Hg(63P,) Photosensitization of 3-Methylbut- 1 -ene Part 2.-Intersystem Crossing and Cyclisation of the 2-Methylbuta- 1,3-diyl Biradical BY DEREK C. MONTAGUE Department of Physical Chemistry, The University, Leeds LS2 9JT Receiued 14th February, 1977 Hg((j3P1) photosensitization of 3-methylbut-1-ene (3MB) yields, among other products, trans- and cis-1,2-dimethylcyclopropane, in a strongly pressure dependent ratio, ranging from 1.37 at 2.5 TOIT to 3.44 at 789.2 Tom. This observation is interpreted in terms of a mechanism involving inter- system crossing and ring closure of both vibrationally excited and thermalised triplet 2-methylbuta- 1,3-diyl (MBD13) biradicals, produced by a 5pp hydrogen migration in excited triplet 3MB. Quanti- tative analysis of the data allows a value for the intersystem crossing rate constant for 3(MBD13)* to be obtained, together with the ratio of dimethylcyclopropanes formed from thermalised MBD13. Addition of oxygen to the reaction system considerably simplifies the observed product spectrum and enables lower limit estimates of the rate constants for intersystem crossing and cyclisation of thermalised triplet and singlet MBD13 respectively, to be derived.The results are compared to those obtained in other systems, and their relevance to the implications of thermochemical and quan- tum chemical analyses of the energetics of propa-l,3-diyl biradicals discussed. In the preceding paper the yields of the products formed by Hg(63P1) photo- sensitization of 3-methylbut-1 -ene (3MB) have been reported. The experimental data were interpreted in terms of reactions of 3-methylbuta-l,2-diyl and 2-methylbuta- 1,3-diyl (MBD 13) biradicals, both initially produced with excess vibrational energy in the triplet state.Application of a stationary-state computer modelling treatment to the postulated mechanism enabled certain isomerization and decomposition rate constants to be derived, and these were in turn used in conjunction with RRKM theory to estimate critical energies for three of the reactions involved. The possible importance of biradicals typified by MBD13 has been recognised for some time. MBD13 itself has been invoked as an intermediate in the structural isomerization of 1,2-dimethylcyclopropane 2 $ (DMCP), and as a precursor to this compound in the photochemical decompositions of both 2,3-dimethylcyclobutanone and 3,4-dimethyl-A1-pyrazoline,5 9 and in the reaction of triplet methylene with b~t-2-ene.~ In this paper attention is focused on the rates of the intersystem crossing and cyclisation processes involved in DMCP formation, both from vibrationally excited and thermalised triplet MBD13.The influence of excitation energy on the stereochemistry of this latter reaction has been recognised, but as briefly noted previously,8 the results now presented demonstrate that the magnitude of this effect is much greater than is generally appreciated. Additional insight into the reaction mechanism has been gained by carrying out photolyses in the presence of molecular oxygen. EXPERIMENTAL Experimental procedure, and the photolysis and analytical apparatus were the same as those described in Part 1.' Oxygen, used as a scavenger in some photolyses, was obtained from the British Oxygen Company, and was used without further purification.277278 3-MET H Y LB U T-1 -ENE PHOTOS ENS IT I Z A TI 0 N RESULTS Both trans- and cis-DMCP are major products in the H S ( ~ ~ P ~ ) photosensitization of 3MB, at all pressures within the range 2.5-790Torr.* The mercury photo- sensitization quantum yields of all the products have been listed in Part 1, over a less extensive pressure range (11.8-764 Torr). Values for the ratio of tDMCP to cDMCP, R, at different experimental pressures are shown in table I. R increases with increasing pressure and appears to approach a limiting value as the pressure tends to infinity.It is however, independent of photolysis light intensity. TABLE VA VARIATION OF THE RATIO tDMCP/cDMCP WITH PRESSURE pressure/Torr pressure/Torr pressure/Torr pressure/Torr pressurelTorr pressure/Torr R R R R R R 2.5 1.37 40.0 1.74 134.9 2.21 254.5 2.64 463.4 3.13 599.0 3.37 5.0 1.39 48.9 1.72 140.8 2.19 274.6 2.77 497.9 3.17 669.8 3.33 10.0 80.8 177.0 305.2 513.5 1.49 1.96 2.38 2.83 3.20 691.7 3.40 aR = tDMCP/( 11.8 86.9 187.3 350.2 