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.
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