System-dependent modified becke-Johnson exchange for quantum transport simulations

A possibility to combine the meta-GGA exchange functional suggested by Tran and Blaha with the LDA pseudopotentials was investigated and a simple extension allowing for the direct reduction of the band gap error was suggested. A set of 19 semiconducting materials was used for testing. The mean absolute value of the relative band gap error was found to be 2.5 times larger than in the case when meta-GGA exchange employs the full-core electron density. The main contribution to the mean error comes from the few materials showing weak response to meta-GGA band gap tuning parameter. At the same time, if the smaller subgroups of semiconductors are used, the extended parameterization presented in the current work allows for the band gap fits within few percent. Such material subgroups can be used to obtain the device-specific meta-GGA parameterizations with a minimal computational effort.