CSA tensors

Angular restraints are another important source of structural information. Several empirical relationships between scalar couplings and dihedral angles have been found during the last decades. The most important one is certainly the Karplus relation for -couplings. Another, relaxation-based angular restraint is the so-called CCR between two dipolar vectors or between a dipolar vector and a CSA tensor. 

Here, ojr is the rate of spinner rotation. I is the proton spin number, 8 is the chemical shift anisotropy (CSA) and q is the asymmetric parameter of the CSA tensor. Thus, the line broadening occurs when an incoherent fluctuation frequency is very close to the coherent amplitude of proton decoupling monotonously decreased values without such interference in Figure 1. 

The characterisation of the angular dependence of the interaction of two dipole tensors A1 A2 and B B2 is therefore straightforward, namely it depends on the projection angle of the two bonds between A1 and A2 and between B1 and B2. The orientation and magnitude of the chemical shift anisotropy (CSA) tensor, which also can cause cross-correlated relaxation, is not know a priori and therefore needs to be determined experimentally or... 

The size and orientation of the 31P CSA tensor have been calibrated from single-crystal solid state NMR data of barium diethylphosphate [31]. The projection angles 6CHa22 and i between the 1H,13C-dipolar coupling and the components of the 31P-CSA-tensor de-... 

Fig. 8.10 31P chemical shift anisotropy (CSA) tensor orientation of a nucleotide from a DNA dode-camer with its helix axis pointing vertically. The DNA structure has been calculated using CSA data obtained under anisotropic conditions... 

The relaxation theory used in the Appendix to describe the principle of TROSY clearly tells us what to expect, but it is always a little more satisfying if one can obtain a simple physical picture of what is happening. We consider a system of two isolated scalar coupled spins of magnitude %, 1H (I) and 15N (S), with a scalar coupling constant JHN. Transverse relaxation of this spin system is dominated by the DD coupling between spins XH and 15N and by the CSA of each individual spin. The relaxation rates of the individual multiplet components of spin 15N are now discussed assuming an axially symmetric 15N CSA tensor with the axial principal component parallel to the 15N-XH vector as shown in Fig. 10.2. 

Fig. 10.2 Interactions of the local magnetic fields eDD(t) with EFSA(t) (see text). 80 s the static magnetic field. The CSA tensor a is displayed by...

Radio-frequency driven recoupling (RFDR) [58] uses rotor-synchronized 180°-pulses to prevent the averaging of the homonuclear dipolar coupling by the MAS rotation. A single 180°-pulse is placed in the middle of each rotor period (Fig. 11.6a), often using an XY-8 phase cycle [66]. The efficiency of the recoupling depends on the isotropic chemical-shift difference of the two spins and the size and relative orientation of their CSA tensors. 

This approach yields spectral densities. Although it does not require assumptions about the correlation function and therefore is not subjected to the limitations intrinsic to the model-free approach, obtaining information about protein dynamics by this method is no more straightforward, because it involves a similar problem of the physical (protein-relevant) interpretation of the information encoded in the form of SD, and is complicated by the lack of separation of overall and local motions. To characterize protein dynamics in terms of more palpable parameters, the spectral densities will then have to be analyzed in terms of model-free parameters or specific motional models derived e.g. from molecular dynamics simulations. The SD method can be extremely helpful in situations when no assumption about correlation function of the overall motion can be made (e.g. protein interaction and association, anisotropic overall motion, etc. see e.g. Ref. [39] or, for the determination of the 15N CSA tensor from relaxation data, Ref. [27]). 

Apart from the relaxation mechanism described here, other mechanisms such as relaxation involving cross-correlation between dipole-dipole coupling and chemical shift anisotropy (CSA) can also provide structural information [48, 49]. The expression for this relaxation rate in case of axial symmetric CSA tensors is... 

Another CCR mechanism is the interaction of the magnetic dipole with the chemical shift anisotropy (CSA) tensor, e.g., the interaction with the carbonyl CSA-tensor in proteins. The dipole-CSA CCR-rate is also dependent on the projection angle 9 between the magnetic dipole and CSA tensors ... 

The CSA tensor is characterised by <5iso (proportional to its trace) and by the parameter span (O) and skew (k), defined as ... 

The determination of the NMR chemical shift or chemical shielding anisotropy (CSA) tensor from quantum mechanical methods remains a crucial... 

A complication encountered in amorphous inorganic materials is the formation of three-dimensional networks, compared to the one-dimensional chains common in synthetic organic polymers. This network formation can lead to a very large number of structural variables that may influence the observed NMR CSA tensor. Due to this increased complexity it therefore becomes crucial to separate and distinguish the effects of different structural variations on the observed NMR spectra. 

Not all 9 components of a are typically reported when describing the chemical shielding tensor. Instead, the 3 principal components (or eigen values) in a principal axis system (PAS) are reported. The CSA tensor can also be described by three additional parameters 1) the isotropic value (or trace), aiso, of the shielding tensor and is defined as... 

The chemical shielding anisotropy (CSA) tensors for the simple phosphate structures listed in Table I, were calculated using ab initio methods. The isotropic tensor value (aiso), the three principal components (aa), the CSA anisotropy (Act) and asymmetry parameter (rj) were evaluated and are given in Table II. 

Table II. Ab Initio NMR CSA Tensor for Simple Phosphate Clusters3...

G(2d,2p) basis set.b Geometry of investigated compounds listed in Table I.c CSA tensor defined using Equations 1-4. d Experimental structure. e Optimized structure.f In the staggered confirmation the phosphorous are inequivalent. 

PH3 The standard PH3 molecule provides a simple example of molecular geometry effects on the CSA tensor. If PH3 maintains C3v there are only two variables that... 

Figure 1 CSA tensor (a) variation with P-H bond distance (rPH) in PH3. The isotropic (aiso) value and principal components (

Figure 2 CSA tensor (a) variation with HPH bond angle (0hpH) in PH3 a) geometry optimization of P-H bond distance performed at each new configuration, b) P-H bond distance fixed at experimental equilibrium distance of 1.415 A.

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