536.5 764.4 1.58 2.00 2.43 2.90 3.28 3.48 :DMCP 20.0 1.56 101.1 2.06 2.54 3.03 3.27 3.44 221.2 374.1 542.0 789.2 24.7 127.8 228.8 407.6 548.8 1.65 2.19 2.55 3.03 3.15 37.5 131.5 251.6 451.2 577.5 1.59 2.21 2.66 3.21 3.32 In a second series of experiments various amounts of oxygen were added to several different pressures of 3MB before photolysis, with the result that the yields of all products formed from monoradical precursors in the unscavenged system, e.g.pent-2-ene, were reduced to trace levels, whereas those of DMCP and 2-methylbut- 2-ene (2MB2) were only partially decreased. In addition the spectrum of C2-C4 products, of which buta-1 ,3-diene7 but-2-ene7 but-I-ene and propylene could be positively identified, changed slightly. The small yields of these compounds prevented TABLE 2.-vARIATION OF THE RATIO tDMCP/cDMCP WITH 3MB AND OXYGEN PRESSURES a 3MB/Torr 0 2/Torr R' 204.9 200.5 299.5 397.0 398.2 402.0 398.1 398.2 402.2 500.0 501.4 500.0 498.8 26.8 54.9 75.5 41.2 98.6 113.9 121.7 137.6 151.9 30.5 60.9 86.4 170.4 2.20 2.04 2.23 2.61 2.32 2.25 2.15 2.21 2.14 2.98 2.65 2.57 2.23 a See text for explanation of symbols.* 1 Torr = 133.3 Pa.D . C . MONTAGUE 279 their quantitative assessment with any confidence, however. Minor amounts of 2-methylbut-1-ene (2MB1) and isoprene were also observed. Other higher molecular weight products were undoubtedly formed but no attempt was made either to detect or to identify them. The only data amenable to a meaningful quantitative interpreta- tion are those of the variation of the DMCP geometrical isomer ratio, with changes in the oxygen concentration and overall pressure. Experimental values of this ratio, symbolised as R’ to distinguish it from the ratio of the same products, R, in the absence of oxygen, are given in table 2. They show that for an approximately constant 3MB pressure, increasing the pressure of O2 decreases R’.DISCUSSION Vi brationally excited triplet acyclic mono-olefins produced by Hg(63P1) photo- sensitization can fragment, unless collisionally deactivated, producing mono-radicals, or isomerize by hydrogen atom migration processes proceeding by cyclic transition ~ t a t e s . ~ For 3MB, 5pp isomerization gives vibrationally excited triplet MBD 13, which can subsequently either decompose, undergo spin inversion leading to DMCP by ring closure, or, less importantly, isomerise by a 1 ,Zhydrogen translocation to 2MB 1 and, presumably, 2MB2 in approximately equivalent yields. OXYGEN FREE EXPERIMENTS The extensive variation of R with pressure can be rationalised by postulating first that the rate of intersystem crossing of excited triplet MBD13 to the ground singlet state is sufficiently slow, so that collisional deactivation often occurs prior to PRODUCTS A I k,5! 0, I k, 6 PRODUCTS A I I k , , 10: I 1‘41 * L 1 1 L k M 7 Pf w) L \ 4 I I [\a/] * k, M PRODUCTS FIG.1 .-Reaction scheme for 3(MBD13)*.280 3-MET HY L B U T-1 -E NE P H 0 T 0 SEN S I TI Z A T I0 N spin inversion, and secondly that biradical ring closure becomes more stereospecific as the biradical excitation decreases. Both deactivation and fragmentation of the excited singlet biradical are ruled out at the pressures of these experiments by its rapid rate of cyclisation. * Geometrical isomerization of newly formed excited DMCP serves only to modify the observed values of R, especially at low pressures; it alone cannot provide an explanation for the data, as the rates are too low (vide infra). The fate of excited triplet MBD13 can be discussed in terms of reactions (1)-(lo), schematically depicted in fig.1. '(MBD13)" and l(MBD13) are enclosed in square brackets to indicate that they may not possess an intrinsic stability. Routes to 2MB1 and 2MB2 from 3(MBD13)* and 3(MBD13) have been omitted as they are negligibly s1ow.l If the usual assumptions of the stationary state hypothesis are applied to the concentrations of '(MBD13)*, 3(MBD13), '(MBD13), (tDMCP)* and (cDMCP)*, then a kinetic analysis of the reaction mechanism enables the expression for R shown in eqn (1 1) to be derived. p(1 +a + cm[M] j + pP R = @(I+ a + p[ MI) + P where and a = k4t/k40 = kst/ksC, 6 = kl/kz, p = k9/k4, $ = k10/k5, p = k7/k--6 and o = ks/k6.It would seem likely that eqn (I 1) could only be fitted to the experimental data to yield meaningful