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and M. Kat& Tetrahedron Lett., 1515 (1971); 0. L. Chapman and D. S. Weiss. Org. Photochem., 3, 197 (1973). For a preliminary account, see E. Dunkelblumand H. Hart, J. Am. Chem. Soc.,99, 644 (1977). For previouspapers, see H. Hart,T. Miyashi, D. N. Buchanan, and S. Sesson. J. Am. Chem. SOC.,98, 4857 (1974); H. Hart and M. Suzuki, Tetrahedron Lett., 3447, 3451 (1975); E. Dunkelblum, H. Hart, and M. Suzuki, J. Am. Chem. SOC.,99, 5074 (1977). For details of the spectrum, and the conformational changes which occur when europium shift reagent Eu(fod)~is added, see E. Dunkelblumand H. Hart, J. Org. Chem., 42, 3958 (1977). Prepared by a modification of the procedure described by E. W. Collington and G. Jones, J. Chem. SOC.C,2656 (1969); see also F. Ramirez and A. F. Kirby, J. Am. Chem. Soc., 75, 6026 (1953). The NMR spectra of the two stereoisomers showed many distinguishing features (for the numbering system, see structure 58). in 58, the LIS slops is much greater for Hll than for Ha. whereas in 5b these slopes are nearly equal. The reason is that H1is "down" in 5a, allowing shlft reagent to a p proach Hll more closely. H1occurs at appeclably lower field in 5b (6 3.17) than in 5a (-2.40) owing to its proximity to the oxygen bridge. In 5b, H1 is easily pulled out of its multiplet with,FH by europium shift reagent, permitting the trans coupling constant ( J = 6 Hz) with H7to be observed. Detailed comparison with the spectra of similar furan adducts'* is consistent with the assignment. lrradlatlon of 4 In an inert solvent such as cyclohexane gave dimers whose structures and mechanism of formatlon wiii be discussed in a separate paper. For related systems with > Jcl0 see S. Kabuss, H. G. Schmid, H. Frlebolin, and W. Falsst, olg. M g n . Reson., 1,451 (1969);M. St.Jacques and C. Vaziri, ibid., 4, 77 (1972). The coupling constants were silghtly different from those of the corresponding protlo compounds, to an extent deflnltely outside the experimental error. For other examples of thls effect, see G. V. Smith, W. A. Boyd, and C. C. Hinckley, J. Am. Chem. SOC., 93, 2417 (1971); J. K. M. Saunders and D. H. Williams, J. Chern. SOC.,Chem. Commun., 436 (1972). P. Chamberlain and G. H. Whitham, J. Chem. SOC.8, 1131 (1969). Analyzed by NMR using the same methods as for the photolnducedaddltions. NMR integration, using the methoxyl protons as a reference, showed that a small fraction of the C2 proton cis to the methoxyl was exchanged, but the product is mainly 3 - 4 . in this case, -50 % of the C7 proton CISto the methoxyl Is also exchanged, owing to the slowness of the addition and the prolongedopportunity for the product to exchange. One cannot, however, strictly rule out the possibillty that some fractlon of the reaction of Iwith methanol may proceed by polar addition to a photoexcited state. For reviews, see P. J. Kropp, Pure Appl. Chem., 24, 585 (1970); J. A. Marshall, Acc. Chem. Res., 2,33 (1969); J. A. Marshall, Sc/ew,170, 137 (1970). For more recent results and additional references, see P. J. Kropp, E. J. Reardon, Jr., 2 . L. F. Gaibel, K. F. Wiillard, and J. H. Hattaway, Jr., J. Am. Chem. SOC.,95,7058 (1973). The addition of CH3COODto transcyciooctene occurs in a stereospecific syn manner, for which a concerted six-centered transition state has been suggested: K. T. Burgoine, S. G. Davles, M. J. Peagram, and G. H. Whitham, J. Chem. SOC.,Perkin Trans. 7, 2629 (1974). Consistent with this notion is the observed isotope effect of -3 for the addition of methanol to adamantene, presumably a more strained alkene
