H. E. O X E A LAND S.W. BENSON
1866
The Biradical Mechanism in Small Ring Compound Reactions' by H, E. O'Neal Department of Chemistry, San Diego State College, San Diego, California
96116
and S. W. Benson2 Department of Thermochemistry and Chemical Kinetics, Stanford Research Institute, Menlo Park, California 94086 (Received December 18, 1967)
The kinetics of dissociation,structural isomerization, and geometric isomerization in three- and four-membered cyclic compounds are discussed in terms of the biradical mechanism. With the exceptions of the cyclobutene isomerizations and the ci~-l,2-alkylvinylcyclopropaneisomerizations, all small ring compound reactions to date are shown to be both qualitatively and quantitatively consistent with the biradical mechanism. Methods for making a priori transition-state estimates of the activation energies and Arrhenius A factors for these reactions are outlined. Estimates are shown to be reliable to about 0.3 log unit in A and about 1.5 kcal/mol in E, on the average. The thermochemistry of fluorine substitution in cyclopropanes and in cyclobutanes along with the effect of such substitution on the mechanism and kinetics of fluorinated small ring compound reactions is also discussed.
Introduction I n spite of the many successes of the biradical mechanism in explaining a large number of cyclic reactions qualitatively and, in some instances, quantitatively, the broad applicability of the biradical mechanism, particularly with regard to the quantitative predictions to which it is so readily and admirably suited, has not been fully exploited. The purpose of this paper is to show that quite accurate and reliable a priori estimates of the Arrhenius parameters of all of the three- and four-membered ring compounds (excluding only those which are known to be concerted processes) can be made by using rather straightforward thermodynamic estimates for the transition states involved. A future paper will show that similar considerations lead to quite acceptable estimates of the Arrhenius parameters of polycyclic compounds and that these reactions also, with some few exceptions, appear to involve biradical intermediates. One of the most interesting and practical aspects of applying transition-state calculations to the biradical mechanism is that the relative rates of the competitive reactions of the biradicals can be estimated. The importance of such relative rates cannot be overemphasized because they are the "key" to understanding the reasons for preferred reaction paths (when they exist) in over-all reactions proceeding through biradical intermediates. Experimental Uncertainties in Arrhenius Parameters Almost all "small ring" compound reactions are extremely well behaved kinetically. They are, for the most part, free from free radical sensitized decomposition and from surface catalysis in wall-conditioned reaction cells. Reported kinetic parameters are, therefore, quite reliable. Assuming a maximum error in rate-constant determinations of *5%, a maxiThe Journal of Physical Chemistry
mum error in the temperature of *0.2", an average temperature of GOO"K, and a temperature range of study of about GO'K, one can estimate3 probable errors in the activation energy ( E ) of about 1.5%. For an activation energy of 55 kcal/mole, this would correspond to an uncertainty of E of about 0.8 kcal/mol and an uncertainty in the A factor of about a factor of 2 (ie., -10*0.30). I n some reactions where concurrent product yields or the temperature range of study are small, errors in IC, A , and E can be appreciably larger. Such cases will be noted. I n spite of the fact that many studies report errors In k and E which are much smaller than the above, it should be remembered that such estimates are invariably based on the precision of the rate data. Since systematic errors in analysis and temperature control are the most significant in kinetics, we feel the error limits given above are realistic average values. Errors in the transition-state estimates are believed to be comparable to the experimental errors. Recent updating of group-additivity values4 allows thermodynamic estimates of the reactants and products to be made with reasonably high accuracy, about =t1.0 gibbs/mol in so and and 1 1 . 0 ltcal/mol in AHf O. Transition-state estimates are also thought to be nearly as reliable. Therefore, we feel that the estimated activation entropies and activation energies should, on the average, be good to better than 1 2 gibbs/mol and 2.0 kcal/mol, respectively.
cpo
(1) This project has been supported in part by a contract with the Office of Standard Reference Data, National Bureau of Standards, Washington, D. C. (2) To whom reprint requests should be addressed. (3) S. W. Benson, "The Foundations of Chemical Kinetics," McGraw-Hill Book Co., Inc., New York, N. Y . , 1960, pp 86-94. (4) S. W. Benson, et al., Chem. Rev., in press; see also S. W. Benson and J. H. Buss, J. Chem. Phys., 2 9 , 546 (1958).
THEBIRADICAL MECHANISM IN SMALL RINGCOMPOUND REACTIONS
1867
Table I : Some Pertinent Group Additivitiesavd
--~
AX!'