information if values for at least four of the seven rate con- stant ratios are known. The inverse half-quenching pressures for geometrical iso- merization of the excited trans- and cis-DMCP formed in reaction (4), p and co, can be estimated by RRKM theory. The calculation was carried out in the same way as those performed previously, 3 using frequencies for the reactants and activated complexes based on those listed by Simons and Rabinovitch,ll and chosen to be commensurate with the Arrhenius A-factors for these rearrangernents.l Similarly critical energies were derived, in the usual way,13 from the measured activation energies. The computed rate constants were converted to the inverse half-quenching pressures p = 0.0110 Torr-l and co = 0.0824 Torr-I, using a calculated collision rate constant of 1.357 x s-l Torr-l (2.517 x 1014 cm3 mol-1 s-l).The magnitudes of p and $ reflect the relative rates of isomerization against cyclisation for excited and thermalised singlet MBD 13 respectively. A comparison of the small yields of 2MB1 with those for DMCP over the experimental pressure range, indicates that p and $ must both be of the order of 0.05. If they are equal then their magnitude is irrelevant, as the term (1 +p)/(l +$) in eqn (12) becomes unity. Their values can be estimated by fitting the variation with pressure of Q, the ratio of the sum of the quantum yields for the isomerization products 2MB1 and 2MB2 to that of DMCP, to eqn (13), which can also be derived from a kinetic analysis of the proposed mechanism.The data used were those tabulated in Part 1 and, as before, it was assumed that reactions (9) and (10) produce eqclivalent amounts of 2MB1 and 2MB2. The same computer modelling approach to that previously employed was used once again.l* lo It was found that good fits could beD . C . MONTAGUE 28 1 found for any value of 6 in the range 30-170 Torr. Thus if 6 = 33.6 Torr as found in Part 1, p = 0.0440 and $ = 0.0514 ; for 6 = 150 Torr, p = 0.0427 and II/ = 0.0554. Satisfactory fits could not be obtained however when either p or $ was set equal to zero. Biradical isomerization must therefore occur, albeit to a minor extent, both from l(MBD13) and l(MBD13)*. As the experimental data are scattered, detailed conclusions should not be drawn from the exact relative magnitude of p and $.Suffice it to say that the near equivalence of these parameters indicates that the energy barriers for isomerization and ring closure of MBD13 must be similar, the difference in the rates of the two reactions being largely brought about by a difference in pre- exponential factors. I I I I J 200 400 600 pressure/Torr FIG. 2.-Variation of Q D ~ P / C D ~ D M C P with pressure. Using the values obtained for p, coy p and $, eqn (11) can be fitted to the experi- mentally observed variation of R with pressure. As p and $ are not only both small but almost equal, their effect is minimal. It was found that the best fits could be obtained by also treating p as a variable parameter.The optimum value derived, 0.115 Torr-l, is within 4% of that calculated by RRKM theory. The optimum values for the other variables are listed in table 3. Fig. 2 shows the best-fit curve computed from these parameters. The effects of neglecting biradical isomerization and interconversion of tDMCP* and cDMCP* were investigated in turn, by equating first p and $, and then, in addition, w and p to zero. Almost equally good fits to282 3-METHY LB UT- 1 -ENE P HOT 0s ENS I TI Z A TI 0 N the data were found, generating the parameter values also listed in table 3 . Clearly a reaction mechanism of the level of sophistication proposed is not strictly necessary. The isomerization reactions (6), (- 6), (9) and (10) have nevertheless been included for the sake of completeness, thereby enabling their minor role to be illustrated. TABLE 3.