QUANTUM TOPOLOGY OF MOLECULAR CHARGE-DISTRIBUTIONS .1

The primary concepts of descriptive chemistry, of an atom in a molecule with its own set of properties, and of a chemical bond, yield to precise definitions in terms of quantum mechanics and the observed topological properties of the charge distribution. The notion of a molecule as a collection of bonded atoms with a definite structure and shape is one which has meaning in real, Euclidean space. It should therefore be a consequence of a property of the system which is itself manifest in real space. It is shown that a particular topological property of the charge density, ρ(r), defines the boundaries between pairs of bonded atoms (it defines an atom) and the network of bonds which link tnem (it defines structure). The definition of the boundary is universal and it defines the boundary of the molecule, as well as of the atoms within it (it defines molecular shape). These definitions apply to both stationary and dynamic systems. Thus the notions of the making and breaking of chemical bonds are also precisely defined. The boundary defined in the usual formulations of quantum mechanics is the one at infinity where the boundary condition on the variation of Ψ is satisfied. These approaches are necessarily restricted in their applications to a total, isolated system. One may obtain a formulation of quantum mechanics which does define the physical subspacesof a system and yields a prediction and description of their average properties. The boundaries of these subspaces are found to be identical with the physical boundaries defined by the topological properties of ρ(r). The observational and theoretical basis for these definitions is presented and illustrated for the diborane molecule. This paper serves as an introduction to a theory of bonding and molecular structure which is entirelydetermined by the observed properties of the charge density. © 1979, American Chemical Society. All rights reserved.