(2.4.7) Kaupp and Arbuznikov : The AC, which has already been invoked in contributions (2.4.2)- (2.4.6) as an important principle for the development of DFAs, is usually applied to the energy functional, where its existence is well established. Increasingly, however, interpolations along local ACs have been used, meaning that the coupling-strength (λ ) integration is applied to the corresponding energy density or even to the exchange-correlation hole followed by integration over one and two spatial coordinates, respectively. While the existence of a "local adiabatic connection" has never been proven rigorously, Becke argued that such an approach does not violate any basic principles and is just a matter of changing the order of integration that is valid for continuous functions 165 -see also, for example, ref.