'
[ .C-(C ) (Hp)I [ *C-(Cd)(Hz)] [ .C-cCo)(Hz)l [ .C-(Cz)(H)I [ *C-(C,)(C)(H)I [ ~c-(co)(C)(H)l
[.C-(C3)1 [ *C-(Cd)(C2)] correction 0 correction cis gauche alkane alkene c-(C ) (H3) C-(C2)(H2) C-(Cd(H) C-(C,)
35 82 35.82 35.82 37.45 37.64 36.35 37.00 37.42 27.6 26.2 1.0 0.8 0.5 -10.08 -4.95 -1.90 0.50 I
30.45 30.13 30.15 10.34 10.47 9.62 -10.67 -10.54 32.1 29.8 C
~
~~
-IJ
~
300
400
500
600
700
800
6.15 5.81 5.81 5.16 4.60 6.19 4.06 3.50 -3.05 -4.61 -1.34
7.08 7.12 7.12 5.67 5.66 6.61 4.25 4.24 -2.53 -3.89 -1.09
8.11 8.20 8.20 6.15 6.45 7.00 4.30 4.80 -2.10 -3.14 -0.81
8 .'84 9.12 9.12 6.63 7.08 7.34 4.59 5.06 -1.90 -2.64 -0.61
9.53 9.86 9.86 7.09 7.57 7.67 4.87 5.37 -1.83 -2.26 -0.50
10.27 10.60 10.60 7.64 8.16 8.09 5.22 5.72 -1.77 -1.88 -0.39
6.19 5.50 4.54 4.37
7.84 6.95 6.00 6.13
9.40 8.25 7.17 7.36
10.79 9.35 8.05 8.12
11.90 10.21 8.68 8.44
13.02 11.07 9.31 8.77
S O
30.41 9.42 -12.07 -35.10
'
The free-radical groups do not include any effects arising from resonance, li For a complete list of alkane additivity values see ref 4. variations in molecular frequencies of groups bonded to radical centers, or from electron spin. Corrections for these effects must be made separately (see the Appendix). The rotational barriers in radicals should be lower than those found in the corresponding alkane because of the increased se,paration of t.he rotating groups which arises from the rehybridization to spa bonding. Neither the rotational barriers to large groups in alkanes nor the rotational barriers to groups around a free-radical center are known. However, it seems reasonable to assume a reduction in barriers by about a factor of '/a for the radical as opposed to the alkane. Fortunately, changes in entropy and heat capacity for such rotational-barrier corrections are essentially independent of the size of the original barrier in the alkane (i.e,,for barriers in the range of 3-12 kcal/mol, see Table 11)and also of the mass of the rotor (excluding methyl and methylene). It should be mentioned that the rotational-barrier corrections made here are not very critical to our transition-state calculations, since in most cases, the corrections are later "removed" in making the transition state entropy estimates. cis-But-2-ene = 1.2 gibbs/mol, cis-pent-2-ene = 0 gibbs/mol, (all other cis) = -0.6 gibbs/mol. The method of estimating the thermodynamic properties of the free-radical groups is illustrated for the C-(C)(Hz) group. Consider the reaction C-(Cz)(H2) + Ha
+ [.C-(C2)(H)] ( R . )
AHt" [( C-( CZ)(Hz)] =
(DH"(C-H) = 98.0 kcal/mol)
- 10.08 kcal/mol
AHfo(H ) = 52.1 kcal/mol A H ~ " ( R . )= DH"(C-H)
+ AHro[C-(Cz)(H2)] - AHf"(H.) = 35.82 kcal/mol
/"\
To obtain the group entropy, the alkane group has been "corrected" for the loss of 2(H moment-of-inertia changes to internal rotation.
H) vibrations and for the barrier and
C
/\
-
Soaoo[*C-(C)(H,)] = S"[C-(C)(Ha)l 2S"(H = 30.41 2(0.03) 4.34
+
-
H)IWIcm-'
- 4.25
+ S"(*CHr+m)z,a - S"(CHa+m)a,s
= 30.44 gibbs/mol
Heat capacity values have been obtained by similar considerations. C
-
/ \
Cp0~oo[*C-(C)(Hz)1= Cp"[C-(C)(Ha)l 2Cpo(H = 6.19 0.20 2.16 2.00
-
+
-
H)
+ Cp"(*CHz+
m)z.a
- Cp"(CHa+
m)a,a
= 6.15 gibbs/mol
Methods of Calculation The thermodynamic path from the reactant to the transition state employed for the A-factor calculations involves estimates of changes in entropy, enthalpy, and heat capacity in the following steps: 1. ring opening to the corresponding biradical (nonresonance
form) at room temperature; 2. incorporation of resonance in the biradical (if resonance exists); 3. Comection of the thermodynamics of the ring-opening reaction (to the biradical) from 298°K to the reaction temperature by using the estimated average reaction heat capacity over this temperature range (i.e., Volume 72,Number 6 June 1968
H. E. O'NEAL AND S. W. BENSON Table I1 : Hindered Internal Rotation: Partition Functions,' Entropies,b and Heat Capacities
2.3 2.6 3.0 3.5 4.0 4.5 5.0 1.0 0.6
8.5 37 46 10.7 37 46 51
5.2 8.0 8.7 5.9 8.2 8.9 9.3
1.0 1.2 1.4 1.5 1.7 1.9 2.1 0.3 0.1
2.16 2.27 2.34 2.00 2.27 2.23 2.19 1.4 1.1
1.96 2.12 2.25 2.12 2.33 2.32 2.29 1.3 1.1
1.78 1.94 2.10 2.07 2.29 2.32 2.33 1.2 1.1
1.61 1.76 1.91 1.96 2.18 2.25 2.29 1.1 1.o
1.49 1.60 1.74 1.85 2.03 2.14 2.22 1.1 1.0
a The partition functions were calculated from the relation &f = [87r31k2'/h2] 'Iz. Entropies and heat capacities for the hindered (h) rotors have been estimated from tables prepared by Pitzer: see G. N. Lewis and M. Randall, "Thermodynamics," revised by K. S. Pitzer and L. Brewer, 2nd ed, McGraw-Hill Book Co. Inc., New York, N. Y., 1961, pp 441-446. These are only approximate barriers. Real values will, of course, depend on conformation of groups around the rotation axis. 2.6-6, Barrier effect: -RH -,-It. ( V V -+ ' / 3 V R H ) ASo/rotor = 0.50 ACpa/rotor: 0 - 0.21 - 0.35 - 0.42 - 0.43. For R > CH3, the changes in entropy and heat capacity in going from the alkane to the radical are relatively insensitive to the original barrier and the mass of the rotor. e Barrier effect: 0.18 - 0.13 - 0.12 - 0.11 - 0.08, for any It,including CI13. -RH + - R . (V = 1.0 -+ V = 0.6) ASo/rotor = 0.25 AC,"/rotor: Values listed are changes per rotor and apply to the following temperatures: A!S"/rotor (300°K); ACPo/rotor (300"K, 400"K, 500"K, 600°K, and 700"K, respectively).
