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AlessandroMariani

Member

Registered: 2021-11-09

Posts: 2

Charge density calculation

Hello,
I am a new Multiwfn user. I would like to calculate the charge density (electron charges/Angstrom^3) for a series of polyatomic ions.
Ions like K+, Cl-, or even (SO4)2- are easy to treat by simply calculating the VDW volume of the overall ion and divide the net charge by that. The tricky part (for which I am asking for help here) comes for ions in which the charge is localised only on a portion of the ion, e.g. Acetate, Triflate, etc.

Is it possible to calculate the volume only of a portion of a molecule and not the entirety of it?
Or, is it possible to derivate the charge density in other ways?

Thank you very much for any advise

Last edited by AlessandroMariani (2021-11-09 13:00:49)

sobereva

Tian Lu (Multiwfn developer)

From: Beijing

Registered: 2017-09-11

Posts: 1,830

Website

Re: Charge density calculation

I don't understand your problem clearly. I think the charge density you mentioned should be electron density, it is not a concept directly relevant to vdW volume. It seems that you confused some concepts.

It is possible to calculate atomic volumes using atom-in-molecules (AIM) partition via basin analysis module of Multiwfn, but it has no directly relationship with charge density. (Note that electron density in an atomic space is different at different positions, if you integrate electron density over the atomic space, you will obtain atomic charge)

AlessandroMariani

Member

Registered: 2021-11-09

Posts: 2

Re: Charge density calculation

Thank you for your reply.
Maybe I was not clear enough.

Silberberg (Chemistry: The Molecular Nature of Matter and Change. 4th ed. 2006) defines Charge Density as:

"The ratio of the charge of an ion to its volume."

The factors playing into the strength of an ion's charge density are therefore the charge of the ion (e.g. 2+ for Mg, 1+ for Na) and the effective volume which that charge acts over - which is where the ionic radius comes in.

Charge density = charge/volume

As the magnesium ion and sodium ion both have the same electronic configuration i.e. that of neon (because Mg has lost 2 electrons and Na has lost 1 and they now both have 10 electrons in total) the charge of the electrons around the ions is the same. But - magnesium has one more proton in its nucleus. This means magnesium has a smaller radius, and thus higher charge density.

For Na+ the ionic radius is 1.16 Å, and the charge is +1
For Mg2+ the ionic radius is 0.86 Å and the charge is +2

The corresponding charge densities are (assuming spherical geometry):
Na+: 1/[(1.16)^3 * 4π/3)] = 0.15 e/Å^3
Mg2+: 2/[(0.86)^3 * 4π/3)] = 0.75 e/Å^3

For ions where the charge is localized only on one portion of the molecule, I need to determine the volume only of that portion, and not the whole ion.

What I want to achieve is something as described here:

https://bcs.whfreeman.com/WebPub/Chemis … 20Ions.pdf

I hope now my question is clearer

Last edited by AlessandroMariani (2021-11-10 10:32:50)

sobereva

Tian Lu (Multiwfn developer)

From: Beijing

Registered: 2017-09-11

Posts: 1,830

Website

Re: Charge density calculation

You can use Multiwfn to perform AIM basin analysis to derive AIM atomic charges and volumes, see Section 4.17.1 of Multiwfn manual for example:

Then you can divide the printed atomic charge by atomic volume to obtain the charge density of the atom of interest.

You can also sum up atomic charges and volumes to obtain charge and volume of a fragment, and then divide them to estimate charge density of a fragment.