VALIDITY OF THE EXTENDED ELECTRON-ELECTRON CUSP CONDITION

The extended cusp condition asserts than h(u)-a0 dh(u)/du greater-than -or-equal-to 0, where a0 is the Bohr radius, u is the interelectronic spacing, and h(u) is the angle-averaged pair density in the ground sta te. We prove that this inequality is obeyed by Hooke's atom for any va lue of the spring constant. However, we also show that this condition is violated by the uniform electron gas of high density. We explain th e qualitative difference between these two systems by subtracting a lo ng-range contribution from h(u), leaving a short-range contribution wh ich is amenable to a local density approximation. Thus the extended cu sp condition is not a universal property of the ground state of inhomo geneous electronic systems.