Unimolecular Hydrogen Chloride Elimination Reaction H. Heydtmann, B. Dill, and R. Jonar, rnt. J . Chem. Kinet., 7, 973 (1975). (a) R. L. Johnson and D. W. Setser, J. Phys. Chem., 71, 4366 (1967); (b) K. C. Kim and D. W. Setser, ibid., 77, 2021 (1973). (a) K. C. Kim and D. W. Setser, J. Phys. Chem., 78, 2166 (1974); (b) K. C. Kim, D. W. Setser, and B. E. Holmes, ibid., 77, 725 (1973); (c) B. E. Holmes, D. W. Setser, and G. 0. Pritchard, Int. J . Chem. Kinet., 8, 215 (1976). (a) P. Cadman, A. W. Kirk, and A. F. Trotman-Dickenson, J . Chem. Soc., Faraday Trans. 7 , 72, 996, 1426 (1976); (b) A. W. Kirk, A. F. Trotman-Dickenson, and B. L. Trus, J. Chem. Soc.A, 3056 (1966). (a) A. Maccoll, Chem. Rev., 69, 33 (1969); (b) P. C. Hiberty, J. Am. Chem. Soc., 97, 5975 (1975); (c) I. Tvaroska, V. Klimo, and L. Valko, Tetrahedron, 30, 3275 (1974). B. E. Holmes and D. W. Setser, J . Phys. Chem., following paper in this issue. (a) H. M. Frey, G. R. Jackson, M. T. Thompson, and R. Walsh, Trans. Faraday SOC.,6, 2054 (1973); (b) J. W. Simons, W. L. Hase, R. S.Phillips, E. J. Porter, and F. B. Growcock, rnt. J . Chem. Kinet., 7, 679 (1975); (c) R. J. McCluskey and R. W. Carr, Jr., J . Phys. Chem., 80, 1393 (1976); (d) R. L. Russell, Ph.D. Thesis, University of California, Irvine, Calif., 1971. P. F. Zittel, G. B. Ellison, S.V. O'Neil, E. Herbst, W. C. Lineberger, and W. P. Reinhardt, J . Am. Chem. SOC.,98, 3732 (1976). R. Srinivasan, J . Am. Chem. Soc., 84, 4141 (1962). E. F. Brittain, C. H. J. Wells, and H. M. Paislsy, J . Chem. SOC. 6, 304 (1968). W. G. Clark, D. W. Setser, and E. E. Seifert, J . Phys. Chem., 74, 1670 (1970). J. F. Meagher, K. J. Chao, J. R. Baker, and B. S. Rabinovitch, J . Phys. Chem., 78, 2535 (1975). (a) S.E. Stein and B. S. Rabinovitch, Int. J . Chem. Kinet., 7, 531 (1975); (b) W. L. Hase and J. W. Simons, J . Chem. Phys., 54, 1277 (197 1). B. E. Holmes, Ph.D. Thesis, Kansas State University, 1976. J. R. Durig and A. C. Morrissey, J . Chem. Phys., 46, 4654 (1967). R. B. Synder and J. H. Schachtschneider, Spectrochem. Acta, 21, 169 (1965); J . Mol. Spectrosc., 30, 290 (1969). H. Kim and W. D. Guinn, J. Chem. Phys., 44, 865 (1966). L. H. Scharpen and V. W. Laurie, J. Chem. Phys., 39, 1732 (1963). G. A. Segal, J. Am. Chem. SOC.,96, 7692 (1974).
The Journal of Physical Chemistry, Vol. 82, No. 23, 1978 2461 (24) "Table of Molecular Frequencies", National Bureau of Standards, Washington, D.C., NBS, 11, 1967. (25) K. S.Pitzer, J. Chem. Phys., 14, 239 (1946). (26) (a) H. M. Frey and R. Walsh, Chem. Rev., 68, 103 (1966); (b) P. C. Beadle, D. M. Golden, K. D. King, and S. W. Benson, J. Am. Chem. SOC.,94, 2943 (1972); (c) A. T. Cocks and H. M. Frey, ibid., 91, 7583 (1969); (d) T. F. Thomas, P. J. Conn, and D. F. Swinehart, ibid., 91, 761 1 (1969); (e) A. Ramakrishna, R.D. Thesis, Rochester, 1970. (27) (a) S. W. Benson and H. E. O'Neal, "Kinetic Data on Gas Phase Unimolecular Reaction", National Bureau of Standards, Washington, D.C., 1970; (b) N. N. Das and W. D. Walters, J. Phys. Chem., 15, 22 (1956); (c) A. F. Patzracchia and W. D. Walters, ibid., 68, 3894 (1964). (26) E. W. Schlag and G. L. Haller, J . Chem. Phys., 42, 584 (1965). (29) (a) T. H. Richardson and J. W. Simons, Chem. Phys. Left., 41, 166 (1976); (b) T. H. Richardson and J. W. Simons, J. Am. Chem. Soc., 100, 1062 (1976). (30) R. J. McCluskey and R. W. Cam, Jr., J. Phys. Chem., 81, 2045 (1977). (31) (a) H. M. Frey, G. E. Jackson, R. A. Smith, and R. Walsh, J. Chem. SOC.,Faraday Trans. 1 , 71, 1971 (1975); (b) A. D. Clements, H. M. Frey, and R. Walsh, ibid., 73, 1340 (1977). (32) P. J. Marcoux and D. W. Setser, J . Phys. Chem., 82, 97 (1976). (33) K. W. McColloh and V. H. Dibeler, J. Chem. Phys., 64, 4445 (1976). (34) (a) J. W. Simons and R. Curry, Chem. Phys. Left., 38, 171 (1976); (b) J. Danon, S. V. Filseth, D. Feldmann, H. Zacharias, C. H. Dugan, and K. H. Welge, Chem. Phys., 29, 345 (1978). (35) J. A. Kerr, B. V. O'Grady, and A. F. Trotman-Dickenson, J . Chem. SOC.A , 275 (1969). (36) (a) 8.0. Ross and P. M. Siegbahm, J. Am. Chem. Soc., 99, 7716 (1977); (b) R. R. Lucchese and H. F. Schaefer, 111, ibid., 99, 6766 (1977); (c) L. B. Harding and W. A. Goddard, 111, J . Chem. Phys., 67, 1776 (1977). (37) (a) S. E. Stein and B. S.Rabinovtch, J. Phys. Chem., 79, 191 (1975); (b) E. W. Hardwidge, B. S.Rabinovitch, and R. C. Ireton, J. Chem. Phys., 58, 340 (1973). (38) D. F. McMillen, D. M. Golden, and S.W. Benson, Jnt. J. Chem. Kinet., 4, 487 (1972). (39) S.W. Benson, "Thermochemical Klnetics", Wiley, New York, N.Y., 1966. (40) R. M. Joshi, J. Macromol. Sei.-Chem., AB, 595 (1972).
