T H E
J O U R N A L
O F
PHYSICAL CHEMISTRY Registered i n U.S . Patent Office 0 Copyright, 1975, by the American Chemical Society
VOLUME 79, NUMBER 5 FEBRUARY 27, 1975
Reactions of Singlet Methylene with Butadiene. High Energy Isomerizations of Vinylcyclopropane P. M. Crane’ and T. L. Rose* Department of Chemistry, Texas A&M University, College Station, Texas 77843 (Received June 24, 1974)
Singlet methylene produced by photolysis of diazomethane at 436 nm was allowed to react with butadiene in oxygen-scavenged systems over a pressure range of 10 to 1400 Torr. In agreement with earlier results six major reaction products were found: isoprene, vinylcyclopropane, 1,4-pentadiene, cyclopentene, cis-1,3pentadiene, and trans-1,3-pentadiene. Isoprene was formed solely by C-H insertion and 1,4-pentadiene only by isomerization of vinylcyclopropane. The relative reactivity favoring methylene C=C addition us. C-H insertion was =22:1 which does not differ significantly from the values obtained in the unscavenged system. The calculated isomerization rates of vinylcyclopropane to cyclopentene and 1,4-pentadiene using the RRKM theory and the thermal Arrhenius parameters were in good agreement with the experimental values. To fit the data for the 1,3-pentadiene isomers, however, it was necessary to adjust the parameters to give the observed experimental rates. The new values agree well with those estimated on the basis of thermochemical kinetic techniques using experimental results on the pyrolysis of l-cyclopropyl-2-methyl-lpropene.
Introduction Although studies on the reactions of methylene are legion,2a there are relatively few investigations on systems with conjugated double bonds. Butadiene has been studied by Franzen,2bby Grzybowska, Knox, and Trotman-Dickenand most extensively by F r e ~The . ~ results of methylene reactions with cyclopentadiene have been reported by our l a b ~ r a t o r y In . ~ the course of this latter work, it became apparent that a reinvestigation of the butadiene system was necessary in light of the new understanding of methylene reactions. For example, the earlier work was done in an unscavenged system so that both the singlet and triplet methylene species contributed to the product spectrum. No quantitative comparison was made between the chemical activation isomerization rates and those calculated by the RRKM theory using the thermal Arrhenius parametem6 The work reported here addresses itself primarily to the question of isomerization of vinylcyclopropane which has been chemically activated by singlet methylene reactions with butadiene. A secondary goal is to evaluate the selectivity of singlet methylene for C-H bond insertion us. C=C bond addition and the relative importance of 1,2 and 1,4 addition which was the subject of a recent theoretical st~dy.~
The principal product from the reaction of methylene with butadiene is highly excited vinylcyclopropane (VCP). Knowledge of the Arrhenius parameters for the subsequent isomerizations of this molecule is very important since it forms the basis for understanding rearrangements of other vinylcyclopropane analogs. In the thermal isomerization of VCPs,9 cyclopentene accounts for 96% of the isomerization products, the other products being 1,4-pentadiene (14P), cis-1,3-pentadiene (c13P), and trans- 1,3-pentadiene (t13P). Thus while the rate data and Arrhenius parameters for the ring expansion product are expected to be quite good, the values for the other isomers may be subject to larger errors. This is especially true for the 1,3-pentadiene isomers since the effect of the equilibrium between the cis and trans formslOJ1 and the polymerization of these products was not taken into account in the thermal study.11 It is possible that these effects are in part responsible for the differences in the experimental and estimated Arrhenius parameters for the 1,3-pentadiene isomers.12J3 In the chemically activated system, the VCP is sufficiently excited that the straight chain isomers, whose reaction pathways involve higher activation energies and higher preexponential factors than that leading to cyclopentene, are formed in higher relative yields than in the thermal system. The data, therefore, are particularly suitable to use 4 03
P. M. Crane and T. L. Rose
404