-
( A C , o > ~ ~ ~; -4. T ) formation of the transition state from the biradical; 5. incorporation of the total change in symmetry, including optical isomers, between the reactant and the transition state. Calculational procedures used in each of the above steps are outlined briefly below and illustrated in the Appendix. Step 1. R i n g Opening. Thermodynamics have been estimated from the appropriate group additivities of hydrocarbons4 and of free radical^.^^^ The methods used in obtaining the free-radical group additivities are discussed briefly in Table I and in more detail elsewherea5'e Step 2. Incorporation of resonance in the biradicals produces lower energy and lower entropy states. The most important resonance stabilization in the small ring compound reactions is that of an alkyl-substituted allyl radical (i,e,, ~ 1 2 . 6kcal/mole).' Resonance tightening, with its effect on radical entropy and heat capacities, has been estimated by replacing the internal rotation about the bond in which resonance is developed with a three-electron torsion. Entropies of internal rotations and torsions are shown in Tables I1 and 111. This method of estimating resonance stiffening has been found to be reliable in other transition-state calculations.8 Step 3. Corrections to bring the thermodynamics of the ring-opening reactions (to the biradicals including resonance) from 298°K to the reaction temperature have been made in the usual way (Le., using the average heat capacity over the temperature range). To obtain the average value, reaction heat capacities, calculated from group additivities (Table I) and the heat capacities of hindered rotors and three-electron torsions (in the case of resonance), Table 11, were The Journal of Phgsicat Chemistry
estimated at 100" intervals from room temperature to the reaction temperature. Step 4. Three kinds of transition states have been encountered in the small-ring reactions : H migration in 1,3 biradicals, decomposition in 1,4 biradicals, and various kinds of ring-closing transition states. The activation energies of these processes from the biradicals at reaction temperatures have been obtained from analysis of the kinetics of the following reactions selected as standards: cyclopropane (H migration) , 112-dimethylcyclobutane (decomposition), cyclopropane (three-membered ring closing), 1,2-dirnethylcyclobutane (four-membered ring closing), and vinylcyclopropane (five-membered ring closing), Extension of the calculations to the other cyclic-compound reactions have been made and are in good agreement with the reported data (Tables IV and V). &lethods for estimating activation entropies from the biradicals to the various transition states have been made at the reaction temperatures by general methods illustrated in the Appendix and also are discussed in detail elsewherea6 Note specifically the assignment of the reaction coordinate in these processes. Step 5 . Activation entropies estimated from group additivities are intrinsic entropies (Le., Sointrinsio = Soobsd R In ( u l n ) ,where u is the product of the external and internal symmetries and n is the number of optical isomers). To obtain the reaction-path degeneracy of a reaction, the total symmetry change between the transition state and ground state, including
+
( 5 ) J. H. Purnell and C. P. Quinn, J . Chem. Soc., 4049 (1964). (6) H. E. O'Neal and S. W. Benson, Int. J . Chem. K k , in press. (7) K. W. Egger, D. M. Golden, and S. W. Benson, J . Amer. Chem. Soc., 86, 5420 (1963). (8) H. E. O'Neal and S. W. Benson, J.Phys. Chem., 71,2903 (1967).
THE
BIRADIC AL n I E C H A N I S h l
I N SMALL
RINGC O M P O U N D REACTIONS
1869
Table 111: Entropies of Free Rotation" and Torsion as a Function of Temperature Hybridization
Free rotors
SPa SP2 SPa SPS spa SP2 sp2
( m )+methyl ( m )+methylene ( m )-ethyl ( m )-&propyl ( m )+butyl (m .Et)
I-(
(m)-(i-Pr.)
----
Qr (300'K) 11.6/3 = 3 . 7 8.4/2 = 4 . 2 37.0 52.5 64.5 35.0 49.7
___--__--Toraionsb
800 (P4e)t 700 (i-Buhe\ 400 (Pae)t (CB4e)t 350 (i-Bae)t 300 (t-Bae)t 250 (2-MB4e)t 200 (c-Bae)t 150 (t-Bae)t 128 (2-MBse)t 100 (2,3-DMBae)t
300'K
400'K
0.2 0.3
0.4 0.5
300'K
500°K
5.9 5.2 8.2 8.9 9.3 8.05 8.75
6.4 5.75 8.7 9.4 9.8 8.55 9.25
Entropies, gibbs/mol----------. 6OOOK 700°K
6.55 5.9 8.9 9.6 9.95 8.75 9.43
Entropies, gibbdmol--500°K 600'K
0.7 0.8
1.0 1.2
6.7 6.1 9.0 9.7 10.1 8.85 9.55
700°K
1.2 1.4
800°K
6.85 6~25 9.15 9.75 10.25 9.0 9.6
--800°K
1.4 1.7
1.o
1.4
1.8
2.1
2.4
2.7
1.2 1.4 1.8 2.2 2.7 3.1 3.4
1.6 1.8 2.2 2.6 3.2 3.6 4.0
2.1 2.3 2.7 3.1 3.7
2.4 2.7 3.0 3.5 4.0 4.4 4.8
2.7 3.0 3.3 3.8 4.3 4.75 5.2
3.0 3.2 3.6 4.2 4.7 5.15 5.6
300'K
400'K
500'K
6OO'K
700°K
800'K
8" C,"
0.03 0.10
0.07 0.30
0.16 0.54
0.28 0.78
0.42 1.00
0.58 1.17
so
0.05 0.24
0.17 0.56
0.33 0.86
0.48 1.10
0.67 1.26
0.84 1.40
4.1 4.5
---Bends
So and Cpo
7
C
(H
/\
H)1450 cm-1
C
/\
(H
C,"
C)ll50 em-'
For an opposing rotor heavier by one carbon group, lower the free-rotor a With equal masses, lower entropy by 0.7 gibbs/mol. entropy by 0.3 gibbs/mol. * Abbreviations are: P, propylene; i-Bu, isobutene; c-B, cis-but-2-ene; t-B, trans-but-2-ene; 2-MB 2-methylbut-2-ene; 2,3-DLMB,2,3-dimethylbut-2-ene.
optical isomers, must be considered. Thus K , = reaction-path. degeneracy = un*/cr*n. Here u and o * and n and n* are the total symmetry numbers and the number of energetically equivalent isomers for these species, respectively. As an example, in the cyclopropane structural isomerization, the transition state is with one optical center ( u = 6 and n* = 2); therefore, K,,n = 12.
