Description of chiral tetrahedral molecules via an Aufbau approach.pdf

1 Description of chiral tetrahedral molecules via an Aufbau approach Salvatore Capozzielloa,* and Alessandra Lattanzib,* aDipartimento di Fisica “E. R. Caianiello”, INFN sez. di Napoli, Università di Salerno, Via S. Allende 84081 Baronissi, Salerno, Italy bDipartimento di Chimica, Università di Salerno, Via S. Allende 84081 Baronissi, Salerno, Italy Abstract We propose a predictive “building-up” of tetrahedral molecules, based on a previously derived “chirality index” { }pn,≡χ , which characterizes a tetrahedral molecule, with n chiral centers, as achiral, diastereoisomer, or enantiomer as a function of the p observed inversions (at most one for each center) under rotation and superimposition to its mirror immage. The set of rules which is identified allows the classification of the new molecule, obtained by the addition of another chiral center, by the determination of the selection rule 0,1? =p with respect to the added center. Keywords: Central molecular chirality; Tetrahedral molecules; Chirality index; Aufbau 1. Introduction The development of mathematical descriptors for the characterization of chemical structures is a subject of increasing interest [1]. Several topological indexes have been proposed to depict 3D molecular structures and shapes [2]. Chirality of molecules has been as well the subject of studies aimed to achieve numerical indexes as a measurament of this property [3], so, discrete and continuous measurements of chirality have been proposed in order to determine the degree of chirality of a molecule. Such measurements are related to the methods for the characterization of physical and chemical features of a given compound. *Corresponding authors. E-mail: lattanzi@unisa.it 2 On the other hand, the empirical classification of organic molecules is based on the properties of functional groups, such as hydroxy group in alcohols, C─C double and triple bonds, CO g