J. W. SIMONS AND B. S. RABINOVITCH
1322
Secondary Intermolecular Kinetic Isotope Effects in the Methylene Radical-cis-Butene-2-d,-cis-l,2-Dimethylcyclopropane-d, System'"
by J. W. Simonslband B. S. Rabinovitch Department of Chemistry, University of Washington, Seattle, Washington (Received October !2S3 1963)
A study of the geometric and structural isomerization reactions of chemically activated cis-1,2-dimethylcyclopropane-d~ (DRIC-do) and DMC-ds is reported. Activation was by addition of methylene, from the photolysis of ketene at 3200 A. and 25O, to the double bond of cis-butene-2-do and -d8. The measured intermolecular isotope effects for the geometric isomerization (k,(H)/k,(D) = 3.8) and for one of the structural isomerization (k,,(H)/kSp(D) = 4.3) reactions are, for the most part, secondary quantum statisticalweight effects. The effect on other structural isomerization processes (k,b(H)/k,b(D) = 5.2)is a mixed primary-secondary isotope effect. Theoretical calculations of rates and of isotope effects are in fairly good agreement with experimental values. Anomalous highpressure product compositions in both the -do and -d8 systems can be explained by the presence of ~ 2 9 triplet 7 ~ methylene radical reaction at high pressures. The addition of oxygen altered the product composition so as to indicate the removal of such triplet methylene reaction. Our earlier work on the isotope effects in singlet methylene radical C-H insertion and C=C addition reactions with cis-butene-2 has been extended. Calculations of the geometric isomerization rates of 1,2-cyclopropane-d2 and 1,2-dimethylcyclopropanehave been made and are compared to the existing data in thermal and chemical activation systems.
Introduction The existence and measurement of large normal intermolccular secondary kinetic isotope effects in uniniolecular decompositions of energized species, which take place in noneyuilibrium systems, have been reported and discussed p r e v i o u ~ l y . ~ -The ~ origin of the isotope effect has been shown to be of a quantum statistical, rather than of a mechanistic, nature. The magnitude of this isotope effect depends on the total degree of isotope substitution and on the absolute and relative magnitudes of ( E ) , the average energy of the energized species, and I&,, thc critical energy for reaction. Thc magnitude of ( E ) is governed by Emin,the minimum energy of the activated species, and hy f(E) dl?, the rionequilibrium distribution function of energy states above E,,,. To date, the isotopic systems studied by chemical activation have involved critical energies Eo in the , very small valucs (a few rcgion 30-33 kcal. i ~ o l e - ~with kcal. i ~ o l c - ~of ) the excess energy ((I?) - Eo) = (C+), as for cthyl radical^,*^,^ or with somewhat
larger values (around 8-10 kcal. mole-'), as for butylzb and propyl5 radicals. The addition of singlet methylene radicals to the double bond of olefins produces vibrationally excited cyclopr~panes.~JThis system offers the interesting possibility of studying these nonequilibrium normal secondary isotope effects at both a very high average energy ( E ) , with minimum energy (1) (a) This work was supported in part by NSF and in part by
(b) General Electric Foundation Predoctoral Fellow: abstracted in part from the Ph.D. thesis of J. W. S. (2) (a) B. S. Rsbinovitch and J. 13. Current, Can. J . Chem., 40,557 (1962); (b) J. W. Simons, D. W. Setser, and B. S. Rabinovitch, J . Am. Chem. Soc.. 84, 1758 (1962): (c) J. W. Simons and B. S. Rabinovitch, to be published. (3) B. S. Itabinovitch and D. W. Setaer, J . Am. Chem. Soc., 84, ONR;
1765 (1902).
J. H. Current and B. S. Rabinovitch, J . Chem. P h y s . , 38, 783, 1967 (1963). (5) W. E. Falconer, B. S. Rabinovitch, and It. J. CvetanoviO, ibid.. 39,40 (1903). (6) G. B. Kistinkoivsky and K. Sauer. J . Am. Chem. Soc., 78, 5699 (1956). (7) H. M. Frey and G. B. Kistiakowsky, ibid., 79, 6373 (1957). (4)
1323
INTERMOLECULAR KINETIC ISOTOPE EFFECTS IN METHYLENE SYSTEMS
--
E,,, 100 kcal. ~ n o l e - ~and , also a t high critical energy, Eo 60 kcal. The addition of methylene radicals, generated by the photolysis of ketene, to the double bond of cis-butene-2do and cis-butene-2-d8, and the relative rates of the geometric and structural isomerization reactions of the energized cis-1,2-dimethylcyclopropane-d, and cis-1,2-dimethylCyClOprOpane-de have been studied and are now reported. The effect of the deuterium substitution on the geometric isomerization rate is a secondary isotope effect; the effect on the structural isomerization rate involves mixed primary and secondary isotope effectsg; both a hydrogen and deuterium atom may move to give different products. During the course of this work, hydrogen-deuterium kinetic isotope effects in the addition of methylene radicals to the double bond of cis-butene-2&, and jin the insertion reactions into the vinylic and allylic carbon-deuterium bonds, were also determined. A preliminary account of these latter effects has appeared.I0 When oxygen is added to the systems, the magnitudes of these effects are somewhat altered. The effect of oxygen is interpreted, a t least in part, as indicating the presence of some ground triplet state methylene radicals in the systcin.
Experimental Materials. Ketene was prepared by pyrolysis of acetone and was purified by low temperature (- 78 ') gas chlomatography on Fluoropak. The purified inaterial contained 1.4% propylene and was stored at liquid nitrogen temperature. Phillips research grade cis-butene-2 (purity 99.89%) was used without further purification, since gas chromatographic analysis indicated the presence of a trace of trans-butene-2 as the only impurity. Phillips research grade ethylene (purity 99.9%) was used without further purification. * A mixture of butene-ds isomers containing minor impurities of propane, butane, butadiene, and some higher hydrocarbons was obtained from hlerck of Canada, Ltd. This riiixture contained 20-25% cisb ~ t e n e - 2 - dwhich ~ was separated and purified by gas chromatography. The chemical purity was 99%, with trans-b~tene-2-d~ as the major impurity. The isotopic purity of this isomer was checked mass spectrographically and found to be approximately 85% butene-&, 14% butene-d?, and -1% butene-&; correction for these impurities would amount to only a 3-47, effect on measured rates. Appamtus and Procedure. All gas handling was performed with a conventional vacuum system. The filtered radiation of a G.E. AH-6 high-pressure mercury
arc lamp was used for all photolyses. The filter was a 1-2-mm. Pyrex glass reactor wall and an aqueous solution of ?JiS04.6H20 and Cos04 7H2011 circulating through a Corex D glass envelope, having a light path through the solution of about 5 nim. The transmission of the filter was measured, and from the known lamp output and variation of ketene quantum yields12 and extinction coefficientsla with radiation frequency, the average wave length for ketene decomposition was determined to be -3200 A. Mixtures of ketene and cis-butene-2, with or without added oxygen, were photolyzed in Pyrex vessels of known volumes for reaction times varying between 30 and 90 min., depending upon the amount of ketene and the size of the reactor. The ratio of ketene to butene used was usually 1:15, and no significant variation in the product proportions of interest occurred as this ratio varied from 1:10 to 1:20. Systems without added oxygen will be designated as "pure," The entire condensable portion of the contents of a reactor was analyzed a t the end of each run. Analysis. Gas-liquid phase chromatography was used for all quantitative analyses. The analytical columns consisted of a 1-m. length of 20% hexainethylphosphoramide on firebrick followed by a 6-m. length of 20% AgKOS-ethylene glycol (saturated solution) on firebrick. A mixture of known composition and coinponents, similar in relative magnitudes to a reaction mixture, was used to calibrate the analytical columns. Since the products 2-methylbutene-1 and 3-methylbutene-1 were not resolved on these columns, only the total of these two components was determined. A correction to the 2-methylbutene-2 was determined for incomplete resolution of propylene from it; this correction was negligible a t high pressures, but increased to 50-70% a t the lowest pressures, particularly in the oxygen runs.
