Multiwfn forum / Electron Density Surfaces For Individual Localised Orbitals

Re: Electron Density Surfaces For Individual Localised Orbitals

dummy@example.com (saeed_E) — Tue, 11 Mar 2025 19:22:18 +0000

Thank you very much.

Saeed

Re: Electron Density Surfaces For Individual Localised Orbitals

dummy@example.com (sobereva) — Mon, 10 Mar 2025 19:29:25 +0000

I agree

Re: Electron Density Surfaces For Individual Localised Orbitals

dummy@example.com (saeed_E) — Mon, 10 Mar 2025 09:53:36 +0000

Dear Tian,
Many thanks for your much valuable comments.
If one wants to compare results of the gas phase and those of the solution, a quite same isovalue should be employed. In this sense, it seems isovalue= 0.001 a.u. to be suitable for both the gas and solution phase. Do you agree?

Sincerely,
Saeed

Re: Electron Density Surfaces For Individual Localised Orbitals

dummy@example.com (sobereva) — Sun, 09 Mar 2025 22:12:49 +0000

Usually rho=0.002 a.u. is used to define the vdW surface in condensed phase, it is larger than 0.001 a.u. because there are mutual penetrations between molecular vdW surfaces.

Re: Electron Density Surfaces For Individual Localised Orbitals

dummy@example.com (saeed_E) — Sun, 09 Mar 2025 20:22:18 +0000

Dear Tian,
In the above replies you indicated:
"the Bader's definition of molecular vdW surface (in gas phase) corresponds to isosurface of electron density with isovalue of 0.001 a.u.;.....". If possible, please let me know what is the suitable isovalue for the vdW electron density in the presence of a desirable solvent.

Sincerely yours,
Saeed

Re: Electron Density Surfaces For Individual Localised Orbitals

dummy@example.com (sobereva) — Sat, 08 Mar 2025 17:16:21 +0000

1 It is also applicable to a molecule without symmetric density distribution. See the equations used by this function in Section 3.200.5 of Multiwfn manual, they are universal.

2 Yes, it is easy. When you plot curve, plane and isosurface maps by main functions 3, 4, and 5, respectively, you can also choose "44 Orbital probability density" as the function to be plotted.

Re: Electron Density Surfaces For Individual Localised Orbitals

dummy@example.com (dcjskea) — Sat, 08 Mar 2025 00:58:29 +0000

Thank you. Following your instructions, I have successfully calculated rdf of probability density for individual orbitals, initially using calculations on single atoms. I note the requirement for spherical symmetry, and I assume that "r" is the distance from a nucleus which has coordinates 0,0,0. Can this type of calculation be carried out in molecules where there are many nuclei, and probably no spherical symmetry?
For the study of localized orbitals and bonding in molecules, can a "spatial" (rather than radial) distribution function of probability density be calculated for each orbital (in a line, plane, or even 3D)? That is, where in a molecule are the electrons most likely to be found?

Re: Electron Density Surfaces For Individual Localised Orbitals

dummy@example.com (sobereva) — Sun, 09 Feb 2025 21:30:51 +0000

I don't know what is "electron density surface"

If you want to obtain rdf of probability density of each orbital (i.e. norm of orbital wavefunction), it can be realized via Multiwfn (Please ensure that you are using the latest version of Multiwfn). In the interface of plotting rdf (i.e. subfunction 5 of main function 200), choose "1 Select real space function", then choose "44 Orbital probability density", then input the index of the orbital you are interested in. After that, you can choose option "0 Calculate radial distribution function and its integration curve" to calculate and visualize rdf.

Re: Electron Density Surfaces For Individual Localised Orbitals

dummy@example.com (dcjskea) — Sun, 09 Feb 2025 18:23:54 +0000

Thank you for your reply of some months ago. I am using Multiwfn, and understanding more of its capability. I would like to visualize the radial distribution function of electron density surface, for each orbital separately. Please let me know if there is a way to do this, and instruct me on how to do it. Many thanks.

Re: Electron Density Surfaces For Individual Localised Orbitals

dummy@example.com (sobereva) — Thu, 29 Aug 2024 12:23:48 +0000

Your statement is correct.

Radial distribution function of electron density corresponds to the 6th user-defined function, see Section 2.7 of Multiwfn manual for detail. To visualize it, you need to set "iuserfunc" in settings.ini to 6, then when you use main function 3/4/5 to visualize it as curve map/plane map/isosurface map, choose "100 User-defined function" as the function to be calculated and plotted.

