In exploring one-electron carbon-carbon bonds, I had noted previously[cite]10.59350/88k04-2×509[/cite] that both hexafluoroethane and ethane itself could each lose an electron to produce such species. A discussion developed in which a molecule isoelectronic with ethane, namely the methyl-λ1-borane radical (H3B-CH3) was proposed by Jacob. The optimised structure at the ωB97XD/6-31G(d) level exhibited a B-C bond length of 1.57Å, with two of the B-H hydrogens forming a a 3c-3e bond with boron and so a one-electron B-C bond was discounted. Here I take a closer look at this system.
At the ωB97XD/Def2-TZVPP level, I located an alternative structure with a longer B-C bond of 1.737Å[cite]10.14469/hpc/14662[/cite] and an “agostic” like interaction between C and one B-H bond.
The electron density difference maps between methyl-λ1-borane and its mono cation is shown below and following it the density difference map between the corresponding anion and methyl-λ1-borane radical. These are very similar to the maps obtained previously for hexafluoroethand and ethane and support the hypothesis that the differences between the two-electron/zero-electron species and the one-electron radical originates at least in part in the B-C bond.
A contour map of the negative region of the electron density Laplacian (-0.04 au) again shows that it lies along the B-C bond, suggesting covalency. Note the -ve Laplacian in the region of the agostic interaction! The NCI (non-covalent-interaction) plot is featureless.
The computed methyl-λ1-borane radical has a B-C stretching vibration corresponding to 494 cm-1, a Wiberg bond order of 0.660 and Wiberg bond index totals of 3.51 for carbon and 3.28 for boron. These can all be reasonably interpreted as a one-electron “half” bond between C and B. With a computed bond length of 1.737Å, it represents the shortest “one electron” bond thus far identified, and hence extends the length range of such bonds to around 1.16Å.
Postscript 1
I also looked at the radical anion of H3B-BH3– which is isoelectronic to methyl-λ1-borane, revealing rB-B 2.124Å and has a classic “ethane” D3d like structure. The electron density difference map between H3B-BH3– and the neutral H3B-BH3 is shown below, revealing in a considerable reorganisation of the electron density, only one aspect being the B-B region and different from the reorganisation of the radical cation of ethane itself. This reveals that simply talking about a two-atom region for this sort of system is very simplistic and misleading. The Wiberg B-B bond index is 0.383 and the B-B stretching vibration is 384 cm-1.
The electron density Laplacian of H3B-BH3– contoured for a -ve value of -0.04 au, again implying a covalent B-B bond.
Postscript 2
Here I add hexamethylethane radical cation to the list. Firstly the density difference map. Note the longer C-C bond (2.31Å) than for ethane radical cation (1.933Å). In this sense, the hexamethyl radical cation has a weaker C-C bond than does the unsubstituted version (191 cm-1) vs 477 cm-1)
The Laplacian shows no -ve value in the C-C region (isosurface value -0.01), again placing it in the weak bond category.
Finally some NCI plots. Here the density cut-off threshold is crucial. Typically a second period element covalent density is taken as 0.05 au, and this is removed from the NCI analysis. The feature seen along the C-C bond at this level is typical of weak covalent interactions however.
Reducing the density to 0.023 (typical of density in which one atom is of the third period, ie Si) removes the central C-C feature, leaving only NCI effects between the hydrogen atoms of the methyl groups. These in fact form a continuous weakly stabilizing surface between the two halves.
So with hexamethylethane radical cation, we get messages that the interaction between the two carbons is both weak, but also not a non-covalent interaction. So this is a very weak covalent bond perhaps, but in this strange region, it is difficult to ascribe a single description to it.
Ooh, another valence-bond isomer! Very cool! Thanks for following up and investigating these; I’m only an amateur and it’s great to see what an expert like you can pull out the simulations.
It’s a little frustrating that one-electron bonds are so strongly affected by nearby substituents. I guess I shouldn’t be surprised: radicals are known to migrate easily. Still, 3-electron bonds and 1-electron pi bonds are much more stable. If I had to guess, some of the instability must arise because 1-electron bonds are so weak; the system is, philosophically, a perturbation on a 2-electron bond skeleton.
Remember also that a “bond” defies entropy! Thus entropy prefers two fragments over just one and hence the free energy of the former will be lower than the latter. With 2-electron bonds and greater, the enthalpy of the bond more than overcomes the unfavourable entropic contribution to the free energy. But with a 1-electron bond, that may no longer be true, so 1-electron bonds may well be vulnerable to the “entropy issue”, unlike higher electron bonds.