  We derive an explicit expression for the functional derivative of the
subleading term in the strong interaction limit expansion of the generalized
Levy--Lieb functional for the special case of two electrons in one dimension.
The expression is derived from the zero point energy (ZPE) functional, which is
valid if the quantum state reduces to strongly correlated electrons in the
strong coupling limit. The explicit expression is confirmed numerically and
respects the relevant sum-rule. We also show that the ZPE potential is able to
generate a bond mid-point peak for homo-nuclear dissociation and is properly of
purely kinetic origin. Unfortunately, the ZPE diverges for Coulomb systems,
whereas the exact peaks should be finite.
