where V nn is the nuclear repulsion, i, j, k, and l are orbital indices, h ij is a one-electron integral, γ ij is the one-electron density matrix, g ijkl is a two-electron integral, and E NE is the nonclassical-energy functional. In most of our work, E NE is written as a function of the electron density ρ and the on-top pair density Π and is called an on-top density functional.