PSI-K SCIENTIFIC HIGHLIGHT OF THE MONTH: A Fractional View of the Exchange-Correlation Functional and Derivative

Abstract

The exchange-correlation functional is the key object in the understanding and appli- cation of density functional theory (DFT). Development of approximations to the exact functional is extremely challenging, as it aims to give a universal functional that works for all densities. To shed light on this issue in any manner is of great importance, and exact conditions offer a possible path forward. By considering the well established formal extension of DFT to fractional occupations at zero-temperature, we formulate perspectives based on fractional numbers of electrons and fractional spins that reveal some very stringent exact conditions of the energy functional. What is possibly even more important is that currently used approximations violate these exact conditions, leading to massive basic errors in very simple molecules and trends in extended systems that explain systematic errors in the elec- tron density, energy and their derivatives from DFT calculations. This is exemplified by the delocalisation error and static correlation error. The further combination of these two concepts leads to understanding of the band-gap and the derivative discontinuity in DFT, sheds light on the calculation of strongly correlated systems, and calls for dramatically new functional forms that have a discontinuous nature. 5.1