J. Phys. Chem. 1986, 90, 394-397
394
-
analysis for each system it appears that a per-bond insertion A factor for Me2Si should be ca. 109.2(*1.0) M-' s-I (a direct, absolute value is not available). The presumption has to be that here the experimental Arrhenius parameters are subject to some distortion. Thus, to proceed we take
Correction via ACpe gives Ap9,+(298 K) = 207 kJ mol-' From AHfe(Me3SiH) = -163 kJ mol-' and Mfe(Me3SiSiMe2H) = -279 kJ mol-] (additivity e ~ t i m a t e ' ~we ) obtain
log ( k 9 / ~ - '=) 14.5 - 217/8'
AHfe(Me2Si) = 91 kJ mol-'
From the experimental data of ref 20 (see text), we estimate
From a similar analysis of other methylated d i ~ i l a n e decom'~ positions, values in the range 88-96 kJ mol-' emerge. Together with other uncertainties this suggests 92 f 8 kJ mol-'. By definition
log (k-g/M-'
S-I)
= 9.2 - 16/8'
At 650 K A p 9 , - 9 = E9 - E-9
+ RT = 206 kJ mol-'
(37) This small adjustment is accommodated within the model used to fit
the Me6Si2* ion breakdown data: T. Baer, private communication. (38) The group notation in parentheses is in accord with recent actions by IUPAC and ACS nomenclature committees. A and B notation is being eliminated because of wide confusion. Group I becomes groups 1 and 11, group I1 becomes groups 2 and 12, group I11 becomes groups 3 and 13, etc.
DSSE(Me2Si) = D(Me3Si-Me) - D(Me,Si-Me) From published values of AHr(Me4Si),28AHfe(Me3Si),9and the above AHfe(Me2Si) DSSE(Me,Si) = 134 f 12 kJ mol-' Registry No. Me2Si=CH2, 61 153-00-2; Me2%:,6376-86-9; Me&+, 28927-31-3; Me3SiSiMe2H, 812-15-7; 1,l-dimethylsiletane, 2295-12-7.
Hexafluorocyclopropane and Octafluorocyclobutane: A Study of the Strain Energies Joel F. Liebman,* Department of Chemistry, University of Maryland Baltimore County, Catonsville, Maryland 21 228
William R. Dolbier, Jr.,* Department of Chemistry, University of Florida, Gainesville, Florida 3261 1
and Arthur Greenberg* Department of Chemical Engineering and Chemistry, New Jersey Institute of Technology, Newark, New Jersey 07102 (Received: July 22, 1985)
The strain energies of hexafluorocyclopropane and octafluorocyclobutaneare discussed in terms of Benson group increments. Unlike the near constancy of t h e heat of formation of the C(H),(C), group as found in a variety of acyclic species, that for its fluorinated counterpart is found to be. very dependent on its next-nearest-neighborenvironment and the groups C(F),(CF,), and C(F),(C), must be carefully distinguished. Regardless of how the group increments are chosen, the strain energy of hexafluorocyclopropaneis found to be remarkably high relative to the parent cyclopropane, while that of octafluorocyclobutane, likewise low relative to cyclobutane.
Introduction Geminal-difluoro substitution provides marked thermodynamic stabilizations in alkyl derivatives which are diminished or absent in substituted cyclopropanes and olefins.' For example, 1,ldifluorocyclopropane has been calculated to have about 12 kcal/mol more strain (relative to the acyclic 2,2-difluoropropane) than cyclopropane (relative to propane)? and this value is reflected in the unusually low barriers to thermal rearrangements of these c o m p o ~ n d s . ~It is a bit surprising that the e x t r a s t r a i n in 1 , l difluorocyclopropane is only about 2 kcal/mol greater than the 4.5-5 kcal/mol increment per F substituent proposed by O N e a l and Benson4 since the thermodynamic favoring of gem substitution' is a measure of nonadditivity. Hexafluorocyclopropane extrudes CF2 under fairly mild cond i t i o n ~and ~ this could arise from extra strain which might be about (1) Sheppard, W. A,; Sharts, C. M. "Organic Fluorine Chemistry"; Benjamin: New York, 1969; pp 20-40. (2) Greenberg, A.; Liebman, J. F.; Dolbier, W. R., Jr.; Medinger, K. S.; Skancke, A. Terrahedron 1983, 39, 1533-1538. (3) Dolbier, W. R., Jr. Acc. Chem. Res. 1981, 14, 195-201. (4) O'Neal, H. E.; Benson, S. W. J. Phys. Chem. 1968, 72, 1866-1887. (5) Birchall, M. J.; Fields, R.; Haszeldine, R. N.; McClean, R. J. J. Fluorine Chem. 1980, 15, 487.
