  In density functional theory (DFT), the exchange-correlation functional can
be exactly expressed by the adiabatic connection integral. It has been noticed
that as lambda goes to infinity, the lambda^(-1) term in the expansion of
W(lambda) vanishes. We provide a simple but rigorous derivation to this exact
condition in this work. We propose a simple parametric form for the integrand,
satisfying this condition, and show that it is highly accurate for
weakly-correlated two-electron systems.