-oPTIMUM RATE CONSTANT RATlQS AND HALF QUENCHING PRESSURES ’ a B G/Torr olTorr-1 p /Torr-1 P Y 1.368 4.435 150.0 0.0824 0.115 0.0427 0.0554 C 1.368 4.435 151.9 0.0824 0.115 O d 0 “ 1.386 4.451 156.0 0 ” 0 ” O d 0 “ See text for explanation of symbols ; b calculated value, see Text ; C fixed value, see text ; d selected value.The value obtained for 6 is a factor of w 4.5 larger than that derived in Part 1 from an analysis of the overall product yields (33.6 Torr, giving k l = 4.56 x lo8 s-l). Attempts to iit the data here treated using the lower value were entirely unsuccessful, as, it will be recalled, were efforts to explain the quantum yield data discussed in Part 1 using a value of 6 in excess of w 50 Torr.This apparent discrepancy can be resolved, however, if the strong collision assumption, invoked in both kinetic treat- ments of the reaction mechanism, does not necessarily apply, and If the energy barrier for triplet MBD13 intersystem crossing is considerably lower than that for its decomposition by reaction (14) The results from the experiments in which oxygen was added to the pliotslysis mixtures demonstrate that this latter postulate must be correct. They show that the minimum intersystem crossing rate constant for thermalised 3(MBD13) is 3.05 x lo6 s-I, approximately two orders of magnitude lower than that for 3(MBD13)‘k, whereas the rate constant for thermalised 3(MBD1 3) fragmentation, calculated from the computed Arrhenius parameters,1 is at most s-l, some fourteen orders of magnitude lower than its value for 3(MBD13)*.These rate constants illustrate that the rate of intersystem crossing is much less sensitive to the level of internal excitation than is that for decomposition. Thus, while a single deactivating collision of 3(MBD13)* with a bath gas molecule might well reduce the excitation level SO as effectively to prevent fragmentation, the rate of intersystem crossing will only be decreased slightly. The proposed reaction scheme implies that the ratio in which the products tDMCP and cDMCP are formed is dependent on the biradical excitation energy. This means that partially deactivated 3(MBD1 3)* will give these products in a ratio intermediate between a and p.Thus the true mechanism has been simplified by assuming that all triplet biradicals that have undergone a deactivating collision give tDMCP and cDMCP in the same ratio p, a condition that in fact only applies to thermalised biradicals formed by multi-step deactivation. It is a consequence of this assumption that the intersystem crossing rate constant for excited (3MBD 13)’:’, derived using eqn (1 l), is too large, its true value, (4.56 x lo8 s-l), being that measured relative to the decomposition rate constant in Part 1. Several conformations of roughly equivalent stability can be envisaged for triplet MBD13. Twisted configurations rather than the preferred (0,O) orientation of the unsubstituted propa-1,3-diyl biradical l4 are probably favoured as a result of the steric interaction introduced by the CH3 substituents.Even if a structure close to the (0,O) form is adopted, two rotational isomers are possible. The population distribution for these various configurations depends on their relative stabilities and 3(MBD13)* 3 CH3 +CK,CH CH *= CH2. (14)D . C . MONTAGUE 283 the internal energy of the biradical. Steric effects will also influence the course of the cyclisation reaction and the consequent relative proportions of trans- and cis- DMCP formed from each of the conformers present. At high levels of excitation these factors will be less important and it is therefore not surprising that less stereo- specifcity is observed under low pressure conditions where ring closure from non- deactivated biradicals predominates.a represents the relative yields of trans- to cis-DMCP" at the zero pressure limit. Its value is clearly energy dependent and may not be equal to the observed ratio of these products due to their subsequent geometrical isomerization. At the other pressure extreme, p is independent of the initial excitation energy, its value being determined by the relative overall cyclisation rates of those biradical configurations in thermal equilibrium. Thus if 3(MBD1 3)" could be produced in this system with differing initial internal energies, plots of tDMCP/cDMCP against pressure should form a family of curves, all of which approach the same /? value at infinite pressure. Moreover as a and 6 increase and decrease respectively with decreasing internal energy, the curves should not cross.Data from other experimental systems should also fit this hypothesis as long as the bath gases used are equally proficient at deactivating 3(MBD13)*. Results from the reaction of CH2(3B1) with both trans- and cis-but-2-ene do indeed exhibit