Desymmetrization distortional

As shown below (Section IV), the lithium enolates are remarkable vectors of asymmetry. Indeed, the development of many chiral auxiliaries has been associated (in particular through their ester derivatives) with the enolate chemistry. We conclude this section with the contribution of a group of mathematical chemists who have tried to quantify the desymmetrization induced on enolate orbitals by common chiral auxiliaries219. This unusual viewpoint suggests that when the allylic stereogenic center is in the / position, the (Z) isomer has more chirality content than its (E) counterpart. This paper also concludes that in the enolates derived from Meyers oxazolines, the lithium cation distorts the structure but has little influence on its chirality. 

P. Murray-Rust, H.-B. Biirgi and J.D. Dunitz Acta. Cryst. A35, 703 (1979). A lucid exposition of the distinction between kernel and co-kernel in terms of distortional desymmetrization of a molecule in a crystalline environment. The Table of Kernels and Co-kernels in Appendix B was adapted from this paper. 

In the preceding subsection we have merely reproduced the familiar prediction once more, but the viewpoint adopted above may perhaps have provided additional insight into its origin. When it is recognized that a reaction that is forbidden by orbital symmetry conservation to take place in a group of high symmetry can be made allowed by an suitable desymmetrizing perturbation, it becomes appropriate to ask whether substitutional desymmetrization, such as that discussed in Section 2.3.2, may not be as effective for that purpose as distortional desymmetrization. 

Tetraaryldisilenes are essentially planar molecules [6, 7] that distort out-of-plane with great ease to a trans conformation [8]. Ignoring the asymmetry imposed by the substituents, the molecule can be regarded as having D2/1 symmetry. When it is placed in the xy plane with the SiSi bond along x, the soft out-of-plane displacement is assigned to b g and desymmetrizes the molecule to a motion that can play no essential role in the isomerization. ... 

Desymmetrization to Sq by a superposition of ai and a2u displacements or - more drastically - all the way down to C, would formally allow the dimerization. The necessary distortions are opposed by large restoring forces, and would not be expected to reduce the activation energy significantly. 

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