Quantification of the various contributors to rate enhancement in nucleophilic strain releasing reactions

Since cyclopropanes are much more reactive than cyclobutanes despite their nearly identical strain energy, it has become clear that rate enhancement in cyclopropanes is partly due to strain release but also partly due to an additional factor about whose nature there is no consensus. Activation and equilibrium energies for a series of nucleophilic reactions of MeO^-, MeS^-, MeNH^-, Me₂N^-, and MePH^- with strained rings ranging from epoxide to aza-cubane were computed at the HF/6-31+G* level. Using the Marcus equation, in combination with the computed intrinsic barrier for the identity reactions of the same nucleophiles with the strain free reference compounds (e.g., MeO^- with Me-O-Me and Me₂N^- with Me₃N), enabled a quantitative determination of the individual contributions of the partial strain release and the additional factor to the overall lowering of the transition state energy. Analysis of the data reveals the following: (a) There is no contribution of the additional factor to rate enhancement in four membered rings for first row elements (O and N) and only a small contribution (∼2 kcal) for second row elements (S and P). This is to be compared with a contribution of 7-17 kcal for three membered rings. (b) A significant synergistic effect is observed. Thus, in housane, for example, the additional factor amounts to 12.7 kcal which is more (by nearly 5 kcal) than the sum of the individual contributions of the isolated three and four membered rings. (c) The magnitude of the additional factor was found to be Periodic Table row dependent.