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I am interested in calculating electronic difference density maps. These have been described for quite a long time by Bader and others. For example, below is the fourth of a series of papers which discusses these extensively.

Cade, P. E., Bader, R. F. W., Henneker, W. H., & Keaveny, I. (1969). Molecular Charge Distributions and Chemical Binding. IV. The Second‐Row Diatomic Hydrides AH. The Journal of Chemical Physics, 50(12), 5313-5333.

The idea is fairly simple. Use some electronic structure method (or in principle experimental data) to calculate the electron density of some atom or molecule by itself (but at the appropriate geometry) and then calculate the electron density of the molecule containing the atoms for which you have reference density distributions. Sum all the reference densities and take the difference from the reference densities. You then get a map with positive and negative regions that show areas of electron enrichment and depletion which hopefully provides some physical insight.

It is simple enough to calculate electron densities with most electronic structure packages and have the program print out the density in terms of expansion coefficients for the molecular orbitals which various other programs are able to read and visualize.

Now with that information in hand, is anyone aware of software packages which can do this operation I am describing? Or am I stuck with doing something like fitting the electron densities numerically and taking the differences in that way? If so, if anyone has done this before, some input in that regard would be useful.

This seems like such a simple thing to calculate, but I've been a bit confused. I know I've seen people make spin density difference plots for open-shell and excited state systems. This is such a similar calculation that it seems like one should be able to use the same tools, but I assume the latter calculations are buried in the electronic structure package somewhere and hence not easy for the user to adapt.

Any help is greatly appreciated.

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  • $\begingroup$ How large are the molecules in question you refer to? Smallish ones? Larger proteïns? Because Xray crystallography routinely uses calculated electron maps to refine structure models (example proteopedia.org/wiki/index.php/Electron_density_maps, or rcsb.org/pages/help/edmaps) I speculate coot (en.wikipedia.org/wiki/Coot_(software), and pymol (e.g., drugdesign.gr/blog/…) may at least adaptable (pymol with Python scriptable) for such a task, too. $\endgroup$
    – Buttonwood
    Commented Mar 23, 2020 at 16:55
  • $\begingroup$ @Buttonwood Quite small molecules. Ya my assumption is that I can kind of hack a number of programs to do this but if there is a standardized way I would rather do that so as to avoid making mistakes and being able to reproduce my results. $\endgroup$
    – jheindel
    Commented Mar 23, 2020 at 17:17
  • $\begingroup$ Possibly you have to align the coordinate systems of the «reference» and the «probe» molecule with each other in a first step, each carrying their electron density map like a knapsack. If both are the same molecule, a Kabsch-like algorithm (e.g., github.com/charnley/rmsd) could be a start, which nicely runs with little manual intervention and offers output of the newly aligned $(x,y,z)$ about the atoms in a .xzy file. $\endgroup$
    – Buttonwood
    Commented Mar 23, 2020 at 17:26
  • $\begingroup$ Right. One definitely needs to be careful about this type of thing. $\endgroup$
    – jheindel
    Commented Mar 23, 2020 at 17:45
  • $\begingroup$ I know you can do this with Gaussian/Gaussview, though I realize that isn't very helpful if you don't have a license. $\endgroup$
    – Tyberius ♦
    Commented Mar 26, 2020 at 1:35

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