Achiral lattice

The photochemical behaviour of 7 OEt is the first example in which the reaction of achiral molecules in an achiral crystal packing does not occur at random but stereospecifically, resulting in a syndiotactic structure. As no external chiral catalyst exists in the reaction, the above result is a unique type of topochemical induction , which is initiated by chance in the formation of the first cyclobutane ring, but followed by syndiotactic cyclobutane formation due to steric repulsions in the crystal cavity. That is, the syndiotactic structure is evolved under moderate control of the reacting crystal lattice. 

Two compounds are diastereomers when they contain more than one chiral center. If the number of dissymmetric centers is given by N, then the number of possible diastereomers is given by 2N. Of these 2 v diastereomers, each will be characterized by its mirror image, so that the number of enantiomers is given by 2NI2. Whereas the physical properties of enantiomers in an achiral environment are necessarily identical, the physical properties (including solubility) of diastereomers are normally different. The differences arise since there is no structural requirement that the crystal lattices of different diastereomers be the same. For instance, the solubility of an (SS )-diastereomer could differ substantially from that of the (/ S)-diastereomer. However, it should be remembered that the solubility of the (SS)-diastereomer must be exactly identical to that of the (I 7 )-diastereomer, since these compounds are enantiomers of each other. At the same time, the solubilities of the (SI )-diastereomer and the (I S)-diastereomer must also be identical. 

As discussed in detail in Ref. 36, for use in optoelectronics only systems crystallizing in non-centrosymmetric crystal lattices are of interest if the use of expensive enantiomers of chiral molecules is to be avoided. This considerably limits the available crystal lattices since most organic achiral molecules crystallize into centrosymmetric space groups. An interesting example of enantioselective inclusion complexation was reported by Gdaniec and coworkers [37]. 

Achiral objects can be assembled into chiral solid-state structures, and this is frequently the case for urea 1 when it encloses guests. Other compounds adopt a chiral conformation in solution and therefore may ultimately produce either chiral or achiral host structures. On the other hand, thiourea 2 forms an inclusion lattice that is achiral. This arrangement is nonetheless very effective in enclosing guest molecules. 

The best-known example of an achiral molecule forming a chiral inclusion structure is that of the hexagonal urea tubulate [4] lattice (Figure 1). Helical assembly... 

Propagation of the lattice through similar use of the second diol hydroxy groups creates a layer. Hence, the crystal structure of (11) (p-chlorophcnol) comprises a series of parallel layers, each of which is chiral. The net structure, however, is achiral because adjacent layers are of opposite handedness (Figure 14). 

An analogous structure is produced when the helical tubuland diol 12 forms a 1 1 co-crystalline adduct with methanol (Figure 15). The lattice, as before, comprises stacked layers of alternating chirality, but overall is an achiral structure [34],... 

Crystallisation of racemic 15 from either chloroform or 1,1,2,2-tetrachloroe-thane yields achiral inclusion compounds that contain both host enantiomers. In contrast, when 15 is crystallised from tetrahydrofuran (THF), a mixture of (+)- and (—)- crystals is produced in space group /J2 2 2 [40], Once again, chirality arises from the lattice structure rather than from self-resolution of the host enantiomers. 

Penzien and Schmidt reported the first absolute asymmetric transformation in a chiral crystal. [10] They showed that enone 4,4 -dimethylchalcone 1, although being achiral itself, crystallizes spontaneously in the chiral space group P2 2 2 (Scheme 1). When single crystals of this material are treated with bromine vapor in a gas-solid reaction, the chiral dibromide 2 is produced in 6-25% ee. In this elegant experiment, it is the reaction medium, the chiral crystal lattice, that provides the asymmetric influence favoring the formation of one product enantiomer over the other, and the chemist has merely provided a non-chiral solvent (ethyl acetate) for the crystallization and a nonchiral reagent (bromine) for the reaction. 

In the envelope conformation (A) the peroxide bond and the two carbon atoms are all coplanar (with the C-O-O-C dihedral angle being close to 0°) while the ethereal oxygen atom can be displaced by as much as 0.65 A to either side of this plane. In conformation B the peroxide bond straddles the plane of the remaining three atoms and this dihedral is around 50°. While conformation A is achiral, B has C.y symmetry. Usually ozonides crystallize in chiral space groups however, both enantiomorphic forms of B are usually encountered in the crystal lattice. Furthermore, disorder of the peroxide oxygen atoms over several occupancies is frequent, and in recent analyses, due mostly to improvement in the structure refinement algorithms, this disorder could be taken into account and suitably refined models could be built from the diffraction data. 

