From Kohn–Sham to Many-Electron Energies via Step Structures in the Exchange-Correlation Potential

Accurately describing excited states within Kohn-Sham (KS) density functional theory (DFT), particularly those which induce ionization and charge transfer, remains a great challenge. Common exchange-correlation (xc) approximations are unreliable for owing, in part, to the absence of derivative discontinuity xc energy (?), relates many-electron difference corresponding KS difference. We demonstrate, analytically numerically, how relationship between energies leads step structures observed exact potential four scenarios: electron addition, molecular dissociation, excitation finite system, transfer. further show that steps can be obtained also with common approximations, as simple LDA, when addressed from ensemble perspective. The article therefore highlights capturing advanced is crucial accurately calculating excitations, well ground-state systems consist distinct subsystems.