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Electronic Structure Calculations with the Tran-Blaha Modified Becke-Johnson Density Functional

We report a series of calculations testing the predictions of the Tran-Blaha functional for the electronic structure and magnetic properties of condensed systems. We find a general improvement in the properties of semiconducting and insulating systems, relative to calculations with standard generalized gradient approximations, although this is not always by the same mechanism as other approaches such as the quasiparticle GW method. In ZnO the valence bands are narrowed and the band gap is increased to a value in much better agreement with experiment. The Zn $d$ states do not move to higher binding energy as they do in LDA+U calculations. The functional is effective for systems with hydride anions, where correcting self-interaction errors in the 1$s$ state is important. Similarly, it correctly opens semiconducting gaps in the alkaline earth hexaborides.It correctly stabilizes an antiferromagnetic insulating ground state for the undoped cuprate parent CaCuO$_2$, but seriously degrades the agreement with experiment for ferromagnetic Gd relative to the standard local spin density approximation and generalized gradient approximations. This is due to positioning of the minority spin $4f$ states at too low an energy. Conversly, the position of the La $4f$ conduction bands of La$_2$O$_3$ is in reasonable accord with experiment as it is with standard functionals. The functional narrows the Fe $d$ bands of the parent compound LaFeAsO of the iron high temperature superconductors, while maintaining the high Fe spectral weight near the Fermi energy.