The Chiral Dipolar Hard Sphere Model

A simple molecular model of chiral molecules is presented in this paper : the chiral dipolar hard sphere model. The discriminatory interaction between enantiomers is represented by electrostatic (or magnetic) dipoles-dipoles interactions : short ranged steric repulsion are represented by hard sphere potential and, in each molecule, two point dipoles are located inside the sphere. The model is described in detail and some of its elementary properties are given ; in particular, it is shown that the that the knowledge of only three multipole spherical components (namely : Q 10 , Q 21 and Q 22) allows to compute all multipole spherical components of the model. Despite, the simplicity of the model, it is shown also that the energy landscape of the interaction between two enantiomers is quite rich, this renders systems of chiral dipolar hard sphere very interesting and complicated to study. Few preliminary Monte Carlo simulation results are also reported in the paper. Last, but not least, this paper is dedicated to Jean-Jacques Weis. Chirality is used to describe a lack of symmetry in compounds : it refers to objects , molecules or structures that are not superposable on their mirror image. The separation of the two optical active forms of the tartaric acid, based on the observation of the symmetry of crystals by Pasteur in 1847, has been a major step in the understanding of optical properties of crystals and liquids [1]. Later, in 1884, Kelvin introduced the term chirality, but it has been extensively and systematically used only eighty years later with the introduction of the Cahn-Ingold-Prelog priority rules [2]. Since Arago, Biot and Pasteur, the ideas and concepts on optical activity of substances and on chirality have had and still have a lot of applications in chemistry, biology and physics. In chemistry and biochemistry, chirality is an important tool in stereochemistry and for the determination of the functions of molecules. The interactions between biological molecules are frequently a consequence of the chiral interactions between them. For instance, as first noted by Pasteur, the two forms of asparagine (dextro and levo) tasted differently ; it was found later that this is a frequent property the two optical active forms of amino acids, because of the chiral structure of the taste bud receptor site (several others interesting examples may be found in [3]). The helical structures of DNA, RNA, proteins, etc. are also important to permit biological …