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

Prediction of the derivative discontinuity in density functional theory from an electrostatic description of the exchange and correlation potential