Quantum chemical counterparts are defined for chemical concepts of bond order (multiplicity) and actual valence of an atom in a molecule by performing an atomic partitioning of the exchange part of the second-order density matrix within the framework of Bader’s topological theory of atoms in molecules. Unlike previous definitions, the present results permit the formulation of the concepts of bond order and valence in a basis set independent manner and extend, therefore, their applicability to the Hartree-Fock limit or even exact wave functions. The numerical results obtained indicate that, in the framework of Bader’s theory, bond ionicities are much greater than usually supposed on the basis of conventional population analyses, and this is reflected by a significant reduction of covalent bond order and valence values.