than the trans-2-cycloalkenones 11and 111: J. E. Gano and L. Eizenberg, J. Am. Chem. Soc., 95,972 (1973). There are, of course, recognizedrisks in drawlng concluslons of thls type: A. J. Kresge, D. S. Sagatys, and H. L. Chen, IbM., SO, 4174 (1968). Indeed, in the only other pertinent study on the stereochemistry of this type (27) of reaction, Ramey and Gardner'O obtained circumstantial evidence for enols belng the initlai products. They studled the photoinduced addition of alcohols to l-acetylcyciohexene.The major products were 2-alkoxyI-acetylcyciohexanes,and the elements of RO-H added predominantly (79-80%) trans. NMR and chemical evidence indicated that the initial products were stereol8omBTlc enols which then ketonizedat different rates. However, there was no evldence that the reactions proceeded via a trans intermediate, and the mechanism may be quite different from the reactions we report on here. The same Is true for Z',another reason why we favor the synchronous 2 P. addltlon, T The stereochemistry of Michael additions has not been studied in detail, but examples of syn addltlon,anti addition, and nonstereoseiectiveaddition are known. For brlef discussions, see S. Patai and 2. Rappoport in "The Chemistry of Alkenes", S. Petal, Ed., Wiley-lntersclence, New York, N.Y., 1984, p 464; see also R. A. Abramovltch, M. M. RcgiE, S. S. Singer, and N. Venkatesevaran, J. Org. Chem., 37, 3577 (1972), and references therein. Ail analyses were by Spang Microanalytical Laboratory, Ann Arbor, Mlch. For numbering, see structure in the text. Spectra were determined on a Varlan HA 100 instrument, and ail assignments were confirmed by decoupling. In a control experiment, no adduct could be detected in the absence of light. R. Huisgen and W. Rapp, Chem. Ber., 85,826 (1952). E. W. Qarbisch, Jr., J. Org. Chem., 30, 2109 (1965). Many such spectra were recorded, with varying ratios of substrate to shift reagent. These resuits are consistent with a rigid geometry for the europium complex,13 with large trans coupling constants for 8.0 Hz and JH3,~,( = 7.5 Hz and a small cis coupling constant, 2.0 Hz. Consistent
--
A;
I I
-
with this, & In the unlabeled complex is small (2.0 Hz).13 H. Houp an&. H. Whitham, J. Chem. Soc.8, 164 (1966). These results are conslstent with a rigid geometry for the europium complex, l3 with large trans coupllng constants, JH2,HQ= 8.0 Hz and &,,n,l =
w\ O--;;,7EU
2 H
D
HC
8.0 Hz, and a small cis coupling constant, &,IGc = 3.0 Hz. Consistent with this conclusion is the small value (3.0 Hz) observed for &2s,H3 in the unlabeled ketone.13
Substituted Acetophenones. Importance of Activation Energies in Mixed State Models of Photoreactivity Michael Berger, Eoghan McAlpine, and Colin Steel* Contributionfrom the Chemistry Department, Brandeis University, Waltham, Massachusetts 02154. Received November 7 , 1977
Abstract: The photoabstraction and phosphorescence of triplet acetophenones requires a mixing between zero-order n,T* and T,R* states with interaction energies 2100 cm-I. The extent of mixing ( b z )and the energy separation ( A E ) of the resultant
states are fundamental properties of the molecule and are independent of the phenomena being observed. However, the best expressions for the radiative rate constants (eq 1) and for the reaction rate constants (eq 6 ) differ since no activation energies are involved in the former while there ?re substantial barriers to reaction in the latter. Variations in photoreactivity between compounds are then mainly manifested as activation energy differences and the reactivity of a given compound changes significantly with temperature. On the other hand the radiative rate constants show essentially no temperature dependence although they do differ widely from compound to compound.
