(4.1.6) Johnson : Development of a DFA that can eliminate the delocalization error is needed. The delocalization error, also known as the many-electron self-interaction error, refers to the tendency of many DFAs to overstabilize systems with highly delocalized electrons or fractional charges on separated moieties. This error affects charge-transfer complexes, extended hydrogen-bonding networks, halogen bonds, organic salt crystals, systems with extended π-conjugation, and transition states of many radical reactions, to list a few examples. It is also responsible for the notorious band-gap problem. While many approaches to reducing the delocalization error have been proposed, none is a panacea. Typically, one can reduce the delocalization error through a (frequently range-dependent) mixing of local, DFA exchange and nonlocal, Hartree-Fock exchange. However, the optimal mixing is known to be highly system and size dependent. Development of a practical and universally applicable DFA with a minimal delocalization error remains an outstanding challenge and would represent a significant advance. It is likely that any advance on the delocalization-error front would also help to resolve some of the issues with strong correlation, given how closely linked the two problems are. DFAs from Gori-Giorgi and Vuckovic that are based on the SCE limit (see contribution (2.4.5)) offer some innovative ways of thinking about both problems. There are various ways to go beyond the RPA. Highly promising are σ -functionals , which are technically closely related to the RPA but formally rooted in many-body perturbation theory along the adiabatic connection. Methods using σ -functionals are distinctively more accurate than RPA based or conventional functionals -they reach chemical accuracy for main-group chemistry and treat noncovalent interactions accurately.