0022-3654/86/2090-0394$01.50/0
27-30 kcal/mol (total strain 55-58 kcal/mol) if one simply employs the O'Neal-Benson increment. Bernett estimated a strain energy of 68.6 kcal/mol for this molecule.6 In an earlier paper,, we employed an experimental value for AHfo(g) for hexafluorocyclopropane,' derived from mass spectrometric rather than calorimetric data, along with a published C(F),(C), group increment (-104.9 kcal/mol)* in order to derive a total strain energy of 80.9 kcal/mol. This value was checked against a value derived from published thermochemical data9 for eq 1 (76.7 kcal/mol) F
x
F
-
3C3Fe- 3CzF6
(1)
F F
and the derived conclusion was that "non-next-nearest-neighbor" corrections are quite small. The purpose of the present paper is (6) Bernett, W. A. J. Org. Chem. 1969, 34, 1772-1776. (7) Bomse, D. S.; Berman, D. W.; Beauchamp, J. L. J. Am. Chem. Soc. 1981, 103, 3967-3971. (8) Dolbier, W. R., Jr.; Medinger, K. S. Terrahedron 1982,38,2411-2413. (9) Pedley, J. B.; Rylance, J. "Sussex-NPL Computer Analysed Thermo-
chemical Data: Organic and Organometallic Compounds"; University of Sussex: Sussex, England, 1977.
0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 3, 1986 395
Hexafluorocyclopropane and Octafluorocyclobutane to reconsider this premise in light of additional data and other models.
C(H)2(C)2and C(F)2(CF2)2Group Increments There are numerous methods for obtaining a C(H)2(C)2group increment which yield virtually identical n ~ m b e r s :(a) ~ homodesmotic logic’O (e.g., eq 2) yields a value of -4.90 kcal/mol; (b) AfZf[C(H)2(C)21 = AHdC3Hd - AHf(C2H6)
(2)
mf[C(H)2(C)21 = 1/n[MdCH3(CH2)nCH3) - AHf(C2H6)I (3) ~ f [ C ( H ) , ( C ) 2 1= 1/(n - 1)[Afff(CH3(CH2)SHJ - AHf(C3HdI (4) the “diagonal approach”,” one-sixth of AHf(g) of cyclohexane, yields -4.92 kcal/mol; (c) eq 3, a generalization of eq 2, yields values between -4.88 and -5.07 kcal/mol, and the closely related approach (d) eq 4, avoiding the use of C2H6 deemed here “atypical”, yields values between -4.88 and -5.26 kcal/mol. In any case, a value around -4.93 kcal/mol is “right” and is hardly affected by the CH, ”endgroup problem” inherent in eq 2 and 3. BensonI2 adopted a value of -4.93 kcal/mol while SchleyerI3 and Allix~ger’~ both adopted values near -5.15 kcal/mol for strainless C(H)2(C)2increments. If one uses the same approach for perfluoroalkanes, some interesting results are obtained. Equation 5 is analogous to eq 2 uf[c(F)2(cF2)21 = AHf(C3F8) - AHf(C2F6)
(5)
and provides a value for the difluoromethylene group increment of -103.5 f 1.8 kcal/mol (precision is the square root of the sum of the squares of the contributing errors in AHxg)). It is, of course, this increment that is tacitly assumed in eq 1. (The reason for the designation used for the group increment in eq 5 will become apparent shortly.) However, if one uses the “diagonal approach”, one-sixth of the experimental AHf(g) of perfluorocyclohexane ~ a value for the C(F),(CF2), group (-566.2 f 2 k c a l / m ~ l ) ’yields increment of -94.4 f 1.8 kcal/mol, considerably higher than that derived from eq 5. In comparison to the hydrocarbon case, there is little thermochemical data on perfluoroalkanes. Only one equation analogous to eq 3 and one analogous to eq 4 can be constructed from known data (see eq 6 and 7 for which associated values for AHf[C(F),(CF2),] are -97.3 f 0.5 and -95.8 f 0.5 kcal/mol, respectively). AHf[C(F)2(CF2)21 = /5[mf(cF3(CF2)5CF3) - AHf(C2F6)l (6) Mf[C(%(CF2)21 = 1/4[mf(cF3(cF2)5cF3) - AHf(C3FS)I (7) One can argue against employing eq 5 and 6 since the terminal group (CF,) problem arises. Although the corresponding CH, problem was shown earlier to be negligible for alkanes, is the terminal group problem negligible in other series? One can readily see that the difference between AHf(CH3X)and AHf(C2H5X) changes significantly with X while the difference between AH,(C2H5X)and AHf(n-C3H7X)is rather ~ o n s t a n t . ’ ~ ~Thus, ” the (10) George, P.; Trachtman, M.; Bock, C. W.; Brett, A. M. Tetrahedron 1976, 32, 317-323.
