  Electronic structures are fully determined by the exchange-correlation (XC)
potential. In this work, we develop a new method to construct reliable XC
potentials by properly mixing the exact exchange and the local density
approximation potentials in real space. The spatially dependent mixing
parameter is derived based on the derivative discontinuity of electron density
and is first-principle. We derived the equations for solving the mixing
parameter and proposed an approximation to simplify these equations. Based on
this approximation, this new method gives reasonable predictions for the
ionization energies, fundamental gaps, and singlet-triplet energy differences
for various molecular systems. The impact of the approximation on the
constructed XC potentials is examined, and it is found that the quality of the
XC potentials can be further improved by removing the approximation. This work
demonstrates that the derivative discontinuity of electron density is a
promising constraint for constructing high-quality XC potentials.
