Spin-orbit splittings and energy band gaps calculated with the Heyd-Scuseria-Ernzerhof screened hybrid functional

We assess the Heyd-Scuseria-Ernzerhof (HSE) screened Coulomb hybrid density functional for the calculation of spin-orbit (SO) splittings and energy band gaps. We have employed a set of 23 semiconductors with available experimental data, including group IV elements, and group III-V, II-VI, and IB-VII compounds. The spin-orbit interaction is included in the calculations using relativistic effective core potentials within a second-variation approximation. HSE errrors are similar to those obtained previously without including SO in the calculation and using a weighted average of the SO split bands for the reference value [J. Chem. Phys. 123, 174101 (2005)]. Here we explicitly show that the same good agreement remains after explicitly including SO interaction in the calculations and comparing directly to experimental energy band gaps.