Introduction Considerable experimental and theoretical activity has gone into trying to determine the factors which influence the 0002-7863/78/1500-5147$01 .OO/O
photoreactivity of carbonyls with respect to hydrogen abRH -,> C O H R-.Yang and straction (ka),>C=O* c o - ~ o r k e r s ' -have ~ shown that the variations in the reactivities
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k
Figure 1. Reactivity surface at 300 K as a function of bZ,the fractional n,n* character of TI, and of AE, the gap between T2 and TI. The contours
join points of equal reactivity.
of a series of acetophenones at room temperature can be correlated with the proportion of n,a* character admixed in the lowest triplet states (TI) as measured by the radiative lifetimes ( T r a d ) in low-temperature glasses. W a g r ~ e r ~ pointed -~ out that T I and T2 might still be essentially pure a,a*and n,a*, reactivity variation being associated with varying thermal population, Le., Boltzmann factors, resulting from differing AE ET^ - ET^). In the most general case one might envisage TI and T2 as states with mixed n,a* and a,x* characters lying sufficiently close together such that Boltzmann factors might also be important.6 Recently extensive physical measurements at low temperatures have provided further evidence for a mixed state description for the triplet states of aromatic carbonyls and have shown that the amount of mixing can vary not only from molecule to molecule but also depends markedly upon the e n v i r ~ n m e n t . ~It- lcan ~ be rather confusing to envisage variations in reactivity as AE and/or mixing vary. In this paper it is shown how such variations can be considered in terms of a reactivity surface. This leads to a method of treating the data which allows estimations of the relative importance of mixing and of Boltzmann factors. Finally examination of the model suggests refinements which appear to be in general accord with experiment.
Results and Discussion Models. We shall first develop the model along standard line^.^,^ Consider a molecule in which states T I and T2 can be regarded as mixed states of two zero-order states n,a* and a,** such that $ T ~ = b$n,n* + ~ ‘ ( 1- b2)+,,,* and h2= -$*, - b$,,,: where b2 is the fractional n,a* character associated with TI.It is further assumed that reactivity of a state be associated with its fractional n,r* character so that kTI = b2kn,,* and kTz = (1 - b2)k,,,*. In general the observed overall rate constant k is the sum of the individual rate constants, ki, for the states weighted by the fraction of molecules in the respective states,fi. Specifically for the twostate system under consideration here
where AE = ET^ - ET,. Figure 1 shows a plot of the relative rate constant ( = k / k,,,:) as a function of b2 and AE for a temperature of 300 K. The reactivity of a given system is then represented by the corresponding point on the reactivity surface. The surface will be the same for other temperatures except that the AE scale is expanded by a factor of (T/300);Le., for a given b2 and a temperature of 77 K, k will have the same value at AE = 154 cm-1 as it had at AE = 600 cm-’ when the temperature is 300 K. The question then arises whether the points representing a series of reactants are simply scattered on the reactivity
Figure 2. Reactivity surface:on the b?-AE plane, bZis plotted as a function of AE, for interaction energies of 50 and 100cm-I. The resultant reactivity for I VI = 100 cm-l is also shown on the reactivity surpathway face. (-e)
surface or whether they are grouped in some simple systematic fashion. Let Ho and % (=No u) be the Hamiltonians associated with the zero-order states and with the “real” states T I and T2, respectively, where u is the perturbation causing the mixing. It can readily be shown that
+
AE =
ET^ - E.rl = (1 - 2 b 2 ) ( A E o+ A K ) - 4b V-
(2)
In the above AEO = En,+ - E,,,* where E,,,* and E,,,* are while K,,,* = the energies of the zero-order states under SO, ($n,n* I u I@n,a*) and = (A,,*I u I A,,*)are small energy terms whose difference AK can generally be neglected. V = (+,,,,*lul$T,,*) is the interaction energy between the zeroorder states, the absolute value of which has lieen estimated by Hirota7 to be -100 cm-l for a wide range of aromatic carbonyls. This value is reasonable for a vibronic interaction. When b2 is small, then by first-order perturbation theory b = I V l / A E o , while, when b2 is close to unity, d(1- b 2 ) - I V l / A E o . Fortunately in the region where the above approximations are not so good the second term, 4 b w V , in eq 2 makes a dominant contribution to AE and so AE =
[
+ 46-1
1
X VI for
b2 < 0.5 ( 3 )
AE = 21 VI for b2 = 0.5 (zero-order states degenerate)
(4)
for b2 > 0.5
(5)
Thus for a given I V I , AE can be obtainzd as a function of b2 and correspondingly specific values for k can be calculated as AE and b 2 vary as prescribed by eq 3-5. Figure 2 shows LIE plotted as a function of b2 for I VI = 50 and 100 cm-’ and also the resultant map of for I VI = 100 cm-’. It is evident that for reasonable I VI values the reactivity points lie on a fairly well-defined pathway on the upper surface. It is important to stress that Boltzmann effects, which rely only on A E , and mixing effects, which depend on b2,should not be considered as independent quantities since changes in AE result in concomitant changes in b 2 and vice versa. The above model can now be expressed in a form which allows an estimate to be made of the degree of mixing. For a given 1 VI,values of AE are obtained as b2 is varied from 0 to 1 using eq 3-5. These values of AE and b 2are then substituted into eq 1 to obtain values of 5; at two temperatures. In this way the reactivity at one temperature can be graphed as a function of the reactivity at another temperature. This has been done in Figure 3 for temperatures of 300 and 77 K. Consider first the case of no mixing; i.e., 1 VI = 0 cm-I.