Energy Disposal by the Four-Centered Unimolecular Hydrogen Chloride Elimination Reaction B. E. Holmes" and D. W. Setser Department of Chemistry, Kansas State University, Manhattan, Kansas 66506 (Received April 17, 1978)
The vibrational energy partitioned to 1-and 3-methylcyclobutene by the four-centered HC1 elimination reactions from 1-,2-, and 3-methylchlorocyclobutanes has been investigated by the sequential unimolecular reaction technique. The chemically activated methylchlorocyclobutanes were prepared with 110 kcal mol-' of internal energy by the insertion reaction of singlet methylene into the C-H bonds of chlorocyclobutane. The elimination reactions give 1-and 3-methylcyclobutenewith enough energy to undergo the cyclobutene-butadiene isomerization reaction. The magnitude and pressure dependence of the rate constants for isomerization of 1- and 3methylcyclobutene to 2-methyl-1,3-butadieneand 1,3-pentadiene, respectively, were measured. Matching model calculations to the experimental rate constants gave an assignment of the vibrational energy retained by the methylcyclobutenes. The available energy was divided into statistical and potential energy components in the model calculations. The former is the excess energy above the threshold, (E) - Eo,for HC1 elimination. A Gaussian distribution, which could be altered in both position and width, was used to represent the potential energy. The calculated best fit for both 1-and 3-methylcyclobutene was for an energy distribution that gave (fv (olefin)) = 0.60. This total energy corresponds to 32% of the potential energy plus the statistical component, which is 80% of the excess energy. The effects of cascade collisional deactivation and formation of methylcyclobutene with excess translational energy upon the matching of the experimental and calculated rate constants are discussed. N
Introduction For only a few unimolecular processes has the energy disposal been well characterized.1 When available, such data provide insight into dynamical features and potential *Address correspondence to this author at the Department of Chemistry, Ohio Northern University, Ada, Ohio 45810. 0022-3654/78/2082-2461$01 .OO/O
energy surface for the latter stages of the unimolecular reaction.2 Although the four-centered unimolecular HX elimination reactions have been extensively in~estigated,~ the energy disposal pattern is not completely understood. Translational energy distributions have been determined for the dehydrohalogenation from alkyl halide ions4 and the hydrogen halide vibrational distributions have been 0 1978 American
Chemical Society
2462
The Journal of Physical Chemistry, Vol. 82,
E,=
No. 23, 1978
B. E. Holmes and D. W. Setser
57c CII
1005
( E )= 109.5
PROGRESS OF THE REACTION
Figure 1. Thermochemistry for HCI elimination from 2- and 3methylchlorocyclobutane. The energles (kcal mol-') in the figure are for 3-methylcyclobuteneisomerizationto 1,3-pentadienes. The threshold energies EoHc'and E: are for HCI elimination and methylcyclobutene isomerization, respectively. The internal energy of MCCB is ( E ), the energy in excess of the HCI threshold is E,, and EPis the potential energy. The AHrn' is the endoergicity of the HCI elimination step. The numbers in the figure apply to 3-methylcyclobutene Isomerization. For E,, and EP values are 16.6, 65.5, l-methylcyclobutenethe AH,,', and 30.4 kcal mol-', respectively, for genesis from 1-MCCB; for formatlon from 2-MCCB the corresponding energies are 13.5, 58.0, and 38.0 kcal mol-', respectlvely.
measured for elimination from some small alkyl halide molecules.6 This paper is the final descriptione of our study of the vibrational energy released to the olefin product by a four-centered HC1 elimination reaction. We previously have reported on energy disposal by the three-centered elimination r e a ~ t i o n . ~ ~ ~ ~ The sequential unimolecular reaction technique is capable of giving the overall vibrational energy distribution, but not the localized internal distribution, for a large polyatomic product molecule. In the present study the sequential reactions were HC1 elimination from 1-,2-, and 3-methylchlorocyclobutane (MCCB) followed by unimolecular isomerization of the 1- or 3-methylcyclobutene product (MCB) formed in the first step. Activation of the methylchlorocyclobutanes was achieved by the C-H insertion reactions of singlet methylene with chlorocyclobutane. Based upon the AH?(CH2,1A1) favored in the preceding paper,8 the average internal energy, ( E ) ,of the MCCB is -110 kcal mol-'. Other thermochemical aspects are summarized in Figure 1 (see also the caption to Figure 1). The overall reaction scheme is outlined in eq 1-3; the
( E ) = 112.5
t
kcal mol-'
HC I
L-l
1
.
