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The Fermi–Amaldi correction to the electrostatic self-repulsion of the particle density is usually regarded as a semi-classical exchange functional that happens to be exact only for one- and closed-shell two-electron systems. We show that this functional can be derived quantum-mechanically and is exact for any number of fermions or bosons of arbitrary spin as long as the particles occupy the same spatial orbital. The Fermi–Amaldi functional is also size-consistent for such systems, provided that the factor N in its expression is understood as an orbital occupation number rather than the total number of particles. These properties of the Fermi–Amaldi functional are ultimately related to the fact that it is a special case of the self-exchange energy formula. Implications of our findings are discussed. [ABSTRACT FROM AUTHOR]