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The construction of density-functional approximations is explored by modelingthe adiabatic connection em locally, using energy densities defined in terms ofthe electrostatic potential of the exchange-correlation hole. These localmodels are more amenable to the construction of size-consistent approximationsthan their global counterparts. In this work we use accurate input localingredients to assess the accuracy of range of local interpolation modelsagainst accurate exchange-correlation energy densities. The importance of thestrictly-correlated electrons (SCE) functional describing the strong couplinglimit is emphasized, enabling the corresponding interpolated functionals totreat strong correlation effects. In addition to exploring the performance ofsuch models numerically for the helium and beryllium isoelectronic series andthe dissociation of the hydrogen molecule, an approximate analytic model ispresented for the initial slope of the local adiabatic connection. Comparisonsare made with approaches based on global models and prospects for futureapproximations based on the local adiabatic connection are discussed.

Exchange-correlation functionals via local interpolation along the adiabatic connection