See ref. 589 for a brief review and ref. 590 for a more in-depth review of DFET 591 and its cousin, potential-functional embedding theory (PFET). The latter can deliver self-consistent embedding potentials for hybrid ECW/DFT systems, albeit at considerable cost. Frankly, we've yet to find cases in which such self-consistency was terribly important, although I imagine such cases will emerge. If one is careful to include sufficient numbers of atoms in the embedded region such that the embedding potential does not overlap the phenomenon of interest but instead is essentially a physical boundary condition, then the frozen exact embedding potential we derive from DFET works very well. Thus we have continued to use DFET/ECW theory rather than PFETwith considerable success -to study problems where conventional DFAs fail, such as for phenomena involving electron transfer 596 and excited states involved in electrochemistry and photochemistry on metals; for a recent review on the latter, see ref. where the same idea of using OEP is applied to density matrices rather than densities. Recent benchmarks that we have conducted comparing electrochemical carbon dioxide reduction modelled by a conventional DFA versus DFET/ECW theory reveals critical insights for modellers: for qualitative conclusions regarding reactions that do not involve electron transfer, the DFA is acceptable. 601 By contrast, for any step involving electron transfer, specifically proton-coupled electron transfer (which we find to be the most favourable pathway), the DFA fails on multiple fronts (specifically it yields results inconsistent with experiments) due to too facile electron transfer (as expected from self-interaction error and the lack of a derivative discontinuity) whereas DFET/ECW predictions agree with experiments and produces qualitatively different products than the DFA 602 -a cautionary tale for DFT modellers of electrochemistry.