  We propose a new approach to approximate the exchange and correlation (XC)
functional in density functional theory. The XC potential is considered as an
electrostatic potential, generated by a fictitious XC density, which is in turn
a functional of the electronic density. We apply the approach to develop a
correction scheme that fixes the asymptotic behavior of any approximated XC
potential for finite systems. Additionally, the correction procedure gives the
value of the derivative discontinuity; therefore it can directly predict the
fundamental gap as a ground-state property.