t
( E )= 109.5
HC I
mcH3 [MI (2b)
kM
( E ) and threshold energies, Eo, are in kcal mol-'. The
strong collisional deactivation mechanism is used for simplicity of presentation; the effect of cascade deactivation is investigated in a later section. No distinction is made between the cis and trans isomers of MCCB. Since 2-MCCB isomerizes to l-methylcyclobutene and 3methylcyclobutene, it is listed in both (2) and (3). Although 3-methylcyclobutene is formed from both 2-MCCB and 3-MCCB, the thermochemistry is the same for each and the interpretation is straightforward. For 1methylcyclobutene allowance must be made for the different energies of (la) and (2a). In this work, the rate constants for the isomerization of the methylcyclobutenes were measured from 0.2 to 80 Torr. The rate constants for the HC1 elimination steps of MCCB were considered in the preceding paper.8 Using specific rate constants for methylcyclobutene calculated from RRKM theory and an assumed functional form for the vibrational energy distribution, the fraction of available energy released to the olefin by HC1 elimination was determined by matching calculated isomerization rate constants to experimental ones. The potential energy released as the transition state geometry changes to product geometry, E = EoHC1 - AHo', and the excess both contribute to the available energy, Ex = (E)- EoHdi, energy. Since the rate of internal energy randomization of chemically activated MCCB is considerably faster than the rate of HC1 e l i m i n a t i ~ nthe , ~ ~energy ~ ~ distribution associated with Ex can be taken as statistical. A Gaussian distribution function, which was variable in position and width, was selected to represent the release of E,, and this was combined with the statistical distribution to give the overall vibrational energy distribution for the methylcyclobutenes. Two special effects that can influence the matching of the calculated and experimental rate constants were considered. Comparison to work in the literaturelOJ1 suggests that 6-10 kcal mol-I of energy should be removed per collision for chemically activated MCCB or MCB with the bath gas (mainly ketene or chlorocyclobutane). Therefore, several collisions probably are needed to deactivate the methylcyclobutene and cascade deactivation, as well as the unit deactivation, was utilized in computing the MCB isomerization rate constants. Secondly, the effect of excess translational energy, which may be released to the products from the HCl elimination reaction, was considered. Excess translational energy will affect the computation of the collisional frequency, which is used to define the experimental rate constants. The excess velocity also could affect the deactivation mechanism by altering the average energy removed per collision; however, this role of the translational energy is unknown and only the effect upon the collision frequency was considered in the calculations.
Experimental Section Hydrogen chloride elimination from chemically activated
The Journal of Physical Chemistry, Vol. 82, No. 23, 1978 2463
Unimolecular Hydrogen Chloride Elimination Reaction
2.0
t
m
ttI
F
,
0
,
01
,
,
,
0 2
I
,
I
0 3
,
04
I
m
I
05
VPRESSURE (torr) 0
c 5
10
15
20
2 5
I/PRESSURE ( t o r r )
Flgure 2. Decomposition stabilization ratio vs. reciprocal pressure plot for isomerization of 1-methylcyclobuteneto 2-methylbutadiene.
1-,2-, and 3-MCCB followed by unimolecular isomerization or collisional deactivation of the 1-or 3-methylcyclobutene are the reactions of interest. The methods used to prepare and purify reagents, the general experimental procedure, and the identification of products were given in the preceding paperns The experiments involved photolyzing mixtures of ketene, chlorocyclobutene, and oxygen followed by product analysis via dual-pass gas chromatography. All samples were prepared to a constant total volume of 2.7 cm3 (STP) with reactant ratios of 1.0:3.0:0.4 for ketene: chlorocyclobutane:oxygen,respectively. The products of interest (cis- and truns-1,3-pentadiene, 2-methylbutadiene, and 1-and 3-methylcyclobutane) were trapped from the helium effluent from a thermal conductivity detection cell from the initial analysis, which used a 12-ft Apiezon-L or a 12-ft Octoil-S column. Quantitative product yield measurements were accomplished in the second analysis which utilized a combination column consisting of a 45-ft silver nitrate saturated ethylene glycol column and 2.53.5-ft hexamethylphosphoric triamide column. The response of the hydrogen flame detector was calibrated with prepared mixtures simulating the actual samples.
Experimental Results The experimental results are product yield ratios of (cis-1,3-pentadiene + trans- 1,3-pentadiene)/ (3-methylcyclobutene) and of (2-methylbutadiene)/(l-methylcyclobutene) at various pressures. The mean value of the experimental cis:trans yield ratio for 1,3-pentadiene was 0.2; the ratio appeared to be pressure independent. Reaction 3b allows for the possibility of direct formation of cis-1,3-pentadiene, as well as formation via isomerization of truns-lj3-pentadiene. The cis-pentadiene was the penultimate component that was eluted and the peak was broad; the yield was quite low and the present data cannot distinguish between the two possible pathways for forming cis-1,3-pentadiene. Fortunately, the mechanism for cis formation is not important for determining the total isomerization rate constant of 3-MCB. Plots of D I S vs. 1/P are shown in Figures 2 and 3 for 1- and 3-methylcyclobutene, respectively. The D I S range was extended to as low a pressure as the sensitivity of the gas chromatographic analysis would permit. It is important to establish that all of the methylcyclobutene molecules are formed with sufficient energy to isomerize. Otherwise that fraction of the distribution extending below the threshold energy must be subtracted from the total stabilization yield before converting the D I S ratio to a rate constant. Fortunately, extrapolation of plots of S I D vs. pressure to zero pressure gave a zero intercept value and all of the methylcyclobutene molecules have
Figure 3. Decomposition stabilization ratio vs. reciprocal pressure plot for isomerization of 3-methylcyclobutene to trans-l,3-pentadiene plus cis-l,3-pentadiene.
*QO'
10
10 0
1000
PRESSURE ( t o r r )
Figure 4. Experimental (H) and calculated rate constants, model I, for 1-methylcyclobutene isomerization as a function of pressure. The upper curve corresponds to 1-methylcyclobutene formed from l-methylchlorocyclobutane and the lower for 1-methylcyclobutene from 2methylchlorocyclobutane. Both calculated curves correspond to a release of 18% of EP to the olefin fragment.
QQO '
10'
I
\
01
10
10 0
100 0
P9ESSURE ( t o r r )
Figure 5. Experimental ( 0 )and calculated rate constants, model I, for 3-methylcyclobutene isomerization as a function of pressure. The best fit (-) calculation is for the distribution shown in Flgure 6 which corresponds to retention of 18% of EPby methylcyclobutene. The u of the Gaussian is 4.0 kcal mol-'; the dotted curve illustrates the effect of changing u to 2 kcal mol-'.
energy greater than the threshold energy for isomerization. With this knowledge the D I S values can be converted to apparent unimolecular rate constants in the usual way, ha = kM[M]D/S. For the simple model (which ignores any excess translational energy carried by MCB) the collision number, k ~ was , calculated using hard sphere collision diameters of 5.5 8,for methylcyclobutene, 4.5 8,for ketene, 5.5 8, for chlorocyclobutane, and 3.6 8, for oxygen; mean collision velocities were taken to be the values a t 300 K. The resulting experimental rate constants are plotted in Figures 4 and 5. The rather wide range of pressure and
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6.E. Holmes and D. W . Setser
the variation of ha with pressure should be noted.
