# Reactivity of propellanes

Why is [1.1.1]propellane considerably less reactive than either [2.2.1]propellane or [2.1.1]propellane as illustrated in the hydrogenation reactions pictured below? The heat of hydrogenation reflects the thermodynamic difference in energy between starting material and product. It is a thermodynamic measure of the difference in stability of the products and reactants. Reactivity, on the other, hand is related to kinetics, a reflection of the activation energy involved in the rate determining step.

Cyclopropane and cyclobutane have roughly the same strain energy (SE=27.5 and 26.3 kcal/mol respectively). To a first approximation, the strain energy of a polycyclic system is the sum of the strain energies of the individual rings in the system.

Each of the 3 starting materials contains a total 3 (cyclopropane plus cyclobutane) rings. Since the SE of cyclopropane ~ cyclobutane, we would therefore expect the SE's of the 3 starting materials to be similar and larger than the SE's of the less strained products. In agreement with this expectation the calculated SE's of the 3 starting materials are 109, 106 and 103 kcal/mol respectively (see fig. 2.2 on p. 37 here), indeed very similar.

The SE's of the final products are 17, 41 and 62 kcal/mol respectively (ref, see Table 3.2 on page 72).

If we calculate the strain released during hydrogenation it is in the same order and very close to the actual heats of hydrogenation reported in your figure.

• $\mathrm{109-17=92}$ kcal/mol
• $\mathrm{106-41=65}$ kcal/mol
• $\mathrm{103-62=41}$ kcal/mol

Clearly, in this series of propellanes the heat of hydrogenation is a measure of the strain released in the process.

Because bicyclo[1.1.1] pentane (the right-most product) has a much higher SE than either of the two other hydrogenated products, the heat of hydrogenation given off when it is formed will consequently be much less.

[1.1.1]propellane is an extremely reactive compound (see here for example). Comparing the thermodynamic heats of hydrogenation in your series of compounds cannot be used to meaningfully predict the kinetic reactivity of these compounds.

• The concept of ring strain needs a reference system how it is calculated. This can be chosen completely arbitrary and the numbers have no meaning whatsoever. Strain cannot be measured, too. – Martin - マーチン Sep 1 '15 at 9:13
• Strain energies have been experimentally measured and reported in countless publications. The same techniques used to measure resonance energies can be used here as well; for example heats of combustion and heats of hydrogenation. Typically, a strain-free reference is chosen. – ron Sep 1 '15 at 13:36
• I took the last statement from the reference you provided, when I tried to find out what theses numbers actually mean. I did not have enough time to dig in deeper into the matter, i.e. finding out what the most common reference is. Since you have used this concept a couple of times before, I trust your expertise: What would be the or a strain-free reference for [2.1.1]propellane? – Martin - マーチン Sep 1 '15 at 14:31
• Probably something like 2-methylhexane adjusted for gauche interactions, etc. – ron Sep 1 '15 at 17:29