Schleyer and Houk1 offer a provocative paper examining the reference compounds that one chooses when trying to evaluate such concepts as ring strain energy and aromaticity. I discuss this at length in Chapter 2 of the book, focusing on the isodesmic, homodesmotic, and group equivalent reactions.

Their work starts with the isodesmic reaction

CH3CH2CH3 + CH4 → 2 CH3CH3

and note that this reaction is endothermic by 2.83 kcal mol-1. They argue that 1,3-dialkyl interactions are stabilizing, and call this effect “protobranching”.

Gronert2,3 has recently described the counterargument – that 1,3-dialkyl groups are repulsive – but whether the interaction is attractive or repulsive is not my concern here. Let’s proceed assuming that protobranching is in fact stabilizing.

Schleyer and Houk demonstrate that the stabilization of protobranching is nicely additive. In Table 1 are simple bond separation (isodesmic) reactions of straight-chain alkanes and cycloalkanes. This can then be extended to argue for why branched alkanes are more stable than their straight-chain analogues – namely, branched chains have more 1,3-dialkyl interactions and these are stabilizing. They note that the group separation reaction of iso-butane is more endothermic than that of pentane, yet the difference is neatly ascribed to protobranching.

Table 1. Energy of reactions and energy per protobranch (PB) using experimental heats of formation.

 

ΔH

# PB

E per PB

CH3CH2CH3 + CH4 → 2 CH3CH3

2.83

1

2.83

CH3(CH2)2CH3 + 2 CH4 → 3 CH3CH3

5.69

3

2.84

CH3(CH2)3CH3 + 4 CH4 → 6 CH3CH3

14.10

5

2.82

(CH2)6 + 6 CH4 → 6 CH3CH3

7.73

6

2.76

CH(CH3)3 + 2 CH4 → 3 CH3CH3

13.65

6

2.58

Now the interesting aspect is when this concept of protobranching is applied to ring systems. The conventional (homodesmotic) reaction for cyclopropane is

(CH2)3 + 3 C2H6 → 3 CH3CH2CH3 ΔH = -27.7 kcal mol-1

Schleyer and Houk argue that protobranching is not balanced in this reaction, and the consequence is that since propane is stabilized by about 2.8 kcal mol-1, the reaction energy should be reduced by 8.4 kcal mol-1. Thus the ring strain energy (RSE) of cyclopropane is 19.3 kcal mol-1. This is essentially the value obtained when one employs the isodesmic reaction to evaluate the RSE of cyclopropane, namely

(CH2)3 + 3 CH4 → 3 C2H6 ΔH = -19.2 kcal mol-1

And this isodesmic reaction has balanced protobrancing (none!) on both sides. The reaction that balances protobranching (two on each side) for obtaining the RSE of cyclobutane is

(CH2)4 + 2 CH4 → 2 CH3CH2CH3 ΔH = -21.0 kcal mol-1

Protobranching corrections need also be made to the question of aromatic stabilization energy or resonance energy of benzene. For example, since cyclohexane is invoked as one of the reference compounds in the following reaction, the resulting energy must be corrected for six protobranching interactions.

2 C2H4 + (CH2)6 → (CH)6 + 3 C2H6

The question now becomes “Is protobranching real and do we need to correct for it?” Further studies should be performed.

References

(1) Wodrich, M. D.; Wannere, C. S.; Mo, Y.; Jarowski, P. D.; Houk, K. N.; Schleyer, P. v. R., "The Concept of Protobranching and Its Many Paradigm Shifting Implications for Energy Evaluations," Chem. Eur. J. 2007, 13, 7731-7744, DOI: 10.1002/chem.200700602

(2) Gronert, S., "Evidence that Alkyl Substitution Provides Little Stabilization to Radicals: The C-C Bond Test and the Nonbonded Interaction Contradiction," J. Org. Chem., 2006, 71, 7045-7048, DOI: 10.1021/jo060797y.

(3) Gronert, S., "An Alternative Interpretation of the C-H Bond Strengths of Alkanes," J. Org. Chem., 2006, 71, 1209-1219, DOI: 10.1021/jo052363t.