John P. Lowe The Pennsylvania State University University Park, 16802
Is This a Concerted Reaction?
If an organic chemist is asked to define what he means by a "concerted" reaction, he is likely to say that a reaction is concerted if two things happen a t once-most typically, if some bond undergoes breakage while a second hond is formed. If the same chemist is presented with a sketch such as that shown in Figure 1 and asked, "Does this potential energy profile correspond to a concerted reaction?," he is likely to say, "No. That reaction goes through an intermediate and therefore is not concerted." The point of this paper is that these two usages of the term "concerted" are not alwavs We favor . eaoivalent.' . the former of these two meanings. BC AB + C. Consider an elementan, example: A In Figure 2 is sketched the co&only chosen coordinate axis system for this reaction, assuming that A, B, and C are collinear. Any point in this Figure defines an AB and a BC distance, so that any (collinear) evolution of the system can be followed by the motion of a single point in the plane of the axes. For instance, when the point is in the region labeled "reactants," the B-C distance is quite short (within a vibrational amplitude of Re for BC) and the A-B distance is greater than some fairly large value. Now, if the reaction proceeds by formation of an A-B hond with simultaneous breaking of the B-C bond, the AB distance must decrease while the BC distance increases. In that case the point will follow a curved trajectory (or "reaction path") something like that labeled "concerted in Figure 2. o n t h e other hand, if the AB hond formsfirst and-the BC bond commences breaking afterwards, the point will follow the intersecting-straight-line trajectory labeled "nonconcerted." Because the familiar collinear D + Hz reaction is associated with a curved trajectory, we would say that i t is concerted in the breaking and forming of bonds. Notice that we are able to make this statement without considering whether the reaction inuolves an intermediate. In short, the term "concerted has been used here to give information about the projection onto the plane defined by the coordinate axes of the least-energy path over the energy surface linking reactants and products. I t tells us nothing about the presence or absence of energy minima along this potential energy profile. An important point is that the word "concerted" as used here is meaningless unless we state (or imply) what the two processes are that occur simultaneously. (This is equivalent to specifying the coordinate axes to which the reaction path will he compared.) In all but the simplest reactions' there are a variety of bonds breaking and forming, angles changing, and internal rotations occurring. It is quite conceivable that a reaction could he concerted in some of these changes but not in others. Let us refer to the processes which are specified to be concerted or nonconcerted as referenceprocesses.
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'For detailed discussions of various usages of the term "concerted" see Andrist, A. H., J. Olg. Chern., 38. 1772 (1973); Baldwin, J. E., and Fleming, R. H., Fortseh. Chem. Famehung, 15, 281 (1910); Baldwin, J. E., Andrist, A. H., and Pinschmidt, Jr., R. K.,Accounts Chem. Res., 5,402 (1972). ZHoffmann, R., and Woodward, R. B., J. Amer. Chem. Soc., 87,2046 (1965). Salem, L., J.Arner. Chern. Soe., SO, 553 (1968).
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re~ctont
product
Reoction Coordinate Figure 1. An idealized reaction potential energy proliie
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Reoctonts
Ii
distonce A-B
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1 I I i i
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Products
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B-C distance Figure 2. Coordinate axes for collinear nuclei A. B, and C undergoing the reaction A + BC AB + C.
