Nonadditive kinetic energy functionals equations

Alternatively, the above equation can be interpreted as defining the nonadditive kinetic energy functional itself [see Eq. (15)] ... 

This equation provides an exact integral constraint, which can eventually be used to test (or constrain) the form of approximate, model functionals. It indicates, that the nonadditive kinetic energy functional should be explicitly dependent upon the subsystem numbers of electrons. This depoidence is missing in the case of the nonadditive fimctionals of Eqs. (11, 12). Neitha- of these approximate functionals satisfies Eqs. (17) and (21). 

From Eqs. (13) and (16) one obtains the following exact equation linking the fiinctional derivatives of the density functional for the nonadditive kinetic energy of the non-interacting system with the subsystem densities and the corresponding numbers of electrons ... 

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