ABSTRACT
Imagine a simple chiral molecule in its R conguration close to T = 0 K in free space. Within the Born-Oppenheimer approximation, its nuclei will be somewhat delocalized from the lowest-energy structure due to zero-point vibrations. A small fraction of the nuclear frame probability density will extend into transitional con-gurations, which are equally far from the R and its mirror image S conguration. By continuity and symmetry, there must then also be probability density in the fully developed S conguration region. In other words, the ground state of the molecule will be a superposition of R-and S-like congurations. It will be symmetric with respect to stereomutation and thus achiral in this approximation. There will also be
3.1 Introduction ..................................................................................................... 39 3.2 Parity Violating Forces ....................................................................................40 3.3 Torsional Chirality in Ethanol .........................................................................40 3.4 Fluorination Effects......................................................................................... 41 3.5 Argon Collisions ............................................................................................. 42 3.6 Argon Attachment ........................................................................................... 42 3.7 Water Attachment ............................................................................................ 43 3.8 Dimerization ................................................................................................... 43 3.9 Chiral Molecule Attachment ...........................................................................44 3.10 Experimental Techniques ..............................................................................44 3.11 Conclusions ................................................................................................... 45 Acknowledgments ....................................................................................................46 References ................................................................................................................46
a nearby stationary state with a wavefunction that changes sign at congurations that are equally far from R and S. Like the symmetric ground state, this antisymmetric ground state is achiral. If we prepare the molecule in a low-energy R con-guration, it is not in a stationary state. Within this approximation, it will oscillate between R and S states with a full period τ, which is the inverse of the energy splitting ∆E between the antisymmetric and the symmetric state, divided by Planck’s constant, h.1 If the probability for transitional congurations is low enough, this oscillation will be slow-ideally, one can store the R molecules in bottles. This is the case for a high barrier toward stereomutation, as we know it from molecules with “asymmetric carbon” atoms. If the barrier is low, such as in many pyramidal amines, one cannot store the R molecules in bottles. The timescale on which such a exible, transiently chiral molecule may still be considered to be chiral is governed by quantum mechanical tunneling and depends strongly on the height and width of the barrier for stereomutation. The width also involves the mass, which has to be dislocated during the inversion process. This simple model of a chiral molecule with a more or less high stereomutation barrier provides the starting point for the present chapter, in which perturbations of increasing complexity will be introduced to the chiral molecule and the consequences of these interactions with other systems will be discussed. If the binding partner is also chiral, the term chirality recognition is used. Depending on the stereomutation speed of the binding partner, chirality discrimination, chirality induction, and chirality synchronization phenomena will be discussed.
