ON THE VALIDITY OF WALLACH RULE - ON THE DENSITY AND STABILITY OF RACEMIC CRYSTALS COMPARED WITH THEIR CHIRAL COUNTERPARTS

Wallach's 1895 rule (Wallach, O. Liebigs Ann. Chem. 1895, 286, 90-143) states that racemic crystals tend to be denser than their chiral counterparts. Although this rule has not gone unchallenged, it has nevertheless given rise to the fairly widespread notion that a collection of right- and left-handed objects can be packed more tightly than a collection of homochiral ones. To test the rule we have identified, with the help of the Cambridge Structural Database, 129 pairs of corresponding racemic and chiral crystals. The quantity DELTA(%) = 100[(V/Z)A - (V/Z)R]/{0.5[(V/Z)A + (V/Z)R]}, where A and R refer to the chiral and racemic crystals and (V/Z) is the molecular volume, is +0.56(22)%, an inconclusive result. When the sample is divided into two subpopulations, one containing achiral molecules and rapidly interconverting enantiomers (group I, 64 pairs) and the other containing resolvable enantiomers (group II, 65 pairs), DELTA(%) is reduced to +0.20(34)% for group I and increased to +0.92(29)% for group II. This difference in behavior can be attributed to statistical bias in the group II population, since this can contain pairs in which the racemic crystal is markedly more stable than the chiral one (obtainable by crystallization of resolved material) but no pairs in which the racemic crystal is markedly less stable. A similar bias contributes to the apparent greater thermodynamic stability of the racemic crystals in the thermodynamic data collected for 36 pairs of racemic and chiral crystals by Jacques, Collet, and Wilen (Jacques, J.; Collet, A.; Wilen, S. H. Enantiomers, Racemates and Resolutions; Wiley: New York, 1981; pp 93-100). The thermodynamic argument given by these authors for the greater stability of racemic crystals is shown to be fallacious. Nevertheless, apart from the bias inherent in all comparisons of racemic/chiral pairs of resolvable enantiomers, there may also be a genuine tendency for racemic crystals to indeed be more stable (and denser) than their chiral counterparts. This need not be a consequence of any special kinds of interactions between opposite enantiomers but could result merely from the additional possibilities for favorable packing arrangements in racemic space groups compared with chiral ones. The possible role of kinetic factors in crystal nucleation and growth from racemic solutions is also discussed.