# What can we learn by inspecting charge densities calculated with DFT?

The charge density is an important physical quantity obtained from first-principles calculations based on density functional theory (DFT). Much useful information about the investigated materials can be extracted from it, such as chemical bonding, charge transfer, and orbital hybridization. Here I post this question to ask:

What can we learn by inspecting charge densities calculated with DFT?

Here is an example answer to this question following this paper:

The author compares the differential charge density accumulation between bilayer PtS$$_2$$ and MoS$$_2$$ and concludes the bilayer PtS$$_2$$ will host a more strong interlayer coupling due to the significant charge accumulation.

• I might be missing the point, but I think it would be hard to write down a complete list. If you know the charge density, then in principle you can determine the electronic Hamiltonian (by the first HK theorem) and therefore nearly anything. Are you asking about common ways DFT charge densities are processed in practice? – wcw Oct 12 '20 at 12:43
• @wcw maybe what you just said in the comment, is precisely what should be put in an answer. – Nike Dattani Oct 12 '20 at 16:46
• @wcw It is true that all information can be hidden in the Hamiltonian, which can be derived from the charge density in terms of the DFT. However, this post is hoping to extract information from the charge density. Because the charge density can be obtained easily from DFT calculation, like the CHGCAR output file of VASP. – Jack Oct 12 '20 at 23:46
• Maybe it is best to clarify, information from the charge density that can be extracted without calculating the Hamiltonian then since otherwise there are too many examples. Edit: Reading your changes I think its okay now. I will retract close – Tristan Maxson Oct 13 '20 at 15:24
• Thanks for clarifying Jack. I think it's an interesting question and worth keeping, although I agree with @TristanMaxon that it is very broad and may not elicit a definitive answer. (Also I made a few edits for extra clarity - hope you don't mind!) – wcw Oct 13 '20 at 16:45

When you see charge densities plotted in the literature, they are usually plotting particular isosurfaces (contours) and are trying to show "where the electrons are". Charge density differences can be useful in trying to understand the changes in a system, for example charge transfer as a molecule approaches a surface (although this often isn't very accurate with common XC functionals). Plotting spin-densities can be very useful to see where the regions of magnetism are, and what nature of magnetism is present (e.g. ferromagnetic or antiferromagnetic).

People often try to use the electron density as a proxy quantity for other properties. For example, if you think there should be a covalent bond between layers, then you would expect to find significant electron density in the inter-layer region. If indeed there is a high electron density in this region, then you might argue that this is evidence of a strong bond. In my opinion this is not a very strong argument, because it assumes local interaction with the density, whereas layers could be interacting strongly via non-local interactions (Coulomb interactions such as in ionic materials, for example, or van der Waals interactions) in which case there is no need for a high electron density in the inter-layer region. In fact it is trivial to compute the inter-layer force constant and essentially "measure" the strength of the interaction, so I would always prefer that.

Note that, in principle, the ground state density tells you everything about the ground state of the system -- this is essentially the 1st Hohenberg-Kohn theorem. However, in practice this is not as useful as it may appear at first, since we don't actually know how most of the properties depend on the density, just that they do!

• Thanks for your answers. [In my opinion this is not a very strong argument, because it assumes local interaction with the density, whereas layers could be interacting strongly via non-local interactions (Coulomb interactions such as in ionic materials, for example, or van der Waals interactions) in which case there is no need for a high electron density in the inter-layer region.] Could you share more details about this viewpoint? – Jack Nov 12 '20 at 6:52