Topological properties of the charge density

The analysis of the topological properties of the charge density which follows can also be applied to the density obtained by an averaging of p over the motions of the nuclei... 

The atomic forms defined by the topology of the charge density are open systems and their boundaries, as defined in real space, satisfy the quantum condition for an open system. Thus all of the properties of an atom in a molecule or a crystal employed in the atomic classification of the properties of matter are predicted by quantum mechanics. The same topological properties of the charge density which define the atom also lead to the definition of bonds, structure and structural stability and the whole of the molecular structure hypothesis is given a basis in physics. ... 

It is to be stressed that a bond path is not to be understood as representing a ond . The presence of a bond path linking a pair of nuclei implies that the corresponding atoms are bonded to one another. As demonstrated later, the interaction can be characterized and classified in terms of the properties of the charge density at its associated (3, — 1) critical point. The complete description of the interaction, however, requires the evaluation of operators over the associated interatomic surface. These are the topics of later discussions At this point we continue with the identification of the elements of molecular structure with the topological properties of the remaining stable critical points, (3, + 1) and (3, + 3) critical points. 

A theory is only justified by its ability to account for observed behaviour. It is important, therefore, to note that the theory of atoms in molecules is a result of observations made on the properties of the charge density. These observations give rise to the realization that a quantum mechanical description of the properties of the topological atom is not only possible but is also necessary, for the observations are explicable only if the virial theorem applies to an atom in a molecule. The original observations are among the most important of the properties exhibited by the atoms of theory (Bader and Beddall 1972). For this reason and for the purpose of emphasizing the observational basis of the theory, these original observations are now summarized. They provide an introduction to the consequences of a quantum mechanical description of an atom in a molecule. 

Frontera, Deya et al. [19] also performed a topological analysis of the charge-density distribution and properties of critical points in the complexes using the AIM method providing an unambiguous definition of chemical bonding between the anion and the tt-system. These calculations were per-... 

Biological. - Pichon-Pesme et /. determined the electron density and electrostatic properties of Tyr-Gly-Gly and Gly-Asp from high-resolution X-ray diffraction data at 123 K. Topological properties of the charge distribution are diseussed and compared with those derived from other experimental studies on peptide molecules, and the characteristics of the BCPs of the C=0, C-N and C-C bonds are analysed. 

A real prospect for a correct definition of molecular structure on the basis of quantum mechanics emerged thanks to a topological approach to the analysis of the electron density p(q) distribution in a system characterized by this density. This approach developed by Bader [19], based on the topological properties of the charge distribution in molecular systems, provides an invariant pattern of the distribution of chemical bonds between the atoms in a molecule and determines unambiguously the type of a molecular structure for both the classical (Butlerov-type) and the nonclassical (see Ref. [20]) molecular systems. 

Mei C, Edgecombe KE, Smith VH, Heilingbnmner A (1993) Topological analysis of the charge density of solids bcc sodium and lithium. Int J Quantum Chem 48(5) 287-293 Weyrich W (1996) One-electron density matriees and related observables. In Pisani C (ed) Quantum-mechanical Ab-initio calculation of the properties of crystalline materials, vol 67, Springer, Berlin, pp 245-272... 

Topological Definition of Atoms, Bonds, and Structure.—The definitions of an isolated atom, of an atom in a molecule, of a chemical bond, and of molecular structure derive from the properties of critical points of the charge density. 

It is shown in this chapter that, while the Lewis model of the electron pair does not correspond to the existence of spatially localized pairs of electrons, it does find a more abstract but no less real physical expression in the topological properties of the Laplacian of the charge density, the quantity V p(r) as defined in eqn (2.3) (Bader and Ess6n 1984 Bader et al. 1984). The... 

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