Calculated Results In order to assign the vibrational energy distributions of 1- and 3-MCB, calculated rate constants must be matched to the experimental values shown in Figures 4 and 5. For unit deactivation the ha values were calculated from eq I by averaging the RRKM specific rate constants, hE,
for isomerization of 1- or 3-methylcyclobutene over the energy distributions which are to be determined. The MCB energy distribution was divided into two parts: a statistical distribution representing the release of the excess energy and a Gaussian distribution representing the release of the potential energy. These were folded together to get the total distribution. The statistical component is fixed by the thermochemistry and the RRKM models for the HC1 elimination reaction of the MCCB molecules. Fitting the data in Figures 4 and 5 consists of varying the parameters of the Gaussian function: the most probable energy (Emp)and the width (a) of the distribution. The computational procedure used to obtain the kE values was the same as outlined in the preceding paper; the models for the molecules and the transition states are tabulated in the Appendix. The transition state models were selected so as to fit the preexponential factors for the isomerization reactions.12 No further adjustments of the models were made. We did do calculations, using the models, to test whether or not the reported Arrhenius parameters12were measured in the true high pressure limit. The calculated k/k, vs. pressure curves showed that the thermally activated studies were done above the pressure required to reach the high pressure limit. Model I. Unit Deactivation. This is the simplest model and the objectives were to (i) establish that the energy release pattern for the 1- and 3-methylcyclobutene reactions were the same, (ii) test the sensitivity of the calculated fit to the parameters of the model, and (iii) obtain an estimate for the fraction of available energy released to the olefin. By the simple model we mean eq I with the unit deactivation formulation was used to match the experimental rate constants in Figures 4 and 5, which were obtained using hard sphere collision diameters and the mean Maxwellian speed to compute k ~ . The critical energy for 3-methylcyclobutene formation from either 2- or 3-MCCB is 52.5 kcal mol-l, and since the AHrXno and ( E ) also are equal, the excess and potential energies are the same for each pathway, see Figure 1. The calculated best fit, the solid curve of Figure 5, was for a Gaussian distribution with E,, = 6.5 kcal mol-l, which corresponds to 18% of the potential energy, and u = 4.0 kcal mol-l. The energy distribution and the RRKM rate constants for 3-methylcyclobutene that gave this fit are shown in Figure 6. Both 1- and 2-MCCB yield 1-methylcyclobutene, but with different thermochemistry, and the interpretation is more complicated. For the 1-MCCB reaction sequence AHrXno, Ex,and EP are 16.6, 65.5, and 30.4 kcal mol-l, respectively; but, for 2-MCCB AHT,", Ex and Ep are 13.5, 58.0, and 38.0 kcal mol-l, respectively. Figure 1 is appropriate for 1-methylcyclobutene but with altered thermochemistry, as noted in the caption. Since the dynamics for HC1 elimination should be similar regardless
ENE RGY ( kca I/mole) Figure 6. The RRKM rate constants for 3-methylcyclobutene isomerization. Superimposed on the methylcyclobutene energy scale is the best fit (model I) energy distribution; 99.4% of the distribution is above the 3-methylcyclobutene isomerization threshold, 30.5 kcal mol-'.
of the position of the methyl group, the Gaussian distribution for each was centered at 18% of Ep. After combining the Gaussian with the statistical distribution, the isomerization rate constants for 1-methylcyclobutene formed from 1-MCCB or from 2-MCCB were calculated and the results are shown as the upper and lower curves of Figure 4, respectively. Although the total available energies are similar for (la) and (2a), the distributions associated with Ex and EP differ and the overall distribution and the calculated k, curves are not the same for the two pathways. Using the method just described, the average energy of 1-MCB is 4.7 kcal greater when formed from 1-MCCB primarily because of the 7.5 kcal greater Ex. As seen in Figure 4, the experimental rate constants approach the 1-MCCB calculated curve a t the highest pressures, but the 2-MCCB calculated results are closer to the data a t the lowest pressures. At the highest pressure, 1-methylcyclobutene predominantly arises from 1-MCCB because of its larger HC1 elimination rate constant (a consequence of the 4.5 kcal mol-l lower EoHC1). At the lower pressures both 1-and 2-MCCB contribute to the 1-methylcyclobutene yield. Thus, that variation with pressure of the 1-methylcyclobutene isomerization rate constants is in reasonable accord with the model calculations. These calculations establish that the internal energy distributions for 1- and 3-methylcyclobutene are selfconsistent and that, according to the simplest model, 18% of EP plus the statistical component of Ex give the vibrational energy distribution of MCB. Since the same (or similar) results were found for both 1-MCB and 3-MCB, further exploration of the dependence of the results upon parameters of the model will be done with 3-MCB in order to avoid the dual channels of the 1-MCB system. The magnitude and pressure dependence of k, are sensitive to both Gaussian parameters, u and Emp.The results for u = 2,6, and 10 for a constant E,, are shown in Figure 7. Increasing u broadens the energy distribution which affects the high and low pressure k, limits. The high pressure limit is only moderately increased because ha" = (hE);the low pressure limit, l/(kE)-I, is reduced much
Unimolecular Hydrogen Chloride Elimination Reaction
PRESSLRE
(torr1
Figure 7. Calculated rate constants (model I) for 3-methylcyclobutene isomerization as a function of pressure for various assignments of the Gaussian parameters.