Results Product Yields and Composition. Eflect os Oxygen.14 The pure systems will be considered first. The total (8) D. W. Setser and B. S. Rabinovitch, Can. J . Chem., 40, 1423. (1962). (9) D. W.Set,ser and B. S.Rabinovitch, J . Am. Chem. Soc., 8 6 , 564 (1964). (10) J.
W.Simons and B. S. Rabinovitch, ibid.,
8 5 , 1023 (1963).
(11) W. A. Noyes and P. A. Leighton, "Photochemistry of Gases," Reinhold Publishing Corp., New York, N. Y., 1941. (12) B. T. Connelly and G. B. Porter, Can. J . Chem., 3 6 , 1640 (1958); J . Chem. Phys., 33, 81 (1960). (13) J. Knox, R. G. W. Xorrish, and G. Porter, J . Chem. Soc., 1482 (1952). (14) A. S . Strachan and W. A. Koyes, Jr., J . Am. Chem. Soc., 76, 3258 (1964); R. A. Holroyd and W. A. Noyes, Jr., ibid., 78, 4831 (1956).
Volume 68, Number 6'
June, 196'4
1324
J. W. SIMONSAND B. S. RABINOVITCH
yield of the CS products of interest, cis-1,2-dimethylcyclopropane (C) , trans-l,2-dimethylcyclopropane(T), 2-methylbutene-2 (PI), 2-methylbutene-1 (P2) 3methylbutene-1 (Pa), trans-pentene-2 (PJ, and cispentene-2 (Ps), varied from -20% of the ketene in the reaction mixture a t the lowest pressures to -60% at higher pressures, for both the -do and -d8 systems. The percentage of photolyzed ketene which these numbers represent is actually higher, since some ketene is diverted by secondary and simultaneous processes, such as undetected polymerization or attack by radicals. Variation of photolysis time in replicate experiments indicated incomplete photolysis of ketene (i.e., lower product yields which increased with exposure times) a t shorter times than those usually employed, and almost complete photolysis, under the actual run conditions a t the higher of the pressures used. Side reaction products of lower molecular weight, such as ethane, ethylene, propane, propylene, butane, etc., and an approximately equal amount of higher molecular weight hydrocarbon compounds (C,-C, and largely unidentified) were -20% of the ketene used at the lowest pressures in the pure systems. The amount of obvious alkyl radical side reaction products decreased considerably a t higher pressures. Although the amount of this side reaction was large (equal to the total amount of Cs products of principal interest, in the worst case), only very negligible amounts of these were Cb hydrocarbons : n-pentane, isopentane, and pentene1. It seems that the main CSproducts result essentially from the reactions represented in eq. a-de8 Some further decomposition of these will occur at lower pressures.
+
CH2
+ cis-butene -+ 6ks
the lowest percentage (1%) of oxygen, the amounts of lower molecular weight (CS), side reaction products were reduced drastically, and large amounts of COz were formed. Large amounts of the products which disappeared arose originally from conventional radical processes.lS#l6In the presence of 5-15% oxygen, the COZ and unidentified (presumably oxy en-containing) higher molecular weight compounds (having longer g.1.p.c. retention times), were the main side-reaction products. These side-reaction products amount to -30% of the ketene used, at the lowest pressures. A visible fog was formed in the reactor at the highest oxygen percentages, undoubtedly due to the formation of high molecular weight oxygen-containing compounds. The effect of varying percentages of added oxygen on the (-do) system (a similar behavior was observed for the ( 4 8 ) system) is illustrated in Fig. 1 for two pressures. An explanation of an important change in CS product composition will be given in the section on
20
IO I-
o a
PS
-%PI
-
-3C*
7
2
P=IOCM
o 4
t %0 2
7
e
12
Figure 1. Variation of Cg product composition in the (-do) system with % 02 in the reaction mixture a t two values of the total pressure; total 1,2-dimethylcyclopropane,C T, 0 ; cis- 1,2-dimethylcyclopropane,C, 0; trans- 1,2-dirnethylcyclopropane, T, X ; 2-methylbutene-2, PI, 0 ; 23-methylbutene-1, PI Ps, A; trans-pentene-2, Pd, A ; cis-pentene-2,
+
..
+
+
Ps,
The addition of oxygen altered the product composition at each pressure (although not in the same way). The total yield of the Cs products of interest was reduced t o 40--50y0of that in the pure systems. Even a t The Journal of Physical Chemistry
(15) E. W. R. Steacie, "Atomic and Free Radical Reactions," 2nd Ed., Reinhold Publishing Co., New York, N. Y . , 1954. (16) H. M. Frey and G. B. Kistiakowsky, J . Am. Chem. Soc., 79, 6373 (1957); J. Bell and G. B. Kistiakowsky, ibid., 84, 3417 (1962).
1325
INTERMOLECULAR KINETICISOTOPE EFFECTS IN METHYLENE SYSTEMS
triplet methylene reaction. It should be noted that, a t both pressures, the oxygen effect on the product composition increased up to 5% oxygen, with virtually no further change, within experimental error, for larger percentages of oxygen. Product Composition and Pressure Dependence. The pressure variation of the amounts of each of the Ca reaction products, expressed as its percentage of the total of these productfl, is shown in Fig, 2-5 for both the pure system and the oxygen (5-15%) systems, with
50 -
5
IO
I
I 8
Pcm 15 I
L
P
U
r\
c-l:
0
340
P
0
30
IO
Prnm 20
too 200
.I
I
I
c
Figure 4.
I
-c-
The same as Fig. 2 but for the pure (4,) system.
-
P.
0
U
I
0 2 0
3
n
0
P
A
I
I
2
3
Pmm 5
15
Figure 2. Variation of C6 product composition with total pressure for the pure (-do) aystem, showing expanded presentations for different pressure regions. Smooth curves are shown t,hrough the data. The same symbols apply as in Fig. 1.
