Properties of Kinetic Energy Functional

The conventional approach to deriving new density functionals is to first make a list of the properties of the exact functional these properties then constrain the types of functionals that need to be considered. 

Most researchers choose to model not the total kinetic energy T[p] but only the Kohn-Sham piece TJp]. This is partly because accurate approximations to the correlation kinetic energy TJp] are already available from KS-DFT. In particular, most OF-DFT programs use the same energy expression that is used in Kohn-Sham, 

The other reason that researchers choose to approximate the Kohn-Sham kinetic energy is that this functional has simpler mathematical properties. For example, the Kohn-Sham kinetic energy is homogeneous of degree two with respect to coordinate scaling of the electron density  

From this equation, one can derive the virial equation for the Kohn-Sham kinetic 

Modern Theoretical Chemistry Electronic Structure and Reactivity 

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