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Broadly given two electron charge density (ECD) fields, is it possible to distinguish between the elements present in both the systems?

Since the ECD does not explicitly present any information on the species present in the system. Is there a possibility that two ECDs exist with similar structures and totally different number of valence electrons, but consist of slightly or vastly different elemental species?

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  • $\begingroup$ A sort of glib chemist's answer is that the answer is yes and no. Certainly ∫𝑑𝑟𝜌(𝑟)=𝑁, so you can distinguish the total number of (valence) electrons (per unit cell). But the existence of the periodic table is evidence that different elements with vastly different electron numbers can behave somewhat similarly, in ways (chemical bonding environments) related to their densities. How to quantify that I'm not so sure. $\endgroup$
    – elutionary
    Nov 14, 2023 at 3:07
  • $\begingroup$ Per the Hohenberg-Kohn theorems you'd need the two systems to have potentials that differ by a constant. Is that actually chemically possible? $\endgroup$
    – Anyon
    Nov 16, 2023 at 7:32

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