Optical activity from racemates.

To the Editor — The relationship between chirality and optical activity is an important consideration for various fields of chemical, physical and biological research. For example, the determination of optical activity is a routine test of enantiomeric purity in organic synthesis. Chiral materials (or other non-centrosymmetric (NCS) materials) are also commonly used in optics and photonics to control the polarization of light. In the solid state, optical activity is intrinsic to the crystal structure. Although it is well established that optically active materials can form from any unit that is appropriately arranged — irrespective of the molecular chemistry of that unit — here we highlight that racemic pairs also fit into this category and can therefore be used to make optically active solids. This presents an important qualification to the widely held assumption that racemates are optically inactive. One rule of crystal packing is that enantiomerically pure units must pack into chiral crystal structures1. Chiral materials may also be synthesized from only achiral building blocks2,3. In the synthesis of materials from achiral units, chirality is usually targeted by using chiral templates or solvents. On the other hand, rightand left-handed enantiomers must be related by symmetry to be strictly considered as a racemic compound4–7 (to be consistent with the IUPAC definition of an enantiomer — one of a pair of molecular entities which are mirror images of each other and non-superposable — we do not consider kryptoracemic compounds as racemic because the enantiomers of opposite handedness are not strictly related by symmetry). Because only improper symmetry operations (that is, inversion centre, mirror plane and/or rotoinversion) can relate one enantiomer to its opposite, racemic compounds can only be classified into the 21 non-enantiomorphous point groups. In other words, whereas enantiomerically pure units must pack into chiral crystal structures, racemates, in the strictest sense of the word, must pack into non-chiral ones. Moreover, not only can the enantiomers of opposite handedness be arranged in these crystal classes8, but their arrangement can also induce such symmetries. Thus, enantiomers of opposite handedness can pack such that they are not related by an inversion centre, but instead by only improper rotations or mirror planes leading to non-centrosymmetric point groups such as 4 –2m (D2d), 4 – (S4), mm2 (C2v) or m (Cs). This is illustrated in Fig. 1 in which the packing of centrosymmetric units (symmetry Oh) leads to a centrosymmetric arrangement with symmetry m3 –m (space group Im3 –m). If these units are pure enantiomers (symmetry D3), the arrangement leads to a chiral, non-polar material. If these units are non-polar racemates (symmetry D3), the same packing induces a polar arrangement with symmetry mm2 (space group Aba2) because only glide planes can relate the rightand left-handed enantiomers. Thus, the alignment of polar units is not the only available method to engineer polar materials. The racemic non-polar units can also be used as building units for this design. The symmetry of the media is known to have an influence on its physical properties, and as stated by F. E. Neumann9, every symmetry element of the point group of a crystal structure must be included in the tensor symmetry of any of its physical properties. It is therefore possible to predict from the tensor symmetries which crystal structure can exhibit specific properties. A general consequence of this is that no property described by polar tensors of odd rank and axial tensors of even rank can be observed in media with an inversion centre. For example, pyroelectricity (first rank polar tensor), optical activity (second rank axial tensor) and piezoelectricity/ linear electro-optic effect (third rank polar tensor) can only be observed in noncentrosymmetric media. In particular, optical activity which can be described by a second rank axial tensor will be specific to the eleven enantiomorphous point groups (1, 2, 3, 4, 6, 222, 422, 432, 32, 622 and 23) and four non-enantiomorphous point groups (4 –2m, 4 –, mm2 or m; Fig. 2a) (refs 10–12). Indeed, optical rotation from non-enantiomorphic compounds has been demonstrated previously13–18. As shown in Fig. 2a, optical activity can be observed in 15 crystallographic point groups. On the other hand, enantiomers of opposite handedness can arrange into 21 crystallographic point groups. Thus, the optical activity and racemic compound groups are not independent: the crystal classes 4 –2m, 4 –, mm2 or m belong to both groups and, consequently, racemic compounds can be optically active. To confirm optical activity in racemic materials, we synthesized Optical activity from racemates