Two-site jump model

The temperature dependent T data are shown in Fig. 9. 7j values decrease from 28 ms at 21°C with increasing temperature, and show a minimum of 6.4 ms at 80° C. These results indicate the presence of the motion with a Larmor frequency of 30 MHz at this temperature. This minimum was found to be attributed to the flipping motion of a phenyl ring from the result of our other experiments discussed in later section.13 The jump rates of the flipping motion were estimated with a two-site jump model that a C-2H bond jumps between two equivalent sites separated by 180°, and that the angle made by the C-2H bond and the rotational axis is 60°. The quadrupole coupling constant of 180 kHz and the asymmetry parameter approximated to zero were used in the calculation. The calculated values for fitting with the... 

The line shapes were calculated for the flipping motion with the two-site jump model described above, and the calculated spectra are shown in Fig. 11 for the higher temperature region. The experimental line shapes at 20 and 30° C are well reproduced showing the motional mode and rates obtained by T analysis are reasonable at least around these temperatures. Above 40°C the calculated line shapes are invariable and remain in the powder pattern undergoing a rapid flipping motion, while the experimental ones... 

Selective inversion recovery experiments i.e. only select frequencies within the powder pattern are excited, have also been performed on 2H for the purposes of studying molecular motion. Initial experiments were performed on deuterated dimethylsulfone (DMS) to demonstrate the utility of the experiment.46 Selective inversion recovery curves were fitted to a suitable motional model, a two-site jump model in the case of DMS, to yield the motional rates as a function of temperature. A significant feature of this work is that the activation energy for the motion so obtained differs markedly from that obtained from earlier 13C chemical shift anisotropy lineshape studies. 

The two-site jump model appears to work well for this polymer. However, it should be noted that the density of transitions is large here due to the larger spin quantum number of deuterium (/= 1), the fact that there are three of them in the isotopically substituted polymeric radical, and that the coupling constant for each deuterium is smaller by a factor of 6.4 compared to the protonated radical. Coupling these facts to the visual fitting process, these fits may not be unique. In fact, when the same model is applied to the temperature dependence of the protonated PMMA spectra (Fig. 14.2), reasonable visual fits could not be obtained with this model. Deuteration of the... 

Fig. 23.18. Comparison of 76.77 MHz spectra of L-[ Hio]leucine labeled KIF with lineshapes generated by a discrete two-site jump model. Spectra at temperatures (a) 26, (b) 5, (c) —23 and (d) -45°C, each an average of 2500 scans. Simulations with two-site half-angle of 54.75°C between two equally populated equilibrium sites with fast and slow jump rate (k and k ) assigned to two different classes of molecules , (e) k = I x 10, k = 1.65 x 10 (f) k( = 5 X 10- k, = 1.65 X lO (g) kf = 6.5 x 10 , k, = 5.73 x 10 (h) kf=k = 3.8 x 10 A 1 1 ratio of slowly and rapidly jumping components is assumed in the simulations.

The quasi-elastic neutron scattering from H2O and D2O, in harmotome, has been further measured in samples with 2, 4, and 12 water molecules per unit cell at 294 K < T < 423 K [98S1]. From the observed coherent scattering relaxation time for D-D correlations, 2 to 11 ps were obtained. Fitting the incoherent quasi-elastic peaks from H2O to a two site jump model, yielded residence times of the protons in the range from 4 to 6 ps [98S1], close to the previous reported values. 

Fig. 15. (a) Normalized pure-exchange CODEX intensities E(tm) as a function of tm for the aromatic ternary CH and the quaternary Cquat in Td-G2(-Me),6 dendrimer (T=363K). The fit curve for the ternary carbons is a stretched exponential cxp[—(rln/rcyi with /I = 0.51 and tc = 401 ms. The dotted line indicates the final CODEX exchange intensities, (b) Motional model of the localized, cooperative dynamics in polyphenylene dendrimers, including two-site jumps of all phenyl substituents of a pentaphenyl benzene building block. As indicated by X-ray analysis and computer simulations, the peripheral aromatic rings are inclined by 30° with respect to an axis normal to the face of the central benzene ring. For details, see ref. 44. 

The temperature-dependent spectra were interpreted in terms of a two-site hop model, in which the deuterons undergo jumps through a dihedral angle of 103°. This type of motion is consistent with gauche-trans conformational transitions. At -88"C these motions appear static on the time scale of the deuterium NMR experiment, and at +85 °C the motions are in the fast exchange limit. The rate constants for these motions were obtained from the calculated spectra. An Arrhenius plot of these data show that the apparent activation energy is 5.8 kcal/mol. (Dynamic mechanical data (20 Hz) fall on the Arrhenius plot.) The transitions have an intermediate rate on the deuterium NMR time scale at 20 °C, with the correlation time for the motion being 7 x 10 6 s at this temperature. 

First, it is worth noting that the activation energy value derived from the 22.6 MHz data strongly depends on the motional model considered. Thus, with a two-site jr-flip jump model, leading to a single exponential correla-... 

With the cylindrical cryptands, each macrocycle may bind one cation so that both mono- and dinuclear cryptates may be formed. Although the 12-membered (N202) macrocycles of ligand 5 are too small to bind two cations within each of the macrocycles, variable temperature 13C-NMR measurements have revealed intramolecular cation exchange between identical sites at the top and bottom of this cryptand, for Ca2+, Sr2+, and Ba2+. Cation jump between the two sites is fast with respect to intermolecular cation exchange, modeling the elementary jump processes of cations between binding sites in membrane channels (91). 

One of the most widely used tools to assess protein dynamics are different heteronuclear relaxation parameters. These are in intimate connection with internal dynamics on time scales ranging from picoseconds to milliseconds and there are many approaches to extract dynamical information from a wide range of relaxation data (for a thorough review see Ref. 1). Most commonly 15N relaxation is studied, but 13C and 2H relaxation are the prominent tools to characterize side-chain dynamics.70 Earliest applications utilized 15N Ti, T2 relaxation as well as heteronuclear H- N) NOE experiments to characterize N-H bond motions in the protein backbone.71 The vast majority of studies applied the so-called model-free approach to translate relaxation parameters into overall and internal mobility. Its name contrasts earlier methods where explicit motional models of the N-H vector were used, for example diffusion-in-a-cone or two- or three-site jump, etc. Unfortunately, we cannot obtain information about the actual type of motion of the bond. As reconciliation, the model-free approach yields motional parameters that can be interpreted in each of these motional models. There is a well-established protocol to determine the exact combination of parameters to invoke for each bond, starting from the simplest set to the most complex one until the one yielding satisfactory description is reached. The scheme, a manifestation of the principle of Occam s razor is shown in Table l.72... 

Two-site Model. Consider a particle bearing charge q, with two resting positions separated by a distance d, between which it makes very rapid jumps at random intervals with mean frequency v. We suppose that in the absence of an applied field the probability, per unit time, of jumping out of whichever site is occupied is the same for both sites, so that on average each site is occupied for half of the time. The polarization with respect to the near position alternates between qdjl and — qd/2, with time-average zero. 

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