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In the above example, our reference processes have been the hreaking of the BC bond and formation of the AB hond. However, it is obvious how the argument can be generalized to any two convenient processes, such as the formation of two different bonds in a Diels-Alder addition. Concertedness in such processes has been discussed earlier.2.3 Salem3 has published diagrams similar to Figure 2 which contrast concerted and nonconcerted Diels-Alder reactions. For reference processes, Salem chose overlap changes between certain orbitals rather than distance changes, hut the essential meaning of the term "concerted" is the same. Suppose the reaction profile for the (collinear) reaction A + BC AB C does in fact have a dip like that in Figure 1, and that this dip is of a nature to lead to formation of a long-lived intermediate. We can describe this situation by saying that the reaction proceeds in two steps, or proceeds through an intermediate. These terms give information about the potential energy profile hut in themselves tell us nothing about its projection on the plane of any axes. Observe that the statement that a reaction proceeds through an intermediate, or that it is a step-wise
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reaction, is meaningful without specifying a n y reference processes. In this regard i t is quite different from t h e statement t h a t a reaction i s concerted. It is natural t o have some difficulty with t h e idea t h a t a reaction c a n proceed in two steps a n d still h e concerted. Certainly, t o many chemists, t h e idea t h a t a two-step reaction is nonconcerted seems right. And i t is right if we define t h e reference processes t o be identical t o t h e changes which occur in-the separate steps. For example, if our A BC reaction proceeded through a n intermediate, we could choose our reference process t o be "partial formation of the AB hond a n d partial breaking of t h e B C bond." T h e other reference process would b e "completion of formation of the AB hond a n d completion of breaking of t h e BC bond." T h e n t h e two-step reaction would indeed he nonconcerted i n these two reference processes since, by design, one is finished before t h e other starts. Thus, a two-step (or even a one-step) reaction c a n always b e forced into being nonconcerted if we choose t h e reference processes t o t h a t end. B u t such reference processes a r e not necessarily useful for t h e usual chemical purposes, such a s application of orbital symmetry a r g u m e n k 4 Several classes of reaction mechanism can be envisaged 1) The reaction proceeds in one step and is concerted in the reference processes relevant to symmetry control (which we shall call relevant reference processes). Electronic symmetry control is expected in many such reactions. Simple electmcyclic reactions are thought to fall into this category.' 2) The reaction proceeds through an intermediate, but is eoncerted in the relevant reference processes. We might imagine, for example, a sigmatropic shift which passes through an intermediate wherein a hydrogen has partially broken the bond to its old site and partially formed the bond to its new site. The cancertedness of these processes promotes orhital symmetry control regardless of the lifetime (or even the existence) of the intermediate. Therefore, the appearance of symmetry control in a reaction cannot he taken as proof that the reaction does not go through some intermediate. 3) The reaction proceeds in one step but is not concerted in the relevant reference processes. Such a reaction should not be controlled by orbital symmetry. But the reaction may be so fast that nuclear scrambling is incomplete so that the product
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configuration bears a relation to the reactant configuration. Such relations between configurations may coincidentally agree or disagree with expectations of orbital symmetry arguments. 4) The reaction proceeds through an intermediate and is also nonconcerted in the relevant reference processes. An example is s reaction which passes through a diradieal intermediate. Here the first step corresponds to a change in one of the relevant reference processes (breaking of a bond) and the other step involves a change in the other reference process (forming of a bond). Here the existence of an intermediate and the absence of electronic symmetry control are closely connected. Again, however, it is possible for such reactions to exhibit stereaseleetivity if the intermediate is short lived in comparison to reorientation times or if steric effects block certain orientations. In summary, two kinds of terminology exist which contain qualitative information5 about reactions. Terms like "stepwise" a n d "intermediate" describe t h e nature of t h e potential energy profile for t h e minimum energy pathway. "Concerted" a n d "nonconcerted" concern t h e reaction path's degree of curvature compared t o specified axes. These are independent pieces of information, a n d i t is not generally safe t o assume t h a t a reaction which proceeds through a n intermediate is ipso facto nonconcerted with respect t o the reference processes relevant t o orbital symmetry arguments, or t h a t a reaction under electronic symmetry control proceeds i n one step. T h e author wishes t o thank Professors D. A. Seeley, 0. H. Crawford, a n d R. Hoffmann for helpful comments. 4 Woodward, R. B., and Hoffmann, R., Angew. Chem., Int. Ed. Engl., 8,814 (1969).
We avoid the problem of defining the point a t which a reaction path becomes curved enough to be labeled "concerted" rather than "nonconcerted," and also the problem of when a reaction is "one-step" or "two-step." While such problems are of great practical importance to chemists, they are not the issue here, where we seek only to distinguish hetween the qualitative meanings of "eoncertedness" and "going through an intermediate."
