Symmetry related sites

In the host/additive systems described above, such as (/ ,S)-ser/(/ ,S)-thr and glycine/(/ ,S)-a-amino acids, the change in crystal habit and the enantiomeric segregation of occluded additive indicates that only a subset of the possible symmetry-related sites may be occupied by an additive depending on through which faces the additives are occluded. Such an effect would lead to a reduction in the overall symmetry of the host/additive crystal. 

Fig. 16. A schematic drawing of the hexokinase dimer showing the location of observed glucose and nucleotide binding sites. The two sugar binding sites are represented by 5 and S. The intersubunit AMP-PNP site I is formed by regions Iu and Id of each subunit. The symmetry related sites are indicated by Iu and Id. The location of the AMP binding sites in the monomeric Bill crystal form are labeled A and A. From Anderson et at. (72).

The all-trcms conformation of both guest molecules was maintained throughout the simulation period, but the molecular axis jumped several times between three symmetry-related sites this corresponds to a rate of 1010-1012 s-1. 

The reader can find a discussion of the relationship of magnetic resonance parameter matrices and symmetry-related sites to the possible crystal symmetries in an available review article.12... 

The vectors between symmetry-related atoms can be found by subtracting the coordinates of one atom from that of another atom at a symmetry-related site. In this particular case these vectors lie at ... 

Another problem that frequently arises with multiple isomorphous derivatives is that of handedness. In space group P2i2i2i, Patterson maps for two independent derivatives may be interpreted to yield a set of symmetry related sites for one derivative and, independently, a second set for the other. Because handedness is completely absent in a Patterson map (because it contains a center of symmetry), there is an equal chance that the heavy atom constellation for the first will be right handed, and the constellation for the other will be left handed, and vice versa. This won t do. The two heavy atom sets will not cooperate when used to obtain phase information. There are ways of unraveling this problem too, and once again, it involves difference Patterson maps between the two derivative data sets and cross vectors. This case can also be resolved by calculating phases based on only one derivative and then computing a difference Fourier map (see Chapter 10) for the other. 

Table 2.2 Principal values (in MHz) and axes of hyperflne and quadmpole coupling tensors observed in the radical H3N CH2CH0S03, in single crystals of 2-aminoethyl hydrogen sulfate X-irradiated at 295 K. The and = = signs refer to two symmetry related sites in the crystal. The direction cosines refer to the orthogonalized a, b, and c axes of the monocUnic crystal system, where c is the normal to the (a, b) crystallographic plane...

A common complication in ESR and ENDOR single crystal studies is the occurrence of different spectra due to identical paramagnetic species that are differently oriented due to crystal symmetry. The species are said to be located in different sites, and the overlap of spectra due to different orientations is referred to as site splitting. In the triclinic crystal system, e.g. for the malonic acid discussed in Chapter 2, there is only one molecule in the unit cell and no site-splitting occurs. Two symmetry-related sites with coordinates (x, y, z) and (-x, y, -z) give identical ESR spectra when the crystal is rotated about the y axis. The result is plausible since the magnetic field... 

Figure 1 High-temperature polymorph of caffeine, in which the molecule occupies a site that overlaps with six symmetry-related sites. A depiction of the caffeine molecule, with hydrogen atoms deleted, is shown (a) along with the disordered model obtained in the refinement.

K and > 383 K indicating that there may be a Cs-Cs dimer between two Cs atoms in adjacent Ge cages. Cs NMR spectra of a single crystal of tetragonal Cs" ( 15-crown-5)21 were obtained as a function of crystal orientation and analyzed to provide the magnitudes and orientations of the Cs chemical shift and quadrupolar tensors for two magnetically nonequivalent and symmetry related sites.The results showed that the local environment of the Cs nuclei is nonaxially symmetric. 

Ordering of octahedral cations between the interlayer and the 2 1 layer is permitted and is observed for all chlorites that have been studied in detail. This is essential to the maintenance of a positive charge on the interlayer sheet. Octahedral cation ordering within each sheet is not determinable in the case of semirandom stacking, but is determinable for all regular polytypes. For 10 of the 12 regular one-layer polytypes in Table II, the three octahedral sites within each sheet consist of two symmetry-related sites and one unique site. For the other two regular polytypes, all three sites are unrelated by symmetry. 

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