Three-Membered Rings There are three basic types of reactions for cyclopropane derivatives : two proceed by biradical mecha-
nisms and the third by a concerted process. The standard reactions which have been used to illustrate these basic types are cyclopropane and 1 ,Zdimethylcyclopropane (type 1), trans-1-methyl-2-vinylcyclopropane and vinylcyclopropane (type 2), and cis-lmethyl-2-vinylcyclopropane (type 3). I n addition, two other interesting reactions confirming the importance of biradical intermediates are discussed : bicyclopropyl- and 2-methylmethylenecyclopropane. I . Cyclopropane (A) ( T y p e I ) . The reaction coordinate-energy diagram for the cyclopropane reaction is shown in Figure 1. The reaction mechanism iss
'IrransitiowState Estz'mates
\I
Aso A Ho steps
Volume 78, Number 6 June 1068
1870
H. E. O'NEALAND S. W. BENSON
Table IV : Three-Membered Ring Compound Reactions
O K
Footnote
772
U
Temp,
Reactant
Product
Cyclopropane
Propylene
Log
b C
Cyclopropane-trans-1 ,2-d2
Cyclopropane-1 ,2-cis-dz
Nle thylcyclopropane
Propylene
723 717 723
Isobutene
738
d e d e
fJ
9
8, h f, B 9, h
1-Butene cis-2-Butene
f,9 91 h
trans-2-Butene
f>9 gJ
Over-all 3-Methylcy clopropane-trans1,2-d2 Isobutene (Fs) 1-Butene (Fa) cis-2-Butene (Fa) trans-2-Butene (Fa) Over-all Over-all 1-Pentene (Fa) cis-2-Pentene (Fa) trans-2-Pentene (Fa) Trifluoroethylpropene Over-all trans- 1,2,3-Trimethylcyclopropane 3-Methylbut-1-ene 2-Methylbut-2-ene Over-all trans-lJ2,3-Dimethylcyclopropane 2-Methylbut-1-ene 2-Methylbut-2-ene cis-Pen t-2-ene trans-Pen t-2-ene 2,4-Dimethylpent-2-ene
3-Me thylcyclopropane-cis1,2-d2 Trifluoromethylcyclopropane
Ethylcyclopropane Trifluoroethylcyclopropane Trifluoroethylcy clopropane cis- 1,2,3-Trimet hylcyclopropane 1,l-Dimethylcyclopropane
1,1,2,2-Tetramethylcyclopropane
725
B h
758
f
742 747
f
i
Aestd
15.17 14.89 15.45 16.11 15.7 15.12 15.20 14.62 14.06 14.95 14.14 14,59 13.97 15.49 14.32 15.45 15.35
15.16
j
752
k
735 689
m
1 n
733
0
Eobsd
Eestd"
15.2 15.4
65 65.2 65.6 65.1 64.2 65.4 65.5 66.0 64.3 64.3 62.0 63.9 61.9 63.1 64.4 65.0 60.5
13.87 14.38 14.17 13.95 14.61 14,40 13.88 13.84 13.69
15.1 14.6 14.2 14.2
69.5 67.3 65.2 65.0 65.6 61.6 63.4 63.3 63.1
63.2 63.2 63.2 63.2
14.39 15.78
16.0
63.6 60.95
61.3
...
696
Lo@:
Aobsd
15.8
14.4 14.7 14.3 14.5
14.75 14.75 15.37 15.25
14.7 14.7
13.93 14.08 13.92 13.96 15.83
14.1 14.1 14.1 14.3 15.8 (14.4)
15.5
65.6 64.2
65.8 63.0 63.0 63.0 64.2 62.1 nn
62.6 62.6 63.6 59.42
61.3 61.3
61.9 62.3 61.4 61.2 64.4
64.1 64.1 61.7 61.7 59.7
61.2
'
a T. S. Chambers and G, B. Kistiakowsky, J . Amer. Chem. Sac., 56, 399 (1964). E. S. Corner and R. N. Pease, ibid., 67, 2067 (1945). ' W. E. Falconer, T. F. Hunter, and A. F. Trotman-Dickenson, J . Chem. SOC., 609 (1961). E. W. Schiag and B. S. Rabino82, 5996 (1960). E. W. Schlag, B. S.Rabinovitch, and K. Wiberg, J . Chem. Phys., 28, 504 (1958). vitch, J . Amer. Chem. SOC., Recalculated from ref 10: D. W. Placaeck and B. s. Rabinovitch, J . Phys. Chem., 69,2141 (1965). g J. P. Chesick, J.Amer. Chem. SOC., 82, 3277 (1960). * Recalculated from ref 10: D. W. Setzer and B. S. Rabinovitch, ibid., 86, 564 (1964). * M. L. Halberstadt and J. P. Chesick, J . Phys. Chem., 69, 429 (1965). H. M. Frey and D. C. Marshall, J . Chem. SOC., 5717 (1963). M. C. Flowers and M. C. Flowers and H. M.Frey, Proc. Roy. H. M. Frey, ibid., 3953 (1959). &I. C. Flowers and H. M. Frey, ibid., 1157 (1962). Soc., A257, 122 (1960). &'I. C. Flowers and H. AI. Frey, ibid., A260, 424 (1961). H. M. Frey and D. C. Marshall, J . Chem. SOC., C. S. Elliott and H. M. Frey, ibid., 900 (1964). * H. &'I. 3052 (1962). Frey and D. C. Marshall, ibid., 191 (1963). ' C. A. Wellington, J . Phys. Chem., 66, 1671 (1962). ' M. C. Flowers and H. M. Frey, J . Chem. SOC., 3547 (1961). ' H. M. Frey and D. C. Marshall, ibid., 3981 (1962). C. S. Elliott and H. &I.Frey, ibid., 4289 (1965). ' R. J. Ellis and H. M. Frey, ibid., 4188 (1964). C. S. Elliott and H. ill. Frey, ibid., 345 (1965). ' R. J. Ellis and H. M. Frey, ibid., 5578 (1964). * R. J. Ellis and H. M. Frey, ibid., 959 (1964). * J. P. Chesick, J . Amer. Chem. SOC.,85, 2720 (1963). H. M. Frey M. C. Flowers and H. M. Frey, J . Chem. Soe., 1689 (1962). and I. D. R. Stevens, ibid., 3865 (1962). cc M.L. Neufeld and A. T. Blades, Can. J . Chem., 41, 2956 (1963). d d K. H. Mueller and