(11) Van Vechten, D.; Liebman, J. F. Isr. J . Chem. 1981, 21, 105-110. (12) Benson, S. W. “Thermochemical Kinetics”; Wiley: New York, 1976;
2nd ed. (13) Engler, E. M.; Andose, J. D.; Schleyer, P. v. R. J. Am. Chem. SOC. 1973, 95, 8005-8025. (14) Allinger, N. L.; Tribble, M. T.; Miller, M. A,; Wertz, D. W. J. Am. Chem. SOC.1971, 93, 1637-1648. (15) Price, S. J. W.; Sapiano, H.J. Can. J . Chem. 1979, 57, 685-688. (16) Montgomery, R. L.; Rossini, F. D. J . Chem. Thermodyn. 1978, 10, 471-481. (17) Sellers, P.; Stridh, G.;Sunner, S. J. Chem. Eng. Data 1978, 23, 250-256.
two values -94.4 (”diagonal approach”) and -95.8 kcal/mol (eq 7) remain. Equation 7 still has the problem of terminal CF3 not present in hexafluorocyclopropane but the presumed error is averaged over three groups instead of only one -CF2- group as in eq 5. Another approach to a C(F),(CF2), increment not associated with terminal CF, groups is to calculate a value for an infinite chain of -CF2- (i.e., polytetrafluoroethylene), an “asymptotically-diagonal” standard. The AHf(so1id) (-99.4 kcal/mol of C)9 can be combined with its heat of sublimation = AHrus which must be estimated. The heat of sublimation, AHvap.The AHf,,, is known from experiment (1.1 kcal/mol of must be estimated. Hydrocarbons and their CIS). The AHvap corresponding perfluorocarbons have comparable boiling points and presumably comparable AH,,,.’ This is explicitly shown by comparing AH,,, data:9 e.g., C6H6, 8.1 kcal/mol; CsF6, 8.5 kcal/mol; n-C~H16,8.7kcal/mol; n-C7F16, 8.7 kcal/mol. We recall a simple formula for estimating AHva for arbitrary hydrocarbons: AHvap= l.l(nc) + R T (kcal/mol),‘{ where nc is the number of carbons. Thus, for each carbon the increment is 1.1 kcal/mol. Therefore, by equating heats of vaporization of corresponding hydro- and perfluorocarbons and so assuming AHvap(-CF2-) is the same as AHvap(-CH2-), the value for AHSub(-cF2-) is 2.2 kcal/mol of C. The derived value for A“f[C(F),(CF,),] is -97.2 kcal/mol, in reasonable agreement with the earlier-cited values of -94.4 and -95.8 kcal/mol. Taking a simple average of the three values yields -95.8 kcal/mol which we will employ in the present work.
