Revisiting the Half-and-Half Functional

Hybrid density functionals typically provide significantly better accuracy than semilocal functionals, but conventional wisdom holds that incorporating more than 20–25% exact exchange is deleterious to thermochemical properties and should be used only 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% exact exchange sacrifices thermochemical accuracy, using a sequence of functionals B(alpha)LYP with different percentages of exact exchange, 0 <= alpha <= 100. We find that alpha = 50, corresponding to BH&H-LYP, is nearly optimal and affords accuracy similar to B3LYP for thermochemistry, barrier heights, and excitation energies. Although atomization energies are significantly less accurate with 50% Hartree-Fock exchange, this emerges as the sole rationale for the taboo against values alpha > 25. Overall, BH&H-LYP emerges as 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 excessive concern over its diminished accuracy for ground-state properties.