1,3-Dipolar Cycloadditions DOI: 10.1002/anie.200902263 What Controls the Reactivity of 1,3-Dipolar Cycloadditions?** Bernd Engels* and Manfred Christl* computational chemistry · cycloaddition · distortion energy · frontier orbital theory · transition states Intensively investigated and systematically studied by Huis- gen, [1] the title reactions have become an important tool for the synthesis of heterocycles. [2] Like Diels–Alder reactions, they are thermal [ p 4 s + p 2 s ] cycloadditions. All available criteria indicate that the great majority of these processes proceed concertedly. [1c, 3] In spite of the complexity caused by the participating heteroatoms, reaction rates [4] and regiose- lectivities [4c, 5] could be rationalized by means of the frontier orbital theory. The great success of these quantum chemical studies implies that all essential features are understood. This appears to be contradicted by recent investigations of Houk et al. , [6] who examined the reactions of the prototypical 1,3- dipoles 1–9 (Scheme 1) with the dipolarophiles ethene and ethyne by highly accurate theoretical methods. [7] Similar calculations had been performed previously, [8] but these new studies encompass significantly more systems and seem to be of greater precision. Regardless, the new calculations result in trends not discussed before. These new trends are quite remarkable. For example, the activation enthalpies of the ethene and ethyne reactions differ only by less than 2 kcal mol À1 . In addition, they decrease within each of the series 1–3, 4, 5, and 7–9 by about 6 kcal mol À1 , and the values of the reactions of 4 and 7 as well as those of 5 and 8 hardly deviate from each other. The values of the reactions of the nitrilium ylide 6, which are too high by about 6 kcal mol À1 , [9] are the only exceptions to this trend. In particular, the finding that the activation enthalpies of the ethene and ethyne reactions of a given 1,3-dipole are the same is surprising. On the basis of the frontier orbital theory, it would be expected that ethene reacts substantially faster, as its HOMO (À10.5 eV) is higher and its LUMO (1.5 eV) lower in energy than the respective frontier orbitals of ethyne (À11.5 and 2.5 eV, respectively). On the other hand, the similar reaction rates are remarkable also because of the thermodynamics of the ethene and ethyne additions, since the latter are much more exothermic, especially if aromatic products result as in the reactions of 1, 2, 4, and 5. Kinetic measurements employing numerous 1,3-dipoles had shown previously that ethenes and ethynes with the same substitu- ents add at similar rates, and that either ethyne or ethene may be favored only slightly depending on the nature of the 1,3- dipole. [1c] Looking for a rationalization of the results, Houk et al. found only a partial correlation of the calculated activation enthalpies with the calculated reaction enthalpies and that other approaches also do not provide an obvious explan- ation. [10] However, there is an unambiguous correlation between the calculated activation barriers DE ° and the distortion energies DE d ° (DE ° = 0.75, DE d ° = À2.9; R 2 = 0.97). The latter is the energy required to distort the 1,3- dipole and the dipolarophile from their equilibrium geo- metries into the transition-state geometries without allowing any interaction between them. [11] Since the cycloaddends do not interact in this partitioning by definition, the total distortion energy amounts to the sum of the distortion energy of the individual reaction partners. The total activation barrier then is the sum of the total distortion energy and the energy of interaction DE i ° between the cycloaddends in the transition state. Further computations show that substituted derivatives of 3 and 6 as well as additional 1,3-dipoles such as H 2 COO, O 3 , and O = NH À O also fit the correlation. About 80% of DE d ° is shown result from the distortion of the 1,3- dipoles (see below). The absolute value of the interaction energy DE i ° , which always has a negative sign, generally amounts to 32–46 % of DE d ° , but it has significantly higher values in the cases of 8 and 9. A linear correlation has also Scheme 1. Structures of the 1,3-dipoles studied by Houk et al. [6] recently. [*] Prof. Dr. B. Engels, Prof. Dr. M. Christl Institut für Organische Chemie, Universität Würzburg Am Hubland, 97074 Würzburg (Germany) Fax: (+ 49) 931-318-5394 E-mail: bernd@chemie.uni-wuerzburg.de christl@chemie.uni-wuerzburg.de [**] B.E. thanks the Sonderforschungsbreich 630, the Graduiertenkolleg 1221, and his research group for valuable support. Highlights 7968  2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Angew. Chem. Int. Ed. 2009, 48, 7968 – 7970