Atomic charges are measurable quantum expectation values: A rebuttal of criticisms of QTAIM charges

The charge on an atom in a molecule is defined by the quantum theory of atoms in molecules (QTAIM) as the expectation value of the number operator, a Dirac observable. An atomic charge is measurable and it, together with its change, contributes to numerous measurable properties: to all molecular moments, to molecular polarizability, to intensities of electronic, infrared, and Raman absorption intensities, and to the polarization of a dielectric. The properties resulting from an applied magnetic field parallel those induced by an electric field, with the induced atomic charge being replaced by the atomic current. The phenomena of polarization and magnetization, permanent or induced, have a common physical basis when described in terms of the physics of an open system, all expressions exhibiting a single underlying structure in terms of their atomic contributions. The paper points out that this physics and the appeal the experiment it affords are lost when one employs other definitions of an atomic charge.