with the RRKM theory to test the thermal Arrhenius parameters. Experimental Section The experimental details are essentially the same as described previ~usly.~ Briefly, diazomethane was produced from N,N’-nitrosomethylurea and KOH and stored at liquid nitrogen temperatures in a butylphthalate matrix. Instrument grade butadiene (99.5%) and bone dry grade oxygen (99.6%) were obtained from Matheson Co., Inc. and used without further purification. The C5H8 isomers used to identify the reaction products were obtained in the highest purity available from Chemical Samples Co. Cyclopentadiene was prepared by cracking the dimer.5 The reaction vessels were 2-in. diameter Pyrex cylinders with Pyrex flats epoxied to the ends and having a volume of about 350 ml. Samples were filled on a high-vacuum line fitted with Teflon high-vacuum stopcocks and diaphram pressure gauges. Most of the reaction mixtures contained about 8% diazomethane and 10% oxygen. Changes in a factor of 2 in these percentages had no significant effect on the relative product yields. Irradiations were done using a PEK 200-W high-pressure Hg arc lamp with a narrow band ( f 1 0 nm) filter to isolate the 436-nm wavelength. For the results reported here the irradiation times were 3 hr. Time studies a t 400- and 50-Torr irradiations from 2 to 6 hr showed changes in the product ratios of less than 10% which is the estimated experimental error. All experiments were run at room temperature, 25 f 3’. The reaction mixture was analyzed by FID gas chromatography using a l/s-in. tandem column of 65 f t of silicone oil SF-96 (lo%),10 ft of PP’-oxydiproprionitrile (30%), and 10 ft of dimethylsulfalone (5%) at room temperature. Relative retention times of the products to 1,3-butadiene were 14P, 1.90; ISP, 2.42; t13P, 2.86; VCP, 3.12; c13P, 3.22; CPD, 3.36; CP, 3.50. Products were identified by comparison of their retention times with authentic samples. No other identification was performed since the product spectrum agreed with that reported earlier4 and no additional products in the C5 range were observed. Peak areas were measured by an electronic integrator. The detector sensitivity was assumed to be the same for all the C5 products. Results Experimental Rates. The product spectrum of the reactions of methylene with butadiene in an oxygen scavenged system was determined over a pressure range of 10 to 1400 Torr. Seven products were obtained: vinycyclopropane, isoprene, cyclopentene, l,l-pentadiene, cis-1,3-pentadiene, trans-1,3-pentadiene, and cyclopentadiene. As reported by Frey, these results are interpreted according to the following initial reactions of singlet methylene with butadiene and the subsequent isomerizations of vinylcyclopropane as shown in Figure 1.
(c13P)
The per cent yields of the products as a function of pressure are given in Figure 2. The Journal of Physical Chemistry, Vol. 79, No. 5, 1975
Q +H2 Figure 1. Reaction scheme for the isomerization of chemically activated vinylcyclopropane produced by reaction of singlet methylene with butadiene. Isomerization to isoprene (k5)is included although the measured rate was essentially zero. w is the rate of collisional stabilization.
1
15
,.
10
-
m
“ 0 5
PRESSURE ( t o r r )
Figure 2. Pressure dependence of the C5 products produced from the 436-nm photolysis of diaz0methane:oxygen:butadiene mixtures. Yields are given in per cent of total C5 products.
Application of the steady-state approximation to this mechanism leads to an expression which may be used to determine the total isomerization rate of vinylcyclopropane ( k =~k l k z k~ k4 k5) and the relative importance of C=C bond addition ( k ~to) C-H bond insertion (kI = k~ kg Kc). Thus
+ + + +
+ +
The left-hand side of eq 1 is the ratio of reaction products other than VCP to VCP. w is the collisional stabilization constant. Assuming strong collisions and diameters of the VCP and butadiene of 5.2 A, w is equal to the collision number of 1.2 X lo7 Torr-l sec-l for our reaction mixture^.^ Figure 3 shows a plot of the experimental data for the left-hand side (decomposition/stabilization) us. the reciprocal of the pressure. The least-squares fit gives k I / k D = 0.14 and k T = 15.2 f 0.7 X lo8 sec-l. The data used to obtain the isomerization rates to 14P and ISP are also given in Figure 3 where D represents the yield of the isomerization product and S the stabilized
Reactions of Singlet Methylene with Butadiene
405
TABLE I: Experimental and Calculated Rates for Isomerization of Chemically Activated Vinylcyclopropane Thermal Arrhenius parameters' 10-ak,xpt, 10-*kcalCa, E,, kcal
/
VCP
/O
VCP VCP
VCP
--*l
k2
k3
-+ k4
1%
set'*
sec-*
mol-'
A,sec"
14P
4.7 I 0.1
4.71
57.3
14.45
t13P
4.2 I 0.5
4.15 3.97
55b
14.1' 13.0
3.05
56b
1.89
56.2
14.1' 13.9
3.50
49.7
13.61
Reaction
c13P CP
3.1
* 0.4
3.3 kO.6
53.6
k5
p-' / 1 0 - ~ t o r r - ' Figure 3. Decomposition (D)lstabilization(S)ratio plotted vs. the reciprocal of the pressure for the total isomerization of vinylcyclopropane ( 0 )and for isomerization of vinylcyclopropane to 1,4-pentadiene (0)and isoprene (0).