more strongly. The k, curves with the same E,, but different CT have virtually a common point at D / S = 1. The calculated ha curves with the same u but different E , have different shapes, as well as absolute positions, because the kE values change more rapidly as E approaches Eo. The dependence of the 3-MCB calculated rate constants upon u for the experimental pressure range is shown in Figure 5. The dashed curve is for u = 2 kcal mol-' rather than the best fit value of u = 4 kcal mol-l. Based upon this comparison and the calculations shown in Figure 7, we judge the uncertainty in CT to be +3 and -2 kcal mol-'. The uncertainty in the mean value of the MCB energy can be evaluated from Figure 7. For a 4 kcal mol-l increase in Emp,the computed k, values increase by about a factor of 2. This also is evident from the inspection of Figure 6 because in the energy range of 50-60 kcal mol-l a 4 kcal mol-1 change in E alters kE by a factor of 2. The experimental uncertainty in the D / S values is less than f40%; therefore, ignoring for the moment the collisional deactivation problem, the error in the mean vibrational energy assignment should be f1.6 kcal mol-'. This assumes that the calculated hE values are reliable. Since fitting transition state models to reliable Arrhenius preexponential factors together with use of accurate threshold energies generally gives good RRKM kE values? we believe that this aspect of the model should be reliable. Previously discussed methods which utilize a subset of the HC1 elimination transition state frequencies were used to calculate the statistical d i s t r i b ~ t i o n . 3 ~Variation ~ ~ J ~ for a few frequencies by even a factor of 2 does not discernibly affect the statistical distribution; the mean energy for the statistical distribution is close to the fraction of the frequencies in the olefin fragment multipled by the excess energy. The method used to calculate the sta%istical distribution should not be a source of significant error. The main quantity of interest is the fraction of EP released to MCB. T o obtain this from the mean vibrational energy, a good knowledge of all thermochemistry is required. The AH? values for MCCB, which are essential for determination of ( E ) , were estimated from group additivity schemes,14and the reported uncertainty for these procedures is f 2 kcal mol-l. The AHH,O(CH,,'A,) directly effects ( E )and thus E, since E, = ( E )- Eo(HC1). The controversy about AHH,o(CH,,lAl) was addressed in the preceding paper and appears to have been resolved in favor of values close to the number used here. A second point related to thermochemistry is the division of the available energy into Ex and Ep. This involves knowing the EoHC' values, which should be reliable to f 2 kcal mol-' according to the analysis of the preceding paper. The uncertainty in the methylcyclobutene energy assignment arising from the factors mentioned above is relatively small and other features relating to conversion of the D / S values to the experimental.rate constants and the mechanism for collisional deactivation actually are more important.
The Journal of Physical Chemistry, Vol. 82, No. 23, 1978 2465
Model II. Cascade Collisional Deactivation. The second model differs from the simple model by (i) recognition of the long-range contribution to the collision cross sections, which was done by including the Q(T),t2collision integral16 in the computation of k M and (ii) using cascade rather than unit deactivation in the calculation of the 3-methylcyclobutene isomerization rate constants. The experimental rate constants were converted to s-l using the D / S data of Figure 3 and k~ calculated from k~ = fl(T)2'27T CJ"s2(( C B ) + ~ ( cM)2)'/2 (11) The terms (CB), and (CM)2are squares of the average speeds of the bath molecules and methylcyclobutene, respectively. The e l k values for chlorocyclobutane (400 K), methylcyclobutene (300 K), and ketene (275 K) needed for finding Q(T)2,2 were estimated by analogy with similar = molecules.16 The geometric mean for c / k gave Q(T)2,2 1.6 for 3-methylcyclobutene colliding with the average bath gas molecule at room temperature. Thus, including the Q(T)2#2 integral increases the experimental rate constants by a constant factor of 1.6. For a bath gas primarily composed of ketene and chlorocyclobutene, stepladder deactivation with 6-8 kcal mol-l removed per collision is expected.l0J1 Calculations of k, were done for 3-MCB using the stepladder model with energy increments of 4, 6, 8, and 10 kcal mol-'; the calculated high pressure rate constants increased by factors of 1.92, 1.64, 1.50, and 1.41, respectively, relative to the unit deactivation result. The pressure dependence of the calculated k, curves for cascade deactivation resembled that for unit deactivation down to pressures of 5 X lo-, Torr. At lower pressures the cascade deactivation rate constants increased more than just the high pressure k,"(cascade)/k," (unit) values. Since the experimental data do not extend below 0.2 Torr, the greater deviation of the cascade model from the unit deactivation results at lower pressure is of no consequence for this work. The !l(T)2i2 collision integral increases the experimental rate constants by a factor of 1.6, while cascade deactivation with a 6 kcal mol-l step size increases the calculated rate constants by a factor of -1.6. These two effects mutually compensate and the 3-methylcyclobutene energy distribution of Figure 6 still can be considered as the best fit to the experimental results for model 11. Model III. Effect of Excess Translational Energy. According to the simple model, only -18% of EP was released as vibrational energy of the olefin. Much of the remaining energy is likely to be partitioned as translational energy. The increased velocity will increase the collision rate constant, kM, relative to that calculated for a Maxwellian speed distribution. We will attempt to estimate the translational energy, its effect upon kM, and the resulting effect upon the assignment of (E,(MCB)). Although the increased velocity also may affect the energy lost per collision, we will neglect this because no information is available on how to estimate the effect. According to the model pr0posed~~3~ for four-centered HX (X = halogen) elimination, the hydrogen rapidly transfers to the X with release of a small fraction of Ep. The remaining potential energy is released as the X subsequently recoils from the olefin taking the hydrogen with it. Based upon this view, a three-body impulsive recoil model should provide an estimate of the potential energy partitioned as translational energy, ET. This model should give an upper limit to ( E T )and, hence, the maximum effect upon k,. The three-body model approximates the olefin as a rigid diatomic molecule and C1-H as a single atom. According to this model, the "available" potential energy, denoted as EA, is partitioned to relative translational energy and
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The Journal of Physical Chemistry, Vol, 82, No. 23, 1978
rotational energy of the diatomic fragment. As an initial estimate of EA, the remaining 82% of the true potential energy was used &e., E A = 29 kcal mol-I). Conservation of energy, linear momentum, and angular momentum gives17the mean center of mass velocity of the olefin, ( V,,), as
