Mg(63PJ Photosensitization of 3-Methylbut-1-enet Part 1 .-Reactions of Vibrationally Excited Triplet 3-Methylbut-1-ene and the 2-Methylbuta-l,3-diyl Biradical BY DEREK C. MONTAGUE* Department of Physical Chemistry, The University, Leeds, LS2 9JT Received 14th February, 1977 3-Methylbut-1-ene has been photosensitized by Hg(63P1) atoms in the gas phase at 245 1"C, producing both vibrationally excited 3-rnethylbuta-ly2-diyl and 2-methylbuta-1,3-diyl biradicals in the triplet state. The pressure dependences of the quantum yields of the various reaction products have been investigated and a computer modelling treatment applied to the proposed reaction mechanism, thereby allowing rate constants for the major decomposition and isomerization reactions of these two intermediates to be derived.In addition RRKM calculations have been performed, enabling rough estimates of critical energies for three of these reactions to be obtained. In a previous paper the results of a comprehensive quantitative study of the Hg(63P,) photosensitization of 3,3-dimethylbut-l-ene have been presented.l Rate constant values and critical energy estimates for various reactions of both the excited triplet olefin and the 2,2-dimethylbuta-l,2-diyl biradical were reported. The com- putational methods of data analysis developed for this previous investigation have now been applied to results from the Hg(Ci3P1) photosensitization of 3-methylbut-1 -me (3MB), thereby allowing similar rate constant and critical energy data to be obtained. Vibrationally excited triplet olefins, formed by energy transfer from Hg(63P1),2 react predominantly by the fission of weak C-H and/or C-C bonds, and by hydrogen atom migration reactions leading to isomerization products.Collisional deactiva- tion of the excited olefin also occurs, and this introduces a pressure dependence of the product yields. In the 3MB system a 174-hydrogen atom transfer will produce the 2-methylbuta- 1 ,3-diyl biradical (MBD13). This biradical has been postulated as an intermediate in the structural isomerization of 1,2-dimethylcyclopropane,4 the photochemical decompositions of both 2,3-dimethylcylobutanone and 3,4-dimethyl-A1-pyrazoline,6 and in the reaction of triplet methylene with but-2-ene.' A complete quantitative understanding of the reactive channels open to this intermediate is clearly essential to the elucidation of the often complex chemical behaviour of these various systems.Achievement of this goal, at least in part,-formed the primary objective of this study. In addition rate data for the reactions of vibrationally excited triplet 3MB were sought. The principal advantage of the method used here is that the reaction intermediates have a reasonably narrow spread in excitation energies, thereby enabling the experimental rate constants to be compared in a meaningful way with those calculated by RRKM theory. In contrast, triplet MBD13 formed from 2,3-dimethyl- cyclobutanone and 3,4-dimethyl-A'-pyrazoline has a much wider spread in vibrational energy due to energy partitioning during CO and N2 loss respectively. Presented in part at the Third International Symposium on Gas Kinetics, Brussels, 1973.262D. C. MONTAGUE 263 EXPERIMENTAL 3-Methylbut-1-ene (3MB), stated purity 99.9 %, was obtained from Matheson Gas Products. It contained no impurities that interfered with the gas chromatographic analysis of reaction products and was therefore used without further purification, other than thorough degassing in uacuo. The grease-free vacuum system, photolysis cell, lamp and analytical apparatus have all been described previously. The percentage conversion of the olefin was always <0.5 %. Reaction mixtures were usually analysed on a 100 m wall-coated polypropylene glycol (PPG) capillary column, fitted to a Perkin-Elmer 452 gas Chromatograph that was equipped with a flame ionisation detector.By operating this column at O'C, the yields of all major products from methane to 2,3-dimethylpentane could be quantitatively measured. Some analyses were also performed on a 45 ft x inch silicone oil and Borapak combination column, using a Perkin-Elmer F11 gas chromatograph with flame ionisation detector. Peak areas on the chart recorder trace, estimated by planimetry, were converted to absolute product yields using previously determined calibration factors. Products were identified by a comparison of their retention times with those of authentic samples of compounds thought to be present. The detector sensitivity was measured for ethane, but- 2-ene, 3MB, 3,3-dimethylbut-l-ene (33Dh4B) and 2-methylpent-2-ene (2MP2), and found to be proportional to the carbon number of the compound, within experimental error.Detector sensitivities for other hydrocarbon products were assumed to be similarly related. Actinornetry was carried out as described previously using the Hg(63P1) photosensitized isomerization of cis-but-2-ene. The mercury photosensitization quantum yield for this process has recently been confirmed as 0.5 at pressures in excess of 30 Torr* and low overall conversion level^.