New perspectives of the weighted spin-density approximation: gradient corrections and the valence-only approach

The current state of the weighted spin-density approximation (WSDA) of dens ity functional theory is discussed and new perspective WSDA approaches are put forward. A gradient correction to the exchange pair-correlation functio n G(x sigma)(hom)(r(12)) Of the homogeneous electron gas is developed in or der to improve its performance for inhomogeneous systems within the WSDA. T he correction factor has the form of a Pade-type approximant of the dimensi onless gradient \del n(sigma)((r) over bar)\/n(sigma)(4/3)((r) over bar) (n (sigma) is the electron spin-density) and of the dimensionless argument (k) over tilde(F sigma)((r) over right arrow)(12) ((k) over tilde(F sigma) is the weighted spin-density Fermi momentum and r(12) is the interelectronic d istance). In the zero-gradient limit the corrected pair-correlation functio n reduces to G(x sigma)(hom), while for atoms the present WSDA with gradien t correction (WSDA-GC) provides a substantial improvement of the calculated exchange energies compared to the standard WSDA based on G(x sigma)(hom). A proposal for the application of WSDA to valence-only calculations is cons idered and a practical scheme of the valence-only WSDA-GC is developed. Wit hin this scheme, an atomic core is represented with the exchange pseudopote ntial and an empirical function giving the partial charge of the Fermi hole attributed to this core. The proper choice of the latter function is expec ted to correct the overestimation of the core-valence exchange produced by the standard WSDA. (C) 2000 Elsevier Science B.V. All rights reserved.