Modern density functional theory (DFT) calculations employ the Kohn-Sham (KS) system of non-interacting electrons as a reference, with all complications buried in the exchange-correlation energy (Exc). The adiabatic connection formula gives an exact expression for Exc. We consider DFT calculations that instead employ a reference of strictly-correlated electrons. We define a decorrelation energy that relates this reference to the real system, and derive the corresponding adiabatic connection formula. We illustrate this theory in three situations, namely the uniform electron gas, Hookes atom, and the stretched hydrogen molecule. The adiabatic connection for strictly-correlated electrons provides an alternative perspective for understanding density functional theory and constructing approximate functionals.
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