^ Using a value of 0.7 nm2 for the absolute quenching cross-section of 3MB, estimated by analogy with the corrected lo cross-section for pent-l-ene,l' a calculation similar to that carried out for 33DMB shows that, in the pressure range of these experiments, essentially all the excited Hg(63P,) atoms are quenched by the olefin. RESULTS In the pressure range 11 3-764 Torr, the Hg(63P,) photosensitization of 3MB yields as major products methane, ethane, trans- and cis-pent-2-ene (tP2 and cP2), 2-methylbut-2-ene (2MB2), 2-methylpent-2-ene (2MP2), 2,3-dimethylbutane (23DMB) and 1,2-dimethylcyclopropane (DMCP).Smaller amounts of 3,3-dimethylbut- 1 -ene (33DMB), 2-methylpentane (2MP), 2,3-dimethylpentane (23DMP), 4-methylpent- 2-ene, 2-methylbut-1-ene (2MBl) and isoprene were found, as were trace quantities (in order of decreasing yields) of buta-l,3-diene, but-2-ene, but-1-ene, isobutene, propane and propylene. Also observed were traces of 2,3-dimethylbut-1 -ene and 3-methylpent-2-ene at pressures below M 100 Torr, and an additional product that was formed in yields lower than those of 33DMB.Despite considerable effort this compound, which eluted from the PPG column between 2MB2 and isoprene, defied identification, many potential candidates, including ethylcyclopropane, buta-l,2-dieiie and 3-methylbuta-l,2-diene being eliminated. Its characterization using conventional techniques was unfortunately precluded by its small yields. Methylcyclobutane was not identified among the products. It cannot be positively ruled out, however, as if it were formed in trace 'quantities, it would not necessarily have been observed, as it would have been incompletely resolved from tP2 in the product chromatogram. Its maximum quantum yield is estimated as Similarly 1 ,I-dimethylcyclopropane could not be characterised as a reaction product as its retention time was almost identical with that of the parent 3MB.Attempts to find an alternative chromatographic column suitable for its analysis were hindered by complications arising from the presence of the other products in the mixture. Data * 1 Ton = 133.3 Pa264 3-METHYLBUT- 1 -ENE PHOTOSENSITIZATION from other mercury + olefin photosensitizations indicate that its yield would probably be minor, however.12 Higher molecular weight compounds were also almost certainly formed, but no attempt was made either to identify them or to assess their yields quantitatively. The mercury photosensitization quantum yields (Q) of the major products are presented in table I. Most of the product yields decrease, within experimental error, as the pressure increases. Notable exceptions are those of DMCP, 2MB2 and methane, all of which appear to pass through a maximum.Other similar examples of this behaviour have been noted previous1y.l Both trans- and cis-DMCP were formed, in a ratio that was pressure dependent. This finding is discussed in greater detail in the following paper.13 reactant pressure /Tom 11.8 24.7 37.5 48.9 86.9 101.0 127.8 140.8 177.0 187.3 221.2 228.8 251.6 274.6 350.2 374.1 407.6 451.2 463.4 497.9 548.8 577.5 599.0 691.7 764.4 TABLE 1 .-Hg(63P1) PHOTOSENSITIZATION PRODUCT (I QUANTUM YIELDS ( x lo3) CH4 C2H6 ZP2 cP2 2R.181 2hfB2 33DbLB 3MP2 23DM5 2MP 23DMP C&12 'DMCP nm nm nm nm 0.30 nm nm nm nm nm ntn nm n:n F.31 ntn nm nix nm 6.03 63.26 35.09 25.25 0.46 1.92 1.01 5.25 6.11 nm nm nm nm 0.37 nm nm nm nm 8.96 40.70 24.03 16.74 0.36 2.35 1.27 8.20 7.08 9.15 37.68 21.21 14.95 0.39 2.56 1.07 6.37 5.21 9.57 29.05 18.08 12.89 0.31 2.54 0.83 4.55 5.52 nm nm 16.24 11.77 0.19 2.31 nm nm nm 10.29 22.31 13.53 9.73 0.22 2.47 0.88 5.12 3.97 9.86 19.8U 12.23 8.93 0.23 2.59 1.06 6.05 4.56 10.01 17.50 10.77 8.06 0.33 2.33 0.88 5.67 4.19 nm nm nm nm 0.14 2.35 0.94 6.58 nm 10.01 14.40 9.56 6.92 0.31 2.39 0.97 5.48 4.13 10.26 12.28 7.89 5.85 0.18 2.25 0.76 4.82 2.96 9.01 9.90 7.34 5.15 0.25 2.23 0.67 4.01 2.77 9.64 8.31 5.25 3.79 0.26 2.08 0.58 3.65 2.11 9.20 8.53 5.95 4.14 0.20 2.25 0.60 4.05 2.26 9.20 7.41 4.86 3.50 0.34 2.14 0.53 3.64 1.81 9.12 6.42 4.28 3.00 0.24 2.05 0.44 3.22 1.7'3 8.74 6.07 4.05 2.86 0.25 2.09 0.53 3.70 1.85 8.35 5.36 3.42 2.42 0.25 2.08 0.39 3.11 1.41 8.97 5.59 3.48 2.46 0.26 2.08 0.33 2.28 1.32 8.13 4.36 2.66 1.96 0.27 1.93 0.35 2.39 1.32 8.51 4.40 2.54 1.90 0.20 2.13 0.34 2.49 1.19 7.02 3.15 1.55 1.31 0.18 1.88 0.25 1.96 0.85 a See text for explanation of symbols ; b 4-methylpent-2-ene ; nrn = nm nm nm nm 0.41 0.51 nm nm 1.14 0.44 0.73 0.64 0.64 nm nm nm 0.61 0.62 0.61 0.47 0.75 0.64 nm nm 0.83 0.45 0.64 0.74 0.69 0.29 0.62 0.61 0.66 0.61 0.59 0.33 0.64 0.54 0.57 0.71 0.57 0.53 0.56 0.48 0.60 0.49 0.59 0.39 0.58 0.31 not measured nm nm 0.19 0.28 0.38 0.25 0.08 nm 0.13 nm 0.i5 0.26 0.15 0.18 0.09 0.10 0.15 0.22 0.23 0.13 0.09 0.06 0.08 nm nm 13.00 14.05 13.49 14.23 14.40 14.30 13.89 13.89 13.00 13.60 12.60 12.71 12.02 12.00 10.71 9.99 10.00 9.50 9.13 8.57 8.16 7.87 7.79 7.05 6.37 A few runs were carried out in which the intensity of the light from the photolysis lamp was reduced by a factor of ten.In these experiments (CD)DMCP remained essentially unchanged at any given pressure. The quantum yield of methane increased, however, while that of ethane decreased considerably. In addition the ratio of Q23DMB to @2MP decreased, as did the values of (Dtp2 and QCp2, although Qtpz/cDcPz was constant. Particular care was therefore taken to ensure that under " normal " experimental conditions, photolyses were performed with as constant an intensity as possible. In a separate series of