Not determined VCP ISP 50.04 a Taken from ref 8 unless otherwise noted. b Adjusted in RRKM calculations to give calculated rates for the sum of k z + k s equal to the experimental value. c Estimated by thermochemical kinetic techniques (see text).
VCP yield. The rates are then determined from the equation D
1
s
o
- = - (IkT
+
k,)
+
I
(2)
where I is the intercept of the line and k, the corresponding isomerization rate for each product calculated from the least-squares fit of the slope and the value of kT determined above. I will be zero for those products which are formed only by VCP isomerization and not by methylene insertion into C-H bonds of butadiene. As is seen in Figure 3 this is the case for 14P. The evaluated rates from eq 2 are given in Table I. The value of k g for ISP formation determined from an intercept of 0.07 f 0.03 and slope of 9.2 f 0.5 Torr is zero within the experimental error, corroborating the reports of both thermal studiess and previous chemical activation ~ o r k that ~ - ~ISP is not a product of VCP isomerization. The rate for VCP isomerization to CP and subsequent decomposition of CP to CPD is determined from the data in Figure 4. Use of eq 2 with I = 0.04 f 0.04 for CP formation and I = 0 for CPD formation gives k4 = 3.3 f 0.6 X lo8 sec-l and k8 = 1.52 f 0.12 X lo8 sec-l. Using only the six high-pressure (400-1400 Torr) points, the intercept for CP formation is -0.015 indicating that it is unlikely that significant CP is formed directly from 1,4 addition of singlet methylene to butadiene.7 The kinetic expression for the derivation of the individual rates of formation of t13P and c13P is extremely complicated since these products are formed by both C-H insertion and isomerization of VCP in addition to the complication concerning their interconversion. At zero pressure the ratio t13P/c13P should give the ratio of the rate constants k7/k6. The experimental ratios over the pressure range from 200 to 10 Torr show only a very slight increase with the extrapolated value at 0 Torr of 1.3 f 0.1 for k7/ks. It is clear that the ratio of the trans to cis isomers is relatively insensitive to changes in pressure over the range studied.
D/S
Flgure 4. Decompositionlstabilizationratio plotted vs.the reciprocal of the total system pressure for isomerization of vinylcyclopropane
to cyclopentene (0)assuming all the cyclopentadiene arises from cyclopentene and for decomposition of cyclopentene to cyclopentadiene (0).
Whether this is due to the fact that k 7 and k6 are much faster than kz and k3 or that k7/k6 = k ~ / k 3cannot be answered from our data. Figure 5 shows a plot of the data for the individual t13P and c13P yields and for the sum. Using eq 2 for the total 1,3-pentadiene yield we obtain a rate of 7.2 f 0.7 X los sec-l. From the experimental ratio of 1.3 f 0.1 for trans/ cis, kz = 4.1 f 0.5 X lo8 sec-l and ks = 3.1 f 0.4 X los sec-l. The intercepts from the plots of the individual yields are 0.017 for t13P and 0.036 for c13P. Because of their small absolute magnitude, the error limits in these values are f100%. Nevertheless the values show that the high pressure ratio of t13P/c13P due to C-H insertion is 0.5, different from the observed ratio arising from isomerization of VCP. Calculated Rates. The rates for the isomerization of VCP to the four C5H8 isomers were calculated using the RRKM theory of unimolecular reactions and adjusting the The Journal of Physical Chemistry, Vol. 79, No. 5 , 1975
406
P.
M. Crane and T. L. Rose
ratio of 2.1 was decidely different from our observed value of 1.3. In an attempt to reconcile these differences we adjusted the transition state frequencies to give A values of 14.1 for both isomers as estimated by the techniques O’Neal and Benson12J3J6 (see Appendix). The activation energies were then adjusted, retaining the difference of 1 kcal/mol for the cis and trans isomerization, until the total isomerization rate agreed with the experimental value. The resulting activation energies are 56.0 and 55.0 kcal/mol for rearrangement to the cis and trans isomers, respectively. As seen in the Appendix these numbers are in good agreement with the estimated values based on the results from the isomerization of l-cyclopropyl-2-methyl-l-propene.17 The calculated trans:cis ratio is also very close to our experimental value.
o=\
P+)’I
o -3t o r r -’
Flgure 5. Plot of decomposition/stabilization ratio vs. the reciprocal of the total system pressure for isomerization of vinylcyclopropane
to the 1,3-pentadiene isomers.
