Gradient correction to the exchange pair-correlation function of the weighted spin-density approximation in the density functional formalism

A gradient correction to the exchange pair-correlation function Gxσhom(r12) of the homogeneous electron gas is developed in order to improve its performance for inhomogeneous systems within the weighted spin-density approximation (WSDA) of density functional theory. The correction factor has the form of a Padé-type approximant of the dimensionless gradient ∇nσ(r)/nσ4/3(r) (nσ is the electron spin-density) and of the dimensionless argument k̃Fσ(r1)r12 (k̃Fσ is the weighted spin-density Fermi momentum and r12 is the interelectronic distance). In the zero-gradient limit the corrected pair-correlation function reduces to Gxσhom, while for atoms the present WSDA with gradient correction (WSDA-GC) provides a substantial improvement of the calculated exchange energies compared to the standard WSDA based on Gxσhom.