In this expression M is the mass, I is the moment of inertia, r,, is the distance from the center of mass of the diatomic fragment to the end that is attached to the chlorine, and 0is the angle between the chlorine and the line described by the diatomic internuclear axis. The subscripts 01 and C are for the olefin and HC1 fragments, res ectively. Using P = 140°, rcm= 1.6 A, and Iol = 99 amu gives (Val) = 1000 m s-l. For computation of kM the mean laboratory speed of MCB and bath gas are needed. To obtain the mean laboratory speed of MCB, ( Col),the center of mass mean Maxwellian speed of methylchlorocyclobutane, ( CMcCB) was added vectorially17 to (Val) and integrated over the surface of a sphere. The results are as follows:
l2
(cciI)
(col)
= (vel)
+ (cMCCB)2/3(vol)
for Yo1 > CMCCB (IVa)
= (CMCCB) + (VO~)~/~(CMCCB) for
vol
< CMCCB (IVb)
(IVa) gives ( CO1)= 1020 m/s, which is larger than the 300 K Maxwellian speed by a factor of 3.8. Using this value together with the thermal mean speed for an "average" bath gas of 267 m/s in eq I1 gives a hM that is 2.5 times larger than the 300 K Maxwellian value. The experimental isomerization rate constants would be increased by the same factor and the mean energy retained by MCB must be increased in order to raise the calculated k , values. To match the new experimental results, 35% of Ep should be retained as the internal energy of MCB and the remaining 65% of EP partitioned to translational and rotational energy. The computation of k~ must be iterated since the previous three-body calculation of ( Col) was for 82% of E p being used as EA, Several iterations give a (Col) of 940 m/s which increases the experimental ha values by a factor of 2.3 rather than the 2.5 factor mentioned above. According to model 111, the best fit to the data is for 32% of EP to be released as internal energy of MCB. When added to the excess energy, this corresponds to 60% of the available energy, Le., (fV(MCB))= 0.60. The main aim of the three-body calculation in the previous section was to set an upper limit for (Col) and kM. However, the fraction of EApartitioning as rotational energy of the pseudo-diatomic fragment (olefin) also can be extracted:"
For the sames values of rcm,P, and Io, given previously, ( E R ) / E A = 0.0005. The lack of significant rotational excitation is a consequence of the rather large reduced mass of the system and moderately large moment of inertia; the choice of p and r,, have little effect. If a three-body model were used in which the olefin was treated as an atom and HCl as the diatomic fragment, the rota-
B. E. Holmes and D. W. Setser
tional excitation of HC1 also would be small. However, such a model ignores the early dynamic features when the hydrogen migrates to the C1 atom. Discussion The best (model 111) fit between the calculated and experimental rate constants for 3-methylcyclobutene is for an energy distribution consisting of the statistical component (MCB retained 80% of the excess energy) and a Gaussian distribution (Emp= 32% of EP and u = 6 kcal mol-I) for the potentia1 energy; this distribution gives (E,(MCB)) = 56 kcal mol-l or (fv(MCB)) = 0.60. The model IT1 result provides an upper limit to (EV(MCB)) since the maximum translational energy was used to calculate kM. The complete neglect of the excess translational energy gave (fv(MCB)) = 0.56 which corresponds to 18% of Ep.Although the uncertainty in (fV(MCB))is small, the limits on the fraction of Epreleased to MCB are substantially larger. We favor a value near -30% of Ep. The remaining 40% of the total energy, which corresponds to 68% of Ep, will be released as ET,ER, or Ev(HX). Using infrared chemiluminescence Polanyi and co-workerssa found that (E,(HF)) was 0.13 for H F from chemically activated CH3CF3*. The observed ER(HF) was small; however, a large degree of rotational relaxation may have occurred. Chemical laser studiessb have reported a similar H F vibrational distribution. Surprisal analysis1 of the H F vibrational distribution5, from CH3CF3*,using a prior distribution that included all rotational and vibrational states of H F and CH2CF2,gives a linear surprisal plot with Xv = -9.2 f 0.3. The extrapolated relative population for V = 0 was very close to the value measured by the laser method.5b The negative slope shows that (fv(HF)) exceeded the statistical prediction and that potential energy is converted to (Ev(HF)). McDonald and G l e a v e ~observed ~~ HC1 formed by elimination from radicals produced by the reaction of oxygen atoms with 3-chlorocyclohexene or 5-chloropentene; the HCl distributions favored higher u levels than the H F distribution from CH3CF3. Using (f"(HC1)) = 0.13 and our results for (fv(MCB)),27% of the total available energy (45% of EP) must be released as translational energy and rotational energy of MCB and HC1 (see Table I). Observation of laser emission from rotational levels of HF formed by elimination from chemically activated CH3CF3*has been interpreted as evidence for substantial rotational excitation of HF.18 The mechanism for forming HF in the high J states is not completely established18and arrested relaxation studies of the HF (or HC1) rotational distributions would be useful. Assuming that (ER(HC1)) and (ER(MCB)) are small ca. 5%, then by difference (fT) = 0.22 or 40% of Ep. This energy is consistent with translational energies measured for HX elimination from ions.4 The ion kinetic energy and photoion-photoelectron co-incidence spectroscopy techniques measure the release of EP since the ions are formed with energy just slightly in excess of the reaction threshold. The energy disposal pattern for the four-centered H X elimination is summarized in Table I. The partitioning of the excess energy was estimated from statistical theory. These estimates should be valid for large molecules with lifetimes as long as MCCB.8 Table I illustrates that large fractions of Ep are converted to EV(HC1) and to ET. According to Table I, an increase in E x (or (E))should have little effect upon (Ev(HC1)). In support of this, Berrysd observed fairly constant vibrational distributions for HC1 formed by elimination from six photolytically excited chloroethylenes, regardless of the level of excitation. The invariance of the HC1 distribution with ex-
The Journal of Physical Chemistty, Vol. 82, No. 23, 1978 2467
Unimoiecular Hydrogen Chloride Elimination Reaction
TABLE I: Energy Disposal for Four-Centered HCl Elimination from Methylchlorocyclobutanea fraction
mode
Total Energy (93 kcal mol-’) 0.60 (Ev(o lef in )) 0.13b (Ev(HC1)) -0.22b (ET)(by difference) ~ 0 . 0 5 ~ (ER)(see text)
energy: kcal mol-’ 56 12 -20 -5
Excess Energy (57 kcal mol-’ ) Calculated Statistical Distribution 0.80 (EV(o1ef in) 45 0.03 (EV(HC1)) 2 0.17 (ER t 10 (by difference)
E’)
Potential Energy (36 kcal mol-’) 0.32 tEv(o1efin)) 11.5 8 0.23 (Ev(HC1)) -0.40 ( E T )(by difference) -14.5 -0.05 ( E R )(see text) -2 a The specific energies in this table are for formation of 3-methylcyclobutene. The Ev(HC1) is from Polanyi’s infrared chemiluminescence data5a and by difference f~ t f~ = 0.27. The individual fT and f~ are speculative.