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1 Photoreactivity of Substituted Acetophenones
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0
4
I Y
Cn 0
-
I +reaction
1
mixing-
I
reaction4
I
Figure 4. Comparison of reaction from a pure n,r* state with reaction from the two mixed states TI and T2 to show possible activation energy differ-
ences. Figure 3. Relative reactivity at 300 K as a function of the relative radiative constants or reactivity at 77 K for interaction energies of 0,50, 100, and 300 cm-' using eq 1. The experimental points (0)are from ref 2. The inset diagram shows the energy levels of the states corresponding to the three regions A, B, and C in the main diagram. 1 representsp-trifluoromethylacetophenone; 2, acetophenone; 3, p-methylacetophenone; 4, 3,4-di-
methylacetophenone. When n,a* is lowest (region A of diagram), thermal excitation to the upper T,P*state decreases the population in the reactive n,a* state. Since this effect is more pronounced a t higher temperatures, the higher temperature reactivity, k3og falls off more rapidly than the low temperature reactivity, k77. At B the n , a * and x,a* states are degenerate. Here thereis a 50% population in n,a* a t all temperatures so that both k300 and k77 decrease by a factor of 2. In region C, the upper state is the n , a * state accessible b l t h e r m a l population so that.the high temperature reactivity, k300, falls off less rapidly than the low temperature reactivity, k77. In the other limiting situation of I VI large, the real states T2 and TI never approach closely since they can never come closer in energy that 21 VI. This means that the reactivity is only dependent on the nature of the lowest state since the upper state is thermally inaccessible. In Figure 3 the straight line with slope of -1 describes this situation, namely, that k77 and k300 behave identically as the lowest state changes from n,x* to a,a*in nature. It is interesting that for 1 VI 1 300 cm-I the curves are indistinguishable from this limiting case. It is difficult to measure chemical reactivities a t 77 K. However, since the oscillator strength of a radiative transition is dependent on the n,a* character of the triplet carbonyl, it is reasonable to assume that radiative rate constants krad, should also obey a relationship similar to that described by eq 1. In Figure 3, reactivity data a t room temperature obtained by Yang et aL2 is plotted vs. radiative rate constants a t 77 K. It is apparent that a model which simply involves Boltzmann effects, Le., the thermal population of close-lying triplets without any mixing, cannot explain both the room-temperature reactivity and the low-temperature radiative lifetimes. It should also be noted that only when T1 has little n,a* character (region C in Figure 3), do the curves for different I VI values deviate significantly enough from one another to enable meaningful distinctions. By using a reasonable value of I VI the model can be made to reflect the experimental trends (Figure 3). However the reactivity of a state is assumed to depend solely on its n,a* character. The inset in Figure 3 shows that, when b2 is small (region C), TI lies about AE lower in energy than the zero-order n,a* state. The rate constant kTl is written a s b2k,,,* = b 2 A e - E b * / R T where E",,. is the
activation energy associated with a pure n,x* state. Therefore, k T I = Ae-(Ek.**+e)/RTwhere 8 =-RT In b2. For example, for b2 = 0.007 and T = 300 K this gives 0 = 1034 cm-', but for b2 = 0.007 and I VI = 100 cm-l, AE = 1212 cm-'. Thus the model in fact predicts that the height of the reaction barrier for T I , which is largely a,a*in nature, lies below that of the pure n,a* state. This seems unreasonable and arises because the model does not allow for additions to the activation energies stemming from variation in the energies of TI and T2 with respect to the pure n,a* state. One way to do this is to introduce additional energy terms reflecting the displacements of T I and T2 from the zero-order n,a* state so that individual rate constants a r e now kT, = b2kn,,*e-(AE-B)/RT and k T 2 = (1 - b2)kn,lr*eb/RT (Figure 4). The overall abstraction rate constant becomes