transition state frequencies to give agreement with the reported prexponential factor obtained from thermolysis of VCP.8 The equation used to calculate the high-pressure unimolecular rate was
where the quantities have been defined previou~ly.5~,~ As was done with the calculations on the cyclopentadiene systhe energy spread in E* is neglected and the approximation of Hoare and Ruijgrok was used for evaluation of the sum and density of the states of the activated complex (A+) and the chemically activated molecule (A*).I4 The average excitation energy of the chemically activated VCP estimated from thermodynamic consideration (see Appendix) was 109.8 kcal/mol. Use of this value in the RRKM calculations, however, lead to calculated rates for all the isomerizations which were too low by at least 25%. Excellent agreement for the isomerization to both cyclopentene and 1,4-pentadiene was obtained by increasing ( E * ) to 111.1kcal/mol. This 1.3 kcal/mol difference can be attributed to uncertainity in the estimated A H t 2 9 8 value of VCP and in the RRKM calculation itself, or to the possibility that the higher ( E * ) value is the result of a higher value in our reactions of E* (CH2), the excess energy carried into the reaction by the methylene. This latter conclusion is consistent with the higher reactivity of butadiene2, compared to cis-butene, the system on which the calculated value was used.15 There were also indications in the work with cyclopentadiene that the excess energy of the methylene was somewhat higher than in the cis-butene system.5c The details concerning the frequencies and moments of inertia for VCP and the transition states leading to each C5Hs isomer are given in Table I1 and the Appendix. The calculated rates are given in Table I along with the Arrhenius parameters used. It is seen that the agreement between the calculated and experimental rates is very good for the CP and 14P isomers using the thermal Arrhenius parameters. For formation of 13P, the total rate for the two isomers was only 80% of the observed rate. Even more important was th6 necessity of making unrealistic assumptions about the structures of the transition states in order to get preexponential factors which differed by 100.9 as required by the thermal data. Finally, the calculated t13PIc13P The Journal of Physical Chemistry, Vol. 79, No. 5, 1975
Discussion There is qualitative agreement between this work and that published p r e v i o u ~ l yin~ the ~ ~ product spectrum and pressure dependence of the yields. We, too, observed no isomerization of VCP to isoprene, k5 < 0.04 X sec-1. Since this is the only study, however, with oxygen scavenging and a narrow irradiation band width, the results can be attributed solely to singlet methylene having a small energy range. Our vinylcyclopropane yield at infinte pressure ( 4 8 % ) is slightly higher than that reported previously3 with the concurrent loss in the 1,3-pentadiene isomers. The resulting value for the relative rates of 1,2 C=C addition to C-H insertion is >22:1 which is about a factor of 2 higher than that reported for most alkene systems.2a Although the error limits are large, methylene seems to react with the vinylic C-H bonds to give isoprene twice as fast as with those to give the 1,3-pentadienes. The higher 1,3-pentadiene yield a t infinite pressure, the higher translcis insertion ratio and the higher 13P/ISP ratio in the unscavenged system all indicated that some 1,3-pentadiene may be formed by triplet methylene adding stepwise to the C=C bond a t the terminal carbons as observed for the cis%butene systems.2aThus
Franzen2b and Grzybowska, et al.,3 have included in their mechanism the direct formation of cyclopentene by 1,4 addition of methylene to butadiene. A recent molecular orbital study has shown that this addition is markedly less efficient than 1,2 a d d i t i ~ nFrom . ~ our intercept for cyclopentene formation in Figure 3, an upper limit of 6% of the singlet methylene reacts by 1,4 addition to give cyclopentene and the 1,2/1,4 ratio is >15 in support of the theoretical analysis. As mentioned previously the high-pressure data indicates that the ratio is probably even higher. The rates of isomerization of VCP in this study are slightly higher than those reported previously. Our h~ is 1.7 times as fast as Frey’s4 value measured in the unscavenged butadiene system at 65’. Since the stabilization rates used in the two systems were essentially the same, the difference is probably not due to a systematic error. Rather, the increase reflects the higher average energy brought into the reaction by the singlet methylene compared to the triplet species. The RRKM calculations show that the differences in rates amount to a decrease in the average excitation energy of VCP of about 5 kcal/mol in the unscavenged system.
