Electron correlation and the structure of the exchange-correlation potential and the correlation energy density in density functional theory

The relationship is established between key quantities in density functional theory, such as tile exchange-correlation energy and potential, and the physics of electron correlation as described by density matrices and exchange and correlation holes. We demonstrate that it is natural to break down the exchange-correlation part of the total Kohn-Sham potential into a kinetic contribution and a screening: or hole contribution, and the so-called responses of these potentials. The kinetic and hole potentials immediately afford the exchange-correlation energy density. The response parts do not enter the energy density directly but it is essential to rise them in the self-consisten Kohn-Sham potential in order to obtain accurate Kohn-Sham orbitals and an accurate electron density. Tile introduced potentials have certain charateristic features (peaks, steps), which carry over to the correlation energy density. The relationship of these features with the physics of electron correlation is demonstrated.