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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.

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    $\begingroup$ Partial charge is a notational fiction anyway. If you're working at the level of detail that your question implies, wouldn't it be cleaner to work directly with real observable phenomena (such as the dipole moment)? $\endgroup$ – zwol Nov 15 '15 at 20:42
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Let me put it this way. There are no atoms in molecules. There is just a continuous cloud of electron density, and as you correctly pointed out, we have no way to pinpoint where one atom ends and another starts. Or rather, we have many ways to do that, all slightly different and all inherently arbitrary. (My personal favorite is the concept of Bader charges, but that's a matter of taste.)

So yes, the very idea of partial atomic charges is unavoidably vague.

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  • $\begingroup$ "There are not atoms in molecules." Some times we talk about "perturbed" atoms. "Most of" the atoms do not change very much when bonded, like the nuclei and core electrons; mostly the valence electrons take part in bonding. So surely it is safe to say that atoms do exist in molecules? But you agree, then, that partial charges cannot be measured experimentally? I am not sure how you answered the question. $\endgroup$ – Yoda Nov 15 '15 at 18:04
  • $\begingroup$ I answered the question with the words you see above; if they don't translate to a clear "yes" or "no" - well, sorry about that, but such is the nature of the matter. Bader charges, though, are measured experimentally. The ambiguity is not in the measurement; it is in the agreement of what to measure, i.e. in the definition of atoms. $\endgroup$ – Ivan Neretin Nov 15 '15 at 18:19
  • $\begingroup$ Perhaps my question has become more philosophical than I intended. I get your point, thank you for clarifying. $\endgroup$ – Yoda Nov 17 '15 at 15:10
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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.

It is possible (though not easy) to map electronic density in a molecule (and somewhat easier in crystalline solids). Having electronic density map it is possible to define interatomic borders as a surface with density lower than in areas the surface divides. This allows to attribute well-defined value of 'atomic charge' to an atom.

Another possible option is to fit the attributed charges (without references to real electronic density) so they produced electric field matching the real electric field. The 'real' field may be calculated from experimental data or ab-initio model. This procedure is implemented in some QC packages, but it is very sensitive to the definition of 'similarity' of the fields.

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  • $\begingroup$ What I read is that "we are able to obtain estimates of partial charges based on experimental data", but not that we can actually measure them. Would you agree with that? $\endgroup$ – Yoda Nov 15 '15 at 18:06
  • $\begingroup$ But then I guess that is the way all things are "measured". $\endgroup$ – Yoda Nov 15 '15 at 18:26
  • $\begingroup$ @AndersMB 'We are able to obtain electron density data from the experiment. There are several procedures that we can use to extract some values from the data. If you accept them as atomic charges is up to you, but they are close enough in some cases.' $\endgroup$ – permeakra Nov 15 '15 at 20:09

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