Adiabatic Connection in the Low-Density Limit

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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.