EXCHANGE-CORRELATION ENERGY DENSITY FROM VIRIAL-THEOREM

The virial of the exchange potential in density functional theory yiel ds the exchange energy, but the virial of the correlation potential do es not yield the correlation energy. Via the adiabatic connection form ula, we define a hypercorrelated potential whose virial is exactly the correlation energy. This exchange-correlation energy density is uniqu ely determined by the exchange-correlation energy functional. We calcu late the virial energy density both exactly and within several popular functionals, LDA, PBE, and BLYP, on several atoms. The well-known dif ferences between the potentials generated by these functionals is refl ected in this energy density. We speculate on how accurately the corre lation energy can be estimated from knowledge of the exact density, an d on the construction of an energy density hybrid.