experiments, discussed elsewhere,13 varying amounts of oxygen were added to several different pressures of 3MB before photolysis. In these runs the yields of all major products, except DMCP and 2MB2, fell to trace levels, while those of C3 and C4 products increased slightly.DISCUSSION Vibrationally excited triplet olefins, formed by energy transfer from Hg(63P,), normally react by one of two processes. Examination of the product quantum yields observed at different photolysis light intensities reveals that both are present in thisD. C. MONTAGUE 265 system. Thus fragmentation to radicals is evidenced by the intensity dependent yields of those products with radical precursors, and, secondly, isomerization by the intensity independent yield of DMCP. In addition, the low overall total product quantum yield shows that many excited olefin molecules are collisionally deactivated before reaction can occur. FORMATION AND REMOVAL OF RADICALS The 3MB molecule contains two equivalent weak C-C bonds /3 to the n-bond.Fission of one of these bonds either in the vibrationally excited triplet olefin 3(3MB)*, or in the excited ground singlet state olefin (3MB)*, formed by inter-system crossing, leads to both methyl and 1-methylallyl radicals. The following mechanism surn- marises the possible reactions : Hg(63P,)+3MB +- Hg(G1So)f3(3MB)" 3(3hIB)* -4 (3MB)" 3(3MB)* 3 CH3 + CH3CH"CHE'-CH2 (3MB)* 3 CH3 + CH,CH"CH-CH, (3) (4) M 3(3MB)* 3 3(3MB) M (3MB)* +- 3MB 2CH3 4 C2H6 ( 7 ) tP2 ( 8 4 (86) 7 CH3 + CH,CH=CH"'CH2 4 cP2 'X 3MB. ( 8 4 1,l-Dimethylallyl radicals are also produced, by rupture of the weak C--H bond fi to the double bond. The hydrogen atoms thus liberated probably lead to the formation of molecular hydrogen, the yield of which was not measured, though a considerable fraction of them appear to be scavenged by the parent olefin, giving the 3-methylbut-2-yl and 3-methylbut-1-yl radicals.At the pressures of these experi- ments both of these radicals are essentially completely stabilised before decomposition can occur. The formation of ethane, tP2, cP2, 33DMB, 2MP2, 23DMB and 2MP can all be explained by combination of the various radicals 33DMB 2MP2 CH3 + (CH3)2CECHECH2 < CH3 + (CH3)2CH(?HCH3 3 23DMB CH3 + (CH3),CHCH2CH2 3 2MP as shown in reactions (7)-(11). The ratio, K,, of tP2 to cP2 was constant, within experimental error, over the pressure range 38-764 Torr. It has been argued that the value of K , , 1.3910.02, reflects the thermodynamic equilibrium ratio of trans- and cis-1-methylallyl radicals at 297+ 1 K, the temperature of these experiments.This value has therefore been combined with data obtained at other temperatures to estimate the differences in entropy and heat of formation of the two isomeric forms266 3-METHYLBUT-I-ENE PHOTOSENSITIZATION of this radical.* Obviously the yield of 3MB from reaction (8c) cannot be measured in these experiments. It can, however, be calculated using data from other experi- ments. The ratio of the quantum yields of 2MP2 and 33DMB formed in reaction (9) is a measure of the relative reactivity, a,,,, of the two reactive centres in the 1,l- dimethylallyl radical. The derivation of aIIi = 6.1 rfi0.6 from the data of these and other experiments has been discussed elsewhere. Alternative pathways leading to 23DMB and 2MP can be postulated.CH3 addition to 3MB gives both the 2-methylpent-3-yl radical and the 2,3-dimethylbut-l-yl radical. Various disproportionation and abstraction reactions of these radicals produce 23DMP and 2MP. Two observations suggest that these pathways are less important than reactions (10) and (1 l), however. First (CH3)2CHkHCH2CH3 (CH3)2CHCH(CH3)eH2 CH3 + 3MB < (CH3)2CHeHCH2CH3 CH3 +{(CH3)2CHCH(CH3)kH2 (1 3) the yields of 23DMP, produced by reaction (13), are low, suggesting that reactions (12~) and (12b) are relatively slow in this sytem ; and secondly, the quantum yield ratio oF23DMB to 2MP is always greater than unity, but decreases as the overall pressure increases, paralleling a concomitant decrease in the rate of other radical combination reactions, e.g.reactions (7)-@). These experimental findings are in line with the proposal that at low pressures the favoured production of 3-methyl-but-2-yl radicals by addition of EI atoms to 3MB, ensures that reaction (10) is important, whereas at higher pressures, the decreased rate of formation of M atoms and the lower overall steady state radical concentrations, lead to a greater fraction of CH3 radicals reacting by addition to 3MB, mainly via reaction (12a), resulting in a relatively increased yield of 2MP. Observations from the reduced light intensity experiments support this qualitative explanation. Under these conditions the rate of radical production becomes so low that radical-molecule reactions compete even more effectively with radical-radical interactions, thereby reducing Q2 DMB/@2MP still further.There are two potential pathways that can contribute to the formation of methane from CH3 radicals, viz., hydrogen abstraction from 3MB, and various disproportiona- tion reactions. The latter routes will be most important at low pressures, where radicals are removed predominantly by radical-radical processes. As the pressure of 3MB increases their importance will decrease relative to H abstraction, which