Kohn-Sham theory exchange-correlation energy functional

H. A. Physical interpretation of Kohn-Sham theory exchange-correlation energy functional and its derivative... 

H. A. PHYSICAL INTERPRETATION OF KOHN-SHAM THEORY EXCHANGE-CORRELATION ENERGY FUNCTIONAL AND ITS DERIVATIVE... 

The partial cancellation of correlation effects arising from the 1- and 2-matrices is a well-known fact in Kohn-Sham theory [1, 2, 72], As is to be expected, it also appears in the Kohn-Sham-type equations for an orbit cty. We would like to emphasize, nevertheless, that all terms in Eq. (82) can be explicitly calculated. In principle, therefore, within a particular orbit cty, the exchange-correlation energy term as well as the Kohn-Sham-type exchange-correlation potential can be explicitly obtained. The accuracy of the results depends, clearly, on our selection of the orbit-generating functions W 6 c Cn and W e c Sn. 

Before embarking on a more detailed analysis of how to design exchange-correlation energy functionals in Kohn-Sham theory, it may be instructive to take a slight detour... 

Eds., NATO ASI Series B, Plenum, New York, 1995, pp. 191-216. Recent Developments in Kohn-Sham Theory for Orbital Dependent Exchange-Correlation Energy Functionals. 

Most practical electronic structure calculations using density functional theory [1] involve solving the Kohn-Sham equations [2], The only unknown quantity in a Kohn-Sham spin-density functional calculation is the exchange-correlation energy (and its functional derivative) [2]... 

Explicit KS expressions for the electron-transfer reactivities (f r), s r), S ) defined by Parr and collaborators or implicit in their work [8-12] were obtained in [2] and reviewed in Sect. 3, cf. Eqs. (20) and (21). All quantities entering those expressions are in principle computable via Kohn-Sham theory, using any given approximation to the energy functional F[p], Eq. (18b), and the exchange-correlation potential v,c(r), Eq. (19). 

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