Figure 5. The aanie as Fig. 4 but with 5-15%
0 2
added.
both butene-do and -ds. The variation of the total percentage of 1,2-diniethylcyclopropaneswith the pressure is also shown. The collision frequency w is proportional to pressure. The Low Pressure Region. From Fig. 2-5 it is seen that the pressure variation of the product coinposition for all the systems in the low pressure region (55 cm. for the -do and 5 1 cm. for the -ds systems) js in qualitative agreement with the mechanism represented in eq. a-d, which is altered in nomenclature, only, from the generally accepted mechanism for the reactions of singlet methylene radicals with butene-2.*>l7 It is seen that for all the systems, as the pressure is decreased [C] decreases and [TI increases, due to geometric isomerization of [C*] to [T*], while IC TI and
+
Pmm Figure 3. The same as Fig. 2 but with 5-15% O1 added.
(17) H. M. Frey, Proc. R o y . SOC.(London), A250,409 (1959); A251, 575 (1959).
Volume 68,Number 8 June, 1004
1326
J. W. SIMONSA N D B. S. RABINOVITCH
Table I : Limiting High Pressure Product Composition (%) for Reaction of Singlet and Triplet Methylene Radicals with cis-Butene-240 and cis-Butene-2-ds
y---Triplet--doa
trans-l,2-Dimethylcyclopropane cis-l,2-Dimethylcyclopropane 2-Methylbutene-2 trans-Pentene-2 2,3-Methylbutene-1 cis-Pentene-2
31.3 24.6 3.7 12.3 8.8 19.3
drb
64.6 24 0 3.3 3.3 5.3
-Experimentalc-do
9.2 40.0 12.0 2.6 3.1 33.3
Correctedd ---Singlet----
,---Oz
resultse--
da
do
ds
dj
ds
19.4 47.9 7.9 1.0 1.1 22.9
0.6 46.0 15.3 -1.1 0.8 38.8
0 58.2 11.3 0 0 30.3
0.6 45.0 16 5 0 0.4 37.5
0 57.1 10.9 0 0 32.0
a Data of I h n c a n and Cvetanovii. (for cis-butene-240). b Calculated from this work assuming 297, triplet, methylene and comparing the pure-ds system with the 02 system. c Experimental results for the pure systems in this work (ketene cis-butene-2-do and ketene cis-butene-2-ds), Data for pure systems corrected for -29% triplet methylene. e Experimental results from this work for (-do) and ( 4 8 ) systems with 5-1570 oxygen added.
+
+
the concomitant insertion products are essentially conTI stant. As the pressure is further decreased, [C decreases and the ZIP1] increases as the slower structural isomerization increases in importance. The maximum in [TI occurs where the decrease in [TI due to structural isomerization of [T*] overtakes the increase in [TI due to the geometric isomerization of [C*] to [T*]. Quantitative agreement with expressions resulting from the mechanism is discussed in later sections. The High Pressure Region. Equations a-c for the primary processes of singlet methylene interaction with cis-butene-2 predict that, a t limiting high pressures, [TI, [P2 P3],and [P4]go to zero, while [C], [PI],and [P6] go to constant values. This is the observed bchavior in the presence of 5-15% oxygen. In both the (-do) and ( 4 8 ) pure systems, a t high pressures [TI goes through a minimum increasing to a constant value; [I’,,], [P2], and [P3]approach finite constant values while [C], [PI],and [Pb] either approach constant values or go through maxima and decrease slightly. The high pressure behavior of the pure systems indicates that, a t least a t high pressures, some other mechanism beside that shown in eq. a-c is operative. An added process in which reaction due to triplet methylene takes place a t high pressures in the pure systems will now be discussed. In Table I the observed high pressure product compositions are summarized for the four systems studied in this work, along with the high pressure product composition for triplet methylene reaction as obtained by Duncan and Cvetanovi61afrom the Hg-photosensitization of ketene in the presence of cis-butene-2. The observed composition for the pure (-do) system was corrected for triplet methylene reaction by assunling that T , P4, and Ps PI at high pressures arose solely from
+
+
+
The Journal of Phylsical Chemistry
triplet methylene reaction. The corrected composition as shown in Table I agrees very well with the O2 systems. The correction corresponded to 29% triplet methylene reaction. The propriety of using here the correction for triplet radical-butene-2 product composition as determined from a Hg-photosensitization system is supported by the fact that a similar product coinposition was also found by Frey,lg who studied triplet methylene produced by inert gas collision-induced transitions to the ground state20 of the singlet state radicals arising from diazomethane photolysis. Frey demonstrated the effect of added oxygen on the triplet methylene reactions by a result in which added oxygen restored the singlet methylene product composition. The product composition from triplet methylene reaction with cis-butene-da was calculated by a comparison of the pure and oxygen-containing systems and by assuming the same percentage of triplet radicals to be present as determined from the pure (-do) system. Geometyic Isomerization. Solution of the steadystate differential equation in [T*] (see eq. d) results in eq. 1, which has been given in previous work in a slightly different form*,:
--+ [TI k,
[CI _
W
k,’
+ k,‘ kb-
(1)
where
The value of k , may be determined from a plot of [C]/[T] us. W , without a detailed knowledge of the (18) F. J. Duncan and R. J. Cvetanovi;, J . Am. Chem. SOC.,84, 3693 (19621, and private communication. (19) H. M.Frey, ibid.,8 2 , 5947 (1960). (20) G. Herzberg, Proc. Roy. SOC.(London), A262, 291 (1961).
INTERMOLECULAR KINETIC ISOTOPE EFFECTS IN METHYLENE SYSTEMS
structural isomerization products. The plot should be a straight line a t all pressures, for a monoenergetic system (ie., IC,, kg', and IC,' all constant, independent of pressure), or slightly curved for a system with only a small energy spread, such as the systems of this study. Figure 6 shows the straight line fit to the results for thle
1327
Table I1 : Geometric Rate Constants (108 sec.-l) and Isotope Effects for Activated Dimethylcyclopropane-do and Dimethylcyclopropane-&
kg(
H)
kg(D)c
NO
+la%
oxygen
oxygenb
1.96f0.05" 0.52 f 0.03n
Theoretical
1.34f0.044 0 . 2 9 f 0.Ola
1.52 0.43
1.68
1.40
1.89
1.43
I
8
4
Pmm
12
16
Figure 6. Plots of the ratio cis-/trans-dimethylcyclopropane a t low pressures for all the systems: pure (-do) system, 0; 515% 0 2 (-do) system, 0 ; pure ( 4 s ) system, 0;5-15% 0 2 (-cis) system, B. The least-square lines (solid) through the data have these equations: 0, [C/T] = O.107Pn,, 0.67; 0 , [C/T] = 0.38P,, 0.59; 0 , [C/T] =: 0.16P,, 0.41; B, [C/T] = O.72Pm, 0.30. The dashed line is the extension of the corresponding least-square line.
