Almost all modern density functional theory (DFT) calculations employ the Kohn-Sham system of non-interacting electrons as a reference, with all complications buried in the exchange-correlation energy (Exc), which can be exactly expressed by the adiabatic connection formula. This traditional approach is almost always good for weakly correlated ground state, however may not for highly correlated ground state, e.g., stretched H2. In this work, we show that DFT calculations could instead employ a reference of strictly-correlated electrons, and correspondingly we can define a "decorrelation energy" (Edc) using adiabatic connection formalism. We relate the new and the Kohn-Sham adiabatic connection integrands and Edc to Exc. We show an example in uniform electron gas. By studying the expansion behavior of the new adiabatic connection integrand, we can derive an exact condition that the traditional adiabatic connection integrand must satisfy in the low-density limit. This work may provide an alternative perspective for understanding density functional theory and constructing approximate functionals.
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