Self interaction correction closed-shell

The XC energy represents the correction to the Coulomb energy for the self-energy of an electron in a many-electron system. The latter is due to both the direct self-energy of the electron as well as the redistribution of electronic density around each electron because of the Pauli exclusion principle and the Coulomb interaction. As an example, we now discuss the case of Fermi hole and the exchange energy in Hartree-Fock (HF) theory [16]. For brevity, we restrict ourselves to closed-shell cases. 

The main advantage of this approximation is that it is exact for two-electron systems (if the correct kf(r) = 0 is utilised in (4.15) before performing the functional differentiation (3.17) required for its application) and also correctly accounts for the self-interaction energies of individual closed shells if a shellpartitioning scheme is used [71]. Furthermore, the RWDA reproduces the asymptotic r proportionality of the exact x-only potential (although with the incorrect prefactor of 1/2 [103]). 

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