will become dominant. The abstraction rate cannot be varying linearly with 3MB pressure, however, as QCzH6 is not constant. The product P = Q&L6 [3MB] reflects the form of the variation. Values of P rise at low pressures but reach a plateau at pressures around 300 Torr, thereafter increasing very much more slowly.In addition, the ratio of P values at 764.4 and 37.5 Torr is approximately four times larger than the corresponding ratio of methane quantum yields, indicating the substantial contribution of disproportionation processes at low pressures. No useful analytical expression can be derived to describe iDCH4 against pressure, as a result of the large number of reactions that influence the interdependent stationary state concentrations of the radicals involved in disproportionation. Radical disproportionation reactions account for the formation of the small yields of buta-l,3-diene, isoprene, 2MB2, 2MP2, 4-methyl-2-pentene, but-2-ene and but-1-ene. A further route to 2MB2 is proposed in the following section.D . C. MONTAGUE 267 ISOMERIZATION REACTIONS Four hydrogen atom translocation reactions are possible in 3(3MB)*.They are, a 1,4-shift (termed l5 a 5pp process) giving the 2-methylbuta-l,3-diyl biradical (MBD13), two 1,3-shifts, namely a 4tp and a 4ps process producing triplet 2MB2 and the 2-methylbuta-l,4diyl biradical (MBD 14) respectively, and a 3ts process giving the 3-methylbuta-l,3-diyl (3MBDl3) biradical. These isomerizations, summarized by reactions (14)-(17), would presumably yield vibrationally excited products in the triplet state : - r r 3(3MB)* + son 3[kH2CH(CH3)kH2CH3]* (14) 4tP '(3MB)* + 4PS 3(3MB)* $ 3(3MB)* + 3ts 3 ( 2 ~ ~ 2 ) * (1 5 ) 3[kH2CH(CH3)CH2cH2]* (1 6) 3[kH2CH2e(CH3)2]*. (17) The appreciable yields of DMCP throughout the experimental pressure range indicate that reaction (14) is important. Addition of oxygen to the reaction mixture only suppresses the yields of 2MB2 slightly, suggesting that reaction (1 5) probably provides the major route to this product.Excited MBD14 would be expected either to fragment to ethylene and propylene or collapse to methylcyclobutane. The failure to observe this latter compound among the products and the minor yields of propylene demonstrate that reaction (1 6) occurs to a negligible extent. Similarly, in the Hg(63P1) photosensitization of 33DMB, the rate of the analogous 5pp process greatly exceeded that of the 4ps process.1 As mentioned earlier analytical difficulties prevented an assessment of the almost certainly minor role played by reaction (17). Following its genesis, 3(MBDl 3)* undergoes either decomposition,l collisional deactivation, or intersystem crossing, as shown in reactions (1 8)-(20) : 3(MBD13)* + CH3 +CH,CH"CH"'CH2 (1 8) M 3(MBD13)* -+ 3(MBD13) + DMCP 3(MBD13)* -+ (MBD13)* -+ DMCP.Both reactions (19) and (20) are included in the mechanism because the ratio of trans- to cis-DMCP was observed to be pressure dependent. Such behaviour cannot otherwise be explained, geometrical isomerization of (DMCP)" being at least an order of magnitude too slow. Cyclisation of 3(MBD13)* takes place via inter-system crossing to the singlet state. The factors controlling processes of this type have been discussed.17 The nature of the " singlet biradicals " thus produced is still a matter of some debate,l* though in this case one may confidently assert that the presence of a high level of vibrational excitation in the molecule ensures that the rate of ring closure would be much faster than that of any decomposition reaction, irrespective of the exact magnitude of any possible cyclisation energy barrier.Thus the extensive decoinposition that occurs via reaction (1 8), vide infra, implies that the biradicals formed in reaction (14) must be in the triplet state, as presumed. Fragmentation by a hydrogen atom loss process analogous to reaction (18) cannot occur to any great extent, as the product 1,2-dimethylallyl radicals would go on to give 2,3-dimethylbut- 1-ene and 3-methylpent-2-ene by combination with CH3, compounds that were only observed in minor trace amounts at pressures below268 3-METHYLBUT- 1-ENE PHOTOSENSITIZATION z 100 Torr.Structural isomerisation of (DMCP)* can also be ruled out at the pressures of these experiments. The small yields of 2MB1 that are found must therefore arise by isomerization of (MBD13)" and/or MBD13. The contributions from 3(MBDB)* and 3(MBD13) are negligible as 1,Zhydrogen shifts in triplet biradicals are particularly unfavourable due to the high energy barrier.12* l9 The much lower barriers operating for singlet biradicals result from energy release accompanying n-bond formation as the isomerization proceeds along the reaction coordinate. If 2MB1 is indeed produced in this way, then approximately equivalent yields of 2MB2 would also be expected to be formed in a parallel rearrangement.? A schematic simplified representation of the major reactions of 3(3MB)* and 3(MBD13)* is shown in fig.1. Minor routes and bimolecular radical reactions have been omitted in the interests of clarity. 3(h) - h \ T M T \ FIG. 1.