Chirality and the Choice of Models

The symmetry of the model of a molecule or of a molecular ensemble depends on the conditions of the relevant physical (or chemical) measurement, and may vary for the same system according to time scale of observation and instrumental sensitivity. Whether the model of a chemical system is chiral or achiral may therefore depend on the conditions of observation. There is no ambiguity when chirality properties are observed the hemihedrality of quartz crystals, the optical rotation of hexahelicene, and the enantiospecificity of hog-kidney acylase, for example, are all unmistakable manifestations of an underlying structural chirality. On the other hand, achirality is not so simply implied by the absence of such observations. 

Consider, for example, a vessel that contains a statistically significant number of molecules, such as a mole of helium atoms at room temperature. With a high degree of probability bordering on certainty, this ensemble is asymmetric at any instant in time because, a priori, any system is expected to be asymmetric unless constrained to be otherwise, and no such 

This analysis may be extended to formally achiral molecules that are composed of four or more atoms. The motions in such polyatomic molecules are restricted by the restoring forces imposed by bonding, and stochastic achirality is here the result of internal vibrations. Thus, for example, molecular deformations in some vibrational states impart chirality to the methane molecule, but the sense of chirality averages to zero under the conditions of measurement. As this discussion makes clear, the conventional symmetry of methane is a property solely of the model. 

Consider a sample of racemic 2-butanol at room temperature, prepared by hydrogenation of 2-butanone under achiral conditions. In contrast to cij-1,2-difluorocyclohexane and ethylmethylpropylamine, molecules of 2-butanoI show no evidence of enantiomerization on the leisurely time scale that is associated with optical rotation measurements or with the separation of enantiomers. Because the probability is exactly one half that any macroscopic sample has an odd number of molecules, there is an even 

As the preceding discussion suggests, conditions may exist under which even the most powerful measuring device available will be incapable of detecting a significant difference between samples of different enantiomeric composition above the noise level of stochastic achirality. We call such a system cryptochiral, because the model demands an excess of one enantiomer over the other in the time domain of observation, while the chirality phenomenon to be observed falls below the threshold of the operational null and thus is undetectable. Note that a cryptochiral substance is operationally indistinguishable from a stochastically achiral one because, at and below the operational null, enantiomorphous systems can be neither differentiated from each other nor distinguished from achiral ones. 

---