4393
Communications to the Editor bands, with slight relative intensity differences, as the 457.9-nm spectrum." (1 1) T. G. Spiro, Princeton University, private communication, 1979. (12) E. Konig and E. Lindner, Spectrochim. Acta, Part A, 28, 1393 (1972).
Richard F. Dallinger, William H. Woodruff* D r p a r t n i r n t of Chemistry, T h e Unicersity of Texas a t Austin Austin, T e x a s 7871 2 Receioed M a r c h 26, I979 Io
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Substituent Effects in Concerted Reactions. .4 Nonlinear Free-Energy Relationship for the 3,3-Shift and the Diels-Alder Reaction 000
Sir:
Prediction of absolute rate constants for and substituent efl'ects on concerted peri lic reactions is useful in synthesis. tiouever. a Hammett LFEK approach is inappropriate since transition-state structure can change dramatically with substituents. For instance, the transition-state structure in 3,3 shifts of variously substituted I ,5-hexadienes as deduced from xcondary deuteriuin isotope effects varies substantially betseen the noncuncertcd alternatives resulting from either C I C ~ bond breaking or C 1 C(, bond making.' This relationship can be quantified using the simplest equation for a three-dimensional energy surface with a saddle point, namely, AG = a x hj' L'XJ' d . and the proper boundary conditions. If the reactant is at x = 0, J = 0 , then AG = 0 and d = 0. If, a t x = I . J = 0, the pure bond-making transition state is achieved, then (I = AG*(BM). If. at x = 0, y = I , the pure bondbreaking transition state is achieved, then b = AG*(BB). If the product is a t an average position x = p , y = p , then c = [ ( ~ % ~ , ~ , /-p AC;*(BB) ) - AG*(BM)]/p. Setting the partial Jcrivativcs of AG' with respect to x and t o y equal to zero allows determination of t he t ransi t ion-sta te posit ion which upon subbtitution in the original equation gives
+ +
+
where p is an empirically determined parameter. Remarkably, for all of the 3,3 shifts, p is a constant and equal to I .5. The calculated and experimental AG* values are shown in Table I . The significance o f p in eq 1 is that it adjusts the magnitude of AG* and therefore represents the extent of coupling of the nonconcerted alternatives; it is the non-LFER equivalent of the Hammett p . Highly notable exceptions to the simple formula are the 3,3 shift of cis- 1 ,2-divinylcyclopropane3 and of allyl silyl enol esters4 (see Table I). A reasonable rationalization for the first is the possible strong coupling of the vinyl groups and the 7r-like electrons of cyclopropane ring in the ground state. The second may be due to inordinant stabilization of the bond-making alternative by, if not actual rearrangement of, the MeISi group. Thus, exceptions to the simple formula may indicate reactions requiring special scrutiny. While derived from a crude model, eq 1 makes chemically reasonable predictions about the response of AG* to substituent changes that affect AG,,,, AG*(BM), and AG*(BB). However, careful scrutiny of eq 1 reveals that it can be applied to neutral or exergonic reactions but not to highly endergonic ones unless certain terms are redefined.'
'I'ahlr I . A(; V;IIUCI ~t 523 K for Various 3.3 Shifts - ... -
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41 (' 35.5: 31/ 3.3-dicyLino32p r /rrc,rJ - 3 ,4-d I Illel 11) I 39h I / i r l a - 3.4-d i plic in! I31' i i \ . I ,2.di\iii~lc!il~)bul.iiic 28J .i11>1 L i i i ! l ether 3 3 "1 JIIJ I pllcn) I crhcr 42" ~l11!1 1 L . 'clatc 45J ~ ~ ~ - l ~ 2 - ~ i ~ i 1 1 ~ l c ~ c l ~ 1 ~ ~ r21' u~~~i1ic .Ill! I \llJI cnol .Icct,llc I hc.il/iiiol for the strain of a cis-1,2-divinyl relationship; s e e j . For a boat diyl. -7 kcal/n-,ol dcstabili7ation over c h i i is Libsullied ' ' I 1 It bchu1l.r and G . W . Murphy, J . An?. Chon?,Soc., 72, 3 155 (1950). ' I Calculated liccording to S. u'.Benson, "Thcrinoiticiiiic,il Kinetics' . 711dcd , It iley. h e w York, 1976; these values Lire a t 298 K . (' For a review. see S . J . Rhoads and R. N . Ra\vlins. Org. /