-Major reactions of 3(3MB)* and 3(MBD13)*. QUANTITATIVE FORMULATION OF THE MECHANISM If the usual assumptions of the stationary state hypothesis are made for the concentrations of 3(3MB)*, (3MB)*, 3(MBD13)*, (MBD13)* and MBD13 during photolysis, application of a kinetic analysis to the reaction mechanism enables the sum of the quantum yields of DMCP, 2MB1 and the 2MB2 formed by isomerization of the singlet biradical, to be expressed as (21) where [MI is the total pressure of 3MB and a = k20/k19, y = k5/k14:, 6 = k18/k19, E = k--14/k19 and p = k'/k14, where k' is the sum of the rate constants for reactions t In the gas phase thermal isomerization of both trans- and cis-DMCP, the ratio of the rate of formation of 2MB2 to that of 2MB1 at the mid-point of the temperature range of the study (727 K) was found to be 1.07.The Arrhenius parameters for both pathways are identical within experi- mental error.20 +@nmi + @Yi% = (a + EMI)/{(I +P +WI)(a + 8 + E + [MI)-&)D . C . MONTAGUE 269 (2j, (3) and (15) plus any other possible reactions of 3(3MB)*. If it is assumed (i) that k14 = 2k-14, i.e. that the rate constants per transferable hydrogen atom for reactions (14) and (- 14) are equivalent, (ii) that the collisional deactivation rate constants for 3(3MB)* and 3(MBD13)*, k5 and k19, are equal, and (iii) that the yields of 2MB2 and 2MB1 from singlet biradical isomerization are equivalent, eqn (21) can be simplified to eqn (22) %MCP+2@2MBi = (a+IMI)/((l +D+[MI/~&)(~+~+E+[MI)-&~. (22) An expression for the ratio of the mercury photosensitization quantum yield of methyl radicals to the sum of the yields of DMCP and the singlet biradical isomeriza- tion products 2MB1 and 2MB2 can also be derived.Again by assuming @)2MB1 = @y$&, this expression reduces to eqn (23) @Me/(@D,MCP+2@2MSl) = ((a+d+&+ [M1)(c+q/(l +e[M1)) +6)/(a+[M1) (23) where = k3/kI4, q = k2/k14 and 8 = ks/k4. QMe is given by @Me = @CH4 + 2a)CzHs + 1 *~(@,Pz + @cP2) + @2)2MP2 + @3 3DMB + Q23DMB + @2Mp + 2@)23DMp + a(4-methylpent-2-ene). (24) Eqn (24) assumes that no other products are formed by methyl radicals. Under these experimental conditions this assumption is reasonable, though minor yields of higher molecular weight compounds produced by the addition of the methyl adduct radicals 2-methylpent-3-yl and 2,3-dimethylbut- 1 -yl to 3MB may be produced. The observed high quantum yield of C2W6 and the low quantum yields of 2MP and 23DMP, imply that the yields would be very small, however.Eqn (22) and (23) have an identical form to those successfully used to analyse the data obtained in the Hg(63P,) photosensitization of 33DMB.l As the complex forms of both equations preclude the use of any simple method to obtain values for the unknown rate constant ratios, it was necessary to adopt a computer modelling approach which employed an iterative procedure that refined initial estimates of the unknown parameters. The " best " values thus obtained were defined as those minimising the sum of the squares of the deviations between the calculated and experimental data points.In view of the large number of unknowns in eqn (22) the error hypersurface defining the agreement between the computed and experimental data was explored using a series of fixed values for a and/or 6, thus enabling corres- ponding estimates for p and E to be obtained. Eqn (23) was similarly treated using the same fixed values for a and/or 6, together with the appropriate E value and 0 = 0.0826 Torr-l, calculated by RRKM theory (vide infra). It was found that the two pairs of a and 6 values that minimised the two error functions were similar, but not identical, presumably as a result of the slight scatter in the experimental data.Compromise values were therefore derived that nevertheless gave good agreement between the computed and experimental values for both sets of data. Table 2 shows the optimum values thus obtained. It is worthwhile re-emphasising that this method of data analysis can sometimes give misleading or meaningless results, as there may be more than one set of parameter values that are commensurate with the data. In this case, however, no evidence could be found for an alternative set of meaningful values, and it would therefore appear that within reasonable error limits, that proposed is unique. Of the unknown parameters the values of E and 5 were very insensitive to changes in ct and 6, only requiring alteration by up to 10 and 15 % respectively, in order to still achieve acceptable fits to the data.An attempt was made to place realistic error limits on the quoted optimum values of cc and 6 despite the difficulties inherent in2'70 3-METHYLBUT- 1 -ENE YHOTOSENSITIZA'TION such an undertaking. The computed results show that they are probably accurate to within factors of 1.5 and 1.2 respectively. Previous experience in treating the results from the H S ( ~ ~ P ~ ) photosensitization of 33DMB suggested that the values derived for 8 and q would be closely inter-related and that equally good fits would be obtained for many different pairs of values for these parameters. Consequently no attempt was made here to derive 8 from the data, its value being calculated using RRKM theory. The optimum fit with a = 33.6 Torr and 6 = 302 Torr gave y equal to zero.Increasing a first to 34 and then to 35 Torr whilst holding 6 constant, TABLE 2.