citation energy led Berry5d to propose a two-step model of HC1 elimination based upon the assumption that all the HC1 vibrational excitation arose from release of Ep. The first step for Berry’s model was a sudden “undressing” of HC1 from its transition state environment which produced HC1 with a highly inverted vibrational population. The second step was a partial relaxation of the HC1 because the time scale for complete product separation is presumed to be long compared to the time necessary for vibrational energy relaxation. Our interpretation6 of the energy disposal and the HC1 elimination model differs from Berry’s. The energy partitioning pattern of Table I suggests the following three-step dynamical model for four-centered HC1 elimination. (1)Rapid transfer of H (on the 0carbon) to the chlorine (on a timescale of 0.5-1.0 X s ) ~ O with release of a portion of the potential energy as rotational and/or vibrational excitation of HC1. (2) Structural changes associated with the relaxation of the carbon to planar geometry which would induce vi-
brational excitation of the olefin (a timescale of 2-4
a CH2rock). This step may occur in conjunction with the third step. (3) Recoil of C1 from the a carbon with an impulsive release of the localized energy associated with the C-Cl bond. Thus, a large fraction of EPis released as product translational energy. For a relative translational energy s is required for a 6 A change of 24 kcal mol-l, -2 X in nuclear separation. As the HC1 and the olefin fragments recoil from each other, a simultaneous contraction of the carbon-carbon skeleton will occur as the C-C bond is formed and some vibrational excitation of the olefin probably occurs. During the third step, some vibrational excitation of the HC1 may occur as the extended HC1 bond contracts to R,(HCl). As discussed in the preceding section, little rotational excitation of HC1 or the olefin is expected in the third step. As Berry has emphasized, the HC1 also may lose energy during the third step. The key experimental facts are the relatively small values for (Ev(MCB)) and (Ev(HC1)),which initially were surprising in view of the extensive structural modification in the elimination reaction. However, the rapid motion of the hydrogen atom essentially allows the reaction to be considered as two or possibly three steps. Since the potential energy is mainly associated with the breaking of the C-C1 bond, this energy is released mainly as translational energy.
Conclusions The sequential unimolecular reaction technique has been used to measure the vibrational energy released to methylcyclobutene molecules formed by HC1 elimination from chemically activated methylchlorocyclobutane, The mean methylcyclobutene vibrational energy is relatively low and correspond to acquisition of only 32% of the potential energy. This explains why previous attempts21 to use the sequential reaction technique only provided upper limits to (Ev(olefin)). A qualitative model is presented which explains some of the main features of the energy partitioning by the four-centered HC1 elimination reactions. Attention also is directed to the possible importance of the excess translational energy in using the sequential unimolecular reaction technique to assign product vibrational energies.
TABLE 11: Summary of Models used for Calculation of the Isomerization Rate Constants for 1- and 3-Meth ylcyclobutene 1-methylcyclobutene frequencies, cm - ’
moments of inertia, amu A
@/I
11 I
2958 (8) 1463 ( 6 ) 1152 (8) 901 ( 5 ) 597 ( 3 ) 350 (2) 1 9 5 (1) 153 43.1 120
2
Sb calcd Arrhenius A factor,c s-’
E , , kcal mol-’
transition state 2958 (8) 1393 (9) 992 (8) 661 (2) 516 (2) 363 (2) 1 9 5 (1) 166 52.7
124
3-methyl. cyclobutene 2973 (8) 1340 (11) 1014 (5) 840 ( 3 ) 603 (3) 352 (2) 201 (1) 133 50.0 106
transition state 2973 (8) 1372 (10) 1014 ( 5 ) 823 (2) 601 ( 4 ) 361 (2) 201 (1)
180 42.1 150
1.17
1.28
2.0 6.17 x 1013
3.23 x 1013
34.0 The reaction path degeneracy. function form; these calculated values are within 5% of the reported experimental values, a Numbers in parentheses are the number of frequencies.
X
s is suggested from the typical vibrational frequency for
1.o 30.5 These are in partition
2468
The Journal of Physical Chemistry, Vol. 82, No. 23, 1978
Acknowledgment. This work was supported by the National Science Foundation (Grant No. MPS 75-02793). We also are grateful for the fellowship provided to B.E.H. by the Phillips Petroleum Company.
Appendix The vibrational frequencies and moments of inertia of the molecule and transition state, the reaction path degeneracies, and thermal Arrhenius parameters are needed to calculate RRKM rate constants. Since the vibrational frequencies, bond lengths, and bond angles for 1- and 3-methylcyclobutene are not available, they were estimated from cyclobutene22by removing either a vinyl or allylic hydrogen and adding the characteristic values of the methyl group from appropriate compounds.23 Our frequency assignments are very similar to those used by Elliot and F r e ~ The . ~ ~transition state frequencies were assigned by comparing the 1-and 3-methylcyclobutene frequencies with those of 2 - m e t h y l b ~ t a d i e n eand ~ ~ ~trans-1,3-pentadiene,26respectively. The transition state frequencies were refined by adjusting the C-C-C deformation frequency to fit the experimental thermal preexponential factors.12 Moments of inertia were computed for the transition state configuration given by an ab initio SCF-CI calculation for the cyclobutene-butadiene transformation.26 It was assumed that the structural parameters of the transition state were not altered by substitution of methyl for hydrogen. For the ab initio calculation the minimum energy pathway leading to the transition state involved the ring-puckering motion. This reaction coordinate naturally results in conrotation of the two methylene groups in cyclobutene in agreement with Woodward-Hoffman rules. For the ring-puckering mechanism two transition state complexes are possible, thus, the reaction path degeneracy for 1-methylcyclobutene is two. However, for the 3-methyl isomer the two transition states result in distinct products, i.e., either trans- or cis-1,3-pentadiene is the exclusive product. In the chemical activation experiments the trans isomer was favored by a factor of 5; thus a reaction path degeneracy of one was used. The models for isomerization of 1- and 3-methylcyclobutene, and the calculated and experimental Arrhenius A factors are summarized in Table 11. References and Notes (1) B. E, Holmes and D. W. Setser in “Physical Chemistry of Fast Reactions”, Voi. 3, I. W. M. Smith, Ed., 1978. (2) (a) J. F. Durana and J. D. McDonald, J. Chem. phys., 84, 2518 (1976);
B.