Reactions of Singlet Methylene with Butadiene
4 07
TABLE 11: Vibrational Frequencies for Vinylcyclopropane and Best Models for Activated Complexes=
--_
Motion Stretches C-C
c=c
C-H Bends CH2(def )
Vinylcyclopropane
1000(4) 1625 3050(8)
14P complex
-___
1000,1300(2),258 1300 3050(8)
1425 (3) 1425 (3) 1000(4),1050(2) 1000(3),1050,340(2) CH, (wag) 800(2), 900 800(2),900 C-C-H (in plane) 1300(2) 1300,r c C-C-H (out plane) 700(2) 700(2) C-C-C + ring 310(2),425 310(2), 500 Hindered rotor 15.3b 100 a Values in cm-1, rc is reaction coordinate. * amu &/molecule. CH,(rock, twist)
C P complex
13P complex
1000(2), 675,1300 1300 3050(8)
1000,1300(2),258 1300 3050(8)
1425(3) 1000(4), 1050(2) 800(2),900 1300(2) 700(2) 225,112(2) rc
1425 (3) 1000(3),1050,680,340 800(2),900 1300,r c 700(2) 310,575,640 135
izations the difference in the activation energies for the cis Application of the RRKM theory and the thermal Arand trans isomers are about 1 kcal/mol, reflecting the usual rhenius parameters for vinylcyclopropane isomerization difference of 1 kcal/mol in the heats of formation of the cis gave calculated rates in good agreement with the experiand trans isomers.16 For the VCP system, the activation mental rates for formation of cyclopentene and 1,4-pentaenergy leading to the cis isomer is 2.8 kcal/mol higher than diene. The transition state frequencies for the isomerizathat leading to the trans form. Equally as uncommon is the tion of 1,4-pentadiene were adjusted according to the exdifference in the preexponential factors of almost a power pected changes if only about one half of the allyl resonance of 10 whereas in most cis-trans studies the A factors differ was retained. For the cyclopentene isomerization we found by less than a factor of 2. The combination of the large difit easier to think of the transition state as developing from ference in the E , and A values lead to about equal rates of the cyclopentene product. The transition state frequencies formation of the cis- and trans-1,3-pentadiene from VCP associated with the ring vibrations were selected as onein the temperature range studied in the pyrolysis study. As half those expected for cyclopentene. l8 Several different seen from Table I, however, at the higher energies involved possibilities were tested as the reaction coordinate. Acceptin chemical activation these Arrhenius parameters predict able agreement with the thermal A factors was obtained, a factor of 2 difference in the formation rates whereas the however, only by letting the reaction coordinate be the inobserved ratio was 1.3. ternal rotor of the VCP. In the product molecule this moFor the 1-cyclopropyl-2-methyl-1-propene system the tion becomes an out-of-plane ring vibration and would be activation energies differed by 0.9 kcal/mol, and the preexthe expected reaction coordinate for the reverse reaction.lg ponential factors were virtually identical. In addition, the The RRKM calculations for formation of the 1,3-pentarate of formation of the cis and trans isomers under the diene isomers using parameters from the pyrolysis study reaction conditions are comparable to formation of the cygave rates in poorer agreement with the observed values clopentene product thereby increasing the reliability of the than for the other products. This descrepancy could be due data. Using these results as a guide for estimating new Arto either the assumption of strong collisions or to a problem rhenius parameters for the VCP isomerization (see Appenwith the RRKM calculation, itself. There is little doubt dix) and adjusting the transition state frequencies accordthat at the excitation energy of VCP cascade deactivation ingly, very good agreement was obtained between the calis occurring. The work of Rynbrandt and Rabinovitch20 on culated and experimental values not only for the total rate the methylene chemically activated cis-dimethylcycloproof isomerization but also for the ratio of k&3. We estimate pane system showed curvature in the D / S curves a t ratios that the accuracies of the E , values at f l kcal/mol and the above 8. Our curves (Figures 3-5) show little curvature over preexponential factor at 10*0.2. the pressure range studied so that we are unable to evaluThe thermaI studiesll of isomerization of the cis and ate the effects of cascade collisional deactivation and detertrans isomers also supports our new parameters. From the mine the unimolecular rates averaged over the resulting enthermal rate expressions, k6 = 1013.3e-52@00/RT and k7 = ergy distribution. These rates are expected to be somewhat 1013.49e-52,000/RT, it is apparent that at higher energies the lower than those reported here for the high-pressure reequilibrium value of k7/k6 approaches 1.5. Use of the thergion. T o a first approximation, however, the rates for the mal parameters for k 2 and k3 give a ratio of 2.1. Even if the isomerizations to all four isomers will be lowered by about subsequent geometric isomerization of the 1,3-pentadiene the same amount. The higher rates may at least in part exisomers is important in our system, the ratio would not deplain the necessity of raising the average excitation energy crease below 1.5 and would not reach the observed value of ( E * ) to fit the CP and 14P data. With this normalization 1.3. Only if the initial ratio of k2/k3 5 1.3 can the observed the calculated rates for 1,3-pentadiene formation were also value be obtained. We have, in fact, assumed from the expected to agree with the observed values using the therpressure independence of the t13P/c13P ratio that h6 and mal Arrhenius parameters. The published valuess for the thermal Arrhenius paramk7 are not important at the pressures of our study. This aseters for the 1,3-pentadiene isomers are surprising in light sumption means that our k2/k3 ratio is an upper limit, and of those reported for cis-trans i s ~ m e r i z a t i o n s ~and , ~ ~ ~ the ~ ~ ,Arrhenius ~~ parameters for the hz and k3 isomerizations for isomerization of 1-cyclopropyl-2-methyl-1-propeneto may be even closer. cis- and trans-2-methyl-2,4-hexadiene.17 For these isomerA final question remaining is reconcillation of the therThe Jourrial of Physical Chemistry, Vol. 79, No. 5, 1975
