Koopmans-compliant screened exchange potential with correct asymptotic behavior for semiconductors

The performance of density functional theory depends largely on the approximation applied for the exchange functional. We propose here a screened exchange potential for semiconductors, with parameters based on the physical properties of the underlying microscopic screening and obeying the requirements for proper asymptotic behavior. We demonstrate that this functional is Koopmans compliant and reproduces a wide range of band gaps. We also show, that the only tunable parameter of the functional can be kept constant upon changing the cation or the anion isovalently, making the approach suitable for treating alloys.