Enantiomorphism and multiple-beam X-ray diffraction

Abstract

It is shown that multiple-beam X-ray diffraction does not provide a means of distinguishing between the two enantiomorphic forms of the same crystal. A detailed proof is presented for the case of benzil. It is also shown that, without anomalous dispersion, multiple-beam diffraction is equally incapable of determining the polarity of acentric crystals. Applications are presented to results published in recent literature.It is well known that multiple Bragg scattering, a situation in which two or more Bragg reflections are excited simultaneously, can be used to determine the phases of structure factors. It is also well known that enantiomorphic forms of the same structure cannot be distinguished in ordinary X-ray experiments since the diffraction patterns are identical. Only when anomalous scattering occurs (i.e. the X-ray energy is not too far from the absorption edge of one atomic species present in the crystal) are certain Bragg reflections, otherwise identical in the two enantiomorphic forms, slightly strengthened or weakened, depending on the space group, thereby making it possible to distinguish between the two enantiomorphic forms.Such has been the case, for example, for a-quartz, which is found with either the P3~2 or P322 space group. It has been shown (De Vries, 1958) that anomalous scattering can indeed be used to determine the absolute configuration, or handedness, of a-quartz.

Right and left in chiral crystals

“…Right and left in chiral crystals. By Statements in the recent crystallographic literature (Colella, 1994;Spence, Zuo, O'Keefe, Marthinsen & Hoier, 1994) may give the impression that there is an ambiguity in the sign of Miller indices such that one cannot distinguish between the lt(hkl) reflection of a given chiral crystal and the -H(-h,-k,-/) reflection of its enantiomorph in the absence of anomalous dispersion. There is no such ambiguity.…”