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Band gap calculations with DFT revisited: restoring the derivative discontinuity via the ensemble approach


  Eli Kraisler  ,  Leeor Kronik  
 Department of Materials and Interfaces, Weizmann Institute of Science, Rehovoth 76100, Israel

 

The band gap is a central property for many materials. Nevertheless, it is usually poorly described in density-functional theory (DFT) using standard approximations. This is in contrast to the success of DFT in accurately predicting various properties of the same materials. The failure in predicting the band gap is often associated with the fact that many of the approximate exchange-correlation (xc) functionals employed lack the property of the derivative discontinuity in the total energy as a function of the number of electrons, when it crosses an integer.

In the current work we show that it is possible to reintroduce the derivative discontinuity for any xc functional, via the ensemble approach in DFT. The derivation is completely ab initio, meaning that no empiricism is required and no approximations are made, apart from specifying the xc functional employed. Furthermore, the derivative discontinuity can be expressed using quantities that are associated with the system itself, thereby avoiding alteration of the number of electrons in the system. The latter condition allows an easy and well-established way to calculate this quantity for periodic systems. The approach is demonstrated by calculating the band gap for eleven representative periodic systems -- insulators and semi-conductors -- within the local density approximation for the xc functional. It is found that the reintroduced derivative discontinuity accounts for a significant part of the overall band gap, and cannot be neglected. Improved correspondence of the calculated results to the experiment is observed.