Bijvoet pair

The Friedel pairs are a subset of the so-called Bijvoet pairs, i.e., pairs of any two reflections which are equivalent by Laue symmetry but not by the point group symmetry of the crystal (see Table 2 a full listing of these reflections is available4 1). All Bijvoet pairs may be used for a comparison, but since the measured intensity differences between general Bijvoet pairs are more likely to be affected by systematic error, the conclusion based on their comparison may be less reliable than in the case of Friedel pairs. 

The overall effect of resonant scattering is to cause the break down of Friedel s law that the Bijvoet pairs of reflections S(/i) and S(—h) are unequal The difference... 

A third difficulty is the question of absolute polarity. The structure is too nearly centric for there to be any dramatic differences in the Bijvoet pairs, and the differences in agreement indices ate not very decisive. It is even more difficult to exclude the possibility of two orientations mixed by twinning. Had the measurements been confined to one octant, as is often the custom, the polar dispersion effect A would have caused a serious uncertainty. With full data that effect disappears, and nearly the same results are obtained with either assumption of polarity. 

Figure 22 (a) The separation of the normal and anomalous components of a Bijvoet pair of structure factors presented on an Argand diagram. The anomalous contribution can be further divided into real (f) and imaginary (f") components that are perpendicular to each other, (b) The Bijvoet pairs are often shown in the same quadrant, so that F-, the complex conjugate of F is drawn. Because f is the same for both (at one wavelength), F+ and F differ only by direction of the f" vector. 

Despite repeated recrystallizations, both diastereomers 43a and 43b were obtained only as amorphous solids. Therefore, the first-eluted fraction (-)-43a was reduced with LiAlH4 to yield enantiopure glycol (-)-42, which was further converted to 4-bromobenzoate (-)-44 (Fig. 9.7a). By recrystallization from EtOH, (-)-44 gave good single crystals suitable for X-ray analysis, and consequently its absolute configuration was explicitly determined as S by the Bijvoet pair measurement of the anomalous dispersion effect of the bromine atom contained (Fig. 9.7b) [40]. 

When anomalous scattering from Bijvoet pairs of a heavy metal atom derivative of a protein occurs, equation (6.5) now needs to be written ... 

The most important consequence of this effect is the breaking of Friedel s law (the observation of the effects of the violation of Friedel s law is conditioned by the wavelength and the atoms in the crystal), and Friedel pairs are more correctly called Bijvoet pairs. 

This breaking can be used to determine unambiguously the absolute configuration of the structure (in chiral crystals) calculating Fc hkl) for a number of Friedel (Bijvoet) pairs, one of the enan-tiomorphs will fit better, and this will be the correct absolute configuration. 

If the protein has anomalous scatters in its molecule, the difference in intensity between the Bijvoet pairs, Fm/( + ) and Fa /( —), can be used for the phase angle determination. In the MAD method the wavelength... 

Bijvoet and co-workers have succeeded in the first determination of the AC of chiral compounds by analyzing the intensity difference between Bijvoet pairs. 

To determine the AC more unambiguously, 16 Bijvoet pairs showing a large intensity difference were selected and their intensities were measured. The structural factors experimentally obtained were compared with those calculated for the (3aR,6S) configuration as listed in Table 55.1, where Fo hkl) and Fc hkl) are the observed and calculated structural factors of the diffraction from the (hkl) plane. Similarly, Fo h k l) and Fc h k I) were also obtained for the —h — k — l) plane. To easily recognize the intensity difference, the ratio Fo hkl) / Fo h — k — I) was compared with the ratio Fc hkl) / Fc h — k — /). It... 

To determine more simply the AC without the measurement of the Bijvoet pairs, the Flack parameter x was introduced as formulated in equation (5)... 

If the parameter x = 0 is obtained, the AC tentatively assigned is correct. On the other hand, if x = 1, the opposite AC is assigned. Thus, the simple method using the Flack parameter has become more popular these days. Recently, a new probabilistic method was introduced, where the measurement of Bijvoet pairs is required." ... 

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