-oPTIhaUM RATE CONSTANT RATIOS AND HALF-QUENCHING PRESSURES a a/Torr G/Torr &/Torr O/Torr-1 4 rl 33.6 302 4.145 0.0826 2.345 6 1 C See text for explanation of symbols ; b calculated value, see text ; C see text. resulted in q values of 0.04 and 0.2. Increasing 6 by 1 % gives y equal to zero and 0.14 for a < 34 and 35 Torr respectively. Clearly these data do not allow y to be defined with any precision, though an order-of-magnitude upper limit of unity could be estimated. Its true value is probably considerably less than this. If y is indeed zero then methyl radicals are not formed by (3MB)" decomposition, reaction (4), in this system. On the other hand the fragmentation of 3(3MB)* must be important, as satisfactory fits to the data could not be achieved with set equal to zero.Thus of the three postulated methyl forming reactions, (3), (18) and (4), only the latter can be classified as not being essential to the mechanism. Fig. 2 and 3 show plots of (QDMCp + 2@2MBI) and @MVle/(CDDMCp + 2@2MB1) respectively against pressure, together with computer generated " optimum fit " curves to the data points calculated from the parameter values listed in table 2. As noted previously it is possible that the exclusion of potential high molecular weight product quantum yields from eqn (24) might result in values of a)Me/(@DMCp+2@e)2MBI) that are low. The effect of increasing OMe by an amount DHMW, arbitrarily set equal to 2@23DMp, was therefore investigated.Using the same 8 value as before, the optimum 6 value 0 I I I I I 1 I 1 200 LOO 600 pressure/Torr FIG. 2.-Variation of (%MCP+ 22QM1-31) with pressure.D. C. MONTAGUE 27 I 0 200 400 600 pressure/Torr FIG. 3.-Variation of the ratio @)M~/(@)DMcP+ 2Qi2m 1) with pressure. was found to decrease by z 3 Torr, while that of a increased by xl Torr and [ by ~ 0 . 0 5 . These small variations are well within the error limits for these parameters. The ratio of rate constants for 3(3MB)'k fragmentation versus rearrangement to 3(MBD13)* is given by 5, while 5/y gives the relative rates of fragmentation and intersystem crossing. The uncertainty in rules out an exact determination of this ratio, but a value below 2 seems unlikely.The most favourable reaction channel available to 3(MBD13)* is decomposition, which is faster than ring closure by the factor 6/a = 9.0. The reactive pattern outlined by these results resembles that found for the mercury photosensitization of 33DMB, and, as in that system, the rate constant for CH, loss from the excited triplet biradical exceeds that from the excited triplet olefin, here measured by the factor 8/2~5 = 15.3, despite a statistical factor of two favouring the latter reaction. Estimating a collision diameter for 3MB of 560pm, by analogy with molecules of similar molecular weight and carbon skeleton, enables the collision rate constant TABLE 3 .-EXPERIMENTAL RATE CONSTANTS AND COMPUTED CRITICAL ENERGIES < 1.13 - - I (2) 226 (3) 2.64 (15.5+0.5) {:::;:$ 206 (4) (1.64+0.55)c (16.6+0.3)d (2S4_+4)e 471 r93 226 1.13 i:' 206 226 206 (128k 9) 226 (10518) 186 (1 8) 41 .O (15.1k0.5) { (20) 4.56 - - - a Estimated ; b error limits result from uncertainty in log (A/+) ; C computed value ; dreported value ;31 e calculated from reported activation energy ;31 fpreferred value.272 3-METHYLBUT- -ENE PHOTOSENSITIZATION to be calculated as 1.36 x lo7 s-I Torr-l (2.52 x 1014 cm3 mol-1 s-l) at 24°C.If it is assumed that the collision diameters of the reactive intermediates are also 560 pm, and that the strong collision assumption holds, the rate constants shown in table 3 can then be computed from the half-quenching pressures and rate constant ratios given in table 2. The value of the rate constant for intersystem crossing of 3(MBD13)* is, within the estimated error limits, the same as that found previously for intersystem crossing of the excited triplet 2,2-dimethylbuta-lY3-diyl biradical. Uncertainty in k , makes a comparison with the analogous rate constafit for 3(33DMB)'y more difficult, but it would appear probable that they are again of a similar magnitude.Quantitative data on the intersystem crossing rate constants for simple triplet acyclic olefins and propa-l,3-diyl biradicals is lacking. The values obtained here are, however, in accord with those estimated by considering the factors controlling the rates of these processes.17 T HER M 0 C 13 E MI S T R Y The heat of formation of the relaxed triplet 31MB biradical was calculated as 216 kJ in01 from the reported standard heats of hydrogenation 21 and formation 2 2 of 3MB (- 127 and -29 kJ mol-l respectively), by the same method as that used to compute the corresponding value for 3(33DMB).1 As reaction (14) is formally thermoneutral, AHf"[3(MBD13)] was also taken to be 216 kJ mol-I.It can be argued, however, that AH,"[3(3MB)] and AHf"[3(MBD13)] could be up to 20 and 40 kS 11101-1 greater respectively, by applying analogous reasoning to that previously used when discussing the heats of formation of 3(33DMB) and the triplet 2,2- dimethylbuta- 1,3-diyl biradica1.l These higher biradical AH," values imply a degree of interactive destabilization between the radical centres. If this interaction is indeed present, then it is probable that its magnitude is different in the two biradicals.In view of these uncertainties the RRKM calculations described below have been carried out using both the estimated minimum and maximum AH; values. The average total