We will call this functional BH&H-LYP, although it sometimes goes by other names in the literature including BHLYP, BHHLYP, and BHandH-LYP. Half-andhalf functionals were quickly eclipsed by Becke's threeparameter "B3" ansatz, leading to the B3LYP functional in 1994, and as a result BH&H-LYP never saw widespread deployment. B3LYP contains 20% exact exchange (E HF x ), a fraction that was determined empirically but is close to the 25% that would later be suggested by appeal to Görling-Levy perturbation theory. That argument is used to justify the use of 25% exact exchange in the PBE0 functional. B3LYP quickly displaced most competing functionals. According to one estimate, BH&H-LYP was used in a mere 1% of density functional theory (DFT) calculations up to 2007, as compared to 80% that used B3LYP. Today, there are undoubtedly better-performing functionals than B3LYP, yet many of them involve complexity of at least the meta-GGA variety. When augmented with an empirical dispersion correction, B3LYP remains a respectable functional. Comparatively recent attempts to re-optimize the B3 parameters have landed on very nearly the same numerical values originally obtained by Becke. This is a remarkable tribute to his insight, given the paucity of data in the original parameterization: 42 ionization energies, 8 proton affinities, and 10 first-row total atomic energies, representing the so-called G1 data set. Even as hybrid GGAs have given way to meta-GGAs and double-hybrid functionals as the most accurate instruments in the density-functional toolkit, BH&H-LYP has persisted. It tends to be used when there is concern regarding artifacts originating in self-interaction error (SIE), which often manifests as anomalous delocalization of charge. Thus, BH&H-LYP has long been used to study charge-transfer (CT) complexes, and systems with extended π conjugation, both of which are sensitive to delocalization error. For similar reasons, BH&H-LYP is a standard approach for computing electron affinities of neutral molecules and electron detachment energies for anions, where the open-shell species is more sensitive to SIE. Finally, BH&H-LYP has been demonstrated to improve the behavior of DFT calculations in cases where convergence is hampered by charge oscillations. For excited-state calculations using time-dependent (TD-)DFT, BH&H-LYP is often used to investigate systems where spurious low-energy CT states may be problematic. Functionals such as B3LYP (with 20% HF exchange) and PBE0 (with 25%) systematically underestimate excitation energies for states with charge-separated character, including core-tovalence transitions. This is primarily a consequence of SIE and is less severe when the fraction of HF exchange is larger. The BH&H-LYP functional performs well in benchmark tests of small-molecule valence excitation energies, although it sometimes overestimates excitation energies for larger molecules. (For spectra of large conjugated molecules, it has been suggested that 40% HF exchange is preferable. ) Furthermore, BH&H-LYP has become the de facto standard for spin-flip TD-DFT calculations, for reasons explained elsewhere, and it shows up in other spectroscopic contexts as well. Despite its utility in mitigating delocalization error, BH&H-LYP was long ago judged to be unfit for general-purpose DFT calculations. Early studies demonstrated that half-and-half functionals exhibit somewhat larger errors for atomization energies and reaction energies, 100,101 as compared to B3LYP, although BH&H-LYP affords slightly smaller errors for barrier heights. The notion that BH&H-LYP is greatly inferior to B3LYP, and thus inferior to even better functionals developed over the past 30 years, has become entrenched. Thus, BH&H-LYP tends to be regarded as a functional of last resort, which should only be used in the context of certain SIE-dominated problems (including TD-DFT), because it will substantially degrade the accuracy of ground-state thermochemical properties.