Published: May 16, 2011 r2011 American Chemical Society 4973 dx.doi.org/10.1021/jo200648h | J. Org. Chem. 2011, 76, 4973–4979 ARTICLE pubs.acs.org/joc Quantifying Asymmetry in Concerted Reactions: Solvents Effect on a DielsÀAlder Cycloaddition Inbal Tuvi-Arad* ,† and David Avnir* ,‡ † Department of Natural Sciences, The Open University of Israel, Raanana 43107, Israel ‡ Institute of Chemistry and The Lise Meitner Minerva Center for Computational Quantum Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel b S Supporting Information ’ INTRODUCTION The original WoodwardÀHoffmann (WH) rules 1 were for- mulated for concerted pericyclic reactions in terms of strict symmetry demands. For the DielsÀAlder (DA) reaction, this implies that the two new bonds are formed in a synchronous manner, preserving a mirror symmetry that bisects the co-aligned olefin and diene. However, this ideal situation is rarely realized either because the olefin and diene do not approach each other in an ideally symmetric manner, or because the solvent induces symmetry distortions, or because substituents scramble that symmetry. WH related to that issue, 1À3 for instance, “A slight perturbation, say substitution by a methyl group, may destroy total symmetry, but cannot be expected to change dramatically the mechanism of a reaction.” 1 We propose a more realistic way of addressing such situations: while WH regard the addition of a methyl as a potential for destruction of total symmetry, we suggest that substitution retains some of the original symmetry, where the word “some” relates to quantification of the degree of symmetry content. Such an approach allows one to establish quantitative relations between the degree of distortion from the ideal symmetry and reactivity. Asymmetry of nuclei geometry in cycloadditions has been evaluated through a parameter termed “asynchronicity”, defined as the difference between the lengths of the new forming bonds at the transition state (TS). 2À4 Its use to describe asymmetry is based on the assumption that distortion of the nuclei geometry is intimately related to a distortion of the reacting π orbitals. Yet these specific bond-length changes are only part of a multitude of structural changes that take place in the whole reacting molecules; practically all bond lengths and bond angles vary, and all are therefore relevant to the reaction analysis and can influence the symmetry of the orbitals. As the WH approach focuses on symmetry as the leading structural feature, we propose that a symmetry measure that takes into account all bond lengths and angles is inherently suitable for analyzing symmetry deviations in reactions governed by the WH rules. A measure of symmetry, the Continuous Symmetry Measure (CSM) 5À7 and the related measures of chirality 8 and of shape, 9À12 which were developed in recent years, have been applied successfully in many symmetry- related studies. 13À16 The measure spans from zeroÀthe mole- cule is symmetricÀto higher values for distorted symmetries (up to 100 in extreme cases). Examples of its use include correlations between tetrahedral symmetry measures and the allowedness of d-d spectral transitions 17 or between NMR chemical shifts 18,19 and more. The CSM method has also been applied to study chemical reactions. 20,21 Thus, in a recent study we applied the CSM to follow the reaction path of the cisÀtrans isomerization of diazene and its isotopomers 22 and developed the concept of symmetry profile of a reaction, a plot that shows the changes in symmetry along the intrinsic reaction coordinate (IRC). Received: March 28, 2011 ABSTRACT: We propose the notion that if asymmetry characterizes a concerted reaction, a quantitative treatment in terms of continuous symmetry can bridge the gap between the WoodwardÀHoffmann (WH) rules, originally formulated for symmetry-idealized unsubstituted reactants, and the fact that these rules hold for a much wider scope of reactions. Instead of focusing on symmetry conservation along the minimum energy path, we suggest that the distortion with respect to the original expected symmetry must attain a certain minimal value, not necessarily zero. To demonstrate this approach we studied the effect of solvents on the symmetry and reactivity of the classical [4 þ 2] DielsÀAlder cycloaddition of (E,E)-1,4-dimethoxy-1, 3-butadiene with tetracyanoethylene, revealing the predictive value of this approach. Calculations of the enthalpy of activation and the charge separation at the transition state (TS) predict increased reactivity with the polarity of the solvent. The symmetry measure is in excellent correlation with the enthalpy of activation and the charge separation at the TS, indicating the higher reactivity of the more symmetric case, thus quantifying the main teaching of the WH rules. The advantages of using a global structural parameter that takes into account all geometrical parameters, i.e., the symmetry measure, over specific ones (e.g., asynchronicity) are discussed.