PMO theory suggests that the effects of substituents on the rate of the Diels-Alder reaction between ethylene and 1,3-butadiene cannot be explained on the basis of a synchronous mechanism. Calculations are reported, using the RHF, UHF, and CI versions of MNDO and AMI, for the Diels-Alder reactions of 1,3-butadiene with ethylene, acrylonitrile, maleonitrile, fumaronitrile, and 1 , I -dicyanoethylene. The results confirm the PMO conclusions, indicating unambiguously that the reactions involving the cyanoethylenes cannot be synchronous. The evidence suggests that Diels-Alder reactions in general proceed via very unsymmetrical transition states, close to biradicals in structure and with energies differing little from those of the corresponding biradicals. The regioselectivities and rates of Diels-Alder reactions can be predicted on this basis, more simply and more reliably than they can in terms of frontier orbital theory. The mechanism of the simplest example. Le., the reaction of ethylene with butadiene, remains uncertain. The mechanism of the Diels-Alder (DA) reaction has been the subject of major interest and controversy, ever since it was discovered 60 years ago.’ The chemical evidence seemed initially to favor a two-step2 mechanism, involving a biradical or zwitterionic intermediate, since the regioselectivity of DA reactions can be interpreted very effectively on this basis (see below). It was, however, recognized that the observed stereochemistry is difficult to explain in such terms, DA reactions almost invariably involving exclusive cis addition to the dienophile. In 1938 Evans and Warhurst) pointed out that the cyclic transition state (TS) involved in a synchronous2 mechanism should be analogous to benzene and hence highly resonance stabilized. They suggested on this basis that DA reactions are in fact synchronous, unlike analogous dimerizations of olefins where the TS would be an analogue of cyclobutadiene. While this work was largely overlooked as a result of World War I1 and while good evidence for a nonconcerted* mechanism was later presented by Woodward and kat^,^ the investigations of pericyclic reactions by Woodward and HoffmannS revived the synchronous mechanism, and most organic chemists have assumed in recent years that DA reactions in general are not merely concerted2 but also synchronous. While the stereospecificity of DA reactions certainly suggests that they are concerted, this argument is not conclusive. The same would be true for a two-step mechanism if the intermediate biradicals or zwitterions collapse to the product faster than they isomerize by internal rotation. Several lines of evidence do, however, show that both of the new bonds are formed to significant extents in the TSs of certain specific DA reactions. These, and the properties involved (in parentheses), are as follows: (a) DA reaction of furan with maleic anhydride6 (kinetic isotope effects); (b) reverse DA conversion of dibenzotricyclo[2.2.2]octadiene to anthracene and ethylene’ (kinetic isotope effects); (c) DA reactions of diphenylisobenzofuran with methyl and menthyl furmarates8 (induced optical activity); (d) DA reactions of anthracene and ‘University of Texas at Austin. 1 University of Barcelona. its benzo derivatives with maleic anhydride’ (comparison of rates with localization and paralocalization energies). However, contrary to claims in the original paper^,^-^ this evidence does not show that any of the reactions in question are synchronous. The arguments to this effect have been given in detail elsewherelo and so need not be repeated here. The only new evidence, an addition” to (c), is also inconclusive.’* On the other hand, comparison of the rates of the DA reactions of 1,3( I ) Diels, 0.; Alder, K. Chem. Ber. 1929, 62, 554. (2) Problems have been caused in the past by loose terminology, the term “concerted” in particular having been used with a variety of meanings. The terminology used here, which now seems to be gaining general acceptance, is as follows. A concerted reaction is one which takes place in a single kinetic step. A two-step reaction is one which takes place in two distinct steps, via a stable intermediate. A synchronous reaction is a concerted reaction in which all the bond-breaking and bond-forming processes take place in parallel, all having proceeded to comparable extents in the TS. A two-stage reaction is concerted but not synchronous, some of the changes in bonding taking place mainly in the first half of the reaction, between the reactants and the TS, while the rest takes place in the second half, between the TS and the products. The new features are the precise definition of the term concerted and introduction of the term two-stage. The latter seems to have been first suggested by Goldstein and Thayer (Goldstein, M. J.; Thayer, J. L., J r . J . Am. Chem. Soc. 1965, 87, 1925). (3) Evans, M. G.; Warhurst, E. Trans. Faraday SOC. 1938,34,614. Evans, M . G. Ibid. 1939, 35, 824. (4) Woodward, R. B.; Katz, T. Tetrahedron 1959, 5, 70. (5) Woodward, R. B.; Hoffmann, R. Angew. Chem., Int. Ed. Engl. 1969, ( 6 ) Seltzer, S. J . Am. Chem. Soc. 1965, 87, 1534. (7) Taagepera, M.; Thornton, E. R. J . Am. Chem. SOC. 1972, 94, 1168. (8) Tolbert, L. M.; Ali, M . B. J . Am. Chem. SOC. 1981, 103, 2104; 1982, (9) Dewar, M. J . S.; Pyron, R. S. J . Am. Chem. SOC. 1970, 92, 3098. ( I O ) Dewar, M. J. S.; Pierini, A. B. J . Am. Chem. Soc. 1984, 106, 203. ( 1 1 ) Tolbert, L. M.; Ali, M . B. J . Am. Chem. Soc. 1984, 106, 3804. (12) The earlier criticisms’0 apply equally ta.this work. The experimental results were explained in terms of compensation between two opposing steric effects. There is no reason to suppose that the cancellation may not be almost exact in any given case. The experiment by Tolbert and Ali was what may be termed a “one way” experiment, Le., an experiment with two possible outcomes, one of which leads to a definite conclusion, whereas the other does not. 8, 781. 104, 1742; 1984, 106, 3804. 0002-7863/86/ 1508-577 1$01.50/0