the predicted b e h a v i o ~ r , ~ ~ but those from the Hg(63P1) photosensitizations of 2,3-dimethyl- cyci~butanone,~ 3,4-dimethyl-Al-pyrazoline and 3-methylpent-4-enal appear at first sight not to conform, in that the plots of tDMCP/cDMCP against pressure intersect that shown in fig. 2. This apparent discrepancy can be traced however to the fact that argon, a relatively inefficient deactivating bath gas, was used in these latter systems. If the experimental total pressures are modified using an argon collisional deactivation eficiency (&) of < 0.23 for the ketone and aldehyde experi- ments, and < 0.14 for the pyrazoline experiments, then the variations of the observed tIIMCP/cDMCP ratios with eflective pressure agree with the pattern suggested by the results from the Hg(63P1)/3MB and methylene systems.The values postulated for IJp are not unreasonable, as pp has been measured as 0.16 for the collisional de- activation of vibrationally excited ground state 2,3-dirnethyl~yclobutanone.~~ An alternative less likely explanation for the different behaviour observed in the ketone and aldehyde (or pyrazoline) systems is that the acyl-alkyl (or diazenyl-alkyl) bjradical initially formed from the triplet precursor molecules could participate directly in the formation of DMCP by a concerted CO (or N2) displacement reaction.Even if such a reaction were possible it would probably not compete effectively with direct loss of CO from the biradical. Estimates of the rate constant for this frag- mentation, computed by RRK theory using thermochemistry calculated from the reported enthalpy of cyclobutanone,18 standard group additivity procedures and Arrhenius parameters assumed equivalent to those for propionyl decomposition,20 show that the rate is very rapid at the excitation levels produced by Hg(63P1) sensit- ization. However at the: lower excitation level resulting from triplet benzene sensit- ization (3Blu, 353 kJmol-l), the calculated rate constant for CO loss from the biradical derived from trans-2,3-dimethylcyclobutanone is only 2 x 1 O6 s-l, indicating that decomposition could be effectively quenched at even moderate pressures.The RRK computations discussed here apply to the ground state acyl-alkyl biradical, in which the acyl group is bent. It is possible, however, that photosensitized de- carbonylation may proceed via an excited state biradical with a linear acyl group, if the theoretical postulates of Turro, Farneth and Devaquet are correct.21 If this is so then decarbonylation would be fast at all levels of excitation due to predissociation. It is unfortunate that product quantum yields were not measured for triplet benzene sensitization of the 2,3-dimethyl~yclobutanones,~~ as they might well have provided284 3-M E T 13 Y L B UT- 1 -EN E P HO T 0 SEN SI T I Z A T I 0 N information on the rate of acyl-alkyl biradical fragmentation, thereby enabling the relative importance as intermediates of the linear and bent forms of the biradical to be determined, OXYGEN SCAVENGED EXPERIMENTS The addition of oxygen to the photosensitization system virtually suppresses the formation of products such as pent-2-ene completely.This observation demonstrates not only that monoradicals are effectively scavenged in these experiments, but that intramolecular methyl migration reactions, analogous to those thought to be present in some other olefin direct photolysis are absent. The slightly reduced DMCP yields in the presence of oxygen presumably result from some O2 quenching of Hg (63P1) and partial removal of the triplet olefin and MBD13 biradical by scaveng- ing reactions, leading to unknown products.In the discussion that follows it is assumed that DMCP is neither formed nor removed by either of these latter processes, or by reactions of excited molecular oxygen produced by 0, + Wg(6’Pl) interaction. The results can be interpreted in terms of reactions (1)-(lo), together with the addi- tional reactions, (15)-(18), also shown in fig. 1. Scavenging of l(MED13)* need not be considered under the conditions of these experiments as it is removed extremely rapidly by the first order reactions (4) and (9).8 If a kinetic analysis is applied to the mechanism then eqn (19) can be derived by assuming that stationary state conditions are achieved. where K = k17/k3, A = kls/k,, 0 = k16/k2, and [MI is the effective pressure for collisional deactivation of (tDMCP)* and (cDMCP)*.Eqn (19) expresses the relationship between the experimentally observed ratio of trans- to cis-DMCP, R’, and the pressures of 3MB1 and O2 in terms of ten rate constant ratios. Of these all but K , 3, and Q have been determined previously (cf. table 3), and the latter can be estimated from data in the literature. If values of the pseudo-pressure Y are calculated, the variation of the magnitude of the 1.h.s. of eqn (19) with oxygen pressure can in principle be computer fitted, thereby generating K and A values. As strong collisions are again assumed to be operative for 3(MBD13)*, the appropriate value of 6 for substitution in eqn (20) is 150.0 Torr. 0 is estimated to be < 0.23 by analogy with other molecules and A lower limit of c = 0 is possible if collisions between 0, and 3(MBD13)* result solely in product formation.However, M was calculated assuming that the collisional efficiency of 0, relative to 3MBl for deactivation of (tDMCP)* and (cDMCP)*, was 0.23. Values of Y calculated from the data shown in table 2 were found to range from 105.5 to 245.3 Torr. Computer fitting eqn (19) to these values by the same iterative random-exploration least-squares method, using CF = 0.23, gave optimum K and A values of 6.64 x and 1.75 x low2 Torr-l respectively. Fig. 3 shows the data plotted according to eqn (19) together with the computer generated best-fit curve. If kl, and k18 have the same approxi- mate value as that suggested 25 as typical for the analogous reaction of alkyl mono- radicals, 1.0 x 10l2 cm3 mol-l s-1, then k3 and k, can be calculated from these optimum K and 3, values as 3.08 x lo6 and 8.13 x lo8 s-l respectively.It was found, however, that almost equally good fits could be obtained with either A or IC set equalD . C. MONTAGUE 285 to zero. Under these conditions maximum values of each concomitant parameter were obtained, viz. for A = 0 then K,,, = 1.77 x Torr-l, and for K = 0, then A,,, = 1.86 x Torr-l. Fixing either parameter at any intermediate value both determined that of the other and resulted in an alternative, but less acceptable fit to the data. The poorest fit, at the limits of acceptability, was found when K = 6.13 x Torr-l. The data therefore suggest that either K $- A or A @ K , and not K N A.Torr-I and A = 6.70 x 1 Y o I I 1 I I oxygen pressure/Torr FIG. 3.-Variation of ([3MB1] +0.23[Q2])/ Y with oxygen pressure. 0 50 100 150 If A is indeed close to zero, then cyclisation of thermalised l(MBD13) must be much faster than its removal by oxygen scavenging, and the corresponding K value, K , , ~ defines the minimum rate constant for ,(MBD13) intersystem crossing k,. Substituting k17 = 1.0 x 1OI2 cm3 mol-1 s-l as before gives k,(min) = 3.05 x lo6 s-l, very close to the optimum value. It is nevertheless only a factor of 2.9 lower than that corresponding to the least acceptable fit. Amax on the other hand allows the minimum ring closure rate constant of l(MBD13), k5, to be computed, and xmin the maximum value of k3. It seems unlikely that k,(max) could exceed kl, however, and therefore, assuming k3(max) = k , = 4.56 x lo8 s-I leads via Kmin = 1.18 x Torr-l and a revised A,,, = 1 .8 0 ~ Torr-l, to k,(min) = 3.00 x lo6 s-l. The errors in k,(min) and k,(min) are largely determined by those associated with kl, and k18 respectively. Thus, whereas k5(min) is largely unaffected by a decrease in k17, a reduction in k18 will lower k,(min) by a similar factor, and vice versa for k (min) . A similar set of K and A values, generated by assuming that o = 0, allows the minimum values 3.38 x lo6 and 3.21 x lo6 s-l to be computed for k, and k5 respec- tively, a change of only 10 % in these rate constants. Neglecting the effects of singlet biradical isomerization by setting t,b and p equal to zero produces even smaller changes.In summary, the results almost certainly demonstrate that 3.05 x lo6 -c k3 c 4.56 x lo8 s-l and k5 2 3.00 x lo6 s-l. The short lifetime of thermalised MBD13 biradicals ensures that their reaction with substrates other than those endowed with a par-286 3-METH Y L B U T- 1 -EN E P €3 0 TOS E N SI TI Z AT I 0 N ticularly high reactivity towards free radical species (with, say k 2 lo9 cm3 mol-I s-l), would not occur at 293 K for normal substrate pressures. Addition to the n-bond of a simple olefin to form a cyclopentane is therefore not feasible. Arrhenius parameters for cyclisation of singlet propa-l,3-diyl biradicals have been estimated by O’Neal and Benson from a thermochemical analysis of pyrolysis data for various substituted cycl~propanes.