Distance ambiguous

NOE-difFerence spectroscopy is particularly valuable for distinguishing stereoisomers, for it relies solely on intemuclear distances, and thus avoids any problems of ambiguity or absence associated with couplings. With smallish molecules, it is best carried out in the above 1D maimer, because 2 s are necessary for tire transmission of the NOE. The transmission process becomes more efficient with large molecules and is almost optimal for proteins. However, problems can occur with molecules of intemiediate size [3f]. A 2D version of the NOE-difference experiment exists, called NOESY. 

In an isolated two-spin system, the NOE (or, more accurately, the slope of its buildup) depends simply on where d is the distance between two protons. The difficulties in the interpretation of the NOE originate in deviations from this simple distance dependence of the NOE buildup (due to spin diffusion caused by other nearby protons, and internal dynamics) and from possible ambiguities in its assignment to a specific proton pair. Mofec-ufar modeling methods to deaf with these difficulties are discussed further below. 

Figure 2 Usejaf unambiguous or ambiguous distance restraints in an optimization calculation.

Figure 5 Schematic representation of a Cartesian dynamics protocol starting from random torsion angles. The weights for non bonded (i.e., van der Waals) interactions, unambiguous distance restraints, and ambiguous distance restraints are varied independently. The covalent interactions are maintained with full weight, co.aie - for the entire protocol. Weights for other experimental terms may be varied in an analogous way. Coupling constant restraints and anisotropy restraints are usually used only in a refinement stage.

Figure 6 Steps in automated assignment. (1) Select the lowest energy structures from iteration / — 1 that are used to interpret the spectra. (2) For each peak, list all possible assignments compatible with the resonances within a frequency mnge. (3) Extract a distance for each assignment possibility from the ensemble of structures. (4) Use the distances to assign ambiguous NOEs. (5) Calibrate the peak volumes to obtain distance restraints. (6) Calculate structures based on the new restraints.

The first theoretical attempts in the field of time-resolved X-ray diffraction were entirely empirical. More precise theoretical work appeared only in the late 1990s and is due to Wilson et al. [13-16]. However, this theoretical work still remained preliminary. A really satisfactory approach must be statistical. In fact, macroscopic transport coefficients like diffusion constant or chemical rate constant break down at ultrashort time scales. Even the notion of a molecule becomes ambiguous at which interatomic distance can the atoms A and B of a molecule A-B be considered to be free Another element of consideration is that the electric field of the laser pump is strong, and that its interaction with matter is nonlinear. What is needed is thus a statistical theory reminiscent of those from time-resolved optical spectroscopy. A theory of this sort was elaborated by Bratos and co-workers and was published over the last few years [17-19]. 

Another noteworthy example is x-ray absorption fine structure (EXAFS). EXAFS data contain information on such parameters as coordination number, bond distances, and mean-square displacements for atoms that comprise the first few coordination spheres surrounding an absorbing element of interest. This information is extracted from the EXAFS oscillations, previously isolated from the background and atomic portion of the absorption, using nonlinear least-square fit procedures. It is important in such analyses to compare metrical parameters obtained from experiments on model or reference compounds to those for samples of unknown structure, in order to avoid ambiguity in the interpretation of results and to establish error limits. 

Total Range Foldover. Radar transmits pulses every Tr seconds and for high PRF situations, following (24), the distance Ar between range ambiguities on the ground (distance between consecutive pulse... 

NOEs that involve groups of protons with degenerate chemical shifts, in particular methyl groups, may be referred to pseudoatoms located in the center of the protons that they represent, and the upper bound is increased by a pseudoatom correction equal to the proton-pseudoatom distance [27, 28]. Another method that usually incurs a smaller loss of information [29] is to treat NOEs for groups of protons with degenerate chemical shifts as ambiguous distance constraints (see Eq. (13) below). 

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