+
+
(-do) and
+
+
systems, in the presence and the absence of added oxygen. The effect of added oxygen is to increase the slopes in Fig. 6 and reduce the rate constant k , by a factor of 0.67 and 0.53 in the (-do) and (-&) cases, respectively, and to lower the intercepts by factors of 0.61 and 0.50, respectively. These results are from experiments in which 5 1 5 % oxygen was added. The average experimental rate constants and isotope effects are summarized in Table 11. Experimental rate constants were calculated from the least-squares lines in Fig. 6. Although oxygen has a marked effect on the rate constants, the isotope effect is increased by only 200j0. The values of IC,' given in Table I1 were calculated from the intercepts, with use of the relation that IC,' -O.llc,', which is a good assuinption since the geometric isomerization rates in this and other related systems8 are -10 times faster than the structural isomerization rates; any error due to this assumption is negligible. The low intercepts for the oxygen results in Fig. 6 may be the result of experimental error and the large extrapolation, but it seems more likely that the addi-. (-cis)
a Calculated from standard deviations of least-squares slopes and intercepts. The values in parentheses are doubtful since the intercepts and therefore k,/k,' for the 0 2 systems are out of line with what would be expected from thermal work2' and other methylene work.8117 c ( H ) and ( D ) refer to light and deuterated molecules, respectively.
tion of oxygen has other effects on the system than can be accounted for solely by elimination of triplet methylene reaction. Structural Isomeyixation. The structural isomerization of 1,2-dimethylcyclopropane-do and -ds follows two principal paths, corresponding to rupture of the two different types of ring bonds; the carbon atonis and their attached atoms, are labeled type a and b
c
c
--!%cis- and trans-pentene-2, (b + a) (e) a v
b
c
@
a
+ kab (2-methylbutene-2, (a
-+ b) 12-methylbutene-1, (a -+ a)
(f>
b
The nature of the atom transfer is indicated i n parentheses; there are two equivalent alternative rupture paths shown in (f). The deuterium isotope effect on IC,, is a secondary one since only H-atom transfer, (b -* a), occurs in both isotopic s y ~ t e r n s . ~The isotope effect on IC,b is a mixed primary and secondary effect; Voltime 68, Number 6
June, 1964
1328
J. W. SIMONS AND B. S. RABINOVITCH
an H-atom transfers in the (-do) system and a D atom transfers in the (-cis) system. The reacting cyclopropane is largely geometrically isomerized prior to structural isomerization, and the evaluation of the structural rate constants from the mechanism in eq. a-d was simplified by taking ksb = ksb' and k,, = k,,', which makes k , = k,', also. This approximation is readily shown to be reasonable : Flowers and Frey have reportedz1that ksb = ksb' in the thermal isomerization of 1,2-dimethylcyclopropane. Also, they obtained k,,/?c,,' = 1.4, and a frequency factor ratio of 0.40. The average energy of the reacting molecules in the thermal system was less than in the present chemical activation system; for this energy increase, a ratio here of ksp/kep' close to unity22is expected. Application of the steady-state hypothesis to [C*] and [T"] and solution of the resulting differential equations gives these expressions
Figure 7. Variation of the ratio of the sums of various pentene products to total dimethylcyclopropane with inverse pressure 5
for the pure and
(-do) systems: Z[Pj], pure system, 0 ;
0 2
5
8
3
5
j-1
Z[Pj], pure system, m; Z[Pj], pure system, A; Z[Pj],
j=4
0 2
j=1
j-1
system, 0. Only low-pressure data are included for the pure system. Solid lines are from the best fit curves of eq. 4.
where 2k,/kd
=
lim [Pl]/[C 0-
where 6k,/kd
=
lim [P6]/[C w-+ m
where ki = 6/c, /ci/kd lim ([Pi1 u-m
I
+ TI;, also
m
+
+ TI; finally
2kv; ICs
=
ksb
+
+ [P61)/([Cl + [TI).
kBp; and
I n Fig. 7 and 8, the appropriate pentenes, as determined from eq. 3, are plotted us. l/pressure for the (-do) and (-ds) systems, respectively. The high pressure behavior in the pure systems was discussed above and is not included. As is appropriate for systems with a narrow energy dispersion, the plots approximate straight lines, the slopes and intercepts of which give rate constants averaged over the whole pressure region. With use of the limiting extrapolated high pressure product conipositions from Fig. 7 and 8, rate constants a t any pressure niay be calculated from eq. 3. Alternatively, to avoid this extrapolation, difference The Journal of Physical Chemistry
I
I
I
I
I
2
3
4
I/prnm-l
Figure 8. The same as Fig. 7 but for the
J
( 4 systems. )
expressions for the structural constants (eq. 4) were derived from eq. 3
(21) M. C. Flowers and H. M.Frey, Proc. Roy. Soc. (London),A257, 122 (1960); A260, 424 (1961). (22) J. N. Butler and G. B. Kistiakowsky [ J . Am. Chem. SOC.,8 2 , 759 ( 1960)] found similar behavior for methylcyclopropane.
INTERMOLECULAR
1329
KINETICISOTOPE EFFECTS IN n4ETHYLENE SYSTEMS
I n eq. 4, the structural rate constants, which vary only a little with pressure, may be taken constant over a small pressure range, pl t o p2,to which the subscripts 1 and 2 refer. I n Fig. 9, the “low pressure” data for the pure (-do) and ( 4 8 ) systems are fitted to eq. 4 by finding the rate constants which fit the data. From the rate constants so determined and from the expressions iin eq. 3, limiting high pressure values of the percentages
attempt was made to separate the total rates into individual k,b and k,, values since very few low pressure data were taken in the oxygen systems. I n Table 111, the average experimental structural rate constants and isotope effectsfor the pure and oxygen systtems are summarized. The agreement for the isotopic ratio, k.(H)/k.(D), is excellent. There is an indication that k. in the presence of oxygen is a little less than in the pure system. This apparent difference could simply be caused by some minor triplet reaction still occurring a t low pressure in the pure system, or it could be due to some unspecified oxygen complications.
5
3
( [ C ] f [TI),
[P,], and j=1
[P,] were calculated to j=4
be 43.7, 14.8, and 41.5, respectively, for the pure (-do) system, and 59.3, 11.1, and 29.6, for the pure (-cia) sys-
Table I11 : Rate Constants and Isotope Effects for Structural Isomerization of Activated 1,2-Dimethylcyclopropane-d~ and 4” Pure systems
Oxygen added
1.82 1.09 0.73 0.38 0.21 0.17 4.8 5.2 4.3
1.25
0.30 4.2
T heore tical”
1.76 0.821 0.939 0.394 0.130 0.264 4.47 6.32 3.56
* ( H ) and ( D ) a Rate constants are in units of lo7 set.-'. refer to the light and deuterated molecules, respectively. These are calculated kE values and ratios for the processes involved, a t an average energy based on those of ref. 8. Calculated rate contains an error of -7%.