Mixing terms do not appear explicitly in eq 6, but it should be remembered that AE and 6 both depend upon V and b2. Also since there is no evidence for energy dependence in radiative processes, the first model, eq 1, should still apply for k r a d . Although the changes may appear to be modest, the two models are quite different in their predictions as to the origin of reaction. For example, according to the first model_for I VI = 100 cm-l and b2 = 0.007, AE = 1212 cm-I, and ka,300 = 0.01. This is the point shown as a cross in Figure 3. Equation 1 shows that only 30% of reaction originates from T2 despite the fact that the latter carries 99% of the n,a* character. On the other hand, when V = 100 cm-' and b2 = 0.012, we obtain A E = 960 cm-', 6 = 9 cm-I, and, according to eq 6, z a , 3 0 0 is again 0.01, but the second model predicts that 99% of the reaction should originate from T2. This is because the higher barrier now associated with TI effectively blocks reaction from this state (Figure 4). A high activation energy for a state that is essentially a,a*in character seems quite reasonable. Despite these apparent differences both models predict decreasing reactivity as the a,a*character of TI increases, and, if a value of -100 c m z l is used for the interaction energy, eq 6 and 1 for ka,300 and k r a d , 7 7 , respectively, still afford a good fit with Yang's experimental data. However, experimentally determinable differences between the models are manifested if the temperature dependences of the reactivities, rather than simply the reactivities at a given temperature, are compared. Model 1 results in rate differences showing up mainly in the temperature independent part, or A factor, of an Arrhenius-type equation ( k , = Ae-Ea/RT). For example, the A factor for ka,300 = 0.01 when I VI = lk0 cm-' is 20 times smaller than the A factor associated with ka,300 =
Journal of the American Chemical Society
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I
i
30
32
34
36
38
40
1 0 ~ ( K1- ’ )~
Figure 5. Variation in the lifetimes of triplet acetophenone in the absence,
open points, and presence of cyclohexane,closed points, as a function of temperature: (A)1 X M p-trifluoromethylacetophenone, (A)with M cyclohexane; (0)1 X M acetophenone,( 0 )with 1.5 1.0 X X lo-* M cyclohexane; (0)1 X M p-methylacetophenone, (H) with 0.25 M cyclohexane. Solvent was acetonitrile.
io-~k,, M-1 s-l at E,, [RH],a M 293 K kcal/mol
a
C 3 cyclohexane; I
0.010 (C)
20.4
Results In order to see which model predicted the experimental behavior best, absolute rate determinations for abstraction by three acetophenones were carried out over a range of temperatures. Yang and Dusenbery2 employed 2-propanol (in benzene) as the hydrogen donor and had variable amounts of cis- 1,3-pentadiene present as quencher. In this study acetonitrile was used as solvent because it affords both ready solubility of the compounds and also long phosphorescence lifetimes in the temperature range under consideration.15 Two hydrogen donors were employed, 2-propanol to form a link with Yang’s work and cyclohexane in case there were any unexpected polar effects with 2-propanol. Typical data are given in Table I and Figure 5. The changes in rate constant for 2propanol follow almost exactly those reported by Yang, while it is obvious that reactivity differences are mainly associated with activation energy changes as predicted by the second model. Some further points may be made. As noted above, in the case of the second model, when T1 is predominantly a,a*in character, reaction originates mainly from the upper state. However, it is important to realize that this comes about not simply from the high n,x* character of T2 but also because of the higher energy barrier to reaction from TI.In contrast, as shown above, in the first model significant reaction can occur from T I even though it is largely x,a*. If it is assumed that reaction arises simply from a pure n,a* state displaced by AEO from a X,T* state (see Figure 4), we obtain
(7) With reference to eq 6, when b2