+
Strain Energy of Hexafluorocyclopropane Comparison of this group increment with the experimental AHf(g) of hexafluorocyclopropane (-233.8 kcal/mo17) yields a strain energy of about 54 kcal/mol, in excellent agreement with the O’Neal-Benson estimate. The 26 kcal/mol excess strain energy, compared to cyclopropane, may well be manifested in the relatively facile extrusion of CF2, although the anomalously high stability of this singlet carbene is very importantS2It is interesting that the extra 26 kcal/mol of strain in hexafluorocyclopropane represents a value of ca. 9 kcal/mol per carbon which is slightly lower than the extra strain in 1,l-difluorocyclopropane. The difference in strain energies of these two molecules almost corresponds to the difference in the energies of activation for CF2 extrusion ( E , = 38.6 kcal/mo120 and E, = 56.4 kcal/mol,21 respectively). However, one must also note that the difference in the enthalpies of extrusion (15 kcal/mo12) in these highly endothermic reactions is also close to the difference in E,. An informative comparison is furnished by examination of energetic and structural data for hexafluorocyclopropane and tetrafluoroethylene and their comparison with the corresponding hydrocarbons. Using the C(H)2(C)2increment as a standard for ethylene allows one to calculate a strain energy of 22.4 kcal/mol for this molecule (Le. ethylene considered as “cycloethane”22). Similarly, taking the C(F)2(CF2)2increment and comparing it to AHr(C2F4)9leads to a strain energy of 43.7 kcal/mol for tetrafluoroethylene. The strain energies in C2F4 and CyC10-C3F6, calculated this way, are virtually double those of the hydrocarbons. It is noteworthy that the carbon-carbon bonds in C2F4 and cyclo-C3F, are both shorter than in the corresponding hydrocarbons while the C-C bonds in C2F6, cyclo-C4F8, and cyclo-C6F12are all longer than in the corresponding hydrocarbon^.^^ An interesting point relates to a published AHf(g) for 1,1,2,2-tetrafluoro~yclopropane~~ obtained via gas-phase reaction ~~
(18) Starkweather, H. W.; Zoller, P.; Jones, G . A,; Vega, A. J. J. Polym. Sci., Polym. Phys. 1982, 20, 751-781. (19) Chickos, J. S.; Hyman, A. S.; Ladon, L. H.; Liebman, J. F. J . Org. Chem. 1981, 46, 4294-4296. (20) Atkinson, B.; McKeagan, D. Chem. Commun. 1966, 189-190. (21) Herbert, F. P.; Kerr, J. A.; Trotman-Dickenson, A. F. J . Chem. SOC. 1965, 5710-5714. (22) Greenberg, A.; Liebman, J. F. “Strained Organic Molecules”; Academic Press: New York, 1978; pp 43-44. (23) Yokozeki, A.; Bauer, S. H. Top. Curr. Chem. 1975, 53, 71-119.
396 The Journal of Physical Chemistry, Vol. 90, No. 3, 1986 between CH2(IA,) and C2F4. The value was calculated by using AHLCH,) = 102 kcal/mol; AHdC2F4) = -155 kcal/mol; and E,, = 85 f 10 kcal/mol, leading to -138 f 10 kcal/mol. Using the Rylance and Pedley value9 for C2F4 leads to -141 f 10 kcal/mol. If one were to assume that a C(F),(C)(CF,) increment has AHf = -100.4 kcal/mol (average of C(F),(C), and C(F),(CF,),), then the strain energy based upon the -138 kcal/mol value would appear to be 65 f 10 kcal/mol. This seems to be too high, especially if one considers that E, for extrusion of CF2 is ca. 10 kcal/mol lower than for hexafluorocyclopropane.,’ Even if one were to use the C(F),(CF,), group increment, the strain energy would be about equal to that in hexafluorocyclopropane, which also seems unlikely. Other support for this view may be gained by calculating the enthalpy of reaction for extrusion of CF, from 1,1,2,2-tetrafluorocyclopropaneusing the value -141 f 10 kcal/mol and AHf(g) for singlet CF, (-44.2 kcal/mo17) and for CH2CF2(-80.1 kcal/mo19). This would make the extrusion endothermic by 17 f 10 kcal/mol. In combination with the E, for extrusion (49 kcal/molZ1),the numbers suggest an E, for addition of CF, to CHzCF2of 32 f 10 kcal/mol which appears implausibly high. A more reasonable