P. M. Crane and T. L.
mal studies with the new data presented here. Calculation of the relative rates a t 630'K using the new data give kl: k2:k3:k4 of 1.5:3.8:1.7:93.0 compared to the reported ratios of 1.5:1.0:1.0:96.5. These differences are not outside the experimental errors considering the assumptions already pointed out in the calculation of the rates reported in this work. There is also the possibility of errors due to the high reactivity these conjugated species,ll especially in the thermal study where the yields of the 1,3-pentadienes were so small. Furthermore, no account was taken in either study of the cis-trans isomerization after their formation. Benson has shown that the equilibrium ratio of trans to cis decreases with increasing temperature.lo In the thermal system, therefore, conversion of relatively more trans to cis a t higher temperatures would make the apparent rate of formation of the trans isomer from VCP not increase as rapidly giving too low an activation energy and A factor. The question remains open as to whether the differences in the Arrhenius parameters for the thermal and chemically activated work are due to experimental difficulties in either study or to a problem with application of the RRKM theory itself. We are currently studying the chemically activated VCP isomerization using methylene produced by photolysis of diazomethane at 366 nm. This data will give us a different excitation energy of vinylcyclopropane and allow us to check the conclusions reached in this paper. In addition, the study will be extended to lower pressures to probe the effect of cascade deactivation and will include explicitly the secondary isomerizations of the cis- and trans- 1,3-pentadiene isomers by the method reported by Carter and Tardy.22 Acknowledgment. The support of this research by the Robert A. Welch Foundation of Houston, Texas, and the Environmental Quality Program of Texas A&M University is gratefully acknowledged.
Appendix RRKM Calculations. An estimation of the average internal energy in the chemically activated VCP molecule was made using the following equation: -(E*) = AHrs,,, - E*(CH,)
+ RT
- (E298
Eg)vib
Rose
tion was 15.3 amu A2/molecule. In the RRKM calculation this rotation was treated as a free rotor. It has been pointed out that this approximation can lead to as high as 20% error in the energy level sums even at high energy.29In our calculation, however, the density of states is used and this value should be adequately calculated by the free rotor approximation a t excitation energies of 100 kcal/mol. For evaluation of the preexponential factor, the hindered rotation contributed 6.8 gibbs/mol of entropy at 600'K. Calculation of AS" and AC," using these parameters gave good agreement with the values calculated using group properties.16 Selections of the final frequencies used in the transition states were based on standard group frequencies for partial bond bending, stretching, and torsional frequencies. In all cases the selected frequencies resulted in entropy changes at 600'K which gave A factors within 10O.l of the thermal, or for the 1,3-pentadienes, estimated values. The same frequencies were used for the transition state leading to c13P and t13P. Vinylcyclopropane has a rotational symmetry (a) of one and only one optical isomer (n = 1).For all the transition states a = 1 and n+ = 2. The resulting reaction path degeneracy defined as an+/a+n is thus two for all the isomerizations. The ratio of the partition functions for the adiabatic rotations was set equal to one for all isomerizations except to cyclopentene. For this case, the transition state was assumed to have the same value for the product of the principle