10-
Figure 9. Plot of various Cb product proportions us. pressure a t lower pressures showing the fit of eq. 4 (solid curves) to the pure systems data: open symbols for the (-do) system and solid symbols for the (-&) system; C T, total dimethyl5
+
3
5
cyclopropane, 0; E[Pj], total pentenes, 0 ; Z[Pjl, A; , E [ P j l , j-1
j=l
]
0.
=4
tem. These values are in fair agreement with the measured results given in Table I for the oxygen systems and with the results from the pure systems corrected for 29% triplet methylene reaction. This suggests, in line with some evidence above from truns-dimethylcyclopropane variation with pressure, that triplet methylene reaction is not as important a t low pressure as a t high. Average values of k , for oxygen-containing systeins were obtained in the same way (Fig. 7 and 8). No
Deuterium Isotope Effects on Methylene Insertion and Addition. I n Table IV the results on methylene radical insertion into the C--H and C-D bonds, and addition to the C=C bonds of cis-butene-do and cis-butene-dy, a t 2 5 O , are summarized. The values for the pure systems are changed only slightly from the values of our preliminary report,lO except in one respect. The present propylene correction to the 2-methylbutene-2 product (see description under Analysis) causes fairly large differences in k , / k , from the earlier report, since k , is measured by the 2-methylbutene-2 formed a t high pressures. The present ratios 1.07 and 1.13 make more sense, and agree better with related deterininations in the literature,* than our previous values of 1.21 and 1.52, respectively. The results froin the oxygen systems accord fairly well with the pure systems, in general. The principal djfference, although not a serious one, is a decrease in the oxygen system of 20y0 I’olume 68, AVumber6
June, 1964
1330
J. W. SIMONS AND B. S.RABIKOVITCH
Table IV : Methylene Insertion and Addition Ratios Pura systema
Oxygen
1.29 0.69 1.87 0.99 0.97 1.02 1.91 1.07 1.13 1.94 1.84
1.22 0.74 1.65 0.79 0.75 1.05 1.73 1.32 1.02 1.61 2.08
a These ratios result from the limiting product composition, derived from curves fitting the low-pressure data in the pure systems, as described in the previous section. Only slightly different values result from the triplet corrected compositions in Table I.
in the ratios, kd(H)/k(E) and kd(D)/k(E) (a somewhat anomalous increase of 25% in k,(H)/k,(H) is considered suspect) ; that some differences do occur, which are undoubtedly not all of fundamental sigficance, is not surprising in view of the varied effects caused by oxygen, not to mention the general difficulty of reproducing any value to within 10% in methylene gas phase systems. I n any case, the ratios of ratios are found less sensitive both to complexities or changes of mechanism and the values for kd(H)/kd(D) and ki(H)/ ki(D) agree with the earlier report.1°
Discussion Triplet Methvlene Radical Reaction. Although the elucidation of the chemistry of these systems was not originally, nor indeed is, the major purpose of the present work, nonetheless, we have had to examine the chemical complications encountered. The higher pressure Cb product compositions and their change upon addition of oxygen is consistent with the increasing importance (2530%) of triplet methylene radical reaction in the pure systems at higher pressures. This hypothesis is by no means proven for this complex system, but it provides a consistent explanation of the results. The existing high pressure data in other methylene systems do not rule out the possibility of some triplet methylene reaction, although the thermal8 and photolytic” decomposition of diazomethane in the presence of butenes at high pressures suggest only a few per cent, or less, of triplet reaction in those systems. I n connection with this and other studies, systematic examination has been made, over a wide range of total reaction The Journal of Physical Chemistry
pressure in each, of the effect of added O2on a variety of systems, including ketene with ethylene, propylene, and butene-1 ; in the latter case, F. H. Dorer has found that the removal of oxygen perceptibly changes the proportions of products (at the high pressure limit) in the direction of the product composition found by Cvetanovik and Duncan for butene-1 with triplet methylene.la I n any case, the presence of oxygen affects these systems to some degree besides merely capturing alkyl radicals; no previous systematic studies are known of the effects due to 0 2 in the presence of a variety of olefin substrates. The mechanism for triplet radical formation, if it occurs, is unknown. At 3100 A,, it is pomible12 that it could involve collision-induced singlet-triplet intersystem crossing of the excited singlet ketene, although the occurrence of this process has not been ~ h o w n . ’ ~ , ‘ ~ For purposes of the present isotopic investigations it appears, fortunately, that the complications designated as “triplet” in nature are relatively unimportant a t lower pressures. The rate constants and isotope effects in both the pure and oxygen systems are nearly the same, and thus do not depend on the correctness of the preceding hypothesis. Structural Isomerization. Theoretical calculations were made of the structural isomerization rate. To simplify the experimental calculations, the reactant cyclopropane was described earlier as a 1 : l cis-trans mixture. This is not quite the correct ratio that applies for all conditions, but the effect on the calculations of a variation from unity is small. An aoerage critical energy for each of the combined reaction paths, defined by ksb and k,,, was recalculated for the c i s t r a n s mixture from the thermal isomerization data of ref. 21; EOb and Eo, differ by less than 0.1 kcal. mole-’ (see Appendix I), The initially formed excited molecules have an energy spread of -10 kcal. mole-’ due to photolysis and thermal energy distributions in the formation reactions ; but since the average excess energy, given by (E+) = ( E ) - Eo = 106 - 60 = 46 kcal. mole-’, is also large, the relative energy dispersion is small. Thus k,b and k,, are well represented by values for the two reactions. The MarcusRice formulation of k , was usedz3
where I , is the partition function ratio for t,he adiabatic degrees of freedom (over-all rotations) of the activated (23) R. A. Marcus and 0. K. Rice, J . Phgs. Colloid Chem., 5 5 , 894 (1951); R. A. Marcus, J . Chem. Phys., 20, 359 (1952).
