HLE16: A Local Kohn–Sham Gradient Approximation with Good Performance for Semiconductor Band Gaps and Molecular Excitation Energies

Local exchange-correlation functionals have low cost and convenient portability but are known to seriously underestimate semiconductor band gaps and the energies of molecular Rydberg states. Here we present a new local approximation to the exchange-correlation functional called HLE16 that gives good performance for semiconductor band gaps and molecular excitation energies and is competitive with hybrid functionals. By the simultaneous increase of the local exchange and decrease of the local correlation, electronic excitation energies were improved without excessively degrading the ground-state solid-state cohesive energies, molecular bond energies, or chemical reaction barrier heights, although the new functional is not recommended for optimizing lattice constants or molecular bond lengths. The new functional can be useful as-is for calculations on semiconductors or excited states where it is essential to control the cost, and it can also be useful in establishing a starting point for developing even better new functionals that perform well for excited states.