moments of inertia as cyclopentene. Using the value of 6.21 X lo5 amu3 A6/molecule taken from Butcher,30Q1+/Q1* was 0.64. Because of the problems in obtaining good agreement between the RRKM calculated rates and the experimental values using the thermal Arrhenius parameters of Wellington,8 we made a new estimate of these values. Benson and O'Neal have previously made two such attempts12J3 leading to different results neither of which gave us improved agreement between the calculated and experimental values. The following estimates use the standard nomenclature and method.13
(4)
where AHr,298 is the heat of reaction for singlet methylene addition to butadiene, E*(CH2) the excess energy brought into the reaction by methylene, and (E298 - EO)"&accounts for the vibrational energy of VCP at 298OK. The RT term takes into account both the corrections for use of enthalpy and energy and the mole change of gas in the reaction from two to one. In calculating the first two terms, Taylor and Simon's value15 of AH;&CH2) E*(lCHz) of 112.6 kcal/ mol was used adjusted to 298'K. The values for f i t 2 9 8 of the other species were taken from Benson and O'Neal's tabulation.13 The resulting value of ( E * ) was 109.8 kcal/ mol. The molecular frequencies used for the RRKM calculations are given in Table 11. The vibrational frequencies for vinylcyclopropane were estimated from the standard group frequenciesl6 and comparisons with the reported frequencies for methylcyclopropane,23~~4 dimethylcyclopropane,2" butadieneF6927 and ethylcy~lopropane.~~ The moment of inertia was calculated using the structural parameters of de Meijere and Liittke.28 The resulting product of the principal moments of inertia was 9.64 X lo5 amu3 A6/molecule. The reduced moment of inertia used for the internal rota-
\
trans
At 600'K AS, = -2(Et
nPr)2.6 - (CH,
6
w),.~ -
+
The Journal of Physical Chemistry, Vol. 79, No. 5, 1975
= -18.0 - 4.1 - 0.33
AS' = 12.6 - 11.30
Eest(t13P)
+
(tBde)t + (P.ie)t 7.25 + 2.8 + 1.08 = -11 -30 gibbs/mol
+
R In 2 = 2.7; Aest =
DH"(C-C) - R a l l y 1 + E ~ . m i g = 53.0 - 8.4 + 10.8 = 55.4 kcal/mol
EeSt(c13P) = EeS,(t13P)
+
1 = 56.4 kcal/mol
The activation energy estimate is based on the results for the isomerization of cyclopropyl-2-methyl-1-propeneto cis- and trans-2-rnethyl-2,4-hexadiene.l7 In this molecule the observed activation energy is 6 kcal/mol higher than
HgpP1) Quenching Cross Sections
4 09
expected assuming an allyl resonance of 4 8 kcal/mol for a dimethyl allyl radical.31 By analogy it is assumed that the transition state leading to the 1,3-pentadiene also loses about one-third of the expected 12.6 kcal/mol resonance energy. This decreased resonance means that the Et nPr rotation can be taken as a hindered rotation with an increased barrier rather than a three electron torsion, which raises the preexponential factor to a value of 1014.1. -+
References a n d Notes, (1) Robert A. Welch Foundation UndergraduateScholarship Recipient. (2) (a) W. Kirmse, "Carbene Chemistry," 2nd ed, Academic Press, New York, N.Y., 1971. (b) V. Franzen, Chem. Rev., 95, 571 (1962). (3) B. Grzybowska, J. H. Knox, and A. F. Trotman-Dickenson, J. Chem. Soc., 4402 (1961); 3826 (1962). (4) H. M. Frey, Trans. Faraday Soc., 58, 516 (1962). (5) (a) T. L. Rose, J. Amer. Chem. SOC., 95, 3500 (1973); (b) J. fhys. Chem., 76, 1389 (1972); (c) T. L. Rose, R. J. Seyse, and P. M. Crane, Int. J. Chem. Kinet., in press. (6) P. J. Robinson and K. A. Holbrook, "Unimolecular Reactions," Wlley, New York, N.Y., 1972. (7) H. Fujimoto and R. Hoffman, J. fhys. Chem., 78, 1167 (1974). (8) C. A. Weillngton, J. fhys. Chem., 66, 1671 (1962).
(9) M. C. Flowers and H. M. Frey, J. Chem. Soc., 3547 (1961).
