C—2H bond

Solid state 2H NMR parameters are almost exclusively governed by the quadrupole interaction with the electric field gradient (EFG) tensor at the deuteron site.1 8 The EFG is entirely intramolecular in nature. Thus molecular order and mobility are monitored through the orientation of individual C-2H bond directions. Therefore, 2H NMR is a powerful technique for studying local molecular motions. It enables us to discriminate different types of motions and their correlation times over a wide frequency range. Dynamics of numerous polymers has been examined by solid state 2H NMR.1 3,7,9 Dynamic information on polypeptides by NMR is however limited,10 26 although the main-chain secondary structures of polypeptides in the solid have been extensively evaluated by 13C and 15N CP/MAS NMR.27,28... 

H NMR spectra are profoundly influenced by motions.1 7 It is possible to calculate the powder spectra in the presence of any type of motion by taking into account the geometry, and amplitudes and rates of motions involved.80,81 Consider a C-2H bond which can jump between three equivalent sites,... 

If a C-2H bond diffuses uniformly over the surface of a cone having semiangle 6C, we have... 

If a C-2H bond diffuses freely with the diffusion coefficient Z)w in a cone of semiangle 9C, then T is given by84... 

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 projections of a single side chain on the plane perpendicular to the helix axis are shown in Fig. 20(a), and the directions of a CK-2H bond are shown in Fig. 20(b). The C 2H bond vectors are distributed nearly symmetrically around the average direction. The same result was obtained for a Cf 2H bond. Therefore, jumps among multiple sites which are axially symmetric about the average direction are a good approximation for the large amplitude motion. 

In addition to the large amplitude motion, the libration is expected to exist at higher temperatures as well as at lower temperatures, so that the libration was taken into account as small angle three-site jumps. As a result, the C-2H bond undergoes motions superimposed with two independent three-site jumps. In the calculations, a 0 value of 14° at room temperature was used as the polar angle of the libration, and its distribution was not... 

The authors also evidenced an increase of the percentages of a-talo-pyranose and a-ia/ofuranose upon 2H substitution at C(l) concomitantly with a decrease of the percentages of (l-conformers. This observed shift on the talopyranose anomeric equilibrium was attributed to the preference of the shorter C-2H bond (relative to the C l l bond) to assume an equatorial orientation. 

In case of a deuterated sample (spin 1 case), the spectra are usually dominated by the quadrupolar interaction, that is, the coupling of the nuclear quadrupole moment with the electric field gradient of the C-2H bond. For deuterons in C-2H bonds this can lead to a splitting of about 250 kHz. As in the case of dipolar interaction, a Pake spectrum is obtained for a powder sample. The z-principal axis of the quadrupolar interaction is oriented along the bond axis which makes deuteron NMR particularly useful for studies of segmental orientations and molecular dynamics (reorientation) [1],... 

The predominant interaction for a 2H spin system is the quadrupolar interaction, which couples the electric quadrupole moment of the 2H nucleus to its electronic surrounding. This interaction is a second-rank tensor Hq which lies approximately along the C-2H bond in organic molecules. Thus, in practice, 2H nuclei may be considered to be isolated. It shows that the 2H NMR formalism is similar to that of an isolated proton pair [8] ... 

In a solid system, the resonance spectrum spreads over a wide frequency range ( 250 kHz), with a structure related to the static orientational distribution of C-2H bonds in the system (powder spectrum). 

VqS is the magnitude of the residual tensor. The averaging factor S is the orientational order parameter, i.e., the degree of motional anisotropy, of a given C-2H bond (with respect to its average direction of orientation) ... 

C-2H bond performs rotational random jumps on the surface of a cone with a full opening angle X = 6° (from Ref. 93). (b) Experimental 2H NMR spectra of chlorobenzene-ds in a mixture with cis-decalin at various temperatures T < Tg and at a long solid-echo delay tp [429]. 

In general, three steps are required to create trajectories by means of RW simulations,76,84 (i) determination of an initial orientation/position so that the equilibrium distribution is obeyed, (ii) random selection of a waiting time tw between two subsequent jumps from a suitable distribution and (iii) calculation of the new orientation/position after the jump. After step (i), the steps (ii) and (iii) are performed alternately until a trajectory of sufficient length in time is obtained. While the time scale of the motion is determined by the distribution of waiting times g(tw) in step (ii), the geometry of the motion comes into play in step (iii). For example, the new orientation 0i+ after a -degree-rotational jump of a C-2H bond can be obtained from the old orientation 0, according to... 

RW simulations were performed to demonstrate that the use of suited inter-pulse delays tp in 2H NMR solid- and stimulated-echo experiments allows one to resolve spatially highly restricted reorientations.76 For this purpose, it was assumed that C-2H bonds (t] — 0) show rotational random jumps (cf Fig. 25) where all possible... 

Fig. 14. Effects of small-amplitude reorientation on 2H NMR experiments, as calculated by means of RW simulations. In the model, C-2H bonds (<5 = 2n 125 kHz, rj = 0) perform rotational random jumps on the surface of a cone with a full opening angle % = 6°. (a) 2H NMR spectra for various solid-echo delays tp (tj = t = 30 pis), and (b) 2H NMR correlation functions Fcos(tm) for various evolution times tp (tj = t = 10ms). (Adapted from Ref. 76.)...

In this model,110 it was assumed that all C 2H bonds perform thermally activated rotational jumps within energy landscapes on the surface of a cone. Specifically, six basins were supposed to be separated by six energy barriers at positions 0, 60,..., 300° around the axis of the cone. For each cone, the barriers were drawn anew from the distribution of activation energies determined for TOL in DS.12,19 Further, it was assumed that all positions on the surface of the cone, except for the barriers, have the same energy, i.e., a random-barrier model was considered. The thermally activated jumps lead to a random new position in one of the two neighboring basins. This means that several back-and-forth jumps occur over relatively low energy barriers until relatively high barriers are crossed. In other words, many... 

By an order parameter S =Sqd thus the residual anisotropy, which is not averaged by fast local motions, is characterised. This is the main information obtained for partially ordered systems, and can be considered a characterisation of the mobility of the C-2H bond, which on the other hand describes the chain packing order in oriented aggregates. 

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