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We introduce a novel non-local ingredient for the construction of exchangedensity functionals: the reduced Hartree parameter, which is invariant underthe uniform scaling of the density and represents the exact exchangeenhancement factor for one- and two-electron systems. The reduced Hartreeparameter is used together with the conventional meta-generalized gradientapproximation (meta-GGA) semilocal ingredients (i.e. the electron density, itsgradient and the kinetic energy density) to construct a new generation exchangefunctional, termed u-meta-GGA. This u-meta-GGA functional is exact for {theexchange of} any one- and two-electron systems, is size-consistent andnon-empirical, satisfies the uniform density scaling relation, and recovers themodified gradient expansion derived from the semiclassical atom theory. Foratoms, ions, jellium spheres, and molecules, it shows a good accuracy, beingoften better than meta-GGA exchange functionals. Our construction validates theuse of the reduced Hartree ingredient in exchange-correlation functionaldevelopment, opening the way to an additional rung in the Jacob's ladderclassification of non-empirical density functionals.

Hartree potential dependent exchange functional