Kinetic energy components, virial theorem

The electron-interaction component Wee(r) was originally derived, as noted previously, by Harbola and Sahni [9] via Coulomb s law. Since this component does not contain any correlation-kinetic-energy contributions, it does not [9,17,18] satisfy the Kohn-Sham theory sum rule relating the corresponding electron-correlation energy E [p] to its functional derivative (potential) vf (r). The sum rule, which is derived [19,20] from the virial theorem, and in which the correlation-kinetic-energy Tc[p] contribution is made explicit is... 

Consequently, Harbola and Sahni [9,18] proposed that a term which accounts for the correlation-kinetic-energy contribution be added to W (r) in order to obtain the Kohn-Sham potential v (r). This term is the work W, (r). Both the components Wee(r) and W, (r) can, however, be derived from the virial theorem and we give here the proof according to Holas and March [11],... 

Recall that the stress tensor is defined as the change in force on the surface of a volume element from a differential change in the area of that element (2). On the other hand, (12) and (13) indicate that the stress tensor is linked not only to the electronic potential energy (which defines the force on the electrons), but also to the kinetic energy. The stress tensor is thus revealed as the key component in the differential virial theorem [30, 35, 56, 57] ... 

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