degeneracy (it is not even necessary to know the exact assignments). It is not possible to fix... 

The effects of parameters linking CO groups on different translationaUy equivalent molecules i.e. on molecules similarly situated within different unit cells) are not accessible, and are assimilated into the apparent stretching parameters. Thus it appears that, while the spectroscopy of solid carbonyls is of deep interest, the relevance of the data obtained to bonding in the isolated molecule is at best indirect. 

We are now close to being in a position to examine the effects on CO stretching parameter, for the isoelectronic isostructural series of first row carbonyl halides considered, of changes in metal, degree of substitution, coordination site, and halide. Along the sequence Cr(0), Mn(I), Fe(II), both 5 a and 2n populations fall. In other words, a higher oxidation state of the metal renders it at once a better a-acceptor and a poorer jr-donor perhaps a predictable result. Numerically the a -effect is the greater, but both are in the same direction, and parameters... 

Bond-Stretching Parameters Angle-Bending Parameters ... 

Here, x represents the elementary relaxation time and the stretching parameter (3 is descriptive for the nonexponential decay process (or distribution of relaxation times), or it physically quantifies the confinement effect that is, the larger (3 is, the stronger the confinement becomes. Figure 1.51 demonstrates the... 

Another problem directly related to the number of atomic types involved is that of actual construction of the parameters system, provided some guess concerning the form of the force fields is accepted. A simple estimate given in [199] on the example of the MM2 type of parametrization specifying 71 atomic types shows the number of van der Waals parameters to be 142, the number of different stretching parameters to be about 900, and that for the bending parameters, about 27000. Finally the number of the torsion parameters tends to exceed one million. This clearly indicates that the amount of available experimental data of the accuracy required to obtain... 

Open the menu item Edit/View, there Force Field and there Bond Stretch Parameters. Move the cursor to the row C03-NT, click on this line, click on the button Delete, confirm and leave the Force field editor with OK. Now, your MOMEC force field does not have any parameters for Com-amine bonds you are ready to develop your own parameterization Actually, see what happens if you try to refine a molecule with a missing parameter Open the [Co(NH3)6]3+ - hin file from Section 17.1 (Setup/Files) or from the CSD and refine it (set the maximum number of cycles (Setup/Optimization Controls) to 2 Execute/Geometry Optimization). At the bottom of the Summary window the Force Field Messages will tell you that there is no bond stretch function for atom types C03 NT. 

Return to the menu item Bond Stretch Parameters under Edit/View and Force Field. Go back to the row that you have deleted, click on the Insert button and type in the top row C03, NT, 2.25, 1.950 and Section 17.10. Confirm these entries with Assign and Save the changes to the force field. You are now ready to refine the two molecules as you have learnt in Sections 17.2 and 17.4 (do not forget to set the number of cycles (Setup Optimization Controls) back to 20 refine the molecules as a Batch-Job and see the results with Batch-Job Results under Edit/ View (see Section 17.4). 

Figure 34 shows the temperature dependencies of the static fractal dimensions of the maximal cluster. Note that at percolation temperature the value of the static fractal dimension Ds is extremely close to the classical value 2.53 for a three-dimensional lattice in the static site percolation model [152]. Moreover, the temperature dependence of the stretch parameter v (see Fig. 34) confirms the validity of our previous result [see (62)] Ds = 3v obtained for the regular fractal model of the percolation cluster [47]. 

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