The Topological Partitioning Method

Dalton s atomic hypothesis, that a molecule is an ensemble of atoms linked together by a network of chemical bonds, is a fundamental principle of chemistry and physics. This atomic hypothesis, which may serve as a basis for the definition of a posteriori 

Bader s atoms are defined through the partitioning of (r) in three-dimensional real space. The atomic regions are bounded by atomic surfaces, which satisfy the following zero flux condition  

The beauty of the above topological definition of the atom in a molecule lies in the fact that it coincides with the rigorous quantum mechanical definition of an open subsystem [27, 33, 34]. In particular, the atomic action integral, which is defined through the atomic one-particle Lagrangian density, is zero within the atomic volume  

It has also been shown that in the atomic regions the virial theorem holds [27, 33]. That is why Bader s partitioning of the electron density is often cited as the virial partitioning method [35, 36]. Bader s theory leads to an unequivocal formulation of the transferability idea the ensemble of atomic properties, in particular the contribution of an atom to the total energy, may be the same in different molecules, provided the charge density of the atomic region is identical [27]. The chemical bonds can be identified with the paths of maximal electron density, which interconnect the various nuclei. This point and several other chemical applications of Bader s theory have been recently reviewed by Wiberg [37]. 

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