'
'
''
The Journal of Physical Chemistry
THEBIRADICAL
n/IECHANISRf I N SMALL
RINGCOMPOUND REACTIONS
Footnote
Log
OK
Aobad
Aestd
Zobsd
Eeetd
694
P
15.08
15.5
58.87
60.4
15.08
15.5
60.07
61.4
Temp, Product
Reactant
cis- 1-Ethyl-2-methylcyclopropane trans- 1-Et hyl-2-me thylcyclopropane 1,l-Diethylcyclopropane
trans-I-Ethyl-2-methylcyclopropane cis-1-Ethyl-2-methylcyclopropane 3-Ethylpent- 1-ene 3-Ethylpent-2-ene 2-Ethylbuta- 1,3-diene CHth Cyclopentene
Isopropenylcyclopropanekk 1-Isopropenyl-1-methylcyclopropane trans-1-Cyclopropylbut-1-ene 1-Cyclopropyl-2-methylpropene
cis-1-Methyl-2-vinylcyclopropane" trans-1-Methyl-8vinyIcyclopropane 1-Methyl-1-vinylcyclopropane E thylidenecyclopropane 2-Methylmethylenecyclopropane Bicy clopropyl
1,4-Pent,adiene cis-1,3-Pentadiene trans-1,3-Pentadiene 1-Methylcyclopentene 1,2-Dimethylcyclopentene
P
14.95 14.84 15.44
14.7 14.7
63.8 63.4 65.9
61.3 61.3
631
r, s
13.61, 13.50 14.43 13.90 13.00 13.89 14.16
13.8
49.7'i
14.2 13.8 13.8 14.1 14.1
49.7, 49.6 57.3 56.2 53.6 50.9 50.5
58.1 55.6 54.6 49.7 49.7 (+)""
13.79 14.0 14.61 13.33 13.25
13.8 14.0 14.6 13.0 13.2
49.8 54.6 56.65 53.0 52.1
49.7 54.0 ( 58.1 55.6 54.6
Monofluorocyclopropane 1,l-Difluorocyclopropane 1,1,2-Trifluorocyclopropane 1,1,2,2-Tetrafluorocyclopropane Perfluorovinylcyclopropane
r t
632 620
U
3-Ethylcyclopentene 3,3-Dimethylcyclopentene 5-blethyl-1,Chexadiene cis-2-lle thy1hexa-1,3-diene trans-2-Methylhexa-1,3diene cis-Hexa-1,4-diene
626 643
W
457
5
11.03
Concerted
31.2
cis-Hexa-1,4-diene 3-Methylcy clopentene 1-Methylcyclopentene
585
X
608
y
14.78 13.67 14.11
14.6 13.6 14.1
48.64 48.64 49.35
49.1 49.1 50.5
2--Methylmethylenecyclopropane E thylidenecyclopropane
488
z
14.0
14.1
40.76
39.3
13.9
14.2
40.26
38.8
Cyclohexene All products NB propylene Acetaldehyde decomposition products Propylene (R) Propylene (Fz) Propylene (Fa) Propylene (F4)
714
ff ff fS
70.8 60.7 33.17 56.9 57.4 61.01 56.35 50.5 48.48
70. l P p 60. 7ji
730 696 602 543
16.8 15.36 13.89 14.13 14.34 14.58 14.09 14.43 15.27
Cyclopentene
404
88
13.9
+
Dimethyldiazirine Ethylene oxide
Log
723
+
Vinylcyclopropane
1871
422 673
2,
aa bb cc dd ee
15.5 14.4 14.5
13.8
+)""
Concerted
59.911
34.6
W. B. Walters, J . Amer. Chem. Soc., 73, 1453 (1951); 76, 330 (1954). ee F. Cassas, J. A. Kerr, and A. F. Trotman-Dickenson, J . F. F. Herbert, J. A. Kerr, and A. F. Trotman-Dickenson, ibid., 5710 (1965). '' R. A. Mitsch and E. Chem. SOC., 3655 (1964). Neuvar, J . Phys. Chem., 70, 546 (1966). hh This reaction is probably heterogeneous, or occurs via a free-radical chain. The products would require a concerted process if the reaction were mimolecular, but the A factor is much too high for a concerted process, '' The cis-1-methyl-2-vinylcyclopropanereaction to 1,4-hexadiene is a concerted process (see Discussion). 3 , An activation energy used as a standard to obtain an activation energy for either ring closing or H migration. kk See discussion of vinylcyclopropane. Opening to the biradical is estimated to be 49.6 kcal/mol endothermic. The observed activation energy suggests an abnormally low H-migration activation energy (Le., 7.0 kcal/mol). This is not unlikely, since the H migration is more exothermic by about 15 kcal/mol than usual (e.g., as in cyclopropane). m m The cis biradical is estimated to have about 3 kcal of extra strain in the case of I-isopropenyl1-methylcyclopropane and 4 kcal extra strain for l-cyclopropy1-2-methylpropene. nn The higher activation energies for trifluoromethylcyclopropane on the average (as compared to methylcyclopropane) suggests some bond strengthening in the ring as a result of the CF3 substitution. '' When not specifically indicated, activation energies are those obtained using the parameters calculated from cyclopropane and vinylcyclopropane (Le., EHmig = 10.8 kcal/mol, E,,, cg = 9.3 kcal/mol, E,,, ca = 8.3 kcal/mol). p p A conjugation of the cyclopropane ring of the order of 4 kcal/mol is postulated in the cyclopropylmethyl radical (see text,),
''
w.
