Density Functionals of Exchange Energy

Starting from the Hartree-Fock framework of exchange energy definition in terms of density matrix (Levy et al., 1996), 

Alternatively, by paralleling the kinetic density fimctional previous developments the gradient expansion for the exchange energy may be regarded as the density dependent series (Cedillo et al., 1988)  

Quantum Nanochemistry-Volume I Quantum Theory and Observability 

Moreover, the as5rmptotic behavior of Fade exchange functional (4.441) leaves with the convergent limits  

Another interesting approach of exchange eneigy in the gradient expansion framework was given by Bartolotti through the two-component density functional (Bartolotti, 1982)  

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