1331
INTERMOLECULAR KINETICISOTOPE EFFECTS IN METHYLENE SYSTEMS
complex (+) and the energized molecule (*); ZP(E+vr) is the sum of the (degeneracies of internal energy states of the active degrees of freedom of the activated complex, over the range from zero to E+; and N * , is the density of internal energy states for the active degrees of freedom of the energized molecule a t the energy E*. Models for the molecule and decomposition activated complex were constructed fron: which values of P(E+vr) and N * , were obtained. The models for the (-do) species were fitted to the existing thermal isomerization data, 21 while conformity to the Teller-Redlich product rule was demanded of the (-ds) models. Discussion of these calculational details is given in Appendix I. The calculated specific rates and isotope effects are summarized in Table 111. The agreement with experiment is good, being somewhat better for the pure systems than with oxygen added. Calculations were also made (Appendix I) for structural isomerization of 1,2-cyclopropane-d2, They give a calculated intramolecular primary isotope effect of k K / k D = 2.5 a t 718°K. for the thermal structural isomerization; the experimental valuez4 is 2.18. The calculated value at the energy of the present chemical activation systems is reduced to 1.58. Recent work on the thermal isomerization of methylcyclopropane-d29 gives isotope effects in general agreement with those found for cyclopropane-d2. The ratio kap(H)/ksD(D)(Table 111) is a measure of the secondary intermolecular isotope effect on structural isomerization in the present system, since an H atom transfers in both cases. Although this secondary effect is mechanistic2* in part, since the two D atoms which are on the ring carbons interact somewhat with the reaction coordinate, the largest part of the observed effect corresponds to a quantum statistical-weight effect due to the lowered vibration frequencies of the deuterated species. The magnitude of this nonequiljbrium effect has been shown to decrease with increasing energy of the reactants above the critical threshold Eo, for a fixed value of thie latter. In the present system, (E+) is fourfold greater than the largest value in previous work on butylzb and propyl6 radicals; together with a partially compensating twofold increase in EO(60 kcal. mole-' relative to 31-33 in the radical studies) and resultant threefold increase in ( E ) = (E+) Eo, this results in a reduced, but still large, statistical isotope effect predicted as 3.6 and measured as 4.3. The ratio kat,(H)/JCsb(D)involves a mixed primary and secondary intermolecular isotope effect. The value should be larger than that for the secondary ratio above
+
and this is found (Table 111) both from experiment ( 5 . 2 ) and calculation (6.3). Although a separation of the two effects into separate contributions is not strictly accurate, the relative increase in the isotope effect for /cab over that for k,,, given as the quotient of the last two entries in Table 111, may be taken as a rough measure of the intramolecular primary isotope effect, The calculated value is somewhat higher than that observed. The niodel used is related to that for cyclopropane-d2. I n view of the uncertainties in the experimental values, the agreement is considered satisfactory and no attempt was made to improve the model or the slightly arbitrary valuez6 of AEo = 1.2 kcal. mole-', between H and D atom transfer, assumed in the calculations. Geometric Isomerization. The thermal and cheniically activated geometric isomerization of 1,2-dimethylcyclopropane-do and -ds, and of 1,2-cyclopropane-dz, provide good tests of theoretical calculations and of proposed activated complex models. Reference 9 describes the mechanism for both geonietric and structural isomerization, but so far quantitative calculations for structural isomerization, only, have been presented in detail. We now consider the calculation of unimolecular rates and fall-off behavior for the geometric isomerization (Appendix I). The fall-off curve for the thermal uniinolecular geometric isomerization of dideuteriocyclopropane has been calculated according to the expression of R R I N theoryz3
where QVr is the molecule vibrational-internal rotation partition function, and other quantities were defined previously. The calculated curves have a fall-off shape (Fig. 10) corresponding to a Slater value of n 12-14, which is close to the experimental (n E 13.5) value.z4 The absolute pressure discrepancy, A log p is only 0.20 log p unit. The calculated value of k,, fits see.-]) ; an experiniental thermal value (Acnlcd= the activation energy was arbitrarily set 1 kcal. mole-' less than the value for structural isomerization (Table V) . This energy difference was discussed in ref. 24. (24) E. W. Schlag and B. S. Rabinovitch, J . Am. Chem. Soc., 8 2 , 5996 (1960). (25) A. T. Blades [Can. J . Chem., 39, 1401 (196111 measured a similar magnitude in the decomposition of cyclopropane-do and -d 8 .
Volume 68, Number 6
June, 1.964
1332
J. W. SIMONB AND B. S. RABINOT~ITCH
~
~
~
Table V : Calculated and Measured Values for Geometric Isomerization of Cyclopropane and Dimethylcyclopropane (DMC)
System
l,2-DMC-do, thermal, 715.4"K. Ketene cis-butene-2-do (3200 b.) CHzNz cis-butene-240 (250') CHzNz cis-butene-2-do (300') CHaNz -t. cis-butene-24 (400') CHzNz trans-butene-2-do (4358 A.) Ketene 4- cis-butene-2-ds (3200 b.) Cyclopropane-dz, thermal, 718'K. Ketene ethylene-& (3340 ethylene-& (3200 A . ) Ketene
+ + + + + +
4.)
106 109 112 116 116 106 102 105
12.7 X 1.96 X 3.5 x 4.4 x 11.5 X 9.0 x 0.52 X 2.0 x 11.8 X 15.8 X
lo-' 10s 108 108 108d 108 108 io-4a
10'0C 10loc
12.2 x 10-4 1.52 X 108 2.31 X lo8 3.47 x 108 5 . 5 4 x 108 5.54 x 108 0.43 X lo8 1.95 x 10-4 3 . 0 6 X 1010 4 . 6 3 X 1010
26.8
10.8 8.1 7.5 11.5 8.9 13.7 12.7 18.7~ 14,2O
24.6 8.85 8.13 7.94 7.37 7.37 11.0 7,556 3.32b 3 . 24b
21 This work
8 8 8 13 This work 24 26 26
a This value of k , is one-half the constant as defined in ref. 24; k , in this table represents the rate constant for formation of one isomer from the other. Part of the difference between the theoretical and experimental ratios arises from a calculational model for Rtructural isomerization which fits the values of A and E, for cyclopropane given by Falconer, Hunter, and Trotman-Dickensona'; their k values are higher than those measured by Pritchard, Sowden, and Trotman-Dickenson, Proc. Rog. SOC.(London), A217, 517 (1963), and (roughly a factor of two) by Schlag and Rabinovitch. Since the experimental geometric isomerization values were also measured by the latter authors,z6 the calculated ratios must be multiplied by this factor to put them on a comparable basis; this makes the calculated and experimental values in the thermal case virtually coincide. c This is a large discrepancy above that mentioned in ( b ) and in view of the intuitively expected and theoretically calculated decline of k,/ka with increased energy, it is quite probable that the experimental result is in error. The experimental value seems to have increased somewhat excessively relative to 300'.
Figure 10. Unimolecular fall-off curve for geometric isomerization of 1,2-cyclopropane-d2 a t 718%. : experimental data of Schlag and Rabinovitch, 0; the solid curve is the theoretical curve from the present work shifted 0.20 log P unit to higher pressure; calculated fall-off curvature corresponds to Slater n 'v 12, while experimental is n 'v 13.5.
Values of le(E, for geometric isomerization in chemical activation systems26 were calculated from eq. 5 a t the average energy of these systems. For the same reasons discussed for structural isomerization, these values are taken as good representations of the measured average IC, values. The extension of the activated complex model for geometric isomerization from cyclopropane-& to 1,2dimethylcyclopropane involved replacement of the CI-ID group by C(CH8)H group frequencies. The The Journal of Physical Chemistry
models fit the experimental thermal high pressure rate constantz7 for the (-do) molecule (Table V). The .models for the molecule and activated complex in the (-de) system have Teller-Redlich product rule agreement with their (-do) analogs. The calculated rates and isotope effects in the present chemical activation system are summarized in Table 11. The agreement with the experimental results for the pure systems is good. The origin of the isotope effects on k, and IC,' is largely of a quantum statistical-weight nature; a smaller mechanistic effect, due particularly to the substitution in the ring near the reaction site, also appears from a straightforward application of the Teller-Redlich product rule and lowering of zero point energies per deuterium substitution and is automatically included (EOD= EOH 0.4 kcal. mole-'). The results of these calculations as applied to a variety of systems in the literature are summarized and compared to experiment in Table V. In view of the neglect in the calculations of anharmonicity effects, of possible inefficient intermolecular energy transfer, and of experimental error which is always present in these systems, the agreement is extremely good. It can be
+
(26) B. S. Rnbinovitch, E. Tsohuikow-Roux, and E. W. Schlag, J . Am. Chern. Soc., 81, 1081 (1959). (27) W. E. Falconer, T. E. Hunter, and A. F. Trotman-Dickenson, J . Chem. Soc., 609 (1981).
