Revisiting the variational nature of the quantum theory of atoms in molecules

A simplified derivation of the variational nature of the real space basins used in the quantum theory of atoms in molecules (QTAM) is presented. We focus on pointing out the non-standard characteristics of the variational problem that is solved, and on clarifying some points that tend to be misinterpreted. An explicit discussion of the meaning of the functional minimized is also presented and used to derive both a new form for the atomic virial theorem and to show how basin chemical potentials may be defined.