In this work, the Kullback-Leibler information deficiency is probed as a chirality measure. It is argued that the information deficiency, calculated using the shape functions of the R and S enantiomers, considering one as reference for the other, gives an information theory based expression useful for quantifying chirality. The measure is evaluated for five chiral halomethanes possessing one asymmetric carbon atom with hydrogen, fluorine, chlorine, bromine, and iodine as substituents. To demonstrate the general applicability, a study of two halogen-substituted ethanes possessing two asymmetric carbon atoms has been included as well. The basic expression of the sum of the local information deficiency over all atoms can be decomposed into separate summations over coinciding and noncoinciding atoms, or into a global and a mixing entropy term, or into a local entropy contribution for each atom individually based on the Hirshfeld partitioning. Avnir's continuous chirality measure (CCM) has been computed and confronted with the information deficiency. Finally, the relationship between chirality and optical rotation is used to study the proposed measure. The results illustrate Mezey's holographic electron density theorem with an intuitively appealing division of the strength of propagation of the atomic chirality from an asymmetric carbon atom throughout the molecule. The local information deficiency of the carbon atom is proposed as a measure of chirality; more precisely, the difference in information between the R and the S enantiomer turns out to be a quantitative measure of the chirality of the system. It may be evaluated as the arithmetic mean of the different alignments, or considering only the alignment resulting in the highest similarity value, or using the QSSA alignment.

Molecular quantum similarity is evaluated for enantiomers possessing two asymmetric carbon atoms, namely halogen substituted ethanes. This study is an extension of previous work performed on molecules with a single asymmetric carbon atom and molecules possessing a chiral axis. Global similarity and its local counterpart based on the Hirshfeld partitioning are evaluated. By these means we quantify the dissimilarity of enantiomers and illustrate Mezey's holographic electron density theorem in chiral systems. Furthermore, the relation between the optical activity and the dissimilarity is studied. Special attention is drawn to the meso compounds, since these isomers enable us to examine local chirality in an achiral system.

Molecular quantum similarity is evaluated for enantiomers in the case of molecules possessing a chiral axis, as an extension of previous studies on molecules with a single asymmetric carbon atom. As a case study, the enantiomers of substituted allenes are examined. Next to studying global similarity, using the already existing similarity indices defined by Carbó and Hodgkin-Richards, we evaluate local similarity using our earlier proposed local similarity index based on the Hirshfeld partitioning, to quantify the consequences of Mezey's holographic electron density theorem in chiral systems. Furthermore, the relation between the optical activity and the dissimilarity is studied.

To refer to or to cite this work, please use the citation to the published version: Janssens, S.; Bultinck, P.; Borgoo, A.; Van Alsenoy, C.; Geerlings, P.; Alternative KullbackLeibler Information Entropy for Enantiomers. J. Phys. Chem. A, 2010, 114, 640-645