Exchange–correlation potential built on the derivative discontinuity of electron density

In Kohn-Sham density functional theory (DFT), electronic structures are fully determined by the exchange-correlation (XC) potential. In this work, we developed a new method for improving the accuracy of XC potentials by properly mixing the exact exchange and the local density approximation potentials in real space. The mixing parameter is derived based on the derivative discontinuity of electron density and is fully first-principle. The mixing parameter is three-dimensional and automatically approaches one in vacuum regions. The obtained XC potentials give reasonable predictions for the ionization energies, fundamental gaps, and singlet-triplet energy differences of various molecular systems. This mixing parameter can also serve as an indicator for identifying one-electron regions. Our work demonstrates that the derivative discontinuity of electron density is a promising constraint for building more accurate XC potentials.