Here’s a real tour de force study combining exciting experiments with detailed computations. It’s a look at the radical cation of propellane performed by Bally and Williams.¹ This paper has been nicely reviewed by Hiberty.²

Propellane 1, whose bridgehead-bridgehead bond has been a topic of an earlier post, has a HOMO that is largely outside of the bridgehead-bridgehead region. Thus, loss of an electron to form the radical cation 1^.+ seems unlikely to lead to any significant geometrical change. However, the ESR of the radical cation of propellane shows two types of hydrogens, one type of four hydrogens and a second type of two hydrogens. This is incompatible with a D_3h structure similar to that of 1. Furthermore, loss of an electron from dimethylenecyclopropane 2 leads to a species whose ESR is nearly identical to that of the radical cation of propellane. Analysis of the ESR suggests that the radical actually produced is 3^.+.

CCSD(T)/cc-pVTZ//B3LYP/6-31G* computations were performed to try to discern a mechanism for this rearrangement. The D_3h structure of 1^.+ is a local energy minimum with most computational methods, though not with B3LYP, where it is a TS connecting mirror image C₂ structures. Breaking symmetry to C₂ leads to a TS (TS1) for cleaving one of the C-C_bridgehead bonds. This TS is only 1.15 kcal mol^-1 above 1^.+, and leads to 4^.+, 7.38 kcal mol^-1 below 1^.+. Cleavage of a second C-C_bridgehead bond passes through TS2, with a barrier from 4^.+ of only 2.89 kcal mol^-1. This leads to 2^.+. Lastly, cleavage of a third C-C_bridgehead bond through TS3, with a barrier of only 2.09 kcal mol^-1 above 2^.+, leads to 3^.+, overall 30.4 kcal mol^-1 exothermic from 1^.+. The structures of these critical points are shown in Figure 1. Quite a neat little pathway – three sequential bond ruptures without ever cleaving what was the weakest bond in the original compound (the bridgehead-bridgehead bond)!

1.+ 0.0	TS1 +1.15
4.+ -7.38	TS2 -4.49
2.+ -24.54	TS3 -22.45
3.+ -30.41

Table 1. B3LYP/6-31G* optimized critical points on the pathway of 1^.+ to 3^.+.
Relative energies in kcal mol^-1

The cool part of this is why the barrier is so small leading out of 1^.+ – vibronic coupling via C_s distortion of 1^.+ with its first excited state leads to an energy lowering of this pathway. This sort of vibronic coupling had in fact been implicated by Heilbronner and Wiberg³ in arguing the photoelectron spectrum of 1.

References

(1) Müller, B.; Bally, T.; Pappas, R.; Williams, F., "Spectroscopic and Computational Studies on the Rearrangement of Ionized [1.1.1]Propellane and Some of its Valence Isomers: The Key Role of Vibronic Coupling," J. Am. Chem. Soc. 2010, 132, 14649-14660, DOI: 10.1021/ja106024y

(2) Hiberty, P. C., "Vibronic coupling: Cage-breaking cascade," Nat. Chem. 2011, 3, 96-97, DOI: 10.1038/nchem.971

(3) Honegger, E.; Huber, H.; Heilbronner, E.; Dailey, W. P.; Wiberg, K. B., "The PE spectrum of [1.1.1]propellane: evidence for a non-bonding MO?," J. Am. Chem. Soc., 1985, 107, 7172-7174, DOI: 10.1021/ja00310a068

InChI

1: InChI=1/C5H6/c1-4-2-5(1,4)3-4/h1-3H2
InChIKey=ZTXSPLGEGCABFL-UHFFFAOYAJ

2: InChI=1/C5H6/c1-4-3-5(4)2/h1-3H2
InChIKey=ZNKWTJLYBOAVHI-UHFFFAOYAT

3^.+: InChI=1/C5H6/c1-4-5(2)3/h1-3H2/q+1
InChIKey=BVWPXIKADZQKEJ-UHFFFAOYAU

The nature of the bridgehead-bridgehead bond in [1.1.1]propellane 1 poses an interesting quandary. The bond involves two inverted carbon atoms, whose hybrids should point away from each other. The internuclear region has in fact much less electron density than for an ordinary C-C bond. Nonetheless, the molecule is stable and the C-C bond is estimated to have a strength of about 6 kcal mol^-1.

Shaik and Hiberty¹ have now proposed that the central C-C bond of [1.1.1]propellane is a charge-shift bond. In classical valence bond theory, we have three configurations for a bond: the covalent structure A↑↓B ↔ A↓↑B, and the two ionic structures A↑↓ B and A B↑↓. The description of a typical covalent bond is dominated by the covalent VB structure with a little bit of the ionic structures mixed in. A charge-shift bond is one where the resonance energy due to the mixing of the covalent and ionic structures mostly accounts for the stabilization of the bond.² Just such a case is found in the F-F bond, and also to for the central C-C bond of [1.1.1]propellane!

References

(1) Wu, W.; Gu, J.; Song, J.; Shaik, S.; Hiberty, P. C., "The Inverted Bond in [1.1.1]Propellane is a Charge-Shift Bond," Angew. Chem. Int. Ed., 2008, ASAP DOI: 10.1002/anie.200804965

(2) Shaik, S.; Danovich, D.; Silvi, B.; Lauvergnat, D. L.; Hiberty, P. C., "Charge-Shift Bonding – A Class of Electron-Pair Bonds That Emerges from Valence Bond Theory and Is Supported by the Electron Localization Function Approach," Chem. Eur. J., 2005, 11, 6358-6371, DOI: 10.1002/chem.200500265

InChI

1: InChI=1/C5H6/c1-4-2-5(1,4)3-4/h1-3H2
InChIKey=ZTXSPLGEGCABFL-UHFFFAOYAJ