internal excitation energy, E'*, of initially formed 3(3MB)* and 3(MBD23)* can be readily computed to be at most 226 kJ mol-1 in excess of the residual average thermal energy, Eth, of 3MB, from the calculated thermochemistry and the known excitation energy of Hg(63P1) atoms (471 kJ mol-I). Using higher AHf" values for 3MB and/or MBD13 reduces accordingly. RRKM ESTIMATION OF CRITICAL ENERGIES RRKM theory enables the energy dependence of the specific rate constant, kE, of a unimolecular reaction, to be related to the critical energy, E,, if the A factor is known. For the triplet biradical reactions studied here the A-factors are not avail- able, and it was therefore necessary to estimate them in order to obtain rough values of the critical energies for these processes.This procedure is not as difficult as might be expected, as experimental pre-exponential factors have been measured for several similar reactions. Except for (3MB)* decomposition, the procedure adopted was to investigate the dependence of kE on Eo for fixed values of E*. In this way the value of Eo that resulted in equivalent calculated and experimental rate constants could be determined. The RRKM computations were performed assuming that all overall molecular rotations were inactive and that the reactants were monoenergetic. The semi-classical Whitten-Rabinovitch approximation was used to evaluate the sums and densities of the molecular quantum states.23 Details of the activated complex models used are given in the Appendix.Calculations were performed for four processes. TheD. C. MQNTAGUE 273 rate constant for (3MB)* fragmentation, k4, was first computed so that a value for 8 might be substituted in eqn (23), thereby reducing the number of variable parameters when computer fitting this equation to the experimental data. The other three reactions treated were the decompositions of 3(3MB)*, reaction (3), and 3(MBD 13)*, reaction (18), and the isomerization of 3(3MB)*, reaction (14). The results of the calculations are shown in table 3. One feature of the results is the difference in critical energies for the decomposition reactions (3) and (1 8).This disparity presumably accounts for the experimental observation that kI8 is some fifteen times larger than k3. A similar conclusion concerning the fragmentations of 3(33DMB)* and the excited triplet 2,2-dimethylbuta- 1,3-diyl biradical was rationalised by postulating that whereas the favoured orthogonal configuration of the two free electron orbitals in the triplet 1,2-biradical inhibits extensive resonance stabilisation in the incipient allylic system, the preferred (0,O) configuration of the propa-l,3-diyl biradical allows allylic stabilisation of the developing radical centre to be immediately realised. Implicit in this conclusion and explanation is the assumption that it is valid to compare calculated critical energies based upon equivalent AH; values for 3(3MB) and 3(MBD13).As discussed above it is quite possible that the method used to calculate these quantities may result in their being underestimated, especially in the case of the triplet olefin. Thus if AHt[3(3MB)] is greater than AHf"[3(MBD13)], the average total internal excitation energy, E*, of 3(3MB) would be less than that of 3(MBD13)* by an equivalent amount, and this could result in a correspondingly lower value for k3. Such an effect could partially explain the difference in k3 and k I 8 , and moreover would lead to a lower computed critical energy for reaction (3). The rate constant discrepancy is, however, too large to be entirely due to an effect of this type, even allowing for error in the relative A-factors for the two reactions. The critical energies for these two processes cannot therefore be the same. The computed critical energy for 3(3MB)* isomerization, reaction (14), lies in the range 82-93 kJ mol-l, the exact calculated value depending on the chosen A-factor and excitation energy.Direct comparison with the critical energies calculated for similar lY4-hydrogen shift processes involved in the isomerization of various alkyl and alkenyl radicals 24-26 is difficult, due to differences in the chosen activated complex models and reaction thermochemistries, though it would seem that they are of the same magnitude. 1,3 and 1,2-hydrogen migrations proceeding by 4sp, 4pv (v = vinyl), 3ss and 3sp processes, are reported to have critical energies of z 130 and 140 kJ mol-1 respect- ively.lgT 26-28 Reaction (16) is a 4ps process, and woufd be expected to be less thermochemically favoured.It is therefore not surprising that products such as methylcyclobutane and propylene, derived from the 2-methylbuta- 1,4-diyl biradical formed by this isomerization, were not detected. The experimental data suggests, however, that despite the low reaction path degeneracy, part of the 2MB2 yield arises via reaction (I 5), a 4tp hydrogen shift, presumably as a result of the exothermic nature of the process. A simple calculation using RRK theory shows that the critical energy for this reaction can be no more than M 115 kJ mol-l. Reaction (17), a potential route to the 3-methylbuta-l,3-diyl biradical, the precursor of 1,l-dimethyl- cyclopropane, is a 3ts hydrogen migration and as such would be expected to make virtually no contribution to