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