Volume 72, Number 6 June 1968
H. E. O'NEALAND S. W. BENSON
1872 Table V : Four-Membered Ring Compound Reactions Temp, Products
Reactants
OK
Ethylene
Cyclobutane
717 728 703 688
+
ethylene Propylene cis-1,2-Dimethylcyclobutane Propylene Ethylene cis or trans-but-2-ene trans-1,2-Dimethylcyclobutane 688 Propylene Ethylene cis or trans-but-2-ene Ethylene 1-butene Ethylcyclobutane 713 1-Pentene n-Propylcyclobutane 70 1 ethylene Ethylene 2-methyl-1-butene Isopropylcyclobutane 708 Ethylene 2-methylbuta-l,3Isopropenylcyclobutane 599 diene I-Methylcyclohexene Ethylene Methylcyclobutyl ketone methylethyl 658 ketone Ethylene diethyl ketone Ethylcyclobutyl ketone 663 Ethylene propionaldehyde Cyclobutanecarboxaldehyde 653 673 Ethylene Methyl cyclobutanecarboxylate methyl propionate Ethylene allene 708 Methylenecyclobutane 723 Methylenecyclobutane-dz Methylenecyclobutane-dz Ethylene ketene 626 Cvclobutanone [See references for cyclobutene (concerted) reactions] Trimethylene oxide Ethylene CHZO 713 828 Perfluorocyclobutane Perfluoroethylene 683 1343 cis-l,2-Dichlorohexafluorotrans-1,2-Dichlorohexafluoro698 cyclobutane cyclobutane trans-1,2-Dichlorohexafluorocis-1,2-Dichlorohexafl~1oro698 cyclobutane cyclobutane 698 cis- and trans-DichlorohexaChlorotrifluoroethylene fluorocyclobutane Methylcyclobutane trans-1,2-Dimethylcyclobutane
Log
Log
Aobsd
Aeatd
Eobsd
Eestd
15.6 15.4 14.4 14.9 15.3 14.7 15.2 15.3 15.3 15.3 15.3 14.2
62.5 62.5. 61.2 61.3 61.6 63.4 60.1 60.4 63.4 62.0 61.6 62.6 51.03
63.3
i
15.6 15.62 15.38 14.57 15.45 15.46 14.81 15.48 15.57 15.56 15.53 15.63 14.64
62.1 61.1 61.4 63.2 60. 'I 60.4' 62.2 61.6 61.6 61.4 49.3
j
14.53 14.53
14.2 14.4
51.03 54.5
49.7 54. 5y
14.51 14.43 14 84 15.08 15.68 Not reported 14.56
14.5 14.2 14.5 15.7
54.2 53.3 57.3 61.5 63.3 49.5 52.0
54.2y 53.3v 57.3y 61.9
14.7
60 74.1 74.3 74.3 60.2
59.0
W
14.78 15.95 16.0 16.3 15.1
W
14.88
60.2
W
15.4
65.3
Footnote
a
b C
d
+
+ + + + +
+ +
+ + + + +
d e e
f B
h
k 1 m n 0
p P
I
14.5 14.7
48.3 52.6
r S
t U 21
60.2
63
a C. T. Genaux, F. Kern, and W. D. Walters, J . Amer. Chem. SOC., 75, 6196 (1953). R. W. Carr, Jr., and W. D. Walters, J. Phys. Chem., 67, 1370 (1963). ' M. N. Das and W. D. Walters, 2.Phys. Chem. (Frankfurt), 15, 23 (1958). H. R. Gerberick and W. D. Walters, J . Amer. Chem. SOC.,83, 4884 (1961). H. R. Gerberick and W. D. Walters, ibid., 83, 3935 (1961). R. E. Wellmann and W. D. Walters, ibid., 79, 1542 (1957). ' S. M. E. Kellner and W. D. Walters, J . Phys. Chem., 65, 466 (1961). M.
'
'
59, 2076 (1963). Zupan and W. D. Walters, ibid., 67, 1845 (1963). R. J. Ellis and H. h4. Frey, Trans. Faraday SOC., L. G. Daig80, 541 (1958). B. C. Roquitte and W. D. Walters, J . Phys. Chem., 68, 1606 (1964). nault and W. D. Walters, J. Amer. Chem. SOC., B. C. Roquitte and W. D. Walters, J . Amer. Chem. SOC., 84, 4049 (1962). M. Zupan and W. D. Walters, ibid., 86, 173 (1964). R. L. Brandaur, B. Short, and S. M. E. Kellner, J.Phys. Chem., 65,2269 (1961). J. P. Chesick, ibid., 65,2170 (1961). W. yon E. M. N. Das, F. Kern, T. D. Coyle, and W. D. Walters, J . Amer. Chem. SOC.,76, 6271 (1954). For Doering, unpublished results. a review of cyclobutene results see: R. Criegie, D. Seebach, R. E. Winter, B. Borretzen, and H. A. Brune, Chem. Ber., 98, 2347 (1965). 2082 D. A. Bittker and W. D. Walters, J. Amer. Chem. Soc., 77, 1429 (1955). ' B. Atkinson and A. B. Trenwith, J . Chem. SOC., (1953); B. Atkinson and V. Atkinson, ibid., 2086 (1957). J. N. Butler, J . Amer. Chem. Soc., 84, 1393 (1962). ' A . Lifshitz, B. Atkinson and &/I.Stedman, J. Chem. Soc., 512 (1962). E ActivaH. F. Carroll, and S. H. Bauer, J. Chem. Phys., 39, 1661 (1963). tion energies used to obtain activation energies for ring closing or decomposition from the biradical. Activation energies used to obtain estimates for resonance energies.
'
2(
AXo, = 2[*C-(C)(Hz)] 2 [C-(C,) (Hz)]
ASo4b = 8"[-2(-CH2+m)2.3
- A correction
(ACpo)3= 2.1 gibbs/mol
A.SOda= -So(C
A
C)350cm-' reaction coordinate (rC)
The Journal of Physical Chemistry
f
/"\
2(P4J2- (H
C)ll50 cm-l rc]
(9) Note that the numbers above the arrows represent the changes in entropy between the states indicated (in gibbs/mol) and the numbers below the arrows represent the changes in entholpy (in kcal/mol). The numbers 1, 3, 4a, and 4b refer t o the steps used in the calculations.
1873
THEBIRADICAL MECHANISM IN SMALL RINGCOMPOUND REACTIONS (1) cis-trans-1 ,bDideuteriocyclopropane Isomeriza-
tion.
+ 1.9 - 2.8 +
AS*c4g = 10.0
R In 3
isomerization and that internal rotation of the methylenes is fast compared to CB ring closing. The rate constant for the methylene internal rotation can be estimated by transition-state methods
= 11.3 gibbs/mol AS*int
rot
-So ( *CHz-tEt)z.a
=
=
(Ka, n = 2) -4.9 gibbs/mol log k i n e r o t = 12.9 - 3.8/8 (log kobad = 16.1 - 65.i/e, log kobyd = 15.7
64.2/8)
The reported activation energies for geometric isomerization are 65.1 and 64.2 kcal/mol. If the higher parameters are adjusted to the calculated A factor, one obtains E,-, = 64.1 kcal/mol. Schlag and RabinoE,-, 2 1 kcal/mol vitch have favored E(propy1ene) and A(propylene)/A,-, < 101a3. The lower values are
-
Thus internal rotation is about ten times faster than ring closing. Even in the unlikely circumstance of rotational barriers as high as 5 kcal/mole, internal rotations will still be faster by about a factor of 5. Other simply substituted alkylcyclopropanes follow the cyclopropane mechanism. I I . cis-1 ,W-Dimethylcyclopropane (Type I ) , T = 689°K. Mechanism.