Losing the Expression Achiral Lattices from Chiral Molecules. 234... 

R,R)-TA crystallizes in different enantiomorphous superstructures on Cu( 110), but at a coverage of 0.25 molecules per substrate atom, the monotartrate species forms an achiral c(4 x 2) or (4 0,2 1) structure [71]. In contrast to the bitartrate in its sawhorse geometry, only a single molecular site is connected to the substrate and chirality is not transferred into the lattice structure. Under these conditions, chiral resolution cannot be expected (see below) [72],... 

With the chiral center located in a side chain that is bent away from the surface, an achiral lattice is formed by the chiral diacetylene isophthalic acid derivative at the 1-octanol/graphite interface [73]. Because of the relatively weak interaction between the dangling chiral side chains, the achiral part of the molecule interacting with the substrate dominated the pattern formation. 

Finally, we mention a remarkable example of lateral resolution reported for supramolecular nanostructures on hopg [96]. Held together by 72 hydrogen bonds, the molecular nanostructure is formed from three melamine-substituted calix[4]arene units and twelve 5,5-diethylbarbiturate molecules (Fig. 31a). The nanostructure, basically a stack of four rosettes, has chiral symmetry. With its components all being achiral, both enantiomers are formed upon self-assembly in solution. Deposition of the tetrarosettes on hopg leaves this nanostructure intact and allows surface self-assembly. AFM studies revealed close-packed 2D lattices formed by the tetrarosettes on hopg... 

The measured crystal optical activity, in general, can be either of molecular origin or due to the chiral helical arrangement of chiral or achiral molecules in the crystal, or both. The two factors are difficult to separate. Kobayashi defined a chirality factor r = (pc — ps)/pc = 1 — pslpc, where pc is the rotatory power per molecule of a randomly oriented crystal aggregate derived from the gyration tensors determined by HAUP, and ps that in solution [51]. It is a measure of the 4 crystal lattice structural contribution to the optical activity and represents the severity of the crystal lattice structural contribution to the optical activity, and represents the severity of the restriction of the freedom of molecular orientation by forming a crystal lattice. Quartz is a typical example of r = 1, as it does not contain chiral molecules or ions and its optical activity vanishes in random orientation (ps = 0). 

Chiral crystal from achiral molecule Chiral crystal lattice Moderate-high enantiodifferentiation... 

Even if a molecule is achiral, chiral crystals can form by spontaneous chiral crystallization [26]. The big advantage in utilizing a crystal as a reactant is that absolute asymmetric synthesis can be achieved by solid-state photoreaction of such a chiral crystal. The initial chiral environment in the crystal lattice is retained during the reaction process, owing to the low mobility of molecules in the crystalline state, and leads to an optically active product. The process represents transformation from crystal chirality to molecular chirality. This kind of absolute asymmetric synthesis does not need any external asymmetric source in the entire synthetic procedure [9-14]. 

The compounds in this report usually contain a chirotopic stereogenic carbon ring atom, and were prepared as racemic mixtures. Hypothetically, if the BC conformation prevails, then one can imagine two enantiomers in solution (reference, 5)-BC 9 and (retro-inverso,R)-BC 9-bar. Since this stereochemistry is complicated, it will be helpful if we refer to the descriptor for only one enantiomer. Therefore, in an arbitrary but consistent manner in this report, we will always define the reference ring chirality and label tropicity to be that of the (S)-enantiomer. For example, suppose a racemic mixture of (reference,S)-BC 9 and (retro-inverso,R)-BC 9-bar affords crystals belonging to an achiral space group so that both enantiomers in the racemic compound are present in the crystal lattice. Let us further suppose that dissolution of these crystals will give the same solution-state conformation. We will write that the solid-state (reference,S)-BC 9... 

Klemperer examined the other cases as well (1) when the molecule is chiral, and (2) when the molecule (either chiral or achiral) is not fixed in a crystal lattice but performs rotations and displacements (in fluids). 

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