Towards the kinetic resolution of mechanically planar chiral rotaxanes

In this work, we reported the synthesis and characterization of two [2]rotaxanes endowed with a central ammonium group and two triazolium recognition stations on either side, acting as complexation sites for a dibenzo-24-crown-8 ether macrocycle. These mechanically interlocked architectures were obtained through the interlocking of a functionalized achiral macrocycle with Cs symmetry (where the symmetry element is a mirror plane corresponding to plane of the ring) and a C∞v symmetric axle (where a mirror plane and a C∞ principal axis are aligned along the axle length). We took advantage of the reversible acid/base triggered molecular shuttling of the ring between two lateral triazolium units to switch the rotaxanes between prochiral and mechanically planar chiral forms, which exists as two rapidly-interconverting co-conformers. We exploited the reactivity of the central amino group to attach an optically pure chiral substituent, with the goal of demonstrating the enantiomeric nature of the co-conformers and to obtain a non-zero diastereomeric excess in the resulting diastereomeric products through a dynamic kinetic resolution. To this end, two enantiopure reagents were chosen that could perform clean and fast reaction with amines: a sulfonyl chloride and an acyl chloride. Only the acyl chloride successfully produced an amide in high yield with the deprotonated rotaxane. The group added to the central amine station acted as a stopper against the shuttling of the macrocycle along the axis, thus preventing the fast interconversion of the two mechanically planar enantiomers. We analysed the results through static and dynamic NMR spectroscopic techniques by varying temperature and solvent used. Indeed, the presence of diastereomers was recorded alongside the configurational isomers resulting from the slow rotation of the CN-CO bond of the amide moiety, thus paving the way for a dynamic kinetic resolution.

Diagnosing criticality in symmetric and chiral clock models

Quantum clock models are statistical mechanical spin models which may be regarded as a sort of bridge between the one-dimensional quantum Ising model and the one-dimensional quantum XY model. This thesis aims to provide an exhaustive review of these models using both analytical and numerical techniques. We present some important duality transformations which allow us to recast clock models into different forms, involving for example parafermions and lattice gauge theories. Thus, the notion of topological order enters into the game opening new scenarios for possible applications, like topological quantum computing. The second part of this thesis is devoted to the numerical analysis of clock models. We explore their phase diagram under different setups, with and without chirality, starting with a transverse field and then adding a longitudinal field as well. The most important observables we take into account for diagnosing criticality are the energy gap, the magnetisation, the entanglement entropy and the correlation functions.