$ Transitiondtate Estimates
4
&-C> split
5
--u
AH0
3
4
4
0.8
1
steps
( U T
&b4
3
Cis
consistent with these estimates. Thus = 64.1 = AHol,-l(T) -I- Ecacyclization (Ec,= 9.3 kcal/mol). ( 2 ) Propylene Formation. AS*(propylene)
=
10.0
+ 1.9 - 9.9 -IR In 12
Eobyd
(AC,")
Ku,,(c-t)
+ 0.8+ EH
2[C-(C,)(H)]
AS"4, = -So(C
= 11.9
AS04b
=
+
Ring closing is faster than H migration from the biradical by about + 'v 22-fold at 750°K. Structural isomerization is, therefore, slow compared to geometric isomerization. The mechanism assumes that ring opening is rate determining in the geometric
C)350 cm-l
2(Et-n-Pr)3.0 - (H
C)1150 cm-l rc
( 1 ) cis-trans Isomerization. =
AS*z = -9.9 R In 16 = -4.3 gibbs/mol
/\
/\
+ R In 3 = + R In 4 =
- 1 cis
So[(CBde), Jr (C, t-Bdo)t C
14.1 gibbs/mol ASe-, = -2.8 0 gibbs/mol
- A correction
C
mig
The preferred parameters for the elementary steps of the cyclopropane reaction are, therefore -1
2-cis 4{ 2-trans
AX", = 2[.C-(Cz)(H)] -
E Hmig = 10.7 kcal/mol
AS"1,
1.9 gibbs/mol
1 K,,(pent-2-enes) =
=
and 101G.20sec-1)
= 65.5 kcal/mol = 54.0
=
= 7.0 gibbs/mol
A *(propylene)eytd = 1015.16 sec-l (Aobsd =
Transition-State Estimates.lo
=
11.5
elc T h
1/2--eAS*'/R
+ 1.6 - 2.7 = 10.4 gibbs/mol 1015.6
set-1 (Aobsd
=
1015.3sec-1)
(IO) Note that only one of the two conformations leading to cispent-sene is likely to be important. This conformation is not as probable as the two leading to trans-pent-2-ene. Volume 72,Number 6 June 1968
H. E. O J NAND ~ S.~ W. ~ BENSON
1874
EC-t
cstd
= 50.1
+ 0.8 + 9.3 = 60.2 kcal/mol
AX* = 3.5 gibbs/mol
(&!"bad= 59.4 kcal/mol)
= 11.5
+ 1.6 - 12.0 + R In 2 = 2.5 gibbs/mol
A *(C-P2),,td = loi4*'SeC-l E(C-PB),td
= 50.1
+ 0.8 f
(Aobsd = ioia-' SeC-') (Eobsd = 61.3
f
0.1)
The /3(C-C) split results are given in Table IV. The most significant aspect of the 1,2-dimethylcyclopropane reactions is that the Arrhenius parameters for olefin production from both cis and trans isomers are identical. This clearly indicates that H migrations are rate determining and that ring closing and rotations from the biradical are relatively fast processes. III. 1,1 ,2,2-Tetramethylcyclopropane(Type I(?)), T = 783°K. This reaction is the only alkyl-substituted cyclopropane isomerization with experimental Arrhenius parameters appreciably different from those calculated in terms of the cyclopropane biradical mechanism. Either the parameters observed are high OT the transition state is near the biradical rather than the olefin. Mechanism.
Transition-State Estimates.
steps
- 2 cis + 2 gauche (olefin)
ASo4b = Xo[2(2-R4B~,),- 2(i-Pr+a)a.o
-
C
/\
(H
C)1150 cm-' rc
1 . For the Transition Stale I with Ring Opening a8 Rate Determining.
AS* = 10.1 gibbs/mol = 10'6*8SeC-'
(Aobsd
= 10'6'8SeC-')
2. For the "Normal" Transition near the Olefin ( I I ) . The Journal of Physical Chemistry
AH: -7 I .8-kcal mole
REACTION COORDINATE
Figure 1. Cyclopropane isomerizations: reaction coordinate diagram. The structure (V)* represents the transition state for (9) geometric (cis Ft trans) isomerization of cyclopropane. The *represents the transition state for structural structure (9) (propylene formation) isomerization of cyclopropane.
1
4)
A *estd
sec-lJ the transition-state calSince Aobsd = culation would appear to lend strong support to the ring opening as rate determining. However, an alternative explanation would be that the experimental
10.7 =
60.6 kcal/mol
A correction
= 1014a4sec-'
(or 1 O l 4 e 7 with cis-trans Me geometry)
(2) cis-Pent-2-ene (c-P2) Formation AS*,,.p,,
A *estd
parameters are not reliable. Since the reaction was studied only over a 30" range, the uncertainties in E and log A are about rt3.5 kcal and rtl.0 units, respectively. 3. Activation-Energy Eslirnate. Eobsd = 64.4 = 46.0 - 0.7
+
Ed(ring close or H migration) Thus E4 = 19.1 kcal/mole. This value is considerably higher than any other H-migration or ring-closing reaction deduced from the kinetics of other cyclopropane reactions and is, therefore, suspect. If the calculated A factor for an H-migration transition state is used to "adjust" the reported Arrhenius parameters, one sec-l. These parameobtains kadjusted = 1014*4-59-7/e ters are more reasonable and are not greatly outside the limits of the experimental errors for the reaction.
