Angular information

RDCs are easy to measure and the interpretation with respect to distance and angular information is readily available. Other anisotropic parameters contain similar information, but are either difficult to obtain experimentally or are more complex in terms of interpretation. In the following, a brief introduction into RQCs, RCSA and PCSs is given. 

A second way of measuring angular information is based on CCR processes. In contrast to empirical relations like the Karplus equation, angular information out of CCR measurements can be directly extracted from fundamental principles. 

As described in Section 9.2.4.5, CCR can be used to obtain dihedral angular information. Since CCR processes depend linearly on the correlation time, the requirements for exchange-transferred spectroscopy are fulfilled similarly to the etNOE. 

Angular information is notably absent from the list of structural parameters normally obtained from XAS. One approach to obtaining angular detail is to make use of multiple scattering effects (17). Unfortunately, this technique is only useful for outer shells (non-nearest neighbor atoms) where there are atoms intervening between the absorber and the scatterer. This technique suffers from complications if the shells of interest overlap in distance with other shells of atoms. 

An alternate method for obtaining angular information is to make use of the plane polarized nature of synchrotron radiation. It has long been known that XAS should exhibit a polarization dependence for anisotropic samples (18) however it is only recently that attempts have been made to exploit this effect. Early attempts to observe anisotropic XAS suffered from the low intensity and incomplete polarization of conventional x-ray sources. This work has been reviewed by Azaroff (19). 

Direct RDCs in biomolecules between protons over a distance of up to 8 A have been measured,1011 allowing in principle an extension of atoms to be correlated. But even more important is that the nature of RDCs allows the extraction of angular information relative to the static magnetic field as an external reference, making it now generally possible to correlate distant parts of a molecule with NMR spectroscopy. 

Although the bulk of detailed work has been undertaken on v-SiOj, in situ x-ray studies of molten silicates at high temperature have confirmed that Si is coordinated to four oxygens in the molten as well as the glassy state (Waseda and Toguri, 1977, 1978) and yielded information on Si-0 bond lengths and some angular information (see Table 8.1). 

EXAFS data from frozen solutions and polycrystalline samples can provide information about the number, type, and distances of atoms coordinated to the molybdenum atom, but not angular information that defines stereochemistry. Mo L-edge spectroscopy has been used to investigate the 2p 4d electronic transitions of the molybdenum atom in sulfite oxidase and model compounds in order to obtain information about the symmetry and electronic structure of the molybdenum center (70). 

Therefore, XAS—especially with respect to EXAFS—has many advantages as a probe of transition metal centers in biological materials. Beyond the absence of a requirement for crystalline materials, the major attractions are the specificity, and sensitivity of the technique and the provision of interatomic distances with an accuracy of 0.02 A within (say) 4 A of the primary absorber. However, it should be noted that (1) no angular information is usually obtained (2) rarely does the structural information extend beyond 4 A, (3) the spectrum sums data for all atoms of a particular element and, if the element of interest is present in more than one chemical form, an average environment is obtained (4) the possibility of radiation damage must be anticipated and the integrity of samples should be monitored after, and if possible... 

Search for GRB Neutrinos. The AMANDA GRB search for correlated v emission relies on temporal (typically less than 100 s in duration) and angular information provided by BATSE and other satellites in the IPN network (Hurley et al., 1998). Initial search strategies for data collected between 1997-2000 (Hardtke et al., 2003) and for individual GRBs (Stamatikos et al., 2004), have assumed nearly concurrent emission within the duration of prompt gamma-ray emission (Tgo). A new search (Kuehn et al., 2004) also scans for neutrino emission prior to the Tgo start time. No excess was observed for either search method above the expected background from atmospheric v and poorly reconstructed... 

Although, the powder method was developed as early as 1916 by Debye and Scherrer, for more than 50 years its use was almost exclusively limited to qualitative and semi-quantitative phase analysis and macroscopic stress measurements. The main reason for this can be found in what is known as the principal problem of powder diffraction accidental and systematic peak overlap caused by a projection of three-dimensional reciprocal space on to the one-dimensional 26 axis, leading to a strongly reduced information content compared to a single crystal data set. However, despite the loss of angular information, often sufficient information resides in the ID dataset to reconstruct the 3D structure. Indeed, quantitative analysis of the pattern using modern computers and software yields the wealth of additional information about the sample structure that is illustrated in Figure 1. Modern... 

Fig. 9. Top H-2D exchange spectrum of dimethylsulfone. The inset shows the corresponding theoretical spectrum for a two-site jump with a jump angle of 106°. The angular information is encoded in the shape of the elliptical ridges perpendicular to the main-diagonal spectrum. Bottom Theoretical ridge pattern (contour plots) for different jump angles. (Adapted with permission from Refs. 138,140.)...

Angular Discriminant For distance-based discriminants, the diagnosis can be posed as a minimization of distance penalties. For angular information, a suitable discriminant can be stated as ... 

The various ID CP NMR spectra of a biaxially drawn industrial PET film are shown in Fig. 14.7. The pronounced sensitivity to the orientation of the sample with respect to the applied magnetic field is also shown [7]. However, the orientation distribution is relatively complicated and, therefore, difficult to quantify from these data. For PET, overlapping resonances from carboxyl and phenylene group carbons are especially troublesome and, consequently, restrict the angular information achievable in ID NMR experiments. 

Due to the fact that the cross-correlated relaxation like the NOE depends linearly on the correlation time of the molecule, it grows with the correlation time and thus the size of the molecule. This is the first and so far only NMR parameter with this property that delivers angular information and thus behaves like the NOE that delivers distance information and also scales with the correlation time. This is an interesting property and helps to study molecules that are weakly bound to larger molecules. 

---