Diffusion tensor molecular frame

If the considered molecule cannot be assimilated to a sphere, one has to take into account a rotational diffusion tensor, the principal axes of which coincide, to a first approximation, with the principal axes of the molecular inertial tensor. In that case, three different rotational diffusion coefficients are needed.14 They will be denoted as Dx, Dy, Dz and describe the reorientation about the principal axes of the rotational diffusion tensor. They lead to unwieldy expressions even for auto-correlation spectral densities, which can be somewhat simplified if the considered interaction can be approximated by a tensor of axial symmetry, allowing us to define two polar angles 6 and

symmetry axis of the considered interaction) in the (X, Y, Z) molecular frame (see Figure 5). As the tensor associated with dipolar interactions is necessarily of axial symmetry (the relaxation vector being... 

The previous discussion is a clear example of the separation of dynamic and structural influences on NMR spectra. Before a detailed analysis of anisotropic spin interaction data can be realized, the dynamic averaging of the tensors must be appreciated. In fact, a detailed description of local dynamics can be achieved in which models of the motions are characterized by an axis fixed in the molecular frame, an amplitude for the motion and a motional model, such as diffusion within an arc or three site jumps, etc. [21]. The data in Fig. 6.4.6 shows that the averaging of the tensor above 200 K for this labeled indole site is anisotropic [22]. 

In order to determine the diffusion tensor that best fits a given trajectory, we use a procedure that was developed for the analysis of NMR relaxation data [45-47], and which is well-suited for adaptation to the analysis of MD simulations. This uses the average (or "effective") correlation time for a particular vector, n (e.g. a backbone N-H bond vector, or a randomly chosen direction in the molecular frame), which can be defined as... 

Euler angles relating local molecular frame and diffusion (order) tensor system (see Fig. 12). 

FIGURE 6.1. A schematic illustration of the coordinate systems used in the evaluation of physical motions in liquid crystals, (a) The rotational diffusion tensor Dr is used to define the molecular frame, (b) n B is used. Both h(f) and Dr are referred to as the space-fixed frame. 

First, a rigid subunit of 5CB is chosen to define the molecular frame (Xm, 1m, Zm)- This subunit should be chosen so that, to a good approximation, the reorientation of this reference axis system relative to the laboratory frame is independent of the internal motions. The rotational diffusion tensor of the whole molecule is supposed to be diagonal in this molecular frame. As a result, the small step rotational diffusion model (Section 7.2.2) may be used to account for the reorientation of the whole molecule. The internal rotation axis Zj) linking the th fragment (CjH2) and j — l)th fragment (Cj iH2) is used to define the Z axis of the jth subunit, while its Y axis is taken to be perpendicular to the Zj and Zj i axes (see Fig. 8.2). The correlation functions for the deuterons on the may be calculated... 

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