The electrostatic theorem is formally exact, but breaks down for nonvariational methodologies and/or finite basis sets, meaning it is of limited use in practice. However, for small systems where variational methodologies can be used with very large basis sets, the theorem is quantitatively applicable, meaning it provides an alternative perspective for viewing the "dispersion problem" of local functionals. Errors in dispersion forces can be understood in terms of errors in electron densities, which in turn can be understood in terms of errors in the exchange-correlation potential in the Kohn-Sham equations. Similar arguments can be applied to other problems, such as static correlation or delocalization errors. (3.5.9) Gori-Giorgi : The relevance of errors in electron densities for capturing dispersion interactions may need some reconsideration, or at least needs to be better understood, especially in the DFT setting. Pragmatically, poor densities can give very good dispersion energies -as an extreme example, it has been shown that it is possible to get exact dispersion energies between two one-electron systems up to and including orders R -10 without any deformation of the monomer densities. The subtle point with the electrostatic theorem of Feynman is that the result depends on whether one performs the derivative with respect to the nuclear position in the original coordinates or in the coordinates in which the electrons are centred on their respective nuclei. In the first case, the interaction energy depends only on the density distortion at order R -7 (for which the underlying wave function must be accurate to second order in the dipole-dipole and dipole-quadrupole interaction); in the second case, the interaction energy depends only on the distortion of the interfragment pair density at order R -3 (for which the underlying wave function must be accurate only to first order in the dipole-dipole interaction). These observations may suggest a route to build approximate exchange-correlation functionals by considering a simplified real-space mechanism, in which dispersion is reduced to the competition between kinetic energy and monomer-monomer interaction (thus keeping the density and pair density of the monomers unchanged, but producing an accurate interfragment pair density). 394 (3.5.10) Dobson : Much relevant physics can be included in energy functionals via use of generalized "densities" assembled from Kohn-Sham orbitals, such as the positive local kineticenergy density τ (r) used in meta-GGAs. Here, however, attention will be focused, as per the title question for this section, on strictly explicit functionals of the electron number density ρ and its space derivatives such as ∇ρ and ∇ 2 ρ.