value could be estimated by interpolating the strain energies of 1,l-difluorocyclopropaneand hexafluorocyclopropane to obtain a strain energy of 47 kcal/mol for the tetrafluoro compound and combining it with the C(H),(C), and C(F),(CF,), increments to yield AHLg) = -159 kcal/mol. With this value, the extrusion reaction would be endothermic by 35 kcal/mol and the energy of activation for attack of CH2CFzby CF2 equal to 14 kcal/mol, both lower and seemingly more “reasonable” numbers. For comparison, use of the same value for CF2 would make the extrusion reaction of hexafluorocyclopropane endothermic by 32 kcal/mol and the E , of the reverse reaction 7 kcal/mol. (It should be noted that a value for AH, (g)(CF,), determined by using very different methodologies, equal to -52 kcal/mol has also been p ~ b l i s h e d . ~ ~ )
Strain Energy of Octafluorocyclobutane The derived value for the C(F),(CF2), increment allows evaluation of the strain energy of octafluorocyclobutane. There are three published experimental investigations providing AHdg) The value cited in the Pedley data for octafluorocy~lobutane!*~~~~ and Rylance compendium9 (-368.7 kcal/mol) is based upon reaction with sodium. A value cited by ONeal and Benson: based upon the gas-phase equilibrium between octafluorocyclobutane and tetrafluoroethylene, employed an older A€& value for the latter compound. If one uses the Rylance and Pedleyg value (-157.9 kcal/mol) for tetrafluoroethylene, then the ONeal-Benson value for cyclo-C4F8 becomes -367.8 kcal/mol. DUUS,~ performed enthalpy of combustion measurements and the derived AHf(g) for cyclo-C4F8 using the Pedley and Rylance value is -365.2 kcal/mol. The agreement between the three values, obtained from completely unrelated experimental techniques, is striking especially when one considers the inherent difficulties in fluorocarbon calorimetry. If one employs the earlier-derived C(F),(CF,), group increment (-95.8 kcal/mol), then the strain energy of cyclo-C4F8 is between 14.5 and 18 kcal/mol, some 8.5-12 kcal/mol kower than in cyclobutane. O’Neal and Benson4 calculated a strain energy for cyclo-C4F8essentially equal to that of the hydrocarbon while Bernett6 derived a value of 32 kcal/mol. No major structural changes are apparent in cyclo-C4F8relative to the parent hydrocarbo11.2~ It has been noted that geminal F- - -F distances in the perfluoro derivatives of cyclopropane, cyclobutane, and cyclohexane are all virtually 2.1 8 A.28 Octafluorocyclobutane’s energy of activation for conversion to CF2=CF2 is 11.7 kcal/mol higher than the corresponding reaction for c y c l o b ~ t a n e . ~ ~ (24) Arbilla, G.; Ferrero, J. C.; Staricco, E. H. J. Phys. Chem. 1983, 87, 3906-391 I. (25) Lias, S. G.; Ausloos, P. In?.J. Mass Spectrom. Ion Phys. 1977, 23, 273. The most recent value is -49 k 3 kcal/mol: Lias, S. G.; Karpas, Z.; Liebman, J. F. J . Am. Chem. SOC.1985, 107, 6089-6096. (26) Duus, H. C. Ind. Eng. Chem. 1955, 47, 1445-1449. (27) Chang, C. H.; Porter, R. F.; Bauer, S. H. J . Mol. Srruct. 1971, 7, 89-99. (28) Glidewell, C.; Meyer, A. Y . J . Mol. Strucf. 1981, 72, 209-216.
Liebman et al. This increment is within the range of the strain reduction of cyclo-C4F8. Once again, however, one must note that the enthalpy of reaction for cyclo-C4F8 (+52.0 kcal/molZ9) is much more positive than that for cyclobutane (+6.5 kcal/mo19). To add to the confusion, conversion of 1,1,2,2-tetrafluorocyclobutaneto C2H4 and C2F4 has about the same activation energy as for c y ~ l o - C , F ~ . ~
Difference between AHdC( F),(C)* and M A C (F),(CF,),] Why is AHf[C(F),(CF2)2] fully 9 kcal/mol higher than AHf[C(F),(C),]? In other words, why are “next-nearest-neighbor” corrections significant? One can simply note the high polarity of the C-C bond in -CH2-CF2- units and realize that there is an reduced energy (more stable) increment associated with it. This is exemplified by eq 8,9 for which the exothermicity parallels most
