Closely related to sDFT/FDE with potential reconstruction are the density and potential functional embedding theories (DFET, PFET) developed mainly by the Carter group . DFET can be regarded as an FDE variant making use of potential reconstruction (specifically: Wu-Yang-type reconstruction ) and additionally introducing the constraint of a common embedding potential for all subsystems . Once the embedding potential is optimized based on embedded DFT calculations for the subsystems, it can also be combined with correlated wavefunction-type subsystem calculations in this framework. In PFET, by contrast, also electron densities for subsystems from correlated wavefunction calculations can be employed to construct input densities for the potential-reconstruction procedure . An implementation of DFET in the framework of the projector-augmented-wave method has been presented in 2015 . Technical challenges associated with the combination of periodic DFT codes and molecular electronicstructure programs have been addressed in Ref. , where the embedding potential is expanded in terms of basis-function products (rather than AO basis functions only). A PFET implementation that allows to use mixed correlated wavefunction/DFT setups has been described in Refs. 112, 113. Later, the method has been generalized to a densitymatrix functional embedding making use of non-local embedding potentials to improve the description of fragments connect through covalent bonds . As an alternative, DFET has been combined with a capped-fragment scheme in Ref. , which shares several features with the 3-FDE method [116]. Hoyer et al. have presented an extension to embedd a subsystem described with a non-collinear two-component electronic-structure method in an environment treated with a collinear approximation . A finite-temperature version of DFET was proposed by Huang and later on used in the framework of an embedded cluster density approximation for the exchange-correlation energy . As an alternative to avoid dangling bonds for covalently bonded subsystems, Huang et al. also proposed a link-atom-style partitioning of each boundary atom into two atoms for which the sum of the (valence) electrons equals that of the corresponding boundary atom .