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My teacher explained that free radicals could have a geometry that is planar or pyramidal(tending to tetrahedral) based on whether or not it is substituted by lone-pair containing atoms.

For example, $\ce{(CH3)_3C}$ would exhibit sp2 hybrid geometry of planar.

But when tri-substituted with Flourine/Chlorine, it will exhibit a geometry that is tending towards tetrahedral(pyramidal) because the free radical electron in the P-orbital repels the lone-pairs on the Halogen.

It does not seem convincing because, the P-orbital is above and below the plane, then why does the electron in P-orbital repel the groups into a geometry tending towards tetrahedral? That's like as if the electron was present only on the top and was repelling the groups down.

Here is a picture that might help visualise the p-orbital above and below the plane: https://www.google.com/imgres?imgurl=https://chemistryonline.guru/wp-content/uploads/2016/09/carbonium-1280x720.jpg&imgrefurl=https://chemistryonline.guru/carbonium-ion/&tbnid=1bNjv-81SP8QxM&vet=1&docid=MPke176Wg2AS2M&w=1280&h=720&source=sh/x/im

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    $\begingroup$ Yes, I agree that the attached groups due to the sp2 hybridisation, are aligned into a planar geometry, but the vacant p-orbital must remain perpendicular to the plane of the sp2 orbitals. So, that means the p-orbital being dumbbell shaped, should be above and below the plane of the sp2 bonds. $\endgroup$
    – Desai
    Dec 16 '20 at 9:56
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    $\begingroup$ .... from here chemistry.stackexchange.com/questions/49754/… $\endgroup$
    – Alchimista
    Dec 16 '20 at 10:42
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    $\begingroup$ And as suggested in a comment therein, a look at en.m.wikipedia.org/wiki/Bent%27s_rule $\endgroup$
    – Alchimista
    Dec 16 '20 at 10:59
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    $\begingroup$ Please don't link through Google tracking algorithms to images. If possible and allowed, please include them directly in your post. Otherwise try a permanent URL. $\endgroup$ Dec 16 '20 at 18:52
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    $\begingroup$ I return here specifically for you. While the explanation given by your teacher might be not accurate (as for the material posted below) however it is not inaccurate because the reasoning leading to your doubt. It doesn't matter that the e is repelling equally from above and belove. It matters that with a more pyramidal or sp3 like geometry all repulsions are minimised. $\endgroup$
    – Alchimista
    Dec 17 '20 at 10:23
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A priori, I would expect substituted methyl radicals to adopt a planar structure due to Bent’s rule.

However, I consider it possible for methyl radicals with electron-withdrawing substituents to adopt a trigonal-pyramidal structure too. In this case, Bent’s rule would imply that the electron-withdrawing substituents are ‘more electron-withdrawing’ than the radical is electron-poor. In such a case, it might be beneficial to distort the planar structure, causing rehybridisation and thus resulting in $\mathrm{sp}^n$ orbitals across the board so that all orbitals together add up to $\mathrm{sp^3}$. This structure may not be perfectly pseudotetrahedral but close enough to have a significant s-contribution to the singly-occupied orbital.

Note that $\mathrm{sp^3}$-type radicals are not inherently unstable (unlike $\mathrm{sp^3}$-type cations) as can be seen in bicyclo[2.2.2]octa-1-yl radicals (or bridgehead radicals in general). This points to $\mathrm{sp^3}$ radicals being accessible and thus the finer electronic environments mattering.


Addendum: Ron has shared links to two other questions he answered (1, 2) which argue the case that methyl radicals would be (slightly) pyramidal rather than planar in their ground state. So my a priori expectation might be wrong. I believe it might be very hard to prove the structure conclusively, as it is expected for a pyramidal radical to rapidly inverse as nitrogen does in ammonia and its derivatives so that any non-short timescale measurements would result in an averaged structure (which would be planar).

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  • $\begingroup$ Hi Jan...I find it difficult to believe that nature would build a molecule where only the 3 two-electron $\ce{C-H}$ bonds are stabilized by mixing in s-character, while the orbital containing a single electron is not stabilized by mixing in at least a sliver of s-character. I've suggested previously (to some objection) that the methyl radical is likely slightly pyramidal due to such s-character mixing. See What is the geometry of an alkyl radical? and $\endgroup$
    – ron
    Dec 16 '20 at 20:01
  • $\begingroup$ Geometries of methyl and silyl radicals. $\endgroup$
    – ron
    Dec 16 '20 at 20:01
  • $\begingroup$ @ron That is a very good point and to be perfectly honest I hadn’t yet fully thought it through all the way. $\endgroup$
    – Jan
    Dec 19 '20 at 11:49

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