the reaction mechanism if its energy of activation were similar to those for 3ss and 3sp processes, even if some allowance is made for its possibly greater exothermicity.A striking feature of all the critical energies calculated here is their remarkable similarity to those computed for the analogous reactions occurring in the Hg(63P1)274 3-METHYLBUT-1-ENE PHOTOSENSITIZATION photosensitization of 33DMB, the A-factors for each reaction pair having been estimated in a mutually consistent manner. Results are also available for the Hg(63P,) +2,3-dirnethylbut-l-ene system and it is intended to give a more detailed discussion of the similarities of these various olefin systems in the report of that study.Information concerning the biradical internal energy dependence of the ratio of trans- to cis-DMCP and the effect of oxygen on the reactions of 3(3MB):k and 3(MBD13)* is given in the following paper.13 APPENDIX RRKM C A L CUL AT1 0 NS (3 MB) * D E c o M P o s IT I o N The frequency assignment for 3MB is that deduced by Taylor and Simons 29 except for the inclusion of realistic energy barriers for the internal rotations about the three C-C single bonds. Activated complex frequencies were assigned by considering the bonding changes as the C(3)-C(4) bond is stretched by a factor of two. This bond extension results in Q,'/Ql = 1.69. The reaction coordinate for both this and the other two decompositions described below was taken to be the stretching frequency of the extended bond.Trenwith has revised his published 30 Arrhenius expression for the unimolecular decomposition of 3MB, now recommending 31 loglo (k/s-l) = 16.6kO.3-(35750 K/2.303 2"). Three complex models, I, I1 and 111, were proposed, corresponding to loglo (A/&) = 16.3, 16.6 and 16.9 (calculated at 712 K). The statistical parameter L* for this reaction is 2. Frequencies (wavenumber/cm-l) common to both reactant and complex were as folIows (degeneracies shown in parenthesis) : 3093 3012 2992 2968(3) 2946 2903(2) 2885 1468(2) 1451(2) 6420 1373(2) 1314 1295 1278 1165 955 913 748 575 418 375(2) additional reactant frequencies : 1650 1152 1000 904 850 790 418 250 211(2) 13 additional complex frequencies : complex I : 1230(2) 550 250 155 150 117 100 70 50 complex I1 : 1230(2) 550 250 155 150 100 70 58 50 complexIII: 1230(2) 550 250 155 150 100 70 50 29.In a few calculations the complex frequencies were modified, but in such a way that the corresponding loglo ( A / s - l ) values were unaltered. The results obtained were very similar to those computed using the listed assignments. 3(3MB)* D E c OM P o SI TI ON Vibrational frequencies for 3(3MB) were obtained by removing two C-H stretching, and four CH3 and CH, deformation modes from the frequency assignment for isopentane given by Snyder and Scha~htschneider.~' In addition the torsional frequencies associated with the C(2)-C(3) and C(3)-C(4) bonds were adjusted. With I,* = 2 and by assuming Q,' /Ql = 1.69, rate constants were calculated using three postulated activated complex models, w, v and VI, having vibrational frequency assignments corresponding to values for 1oglo(A/s-l) of 15.0, 15.5 and 16.0 respectively (calculated at 450 K), estimated to be intermediate between those for fragmentation of 3MB and the 3-methylbut-2-yl radical. Common reactant and complex frequencies :D.C. MONTAGUE 275 2962(3) 2952 2938 2926 2873(3) 2852 1384 1377 1366 1351 1337 1298 101 1 952 . 910 796 412 368 additional reactant frequencies : additional complex frequencies : 1268 1037 969 917 764 459 260 204 coniplex IV: 1220(2) 300 250 200(2) 155 complexV: 1220(2) 300 250 200(2) 155 complexVI: 1220(2) 250 195 155 1 SO(2) 1475 1455(3) 1176 1149 198 140 15 100 79 75 100 75 25 100 75 21. 3( MBD 13)* D E c o M P o s I TI o N Vibrational frequencies for 3(MBD13) and the three chosen activated complex models, VII, VIII and IX, corresponding to log,, (A/s-l) = 14.6, 15.1 and 15.6 respectively, were assumed to be identical to those assigned to 3(3MB) and complexes IV, V and VI, with the exception of one reactant frequency at 204 cm-' which was lowered to 150 cm-,.For this reaction E* = 1 and Q,'/Ql = 1.69. (3 MB)* IS o M E R I z AT I o N The vibrational frequency assignment of 3(3MB) is given above. Two five-membered ring activated complex models, X and XI were postulated, corresponding to log,o(A/s-') = 11.2 and 11.5, calculated at 450 K, their frequencies being estimated by analogy with those for the proposed ' complex models involved in the isomerization of 3(33DMB)*. The reaction coordinate was taken to be one of the ring deformation modes involving motion of the H atom.I,* = 6 and Q,'/Ql was assumed to be unity. Complex X frequencies : 2960(3) 2920(2) 2880(2) 2860(2) 1470(2) 1450(3) 1255(2) 1215 1150(3) llOO(2) 1040(2) 1020 lOOO(4) 930 895(2) 870 550 400 360 290 198 The two ring deformation modes at 870 and 290 cm-1 were reduced to 550 and 200 cm-I to obtain the frequency assignment for complex XI. The author is grateful both to Prof. H. M. Frey at the University of Reading, where much of the experimental work was carried out, and to Prof. P. Gray, for the provision of laboratory facilities. Acknowledgement is also due to P. E. Montague for assistance with computing. D. C. 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