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**Uhu22****Member**- Registered: 2023-11-25
- Posts: 3

Dear forum users,

I am trying to analyze the topology of the spin density for an organic radical and to visualize concentration/depletion regimes of spin density via its LaPlacian. While I was able to obtain critical points and real space values of the spin density, I am struggling to plot the LaPlacian of the spin density. In MultWfn, the standard settings for outputting a property in a plane allow to either plot the spin density or the LaPlacian of the electron density, however there seems to be no direct way to plot the LaPlacian of the spin density. Has anyone tried to do this/an idea for a workaround for this?

Thank you!

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Directly plotting Laplacian of spin density is not directly feasible, but thanks to the high flexiblity of Multiwfn, and due to the fact that Laplacian operator is a linear operator, there is an easy workaround:

(1) Obtain cube file of Laplacian of alpha density, and Laplacian of beta density.

For example, to obtain Laplacian of alpha density, after loading wavefunction into Multiwfn, you should enter main function 6 and then subfunction 26, set occupancy of beta orbitals to zero. Then return to main menu, using main function 5 to calculate Laplacian of electron density and then export the grid data to a cube file. Assume that the file is named as alpha.cub. Similarly, obtain beta.cub.

(2) Boot up Multiwfn, use main function 13 of Multiwfn to obtain cube file corresponding to alpha.cub minus beta.cub (see Section 4.13.2 of Multiwfn manual on how to obtain difference cube file between two given cube files). The resulting cube file directly corresponds Laplacian of spin density.

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**Uhu22****Member**- Registered: 2023-11-25
- Posts: 3

Dear Dr. Lu,

Thank you so much for your quick reply, with your instructions I was able to generate cube files of the Laplacian of the spin density. However, if i reboot MultiWfn and load the generated cube file to plot the LaPlacian as a plane I can only choose between Promolecular electron density, Electrostatic potential from nuclear charges, Reduced density gradient, Sign(lambda2)*rho and Delta_g, none of which resemble the 3D representation of the LaPlacian. Is there a way to print the newly generated LaPlacian as a plane?

Thank you, and all the best!

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Because Laplacian of spin density is not a real space function directly supported by Multiwfn, if you need to plot it as a plane map, you need to plot interpolated function based on grid data of Laplacian of spin density. To do so, you should set "iuserfunc" in settings.ini to -1 (linear interpolation) or -3 (B-spline interpolation), then boot up Multiwfn and load cube file of Laplacian of spin density, then use main function 4 to plot plane map. When Multiwfn asks you to choose the function to be plotted, choose "100 User-defined function", which currently corresponds to interpolated function based on the grid data in memory.

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**Uhu22****Member**- Registered: 2023-11-25
- Posts: 3

Dear Dr. Lu,

Thank you so much again for your detailed reply! I was able to successfully plot the spin density LaPlacian in a plane. I am now trying to obtain the real-space values of the spin density Laplacian at critical points via topology analysis of the spin density LaPlacian cube file. The critical points were taken from a previous search on the spin density of the parent wfn file. So far I could only obtain LaPlacian values that are identical to the ones directly obtained from electron density LaPlacian. How can I get MultiWfn to print the CP properties of the spin density, rather than the electron density?

Thank you so much!

*Last edited by Uhu22 (2023-11-28 16:05:14)*

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After performing topology analyisis, record the coordinate of obtained critical points in a text file. Then set iuserfunc to -1 or -3, boot up Multiwfn and load cube file of Laplacian of spin density, enter main function 1, input the critical point coordinate, the "User-defined function" show on screen now corresponds to the value of Laplacian of spin density at the critical point.

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