~ They deduce an activation energy of 38.9 kJ inol-l, and log (Als-l) = 13.6, calculated at 700 K.Several theoretical studies dispute these estimates however, suggesting instead that the ring closure activation energy lies in the range 0-10 kJ mol-? A lucid account of the implications of these conflicting proposals has been presented by Stephenson, Gibson and B r a ~ r n a n . ~ ~ The data obtained here can be used to support either postulate. Thus while the experimental k5(min) value is close to that calculated from O’Neal and Beplson’s suggested parameters, uiz., 5.8 x lo6 s-l, the higher, equally acceptable k5 values are compatible with lower cyclisation activation energies. The latter situation is perhaps to be favoured however, in that as intersystem crossing rate constants invariably show an energy dependence, it would be surprising if kl were not > k3, especially as the energy difference of ’(MBDl3)* and 3(MBD13) is some 186-226 kJ mol-l.This assumption implies that the optimum value for k3 is k3(min) (3.05 x lo6 s-l) rather than k3(max) (= kl), intermediate values having been shown to give less acceptable fits to eqn (19); the argument concludes that k5 approaches k,(max). This con- clusion does not allow the ring closure activation energy to be defined precisely however, as any value in the range 0-35 kJ mol-I will satisfy its proposals assuming the postulated A factor to be correct. The values of kl and k3 allow the “ Arrhenius parameters ” for 3(PJIBD13) inter- system crossing to be roughly estimated using RRM theory.Input data required for this calculation are the biradical excitation energy, initially taken to be 226 kJ mol-1 and the number of active vibrational modes, s. A value of 19 was chosen for s as this enabled good agreement to be obtained between the RRK and RRKM calculated rate constant for 3(MBD13)* deconiposition.l Use of the minimum value for k3 leads to upper limits for the activation energy, EISC, and A-factor. Thus by sub- stituting k3 = 3.05 x lo6 s-l, the intersystem crossing rate constant, kIsc, can be expressed as kIsc = 1.64 x lo9 exp (- 1870/T) s-l. Decreasing k17 by an order of magnitude reduces k3 by a similar factor and gives kIsc = 3.10 x lo9 exp (-2740/T) s-l . Uncertainty in the heat of formation of MBD 13 results in a minimum biradical excitation energy of approximately (1 86 + EIsc) kJ mol-l.A lower value would imply that the heat of formation of I(MBD13) would probably have to be larger than the maximum value dictated by the activation energy for DMCP structural isomer- ization. Using this minimum excitation energy leads to kIsc = 2.01 x lo9 exp (- 1930/T) s-I if k l , = 1 x 10l2 cm3 mol-1 s-l. These calculations show that the uncertainty in the upper limit of the intersystem crossing activation energy is largely brought about by error limits associated with the value of k l , rather than with the excitation energy. Theoretical studies have suggested that the ground state of MBD13 is a triplet.26* 27 It would therefore be anticipated that triplet-singlet intersystem crossing would involve a small positive activation energy.The maximum values postulated here are consistent with this expectation and go some way towards assessing the magnitude of the difference in lowest triplet and singlet state enthalpies. D. C. Montague, J.C.S. Faraday I, 1978, 74,262. M. C. Flowers and H. M. Frey, Proc. Roy. Soc. A, 1961,260,424. H. E. O’Neal and S. W. Benson, J. Phys. Chem., 1968, 72,1866. J. Metcalfe and E. K. C. Lee, J. Arner. Chern. Soc., 1972, 94, 7.D . C . MONTAGUE 287 R. Moore, A. Mishra and R. J. Crawford, Cunud. J. Chem., 1968, 46, 3305 ; E. B. Klunder and R. W. Carr, Chem. Comm., 1971, 742. E. B. Klunder and R. W. Carr, J. Amer. Chem. Soc., 1973, 95,7386. F. J. Duncan and R. J. CvetanoviC, J. Amer. Chem. Soc., 1962, 84, 3593 ; F. S. Rowland, P. S.-T. Lee, D. C. Montague and R. L. Russell, Disc. 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