THE definitions currently used to classify chemical bonds (in terms of bond order, covalency versus ionicity and so forth) are derived from approximate theories(1-3) and are often imprecise. Here we outline a first step towards a more rigorous means of classification based on topological analysis of local quantum-mechanical functions related to the Pauli exclusion principle. The local maxima of these functions define ’localization attractors’, of which there are only three basic types : bonding, non-bonding and core. Bonding attractors lie between the core attractors (which themselves surround the atomic nuclei) and characterize the shared-electron interactions. The number of bond attractors is related to the bond multiplicity. The spatial organization of localization attractors provides a basis for a well-defined classification of, bonds, allowing an absolute characterization of covalency versus ionicity to be obtained from observable properties such as electron densities.