_
_
1333
INTERMOLECULAR KINETICISOTOPE EFFECTSIN METHYLENE SYSTEMS
considered evidence in support of these activated corn-. plex models and of levels of energy which are consistent with those in ref. 8.
Appendix I Rate Calculations The molecule models were based on known, or trans-. ferred, frequency assignments. The activated complex models were assigned to fit the experimental high pressure frequency factors where these rate data were available. Teller -Redlich product rule agreement, within 10% was accepted for the frequency assignments of deuterated models. The zero-point energy differences (AE,) fall in the range 1.8-2.0 kcal. per deuterium atom. In the application of the product rule to activated coimplexes, the groups which were defined to separate along the reaction coordinate (C-H or C-D stretch primarily for structural isomerization, and C-C stretch for geometric isomerization) were used in the reduced mass calculations; ref. 9 should be consulted for further diricussion on this point. Moment of inertia ratios of the light and deuterated molecules are known for cyclopropane-do and -dez8 and were closely estimated for dimethylcyclopropane species. Eo was’calculated from the Arrhenius E, values with use of the standard expressions.29 The evaluation of L’P(E+vr)and N*n from the models was done by direct, ~ energiea summation or accurate a p p r o ~ i m a t i o an t~high using programs written by Mr. G. !A. Whitten for the IBM 709 computer; no frequency grouping was required for molecules. Vibrations were treated at3 harmonic. A modification4vS1of the expression given by Marcus2*for the density of free internal rotational states was used. Tabulations of energy sums and d e n sities a t various energies for all species described below may be found in ref. 31. The symmetry number ratio and number of reaction paths were included in I,. 1,W-Cyclopropane-d2. The vibrational frequencies for the molecule (Table VI) were deduced from those given by Cyvina2for cyclopropane-do and -ds. The observed fundamentals rather than the corrected fre-. quencies are used, since the former provide a partial correction for anharmonicity. The geometric isomtvization compiez for 1,2-cyclopro-. pane-dz was derived from the molecule on the basis of the expanded ring 1node19~~~; the frequencies of propane,33 propylenelS4butane,33 and cyclobutanegswere used as a guide. A ring mode was taken as the reaction coordinate; two methylene twisting vibrations became hindered internal rotations. Other changes in the molecule frequencies were very minor. There are two different complexes, one with two CHD rotors (reaction path weight of 1) and the other with one C H D and one
Table VI : 1,2-Cyclopropane-d~Frequencies4 Mode
C-H stretch C-D stretch C B Zdef. CND def. CB2 twist C B D twist Ring mode CBZwag CBD wag CHI rock CWD rock a
E,
= Zl/phv =
w , am.-’
3103, 3082 (2), 3028 2236, 2211 1442 1378, 1258 1188 1072, 970 1104, 982 (2) 869 870, 795 739 734, 633 45.40 kcal. mole-’; AE, = 1.97 kcal. mole-”
per D atom.
CHz rotor (reaction path weight of 2); a weighted average of these wa,s taken for the actual model. The grouped frequencies are (cm.-I) : 2973(4), 2160(2), 1260(4), 869(4), 702(3), hindered CHD rotor, hindered [2/3CHz ‘/&HD] rotor; E , = 39.82 kcal. An internal rotation barrier of -3.5 kcal mole-’ was used to fit the experimental thermal rate. Hindered internal rotational entropies were determined from the tables given by Pitzer.a6 A barrier of 5 kcal. together with some small terminal methylene frequency lowerings would also fit the data. The value of Eo is 61.80 kcal. mole-], based on E, = 64.10 kcal. mole-’ for geometric isomerization. The value of’(I+ABC/IABC)‘’’ used was 1.30, slightly larger than the value 1.2lZ8which applies for the structural isomerization of cyclopropane-do. The reaction path degeneracy is 3 for this geometric isomerization. A 709 program written previously by D. W. Setser was used in the fall-off calculations. The structural isomerization complexes for 1,2-cyclopropane-dz were based on the model given previously for cyclopropane-do.* A small difference in these models resulted from the use of Cyvin’sazassignments of CHz
+
(28) D. W. Setser, Ph.D. Thesis, University of Washington, 1961. (29) S. Glasstone, K. J. Laidler, and H. Eyring, “The Theory of Rate Processes,” McGrrtw-Hill Book Co., New York, N. Y., 1941. (30) G. Z. Whitten and B. S. Rabinovitch, J . Chem. Phys., 38, 2466 (1963). (31) For details, see J. W. Simons. Ph.D. Thesis, University of Washington, 1964. (32) 5. J. Cyvin, Spectrochim. Acta, 16, 1022 (1960). (33) J. H. Schaotschneider and R. G. Snyder, ibid., 19, 85, 117 (1964). (34) I. M. Sverdlov, Proc. Akad. Sci. USSR, C‘hem. Sect., 106 (1956).
(35) G. N. Rathjens, Jr., N. K. Freeman, W . D. Gwinn, and K . S . Pitzer, J . Am. Chem. SOC.,75, 5634 (1953). (36) K . S. Pitser, “Quantum Chemistry,” Prentice-Hall, Inc., New York, N. Y., 1958.
