Can we measure atomic partial charges in molecules experimentally? The charge of isolated ions can be measured, but when atoms are part of a molecule, the case is much more difficult. We do not really know where one atom starts and where another one stops (the atomic radii are diffuse). So I am inclined to say that partial charges must be based on theoretical concepts, such as the Mulliken population analysis (or a range of other methods), or be derived (estimated) from measurables such as dipole moment.
However, is it possible to probe molecules at the atomic level, using STM, TEM, or some other electron probing technique, and get the partial charges that way, perhaps based on electron-electron repulsions? Still, it seems to me, that the border between the atoms need to be properly defined in order to get the partial charges.
According to the Wikipedia page "Partial charge", several experimental techniques can be used to estimate the partial charge, e.g. XPS, NMR, EPR, UV/vis, with more. But do these techniques measure something which is a direct result of the effect of partial charge, or is some other physical observable measured, from which the partial charges are "guessed"? For example, using XPS to get the kinetic energy of the photoelectron seems like a "direct" measurements (although I know that what the detector sees is not really the kinetic energy, but something with which the kinetic energy correlates: calibration is needed). However, the idea of partial charge seems to be somewhat vague. Numerical values of partial charges depend on the definition of where one atom starts and where another ends, which is an abstract concept: this border cannot be observed or measured.
Another issue that comes to mind, is that the partial charge is not necessarily uniformly distributed around each atom, but will depend on bonds, lone pairs, interactions with other molecules, etc.