# Electron Density vs Electron Density Difference

• handsomecat
In summary, the conversation discusses the use of DFT calculations in atomic systems and the interpretation of charts displaying the electron density and electron density difference. The difference between the two is explained as well as the implications for understanding bonding in the system. The use of Bader's method for interpreting these diagrams is suggested as a more reliable approach.
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!

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"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

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.

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

Thank you!

## 1. What is electron density?

Electron density refers to the measure of the probability of finding an electron in a particular region of space. It is often represented by a three-dimensional map that shows the distribution of electrons around an atom or molecule.

## 2. What is electron density difference?

Electron density difference is the comparison of electron density between two different states or molecules. It is calculated by subtracting the electron density of one state or molecule from the electron density of another.

## 3. How is electron density related to chemical bonding?

Electron density plays a crucial role in chemical bonding as it determines the strength and type of bond formed between atoms. A higher electron density between two atoms indicates a stronger bond, while a lower electron density suggests a weaker bond.

## 4. What is the significance of studying electron density vs electron density difference?

Studying electron density and electron density difference can provide valuable insights into the electronic structure and properties of molecules. This information can be used in various fields such as drug design, materials science, and nanotechnology.

## 5. How is electron density measured and calculated?

Electron density can be measured experimentally using techniques such as X-ray crystallography, neutron diffraction, and electron microscopy. It can also be calculated theoretically using quantum mechanical models and computational methods.

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