Some Remarks on the Concept of Molecular Topology

The topology of a molecule can be described as a neighbourhood (Hausdorff) topology defined in the vertex set of a (connected) molecular graph. The vertex set together with its neighbourhood topology forms the molecular topological space. It contains the totality of information about the mutual connectedness of all pairs of atoms of the molecule but it does not contain any information about the kind of atoms present and the geometry of the molecule (bond lengths and angles) [1]. It is now a well-established (but not at all trivial) fact that the physical and chemical properties of many chemical substances are related to the topological spaces associated with the molecules (see e.g. [2]). In the present communication some more general considerations regarding the concept of molecular topology are presented. All kinds of structural characteristics of a molecule that are not topological in nature will be termed material characteristics, i.e. kind of atoms present, bond lengths and angles, charge, etc. For sets of compounds three cases can be distinguished: