TOPOLOGY OF THE CHARGE DENSITY

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.  

This chapter, which describes the application of the theory of atoms in molecules to the chemistry of the alkanes, gives only a curtailed account of the quantum mechanical basis of the theory, as full accounts have been presented elsewhere The development of the theory of molecular structure is presented in somewhat more detail and the application begins with a review of the topological features of molecular charge distributions and the associated definitions of atoms, bonds and molecular structure. 

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The value of the charge density at a bond critical point can be used to define a bond order (Bader et al. 1983 Cremer and Kraka 1984). The molecular graphs for ethane, ethylene, and acetylene are shown in Fig. 2.8. In each case the unique pair of trajectories associated with a single (3, — 1) critical point is found to link the carbon nuclei to one another. Multiple bonds do not appear as such in the topology of the charge density. Instead, one finds that the extent of charge accumulation between the nuclei increases with the assumed number of electron pair bonds and this increase is faithfully monitored by the value of p at the bond critical point, a value labelled p, . For carbon-carbon bonds, one can define a bond order n in terms of the values of Ph using a relationship of the form... 

Popelier and Logethetis were the first to apply the AIM theory to the study of the nature of the agostic interaction [46]. They analysed the topology of the charge density (computed at the HF, BLYP, and MP2 levels) for CH3TiCl2 (12a), C2H5TiCl2" (12b), and C3H7TiCl2 (12c). 

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