UNAMBIGUOUS EXCHANGE-CORRELATION ENERGY DENSITY

An exact exchange-correlation energy density is constructed using only knowledge of the density dependence of the exchange-correlation energ y functional, E-XC. The energy density does not depend on the choice o f origin, and allows direct comparison between any functional approxim ation and the exact quantity. The asymptotic behavior of this energy d ensity contains the exact ionization potential. The relative performan ce of approximation energy functionals is reflected in this energy den sity, i.e., the local approximation is moderately accurate, generalize d gradient approximations work better, while hybrids with exact exchan ge work best. The intershell spike in atoms is highlighted in this ene rgy density. The energy density can also be calculated for solids, and has implications for many areas of density-functional theory. (C) 199 8 American Institute of Physics. [S0021-9606(98)30243-3].