Analysis of enantiotopic discrimination in the NMR spectra of prochiralsolutes in chiral liquid crystals by symmetry factorization of the Saupeordering matrix

摘要

The enantiotopic discrimination in the NMR spectrum of prochiral molecules dissolved in chiralliquid crystals (CLCs) is governed by the ordering of the solute molecules. The lifting of the spectraldegeneracy of enantiotopic sites in such solvents stems from the nonequivalence in their effectiveordering. This, in turn, is brought about by a change in the directions (or the equivalence) of theprincipal axes of their ordering tensor, relative to those in achiral liquid crystals. This discriminationmechanism can only occur for solute molecules belonging to a limited number of ("allowed")improper point groups, viz., D_(2d),C_(2v), C_s, andS_4[D. Merlet, J. W. Emsley, P. Lesot, and Courtieu,J. Chem. Phys. 111, 6890 (1999)]. In this work it is shown that the ordering tensor of such prochiralsolutes in CLC, S~(CLC),and likewise, the tensors,7~k,describing anisotropic magnetic resonanceinteractions of enantiotopic pairs, can be partitioned into symmetric and antisymmetric (andirrelevant) parts. The NMR results in such solvents can be cast into separate sets of equationsdepending on either the symmetric or the antisymmetric parts of SCLC and 7~k. The discriminationobserved in such solvents depends only on the latter set of equation, while the former applies to theaverage splitting of enantiotopic pairs as well as to diasterotopic or homotopic sites in the prochiralmolecules. The factorization procedure greatly facilitates the analysis of the ordering properties ofprochiral solutes in CLC and provides new insight on the discrimination mechanism. In particular,it allows correlation between independent enantiotopic partners and the identification of NMRsignals belonging to common prosterogenic faces in the molecule. Expressions relating NMRobservables with the symmetric and antisymmetric parts of S~(CLC)are derived for each of the fourallowed groups. Model examples are presented and discussed.