Communication: A new hybrid exchange correlation functional for band-gap calculations using a short-range Gaussian attenuation (Gaussian-Perdue–Burke–Ernzerhof)

We have developed a new hybrid functional [Gaussian-Perdue-Burke-Ernzerhof (Gau-PBE)] that is suitable for the calculation of solid state bandgaps using a periodic boundary condition. The characteristic of this functional is the use of a Gaussian attenuation scheme (Gau) to include a short-range Hartree-Fock (HF) exchange. This new functional can perform barrier height calculations with an accuracy comparable to the middle-range hybrid functional and bandgap calculations with an accuracy comparable to the Heyd-Scuseria-Ernzerhof (HSE) functional. However, the point is that the performance can be achieved using a Gaussian HF exchange, while the HISS functional calculates twice HF-exchange integrations using an error function to obtain both performances. In addition, Gau-PBE functional can decrease the time cost of bandgap calculations by an average of 40% compared to the HSE functional.