Diastereomeric Xe chemical shifts in tethered cryptophane cages

Cryptophane cages serve as host molecules to a Xe atom. Functionalization of cryptophane-A has permitted the development of Xe as a biosensor. Synthetic routes used to prepare cryptophanes result in racemic mixtures of the chiral cages. In the preparation of a tethered cryptophane-A cage for biosensor applications, some achiral and chiral substituents such as left-handed amino acids have been used. When the substituent is achiral, the NMR signal of the Xe atom in the functionalized cage in solution is a single isotropic peak, since the Xe shielding tensor components in the R and L cages differ by no more than the signs of the off-diagonal elements. Chiral substituents can split the cage-encapsulated Xe NMR signal into one or more sets of doublets, depending on the number of asymmetric centers in the substituent. We carry out quantum mechanical calculations of Xe nuclear magnetic shielding for the Xe atom at the same strategic position within an L cryptophane-A cage, under the influence of chiral potentials that represent r or l substituents outside the cage. Calculations of the Xe shielding response in the Lr and Ll diastereomeric pairs permit the prediction of the relative order of the Xe chemical shifts in solutions containing the Rl and Ll diastereomers. Where the substituent itself possesses two chiral centers, comparison of the calculated isotropic shielding responses in the Llr, Lrl, Rll, and Lrr systems, respectively, permits the prediction of the Xe spectrum of diastereomeric systems in solutions containing Llr, Rlr, Lll, and Rll systems. Assignment of the peaks observed in the experimental Xe NMR spectra is therefore possible, without having to undertake the difficult synthetic route that produces a single optically pure enantiomer.