(IO) K. W. Egger and S. W. Benson, J. Amer. Chem. SOC., 87, 3311, 3314 (1965'); 88, 241 (1966). (1 1) H. M. k e y , A. M. Lamont, and R. Walsh, J. Chem. SOC.D, 1583 (1970). (12) H. E. O'Nealand S. W. Benson, J. fhys..Chem.,72, 1855(1968). (13) S. W. Benson and H, E. O'Neai, Net. Stand. Ref. Data Ser., Net. Bur. Stand., 2'f, 63 (1970). (14) M. R. Hoare and T. W. Ruijgrok, J. Chem. fhys., 52, 113 (1970). (15) (a) J. W. Slmons and G. W. Taylor, J. fhys. Chem., 73, 1274 (1969); (b) G. W. Taylor and J. W. Slmons, IbM., 74, 464 (1970). (16) S. W. Benson, "Thermochemical Ktnetics," Wiley, New York, N.Y., 1968. (17) C. S. Elllot and H. M. Frey, J. Chem. SOC.,345 (1965). (18) H. E. O'Neal and S. W. Benson, J. Chem. Eng. Data, 15, 266 (1970). (19) H. E. O'Neal and S. W. Benson, Int. J. Chem. Kinet., 2, 423 (1970). (20) J. D. Rynbrandt and B. S. Rabinovitch, J. Phys. Chem., 74, 1683 (1970). (21) D. W. Setser and E. E. Siefert, J. Chem. fhys., 57, 3623 (1972). (22) W. P. L. Carter and P. C. Tardy, J. Phys. Chem., 78, 1579 (1974). (23) G. B. Kistiakowsky and B. B. Saunders, J. Phys. Chem., 77,427 (1973). (24) F. H. Dorer and B. S. Rabinovitch, J. fhys. Chem., 69, 1973 (1965). (25) G. W. Taylor and J. W. Simons, Int. J. Chem. Kinet., 3, 25 (1971). (26) L. M. Sverdiov and N. V. Tarasova, Opt. Spektrosk., 9, 160 (1960). (27) R. K. Harris, Spectrochlm. Acta., 20, 1129 (1964). (28) A. de w e r e and W. Luttke, Tetrahedron, 25, 2047 (1969). (29) S. E. Stein and B. S. Rabinovitch, J. Chem. Phys., 58, 2438 (1973). (30) S. S. Butcher and C. C. Costain, J. Mol. Spectrosc., 15, 40 (1965). (31) A. S. Rodgers and M. C. R. Wu, J. Amer. Chem. SOC.,95, 6913 (1973).
Further Mercury( 3P1) Quenching Cross Sections S. D. Gledltsch and J. V. Michael* Department of Chemistry, Carnegie-Melon University, Pittsburgh, Pennsylvania 752 13 (Received September IS, 1974) Publication costs assisted by the U S .Atomic Energy Commission
Quenching cross sections of mer~ury(6~P1) with Hz, HD, Dz, C3H6, l-C4H8, l-CbH10, CdHs, and CzHz have been determined from modified Stern-Volmer plots in a steady-state photolytic experiment. Low mercury atom concentrations were maintained to prevent imprisonment of 2537-A radiation. The cross sections which have been determined in this study are compared with those reported by other investigators. Preferred quenching cross sections are proposed for 11molecules.
Introduction The quenching of mercury 2537-A resonance radiation by a foreign gas is the most extensively investigated photochemical system and has been the subject of thorough re~ i e w . l -This ~ study has investigated the efficiency with which mercury atoms are quenched by a variety of molecules. The technique of the present study was recently presented along with measurements of cross sections for nine mole c u l e ~Phosphorescence .~ as a function of absorbed intensity is measured, and classical Stern-Volmer plots are obtained. From a knowledge of the Hg(3P1) emittive lifetime, bimolecular quenching rate constants can then be inferred from slope to intercept analysis, and cross sections are calculated from the usual kinetic theory of gases expression. This type of measurement has been known for over 50 years5 and has been used by numerous workers in mercury quenching e~periments.l-~ The feature of the earlier work4 and this work which is unique is that the measurements were taken at sufficiently low [Hg]1 that radiation imprisonment is negligible or nearly so. The problem of radia-
tion diffusion has been discussed previously,6-10 and its effects on quenching rate constants has been assessed.4 Eight cross sections have been measured including two which were previously measured. Analysis of all data has led to preferred cross sections for 11 molecules. Use of these preferred values will allow many more cross sections to be accurately inferred. Experimental Section The experimental apparatus which was used in this study is the same as that fully described by Michael and S u e ~ sRadiation .~ from a low-pressure mercury resonance lamp is cooled by a flow of compressed air to minimize reversal of the 2537-A resonance line. The radiation is collimated by a quartz lens after passing through an interference filter. The collimated beam passes through a quartz photolysis cell in which an observation window is oriented perpendicular to and midway between the end windows to facilitate detection of phosphorescence radiation emitted at right angles to the incident beam. The photolysis cell is separated from a conventional Pyrex high vacuum line by a The Journal of Physical Chemistry, Vol. 79, No. 5, 1975
