Formalism of polarizable embedding with AMOEBA in DFT context In DFT, a many-electron problem is reformulated in terms of the electron density instead of the many-electron wavefunction. In the most common flavor of DFT, i.e., Kohn-Sham DFT, the electron density ρ is expressed in terms of one-electron wavefunctions or Kohn-Sham orbitals φ i that are expanded in a series of basis functions, typically either Gaussian-type orbitals or PWs. Their expansion coefficients are then determined by applying the self-consistent field (SCF) procedure to solve a set of one-electron Kohn-Sham equations that, that under the Born-Oppenheimer approximation take the form