Re: Electron Density Surfaces For Individual Localised Orbitals

dummy@example.com (dcjskea) — Thu, 29 Aug 2024 11:09:27 +0000

Thank you for your reply. I think I now understand that isovalues are different depending on the parameter being visualized. For Multiwfn, can you confirm:

When plotting wavefunction, the units of the isovalue are (effectively) sqrt(1/Bohr^3)

When plotting electron density, the units of the isovalue are 1/Bohr^3

Please, now, forgive me for asking this question: is there a way of visualizing the radial electron density function surfaces (4 x pi x r^2 x psi^2) for an atom or molecule?

Many thanks. Regards.

Re: Electron Density Surfaces For Individual Localised Orbitals

dummy@example.com (sobereva) — Wed, 28 Aug 2024 22:17:45 +0000

The suitable isovalue(s) for visualizing grid data is different for different functions and purposes. For example, the Bader's definition of molecular vdW surface (in gas phase) corresponds to isosurface of electron density with isovalue of 0.001 a.u.; so , if you visualize rho=0.001 a.u. isosurface (note that the "rho" in this context is total electron density rather than probability density of an orbital), the vdW profile can be understood. You can also visualize such as rho=0.05 a.u. isosurface, but it doesn't have a known meaning.

As I noted, orbital wavefunction is dimensionless. If you visualize orbital wavefunction in Multiwfn, VMD, GaussView, chemcraft... with the same isovalue, then you will see exactly the same isosurface. I am not a IQmol user so I am unable to comment it.

Re: Electron Density Surfaces For Individual Localised Orbitals

dummy@example.com (dcjskea) — Wed, 28 Aug 2024 20:14:11 +0000

Many thanks for your reply. Once again, it has been very helpful. If I may, I have a few more questions relating to isovalue units.

Using Multiwfn, I have been visualizing wavefunction surfaces using an isovalue of 0.05. If I then switch to your electron density surface, I notice that the isovalue defaults to a much smaller value. Could you explain the change in isovalue? And please confirm the units of your isovalues in both cases.

In trying to understand wavefunction visualization, I have compared the visual outputs from Multiwfn and another software (IQMol). I guess this may be a difficult task since the output is very sensitive to the isovalue, and the computation methods may be different. I find that wavefunction visualizations from IQMol (at isovalue 0.05 / Angstrom^3) correspond very closely to visualizations from Multiwfn (at isovalue 0.03 / Bohr^3). I can't make sense of this, assuming your units are /Bohr^3. Perhaps IQMol is not the best?

In the past I have used different visualization software - Avogadro, IQMol, VMD, Molden, wxMacMolPlt, Gabedit - some with success, others not. I would be interested in your views on the subject of visualization - is it a science, or more of an art?

Thank you. Best regards.

Re: Electron Density Surfaces For Individual Localised Orbitals

dummy@example.com (sobereva) — Mon, 26 Aug 2024 21:34:51 +0000

There are two common units of electron density (B), including a.u. (1/Bohr^3) and 1/Angstrom^3. Multwfn always uses the former.

According to the unit you given for C, C should be referred to as radial density function of electron density, and should never be confused with electron probability density function.

Orbital wavefunction is dimensionless. However, if someone forces you to give it a unit, according to Born's probability interpretation of wavefunction, the unit may be sqrt(1/Bohr^3).

The word "orbital density" or "orbital probability density" always corresponds to B.

Re: Electron Density Surfaces For Individual Localised Orbitals

dummy@example.com (dcjskea) — Mon, 26 Aug 2024 11:21:17 +0000

Thank you for your reply. It has been very helpful. I would like to ask you to clarify some of the terminology you are using. I think it is important to get this right in my mind. From my understanding we have different parameters:

A Orbital (wavefunction) - a number, plus or minus
B electron density (wavefunction squared) - electrons per unit volume, e / Angstrom^3 ??
C electron probability density function (4 x pi x r^2 x psi^2 x dr) - a number, probability

Using Multiwfn, if I choose to calculate and visualize a "wavefunction" surface, what are the units of the isovalue I choose? Many visualization programs have the units as e / Angstrom^3 (electrons per cubic Angstrom). Is that true of Multiwfn?

Using Multiwfn, if I choose to calculate and visualize your "Density" surface, do you mean B or C? And what are the units of the isovalue in this case?

I hope my questions make sense. I look forward to your reply. Many thanks and regards.