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# Harris Foulkes functional

${\displaystyle E_{\mathrm {HF} }[\rho _{\mathrm {in} },\rho ]=\mathrm {bandstructure} \mathrm {for} (V_{\mathrm {in} }^{H}+V_{\mathrm {in} }^{xc})+\mathrm {Tr} [(-V_{\mathrm {in} }^{H}/2-V_{\mathrm {in} }^{xc})\rho _{\mathrm {in} }]+E^{xc}[\rho _{\mathrm {in} }+\rho _{c}].}$
It is interesting that the functional gives a good description of the binding-energies, equilibrium lattice constants, and bulk-modulus even for covalently bonded systems like Ge. In a test calculation we have found that the pair-correlation function of l-Sb calculated with the HF-function and the full Kohn-Sham functional differs only slightly. Nevertheless, we must point out that the computational gain in comparison to a self-consistent calculation is in many cases very small (for Sb less than ${\displaystyle 20~\%}$). The main reason why to use the HF functional is therefore to access and establish the accuracy of the HF-functional, a topic which is currently widely discussed within the community of solid state physicists. To our knowledge VASP is one of the few pseudo-potential codes, which can access the validity of the HF-functional at a very basic level, i.e. without any additional restrictions like local basis-sets etc.