Pair-correlation effect and virial theorem in the self-consistent density-functional theory

The self-consistent derivation of density-functional theory by cluster expansion gives each electron half of the interaction energy. The pair correlation effect maximizing the probability of particle separation recovers a missing energy that increases with the total number of electrons. It provides the first evidence that the virial theorem holds true for atomic and molecular systems. The 3d finite element method calculation of water molecule is also presented.