Plateaus in the Kohn-Sham potential of density-functional theory: analytical derivation and useful approximations

Density functional theory (DFT) is the leading theoretical framework for electronic structure calculations, successfully describing a variety of materials and processes. However, the accuracy of DFT calculations crucially depends on the quality of the approximation used for the exchange-correlation functional, for which there is no exact expression. One of the features of the exact exchange-correlation potential which common approximations do not capture is the appearance of sharp spatial features, e.g. steps and plateaus. Their role is crucial for the description of such processes as ionization, dissociation and charge transfer.

In my talk I present an exact analytical expression for the spatial plateau function in the Kohn-Sham (KS) potential that forms when the number of electrons in the system is varied. The origins of the various features of the plateau function are discussed. I further show how the exact expression for the plateau function can be efficiently approximated. Analytical findings are then illustrated with numerical results for the exact KS potential obtained from Full Configuration Interaction calculations. Moreover, I show how one can extract plateaus even from approximate KS-DFT results, using even the simplest local spin-density approximation (LSDA).

Analytical description of the plateau functions I plan to present paves the road: (a) to further investigation of steps and plateaus of the KS potential, e.g. in the cases of dissociation and charge transfer; (b) to development of advanced approximations to exchange and correlation that will correctly simulate steps in the potential and significantly extend the ability of DFT to describe important physical processes.