+ other AA + BB
-
CF3CF3 CH3CH3
-
2 CH3CF3, AH -13
kcal/mol
(8)
2AB reactions. For the C(F),(C), increment, two polar C-C bonds are involved (two such bonds are created in eq 8) and one may estimate that the extra stabilization is 2/3(13 kcal/mol) - 9 kcal/mol in agreement with the difference between the two group increments. A reported AHf(g) for 2,2-difluoropropane (-129.8 f 3.0 kcal/moPO)is more negative by 4.5 f 3.0 kcal/mol than the value calculated through use of Benson’s C(H),(C)I2 and Dolbier’s C(F),(C)28 increment. A value based upon the 9 kcal/mol correction would be lower still (-134 kcal/mol). The need for these corrections is ample reason for avoiding use of terminal groups as in eq 1 and opting instead for the “diagonal” or “asymptotically-diagonal” approaches discussed above. It is also worthwhile to briefly recall the analogy between gem-difluoro and carbonyl carbons employed e1sewhe1-e.~’One can calculate a destabilization energy arising from adjacent carbonyl groups using eq 9 or 10. Equation 10 employs sp2-hybrid H(C0)-(C0)H = 2H(CO)CH3 - CzH6, AH = -8.5 kcal/mol (9) H(C0)-(C0)H = 2CH,=CHCHO CH2=CHCH=CH2, AH = -9.8 kcal/mol (10) CH,(CO)-( CO)H = H(CO)CH3 CH3(CO)CH3- C2H6, AH = -6.7 kcal/mol (1 1)
+
CH3(CO)-(CO)CH3 = 2CH3(CO)CH, - CzH6, AH = -5.6 kcal/mol (12) carbons and is probably a more relevant model, but there is some resonance stabilization in acrolein, AHf(g) estimated from AHLg)9 values of trans-2-butena1, propene, and ethylene, which decreases its utility. Similarly, eq 11 and 12 also illustrate this a-dicarbonyl destabilization which is fairly similar to that in -CF2-CF,- units.
Conclusions The value of AHf[C(F),(CF2),] is 9 kcal/mol more positive than that of AHf[C(F),(C),] due to stabilizing polar C-C bonding in the latter. Use of the C(F)2(CF2)2increment to calculate the strain energies of cyclo-C3F6 and cyclo-C4Fs gives values of 54 and 14.5-18 kcal/mol, respectively. Both cyclo-C3F6 and C2F4 have strain energies double those of the corresponding hydrocarbons and this may reflect similarities in structural trends between the four molecules. The strain energy in cyclo-C3F6is essentially that predicted from O’Neal and Benson’s early assumption of 4.5-5 kcal/mol of extra strain per F on cyclopropane, but it is not quite an additive function of three 1,l-difluorocyclopropane molecules. While E , for CF2 extrusion follows a trend seemingly related to strain energies, it also reflects the relative heats of extrusion for these highly endothermic reactions. (29) Butler, J. N. J. Am. Chem. SOC.1962, 84, 1393-1398. (30) Williamson, A. D.; LeBreton, P. R.; Beauchamp, J. L. J. Am. Chem. SOC.1916, 98, 2705-2709. (31) Greenberg, A,; Tomkins, R. P. T.; Dobrovolny, M.; Liebman, J. F. J . Am. Chem. SOC.1983, 105, 6855-6858.
J. Phys. Chem. 1986, 90, 397-400 cyclo-C,F, appears to have a reduced strain energy, the origin of which is not definitely known. One interesting possible explanation for the reduced strain energy of octafluorocyclobutane relative to the parent hydrocarbon notes the importance of 1,3-repulsions in the energetics of cy~ l o b u t a n e s .Paralleling ~~ a recent discussion of the strain energies of substituted bicyclo[ 1.1.11pentanes,33 decreasing the electron (32) Bauld, N. L.; Cessac, J. J . Am. Chem. SOC.1977, 99, 942-943. Bauld, N. L.; Cessac, J.; Holloway, R. L. Ibid. 1977, 99, 8140-8144.
397
density on the carbons in a cyclobutane is expected to decrease this repulsion and total strain energy. Equivalently, perfluorination of cyclobutane affects a decrease in strain.
Acknowledgment. The authors gratefully acknowledge the helpful comments and criticisms of Dr. Bruce Smart. Registry No. Hexafluorocyclopropane, 93 1-9 1-9; octafluorocyclobutane, 115-25-3. (33) Wiberg, K. B. Tetrahedron Lett. 1985, 26, 599-602.
