Virial partitioning method

When space is partitioned with discrete boundaries, as in Eq. (6.7) and in the Bader virial partitioning method, the moments can be derived directly from the structure factors by a modified Fourier summation, as described for the net charge in chapter 6. 

Since difference electron densities, deformation densities or valence electron densities are not observable quantities, and since the Hohenberg-Kohn theorem64 applies only to the total electron density, much work has concentrated on the analysis of p(r). The accepted analysis method today is the virial partitioning method by Bader and coworkers67, which is based on a quantum mechanically well-founded partitioning of the molecular... 

Dissection of the energy into atomic energies with the help of the virial partitioning method. 

TABLE 7. Atomic energies and atomic charges of cyclopropane, cyclobutane and propane as calculated by the virial partitioning method"... 

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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