Eelctron Localization function and electron density

[ams_nanolab]

How are the electron localization function and the electron density calculated in ATK fundamentally different? And what more information may be derived from the electrostatic difference potential as compared to the electron difference density?

[Petr Khomyakov]

Regarding the first question, you may have a look at https://en.wikipedia.org/wiki/Electron_localization_function to see the difference between the ELF and electron density. You may also have more insight by reading the original work on ELF by A. D. Becke and K. E. Edgecombe, A. D.; Edgecombe, K. E. (1990). "A simple measure of electron localization in atomic and molecular systems". J. Chem. Phys. 92: 5397–5403.

Regarding the second question, I guess the answer depends on what you actually want to use these two different physical quantities for. For example, the electrostatic difference potential may give you a better insight on band bending in semiconductor heterostructures, whereas the electron difference density is more for visualizing interface dipoles in the same structures.  But both are related quantities indeed.