Mathematical description of molecular structure: Molecular topology.

The concepts of the topology of finite point sets are applied to a mathematical description of molecular structure. The combinatorial properties of the "bond topology," which arises naturally from atomic adjacency relationships within a molecule, are investigated in detail. The collection of closed sets, the cotopology, is found to be related to bonding. Combinatorial weights of bonds over the cotopology are defined and explicit expressions for a general molecule are derived. The bond weights are found to parallel molecular orbital bond orders. It is concluded that much of the variation in pi bond orders is topological in origin.