Parameters of Activation Barriers from Curved Arrhenius Plots: CH,
+ RH
-
R iCH,
H. Furue and P. D. Pacey* Chemistry Department, Dalhousie University, Halifax, Nova Scotia, Canada, B3H 4J3 (Received: July 22, 1985)
Expressions have been fitted by least-squares methods to curved experimental Arrhenius plots for the reactions of CH3 with HZ,C2H6, C(CH3),, H2C0, and (H3C)20. The heat capacities of activation ranged from 41 (for reaction with H2) to 95 J K-I mol-' (for C2H6). Expressions incorporating tunneling through one-dimensional Eckart barriers were capable of fitting the data within experimental uncertainty. The temperature-independent factor A , the effective barrier height, and the characteristic tunneling temperature were treated as adjustable parameters. For reaction with H2, the fitted parameters were compared with the predictions of transition-state theory based on ab initio potential energy calculations. Agreement was best for the factor A and the barrier height if two bending degrees of freedom were treated as internal rotations. The effective width of the barrier at half its height was found to be relatively consistent for the other four reactions.
Introduction The tunnel effect can contribute to the observation of curved Arrhenius plots for hydrogen atom transfer reacti0ns.l The size of the tunnel effect depends on the shape of the activation barrier. Kineticists have long hoped, therefore, to learn about the shapes of activation barriers by studying the shapes of Arrhenius plots. With the exception of the pioneering work of LeRoy and coworkers2on the reaction of H with H2, most work on the gas phase has been based on deductive logic. Tunneling factors have been deduced from first principles; comparison with experiment has usually occurred at the end of a study.'s3" In condensed phases and in ref 2, expressions for the tunnel effect have been fitted to experimental plots in order to inductively estimate parameters for the activation barriers.' The objective of the present work is to learn about the tunnel effect for gas-phase reactions of methyl radicals using the latter approach. Data Sets Five reactions, eq 1-5, have been chosen for study. All the CH3 + H2 CH4 + H (1) CH3 C2H6 CH4 C2H5 (2) CH3 + C(CH3)d CH4 + (CH3)3CCH* (3) CH3 H2CO CH4 H C O (4) CH3 + (H3C)2O CH4 + H3COCH2 (5)
--+
+
+
-
---+
+
+
600 K in several laboratories; all exhibit curved Arrhenius plots. In each reactant, all hydrogen atoms are equivalent. Most of the experimental work has been reviewed elsewhere.' Most studies of methyl radical reactions have used one reference reaction, eq 6, as a measure of the radical concentration. In other
cases, rates of reactions 1-5 have been measured relative to another reaction of methyl radicals, which has in turn been measured relative to reaction 6. Use of a common standard reduces discrepancies between measurements in different laboratories. Reaction 6 has been thoroughly studied and does not exhibit Arrhenius plot c u r v a t ~ r e . ~At ~ ~high temperatures and low pressures the value of k6 is reduced because of the limited rate of collisional energy transfer; it is necessary to extrapolate to find the limiting, high pressure value of k6. We shall adopt the value, log k6 (L mol-' s-') = 10.34, as recommended in ref 7. The measured quantities are kx/k6'I2,so that the abstraction rate constants, k,, are affected by only half the uncertainty in k6. For instance, replacing the value of log k6 above by the expression of ref 8 would change temperature-independent factors quoted herein by only -0.06 log units and activation energies by -0.6 kJ mol-'. Data for three of the reactions are shown as the points in Figures 1-3. Data for reactions 4 and 5 (not shown) were taken from ref 23-3 1. The measure of CH3 concentration was reaction 6,
reactions have been studied over temperature ranges of more than (1) Bell, R. P. "The Tunnel Effect in Chemistry"; Chapman and Hall: London, 1980. (2) LeRoy, D. J..; Ridley, B. A.; Quickert, K. A. Discuss. Faraday Sor. 1967, 44, 92. ( 3 ) Johnston, H. S. "Gas Phase Reaction Rate Theory" Ronald: New York, 1966. (4) Clark, T. C.; Dove, J. E. Can. J . Chem. 1973, 51, 2147, 2155. (5) Truhlar, D. G.; Isaacson, A. D.; Skodje, R. T.; Garrett, B. C. J . Phys. Chem. 1982, 86, 2252. ( 6 ) Schatz, G.C.; Wagner, A. F.; Dunning, T. J. J . Phys. Chem. 1984, 88,22 1.
0022-3654/86/2090-0397$01.50/0
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0 1986 American Chemical Society
