Correlation and coherence in many-electron system

The inclusion of the correlation effect in many electron system was shown in the self-consistent density functional theory to yield the virial theorem, an important relation between the kinetic and the potential energies. This provides a correspondence principle and an accuracy that could rule out mechanisms not begetting results within the error limit. The coherence effect of exchange antisymmetry for fermions can readily couple with the correlation effect to result in rich physics. We show from a variational quantum Monte Carlo code that in the excited states of helium atom, the triplet state of like spins tends to have less repulsive dispersion than the singlet state of opposite spins.