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In typical software like Gaussian or GAMESS, the molecular orbitals (or even the basis functions) can be displayed as surfaces.

I understand that the surface is probably constructed from a series of points that give a fixed value when substituted into the wavefunction. However, how are these points calculated? Since typical software usually use GTOs, I’d like a formula if possible using those.

Thanks!

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    $\begingroup$ I think this question is too broad because (1) it depends what you are plotting and (2) it depends on what you are using to plot. There is no universal rule, only common sense guidelines, depending on what you are plotting. For instance, if you output electron density with Gaussian, you specify the size and resolution of the grid to output. It is then up to another software to decide how to display that data. Usually you set a cutoff for what you think is reasonably close to insignificant density, and then generate an isodensity surface to display. $\endgroup$ – Buck Thorn Sep 27 at 6:38
  • $\begingroup$ When displaying orbitals things are a little more tricky because you have not just amplitude but phase to display. You display one phase with one color and opposite phase (negative amplitude, or pi radians out of phase) regions with a different color. In other words, you choose to display either just real or just imaginary components of the wavefunction, and use different colors for positive and negative amplitude. $\endgroup$ – Buck Thorn Sep 27 at 6:45
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Only the program that you used to calculate the electronic structure knows all the idiosyncrasies of the computation to correctly evaluate the orbitals. Therefore, what most people do is to export the evaluation of the orbitals in a grid. Then, a plotting program performs an extraction of a polygonal mesh with a marching cubes (or similar) algorithm.

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    $\begingroup$ That is not really true. The question specifically refers to GTO codes (Gaussian and GAMESS). Here the molecular orbitals are well defined by the basis set and their coefficients, both may be found in the output file. Using for example the molden software, the Gaussian output can be opened directly and it will calculate and plot the grid points required for the 3D isosurface of each MO. $\endgroup$ – Feodoran Oct 6 at 20:43
  • $\begingroup$ I would not say that it is not possible, but that it is not straightforward. You can not blindly rely on molden because there have been errors disclosed in the past. E.g. github.com/psi4/psi4/issues/60. In that case the programs were not writing on file a correct representation of the internal parameters. You have to be prepared to inmerse in others code to get an answer because the documentation may be lacking or is incorrect. The authoritative source is the code. Besides, in some cases the relevant information is not even written in a molden format. $\endgroup$ – Zythos Nov 13 at 12:18

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