Virial field

R. F. W. Bader and P. M. Beddall, /. Chem. Phys., 56, 3320 (1972). Virial Field Relationship for Molecular Charge Distributions and the Spatial Partitioning of Molecular Properties. 

G(r) is the positive definite form of the kinetic energy density [11] and the virial field v(r) may be expressed as... 

Bader s main argument is that there is a homeomorphism between p and the virial field,167 which determines the system s potential energy. As a result every bond path is mirrored by a virial path, along which the potential energy density is maximally negative, i.e. maximally stabilising with respect to any neighbouring line. 

Bader RFW, Beddall PM (1972) Virial field relationship for molecular charge distributions and spatial partitioning of molecular properties. J Chem Phys 56 3320-3329... 

Keith TA, Bader RFW, Aray Y (1996) Structural homeomorphism between the electron density and the virial field. Int J Quant Chem 57 183-198... 

The additive energy is constructed to mimic the standard energy density used in the QTAIM, g(r), this time without the constraints imposed by the need of the latter to satisfy the virial theorem [1]. It is generally assumed that Eg r) = G r) + i r), where i r) is the local virial field, so Ee r) =—K r), the Hamiltonian kinetic energy density. 

Figure 12 Contour maps of the electron density p(r) in a, of the kinetic energy density G(r) in b, and of the virial field V(r) in c for a methylene group adjacent to a methyl group in n-butane and w-pentane. The plane shown contains the carbon and hydrogen nuclei. The C-H bond cps and the associated bond paths and intersections of the interatomic surfaces are shown in a. The corresponding cps and virial paths are shown in c. This group and its properties are transferable between these two molecules to within the experimental accuracy of heats of formation. All three fields are locally proportional to the total energy density, G(r) and V(r) by theory, p(r) by observation...

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