(3)
(4) (5)
(6) (7) (8) (9) (10)
(11)
(12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23)
(24) (25) (26)
E. Holmes and D. W. Setser
(b) J. G. Moehimann and J. D. McDonald, ibld., 82, 3052 (1975); (c) J. M. Farrar and Y. T. Lee, ibid., 83, 3639 (1975); 85, 1414 (1976); (d) K. Shobatake, Y. T. Lee, and S. A. Rice, ibid., 59, 6104 (1973); (e) J. D. McDonald and R. A. Marcus, ibid., 85, 2180 (1976). (a) D. W. Setser, MTPInt. Rev. Sci.: Phys. Chem., Ser. One, 9, 1 (1972); (b) K. C. Kim and D. W. Setser, J. Phys. Chem., 77, 2021 (1973); (c) ibid., 78, 2166 (1974); (d) H. Heydtmann, B. Dill, and R. Jonas, Int. J . Chem. Kinef., 7, 973 (1975); (e) B. Dill and H. Heydtmann, Ibid., 9, 321 (1977). (a) K. C. Kim, J. H. Beynon, and R. G. Cooks, J . Chem. Phys., 81, 1305 (1974); (b) K. C. Kim, ibid., 84, 3003 (1976); (c) 8. P. Tsai, A. S. Werner, and T. Baer, ibid., 83, 4384 (1975). (a) P. N. Clough, J. C. Polanyi, and R. T. Taguchi, Can. J. Chem., 48, 2919 (1970); (b) M. J. Berry and 0. C. Pimentel, J. Chem. Phys., 49, 5190 (1968); (c) E. R. Sirkln and M. J. Berry, I€€€. J . Quant. €lectron., QE-10, 701 (1974); (d) M. J. Berry, J. Chem. Phys., 81, 3114 (1974); (e) J. T. Gleaves and J. D. McDonald, ibid., 82, 1582 (1975). B. E. Holmes and D. W. Setser, J . Phys. Chem., 79, 1320 (1975). B. E. Holmes, D. W. Setser, and G. 0. Pritchard, Int. J. Chem. Kinet., 8, 215 (1976). B. E. Holmes and D. W. Setser, J . Phys. Chem., preceding paper in this issue. A. H. KO, B. S. Rabinovitch, and K. J. Chao, J . Chem. Phys., 88, 1374 (1977). (a) P. J. Marcoux, E. F. Siefert, and D. W. Setser, Int. J. Chem. Kinet., 7, 473 (1975); J. Phys. Chem., 82, 97 (1978); (b) G. Rlchmond and D. W. Setser, J. Phys. Chem., to be submitted; (c) D. W. Setser and E. E. Slefert, J. Chem. Phys., 57, 3613, 3623 (1972). (a) A. D. Clements, H. M. Frey, and R. Walsh, J. Chem. Soc., Faraday Trans. 7, 73, 1340 (1977); (b) R. J. McCluskey and R. W. Carr, J. Phys. Chem., 80, 1393 (1976); (c) T. H. Rkhardson and J. W. Simons, J. Am. Chem. Soc., submitted for publication. (a) H. M. Frey, Trans. Faraday Soc.,58, 957 (1962); (b) ibid., 80, 83 (1964): (c) H. M. Frey and D. C. Marshall, ibid., 81, 1715 (1965); (d) M. K.’Knecht, J. Am. Chem. Soc., 91, 7667 (1969). B. E. Holmes, Ph.D. Thesis, Kansas State University, 1976. S. W. Benson, “Thermochemical Kinetics”, Wiley, New York, N.Y., 1968. Y. N. Lin and B. S. Rabinovitch, J . Phys. Chem., 74, 1769 (1970). J. 0. Hirshfelder, C. F. Curtiss, and R. B. Bird, “Molecular Theory of Gases and Liquids”, Wiiey, New York, N.Y., 1964. J. R. Partington, “An Advanced Treatise on Physical Chemistry”, Voi. 1, Longmans Green and Co., London, 1949, p 288. E. Cuellar, J. H. Parker, and G. C. Pimentei, J. Chem. Phys., 81, 422 (1974). D. J. Bogan and D. W. Setser, J . Chem. Phys., 84, 586 (1976). R. L. Johnson, K. C. Kim, and D. W. Setser, J. Phys. Chem., 77, 2499 (1973). W. G. Clark, D. W. Setser, and K. Dees, J. Am. Chem. Soc., 93, 5328 (1971). (a) R. C. Lord and D. G. Rea, J. Am. Chem. SOC.,79, 2401 (1957); (b) B. Bak et al., J. Mol. Sfruct., 3, 369 (1969). (a) R. G. Snyder and J. H. Schachtschneider, Spectrochem. Acta, 21, 169 (1965); (b) V. W. Luttke and S. Braun, Ber. Bunsenges. Phys. Chem., 71, 34 (1967); (c) N. V. Tarasova and L. M. Sverdiov, Opt. Spectrosc., 21, 176 (1966). C. S.Elliott and H. M. Frey, Trans. Faraday Soc., 82, 895 (1966). N. V. Tarasova and L. M. Sverdlov, Opt. Spectrosc., Suppi. III, 71 (1967). K. Hsu, R. J. Buenker, and S.D. Peyerimhoff, J. Am. Chem. Soc., 94, 5639 (1972).
