  Aiming to remedy the incorrect asymptotic behavior of conventional semilocal
exchange-correlation (XC) density functionals for finite systems, we propose an
asymptotic correction scheme, wherein an exchange density functional whose
functional derivative has the correct (-1/r) asymptote can be directly added to
any semilocal density functional. In contrast to semilocal approximations, our
resulting exchange kernel in reciprocal space exhibits the desirable
singularity of the type O(-1/q^2) as q -> 0, which is a necessary feature for
describing the excitonic effects in non-metallic solids. By applying this
scheme to a popular semilocal density functional, PBE [J. P. Perdew, K. Burke,
and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)], the predictions of the
properties that are sensitive to the asymptote are significantly improved,
while the predictions of the properties that are insensitive to the asymptote
remain essentially the same as PBE. Relative to the popular model XC potential
scheme, our scheme is significantly superior for ground-state energies and
related properties. In addition, without loss of accuracy, two closely related
schemes are developed for the efficient treatment of large systems.
