Revisiting the Half-and-Half Functional

Hybrid density functionals typically provide significantly better accuracy than semilocal functionals. Conventional wisdom holds that incorporating more than 20-25% exact exchange is deleterious to thermochemical properties and should only be used as a last resort, for problems that are dominated by self-interaction error. In such cases, the Becke-Lee-Yang-Parr "half-and-half" functional (BH&H-LYP) has emerged as a go-to choice, especially in time-dependent density functional theory calculations for excitation energies. Here, we examine the assumption that 50% Hartree-Fock exchange sacrifices thermochemical accuracy. Using a sequence of functionals B(α)LYP, with different percentages of exact exchange (0 ≤ α ≤ 100), we find that BH&H-LYP (with α = 50) is nearly optimal and affords accuracy similar to B3LYP for thermochemistry, barrier heights, and excitation energies. Although BH&H-LYP is significantly less accurate than B3LYP for atomization energies, this emerges as the sole rationale for the taboo against values α > 25. Overall, BH&H-LYP is a reasonable choice for problems that are dominated by self-interaction error, including charge-transfer complexes and core-level excitation energies. While B3LYP remains more accurate for valence excitation energies, the use of 50% exact exchange appears to be an acceptable compromise, and BH&H-LYP can be used without undue concern over its diminished accuracy for ground-state properties.