# Dresden 2014 – wissenschaftliches Programm

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# HL: Fachverband Halbleiterphysik

## HL 99: Electronic structure theory

### HL 99.4: Vortrag

### Donnerstag, 3. April 2014, 15:45–16:00, POT 151

**Energy Curvature of Solids with Fractional Charge in DFT** — •Vojtech Vlcek^{1}, Helen Eisenberg^{2}, Gerd Steinle-Neumann^{1}, Leeor Kronik^{3}, and Roi Baer^{2} — ^{1}Universitat Bayreuth, Germany — ^{2}Hebrew University, Jerusalem, Israel — ^{3}Weizmann Institute of Science, Rehovoth, Israel

DFT often does not perform well in terms of prediction of electron removal and addition energies. In exact DFT, the total energy of the system E versus number of electrons N upon addition/removal of a fraction of an electron is a series of linear segments between integer N. At these points the exchange-correlation potential can jump discontinuously by a derivative discontinuity (DD), which contributes to the change of the derivative of E and thus to the fundamental band gap. Without employing ensemble-DFT, commonly used approximations, however, do not satisfy the straight line condition and lack DD. In finite systems, this error is manifested by a curvature of the energy which has been studied extensively over the past decade.

The concept of energy curvature in infinite systems is still under debate. Competing concepts have emerged: 1) curvature was shown to approach zero in the infinite system size limit; 2) the energy per unit cell was shown to have curvature if the electron addition/removal per unit cell is considered. Here we analyze the missing DD by introducing a new measure for the curvature in an infinite periodic system. This allows us to compute the curvature in the thermodynamic limit when only an infinitesimal amount of electronic charge is removed or added to the system.