Fuzzy Measures of Molecular Shape and Size

Mathematical Chemistry Research Unit Department of Chemistry [Pg.139]

All aspects of molecular shape and size are fully reflected by the molecular electron density distribution. A molecule is an arrangement of atomic nuclei surrounded by a fuzzy electron density cloud. Within the Born-Oppenheimer approximation, the location of the maxima of the density function, the actual local maximum values, and the shape of the electronic density distribution near these maxima are fully sufficient to deduce the type and relative arrangement of the nuclei within the molecule. Consequently, the electronic density itself contains all information about the molecule. As follows from the fundamental relationships of quantum mechanics, the electronic density and, in a less spectacular way, the nuclear distribution are both subject to the Heisenberg uncertainty relationship. The profound influence of quantum-mechanical uncertainty at the molecular level raises important questions concerning the legitimacy of using macroscopic analogies and concepts for the description of molecular properties. [Pg.139]

Fuzzy set methods have been developed for a variety of applications, initially mostly in engineering and technology. However, many applications in the natural sciences quickly followed. The Heisenberg relationship and many other aspects of quantum mechanics can be interpreted in terms of fuzzy sets. A straightforward extension of these ideas to some of the elementary concepts of chemistry suggests the following rather [Pg.139]

Copyright 1997 by Academic Press. All rights of reproduction in any form reserved. [Pg.139]

In some of the preceding representations, a natural interrelationship between fuzziness and resolution is used, leading to resolution-based chirality, symmetry and similarity measures. [Pg.140]

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