Electron Density vs Electron Density Difference

[handsomecat]

From articles reporting DFT calculations in atomic systems (eg. unit cells of metallic systems), I have seen charts that display contours of the "Electron Density" and "Electron Density Difference". Would appreciate it if someone could give a brief explanation of

(1) what the difference between the two is? and,
(2) how do I interpret the nature of the bonding in the system from these charts?

I'm interested because I am performing DFT calculations, but don't have the benefit of a formal grounding in physics and chemistry ( I come from a mechanical engineering department ...)

Just to give a heads-up, I've seen the answer to question 12 in the following URL, but I'd like to know if there's anything fundamental that I should know, or anything that I need to note.

http://www.tcm.phy.cam.ac.uk/castep/dftexercises.html

In fact, if there's anyone out there who could help interpret these diagrams, please let me know! Any assistance will be acknowledged appropriately!

 

[JPRitchie]

"Electron Density" is usually denoted by the greek symbol rho. Quantum mechanically, it is the number of electrons times the value of the wavefunction times its complex conjugate. In the fields you refer to, values of rho are computed at points on a mesh and then plotted. The electron density is the scattering medium in x-ray crystallography. In DFT theory, the electron density (the D in DFT) is taken as the independent variable to obtain atomic and molecular energies.

"Electron Density Difference" is typically the difference between an assumed standard or model electron density and the actual observed or DFT computed electron density. For example, one can make a difference plot by subtracting superposed sphericalized (faked) atomic densities from the density of a molecule. People write papers and books about how to interpret electron difference maps in terms of chemical bonding.

Theoretically, a method based on Schwinger's principle of stationary action has been developed by Richard Bader. See: "Atoms in Molecules: A Quantum Theory". For experimental work, see: "X-Ray Charge Densities and Chemical Bonding" by Philip Coppens.

-Jim Ritchie

 

[handsomecat]

Thank you.

One last question. I wonder if I can rely on the answers to question 12, ( see link in first post) as an aid to interpreting the electron density diagrams that I generate.

 

[JPRitchie]

If it were me, I'd use Bader's method. It's quantitative and theoretically sound. Looking only at difference maps can lead to problems. For example, using spherical atoms, one sometimes finds negative differences in covalent systems; flourine molecule is an example.
Jim

 

[handsomecat]

Thank you!