Bijvoet pair measurement

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]. 

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. 

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. 

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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