Derek Lowe reports the story[1] that the recently synthesized octafluorocubane can absorb one electron to form a radical anion – an electron in a cube. So I thought it would be fun to compute exactly where that electron sits!
A ωB97XD/Def2-TZVPPD/SCRF=chloroform calculation (DOI: 10.14469/hpc/11090) is carried out on the neutral system (optimizing its geometry) and then the radical anion at the same geometry. Cubes of total electron density are evaluated for both and then the neutral form is subtracted from the anion. The result is shown below (density isosurface value 0.0025 au; click on the image to load a rotatable 3D model of the density difference).
The below is at the optimised anion geometry for both species;
The colour code is that blue represents the location of the additional electron, and red indicates reduced electron density compared to the anion. Arrow 1 shows an additional sphere of density inside the cube – yes, an electron in a cube. But you probably would not have anticipated that the outer surface of the cube (arrow 2) is also surrounded by that electron and there is a reduced density layer on the inside surface of the cube. The C-F bonds have regions of both additional density and reduced density.
Postscript: Perfluorododecahedrane added as per comment
Postscript: Perfluorotetrahedrane added for completeness
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This is an interesting molecule. I looked at the C8F8(-) system at the same level of theory as you and analyzed it via QTAIM, a while ago. The inner part of the cube that is the C8 moiety remains still positively charged but gains more electron compared to neutral C8F8. Then I thought what if we replace F with Cl, Br, and I to reduce electronegativity and make the electron stay in the cube. The strategy works to some extent. I was hoping to find a non-nuclear attractor in C8I8(-) but it didn't happen. So, I would say the electron is wrapped around the box in C8F8(-) and goes more and more inside the box in C8X8 systems as X becomes less electronegative.
I also tested hydride inclusion. The systems are highly unstable but follow a nice trend. Encapsulation energies of H- in C8X8 in kcal/mol is +55.5, +72.8, +62.9, and +55.2 for X = F, Cl, Br, and I, respectively. Interestingly enough the H becomes octavalent with a noticeable covalent character and the systems have no imaginary frequencies. I am not sure if all the results are worth publication but some lovely trends are there. Maybe, if we look at C8(TeH)8, or a similar system, we can find a non-nuclear attractor. Or, possibly we need a bigger box decorated with I. If I were not so busy, I would play more with the idea.
Perfluorododecahedrane?
I bet on periodo to accommodate a non-nuclear attractor. I doubt about perfluoro one.
If you share the geometry or (even better) FCHK file of perfluorododecahedrane, I'll add its QTAIM analysis to see if it has a non-nuclear attractor or not yet.
Cina, Follow the DOI data link given in the post for the .fchk files. My own QTAIM program (AIMALL) appears not to have been updated since 2019 (http://aim.tkgristmill.com ) and currently does not run due to "wrong architecture" errors for 64-bit binary running on a 64-bit Mac.
I appreciate sharing the files. I'll look at both total and alpha- electron density to see what's going on and share them with you.
re: Sharing - I practise both FAIR and OPEN data sharing. Also, always a fchk file as well as a log file to enable exactly situations such as these.
re: AIMALL, it seems the error can be narrowed down to /Library/Frameworks/QtGui.framework/Versions/4/QtGui: no matching architecture in universal wrapper
In other words, the QtGui libraries used in AIMALL appear to be out of date and incompatible with current MacOS.
The good news is that C20F20 indeed has an NNA in its centre. So, making the box bigger helps to identify electron accumulation in the centre. However, the NNA is extremely small; in fact, the smallest NNA I've ever seen. The charge of the NNA is merely 0.007! It's a ripple in the ocean of electrons.
Cina, send me an image and I will add it to your comment.
Re: replacement for AIMALL, https://github.com/kjelljorner/homebrew-multiwfn describes how to install Multiwfn. After a little while, I did manage to compile, but have no GUI for the program. That is the next task to sort out.