(3.7.6) Gould : On point ii) of contribution (3.7.4), the ability to rigorously define E Hx 427 and then break it down into E FDT H and E FDT x 428 has offered insights into adapting existing approximations to ensembles -because the exact-exchange functional of more complex excitations can obey combination rules that relate it to simpler pure-state systems for which approximations already exist. I showed that using exact-exchange relationships for ensembles allowed ensemble DFT to outperform the ∆SCF and TDDFT methods using the same DFAs. This success has been partially transferred to double excitations. Despite improvements from using the ensemble version of the on-top pair density Π(r, r) given for pure states in eqn ( ), 443 how to effectively reuse existing correlation DFAs remains an outstanding problem.