Volume 68, Number 6 June, 1964
1334
J. W. SIMONS A N D B. S.RABINOVITCH
twist and rock vibrations as compared to those of Table VI1 : 1,2-Dimethylcyclopropane-d0Frequencies“ H e r ~ b e r g . There ~~ are three H transfer complexes: (a) H atom transfer from CH, to a CHD group (reaction Mode w , om. path weight of 4) ; (b) H atom transfer from a CHD to ( C H Z )C-H stretch 3103, 3083 the CHz group (path weight of 2); (c) H atom trans( C H ) C-H stretch 3038, 3028 fer from a CHD to the other CHD group (path weight (CH3) C-H stretch 2990 (3), 2950 (2), 2900 of 2). An average of these complexes was used: CH3 def. 1465 (2), 1450 (2), 1380 (2) CH, def. 1442 3040(3), 2200(2), 1230(5), 880(3), 710(6), 510; E , = C-H bend 1200 (2), 650 ( 2 ) 38.72 kcal. mole-I. The E&H value for cyclopropane-do Ring def. 1120, 960 ( 2 ) was used,27which gave Eo = 62.73 kcal. mole-’. Apart CH3 rock 1040 (2), 960 ( 2 ) from reaction path degeneracy, I , is closely similar to CH2 twist 1188 the value for cyclopropane-do. CH3-C stretch 950, 890 CHZwag 869 There are two activated complexes for D transfer: 740 CHz rock (a) a D atom transfers from a CHD to the other CHD 700 (2), 400 ( 2 ) CHa-C- bend group (path %eight of 2) ; (b) a D atom transfers from a CH3-C- torsion Free rotor ( 2 ) CHD to the CH2 group (path weight of 2). An average a E, = 82.39 kcal. mole-’. was taken for the D transfer model; this model was deduced from the molecule in the same way as the H transfer model: 3050(4), 2190, 1230(5), 880(3), 712(6), trans isomer. This fraction (which is one-half for 510; E , = 39.97 kcal. mole-’. Thus EOD - EOH = cyclopropane-dz) was estimated as 0.67 from the ther1.25 kcal. mole-’ was obtained; this is consistent with inal cis-tyans equilibrium constant21 and from the the measured value of the intermolecular critical energy equilibrium ratio in chemical activation systems (ref. 8 difference for cyclopropane-do and -d6.25 The moand Table 11). ment of inertia ratio is virtually the saine as for the H The structural isomerization “b-complex” for formatransfer complex. tion of 2-methylbutene-2 and 2-methylbutene-l re1,d-Dimethylcyclopyopane-do. The vibrational fresembles the cyclopropane-dz complex in which the H quencies of the 1,2-dimethylcyclopropane-domolecule atom transfers from a CHD group to the other CHD are given in Table VII. The ring and skeletal motion group or to the CHz group. The grouped frequencies frequencies were taken from those for cyclopropane 1350(10),946(10), 685(5), 400(2), are (em.-’): 2985(9), and from a partial assignment for 1,l-diniethylcyclofree CH3 internal rotations (2); E , = 77.27 kcal. pr0pane.3~ The CHz group frequencies were those for mole-’. This model fitted the observed thermal rate, cyclopropane. The C (CH,) H group frequencies were 1014.32e-62~1101RT and gives Eo = 60.47 kcal. mole-’. assigned to be consistent with those for c i s - b ~ t e n e - 2 , ~ ~ The ratio (I+ABc/IABc)~” used was 1.1, as in the earlier pr0pylene,3~and a model for methylcyclopropane given work.8 The reaction pathways are 4 for the b-complex. by Wieder.40 This frequency assignment is partially The structural isomerization “p-complex” for formation altered from that used earlier,a but in view of the inof cisand trans-pentene-2 is analogous to the cyclosensitivity of the calculations to the detailed assignpropane-dz complex in which an H atom transfers from ments, the agreement is satisfactory. The grouped frethe CH2 group to a CHD group. The geometric isomerization,complex is similar to that : 2985(9), 1327(11), 957(8), 679(6), quencies are (cm.-’) for cyclopropane-dz. Different reaction paths were 400(2), free CH3 internal rotation (2); E , = 77.10 averaged into a single model. The grouped frequencies kcal. mole-’. The model fitted the thermal rate, are (cm.-’) : 2982(10), 1350(10), 952(9), 682(3), 400(2), 1014~3ge-62~040/RT; Eo is calculated as 60.38 kcal. free CHI internal rotation (a), hindered C(CH3)R inmole-’. I , is the same as for the b-complex. ternal rotation, hindered [’/3CHZ ‘/3C(CH3)H] in1 ,d-Dimethykyclopropane-d8. The vibrational freternal rotation; E , = 78.60 kcal. mole-’. An internal quencies assigned to 1,2-diinethylcyclopropane-d8are rotational barrier of -20 kcal. mole--’ gave a fit of the observed thermal rate,21 1 0 1 6 ~ 2 ~ e - 5 9 ~ 4 2the 0/RT model ; (37) G. Heriberg, “Infrared and Raman Spectra of Polyatomic gives Eo = 57.80 kcal. mole-l. A value of (I+ABc/ Molecules,” D. Van Sostrand and Co., Princeton, N. J., 1945. I A B C ) ’ ” was estimated at 1.15. The activated com(38) F. F.Cleveland, M. J. Murray, and W. S. Galloway, J . Chem. Phys., 15, 742 (1947). plex described is for the formation of a “biradical” inter(39) C. M. Richards and J. R. Xielsen, J . O p t . Soc. Am., 40, 442 mediate; in order to represent IC, for the formation of (1950). the lrans from the cis isomer, the rate must be inulti(40) G.M .Wieder, Ph.D. Thesis, Polytechnic Institute of Brooklyn, plied by the fraction of biradicals that recyclize to the 1961. -1
+
The Journal of Physical Chemistry
INTERMOLECULAR KINETIC ISOTOPE EFFECTS IN XETHY LENE SYSTEMS
given in Table VIII. The activated complexes for the (-ds) system were derived in the same way as for the (-do) system. The I , ratio is the same as for the (-do)
Table VI11 : 1,2-Dimethylcyclopropane-dsFrequenciesu
1335
system. The grouped frequencies for the geometric isomerization complex are (em.-') : 3043(2), 2231 (8), 1440, 1043(9),814(10), 500(2), 340(2), free CD3internal rotation (a), hindered C(CD,)D internal rotation, hindered [2/3CH23- '/,C(CD3)D] internal rotation; E , = 64.03 kcal. mole-' and AE, = 1.82 kcal. mole-' per D atom. The critical energy difference is eo^ = EOH 0.44 kcal. mole-'. The structural isomerization b-complex for D transfer is analogous to the D transfer complex of cyclopropanedz. The grouped frequencies are (em.-') : 3043(2), 2218(7), 1440, 1020(11), 801(9), 550(4), 340(2), free CD3 internal rotation (2); E , = 63.42 kcal. mole-'. We also obtain AEo for the intermolecular primary isotope effect of 1.16 kcal. mole-], slightly smaller than the value for the intramolecular effect for cyclopropane-d2. The group frequencies for the structural isomerization p-complsx are (cm.- I ) : 3003, 2231(8), 1350, 1053 (lo), 811 (lo), 5 5 5 ( 5 ) , 340(2), free CD3 internal rotation (2), E , = 62.17 kcal. mole-' and AE, = 1.88 kcal. inole-' per D atom. Eo is the same as in the (-do) system since E , was lowered the same for the molecule and the activated complex.
+
(CH2) C-H stretch ( C D ) C-D stretch (CD3) C-D stretch CH2 def. CH2 twist CDs def. Ring def. C-D bend CH2 wag CH2 rock CD3 rock CD3-C stretch CDa-C bend CDa-C- torsion a
E,
atom.
=
67.38 kcal. mole-';
3103, 3083 2264, 2256 2246, 2236 (2), 2216 (2), 2179 1440 1150 1085 (e), 1070 (4) 1050, 890 (2) 950 (2), 500 (2) 860 740 856 (2), 770 ( 2 ) 813, 762 610 (2), 340 (2) Free rotor (2)
AB,
=
1.88 kcal. mole-' per D
Volume 68, Swmber 6 June, 1864