1875
THEBIRADICAL MECHANISM IN SMALL RINGCOMPOUND REACTIONS Now E ~ mig H = 14.4 kcal/mol, which is quite a likely value for H migration in this system. The transition state must be planar, Dreiding models
put nonbonded H----H distances in the methyls at 1.4 compared to the normal 2.1 A. Thus steric repulsions between the methyls are probably considerab1e.l'
11
We prefer the choices of the normal mechanism with the H-migration transition state, the lower adjusted Arrhenius parameters, and the "abnormal" H-migration activation energy (Le., high by an excess strain of about 4 kcal/mole). IV. Vinylcyclopropane (Type 11). The major products of vinylcyclopropane reactions are cyclopentenes; however, some diene products are also formed. Frequency factors close to normal require that entropies of activation are small. There are two possible loca-
tions for the cyclopentene formation transition state : between the reactant and biradical with ring closing as rate determining or between the biradical and cyclopentene with Csring closing as rate determining. Analysis of the kinetics of both cis- and trans-l-vinyl-2methylcyclopropane very strongly supports the latter position (see Discussion). Recent results of Willcott and Cargle12have shown that complete geometric equilibration (trans to cis) of 1-vinyl-2-deuteriocyclopropane occurs within the first 6% of the irreversible formation of cyclopentene. They have estimated that Cs ring closing is a t least five times faster than Cg ring closing. Thus there can be little doubt that the transition state for cyclopentene formation is located between the biradical and cyclopentene. The reaction coordinate-energy diagram for vinylcyclopropane is shown in Figure 2. Transition-Sta,te Estimates, T = 633"K.
A A
= 1 cis (cyclopentene) =
0 (other products)
(ACPo)l = 1.1 gibbs/mol
(ACpo)z= 0.9 gibbs/mol
K,,,(cyclopentene) = 2; KUJ1,4) = 4;
AXOi = [*C-(C)(Hz)l
+
[ * C-(C) (C,) (HI 1 - [C-(C2) (H2) 1 [C-(C2)(C,)(H)] - A correction
+A
1. Cyclopentene (c-P). AS04a = -So(Et-+n-Pr)8.3
ASoz(cis) = So [ - (Et-tn-Pr)o.s
+ (CBa,) ,]
The rotational barrier of 8.3 kcal/mol to the reaction coordinate has been chosen on the basis of the Cg ring closing activation energy (see below). This is not an unreasonable barrier, since the cis-cis conformation of the biradical has an extra steric strain of about 3 kcal/mol'l and the normal "barriers" to rotation of I
REACTION COORDINATE
Figure 2.
(11) H.M.Frey and R. J. Ellis, J. Chem. SOC.,4470 (1965). In the structurally similar compound (I), an excess strain energy of 3.5 kcal/mol has been found. (12) M. R. Willcott and V. H.Gargle, J. Amer. Chem. SOC.,89, 723 (1967). Volume 72. Number 6 June 1068
1876
H. E. O'NEALAND S. W. BENSON
ethyl groups in linear alkanes are of the order of 4-5 kcal/mol. AS*(c-P) = 10.5
- 5.6 + 1.5 - 6.7 +
C
R In 2 = 1.1 gibbs/mol A *(c-P)estd
cannot be planar while the trans transition state can be planar and closely related to lJ4-pentadiene.
= 10133 sec-1
(trans) AS04,
49.7 = 53.3
+ (ACpo)l+2AT - R(ally1) + Ec,
+ 0.7 - 12.6 + Ec,
Ec,ring closing
=
ASitrans= 11.1 - 5.0
8.3 kcal/mol
A *trans
or (ccs) ,estd
-
E1,3--cls
-
(ASo2(633) = -4.4 gibbs/mol)
C
/\
+ (b-Bde)t - (H
HI1
= -7.4 gibbs/mol
AS*(1,4-P) = 11.1 - 5.0
+ 1.5 - 7.4 +
A(1,4-P)estd = 1014.2sec-1
+
R In 4
= 3.0 gibbs/mol
(Aobsd
=
1014e4sec-1)
+
E(lJ4-P),,td = 52.3 0.7 10.7 - 5.6 = 58.1 kcal/mol (Eobsd = 57.3 kcal/mol) 3. 1,3-Pentadienes (1,3-P). The cis transition state The Journal of Phpsical Chemistry
+ (t-B4JtI + -9.8
gibbs/mol
+ 1.5 - 7.4 +
=
1013.8
sec-1;
+ +
52.3 0.7 10.7 3.5 = 54.6 kcal/mol (Eobsd = 53.6 kcal/mol)
=
E113-$ran8
+ Lis = 55.6 kcal/mol (Eobsd
= 56.2 kcal/mol)
Note that the activation energies observed for the 1,3-diene formations from l-cyclopropyl-2-methylpropene are very close to the estimated value for E l , & t r a n s , as one would expect from their low A factors. I V . irans-l-Methyl-2-vinylcyclopropane (Type 2). cis-1 -Methyl-2-vinylcyclopropane (Type 3 ) . The products of the trans reaction are cis-hexa-lJ4-diene (1,4-H) and 3-methylcyclopentene (3MeC6). The trans reaction can best be understood by first considering the isomerization of cis-l-methyl-2-vinyl cyclopropane. The latter is a concerted ene reaction analogous to the isomerization" of 4-methylpenta-1,3-diene (1) and its inverse (- 1) and follows a six-center mechanism
Arrhenius parameters for the reactions are very comkl = 1 0 i i . 7 2 - a 6 . 1 ~ / 0 . J k-l = 10ii.z4-az.7a/s.7 k3 = 1011.03-31.2/O
- (Et-m-Pr)z.e +
(P4e)t
+
Activation Energies.
H
Note that in this model there are formal charges of I / z e at the right- and left-hand C atoms. This represents an expenditure of work to separate charge, since in the biradical with allylic resonance the formal charges are on the first and third C atoms. The amount of work required can be estimated at 7 kcal from the comparison of the difference in stabilization energies of the pentadienyl and cyclohexadienyl free radical^'^ which show a similar charge separation. The net stabilization is thus 12.6 - 7 5.6 kcal and would correspond to a 1.4 gibbs/mol loss in entropy of internal rotation. The 1,3-pentadiene transition state has basically the same delocalization energy and semiion-pair charge separation as the 1,4-pentadienej but the final product is 7 kcal more stable. We may expect the activation energy to be diminished by some fraction of this, perhaps by one-half.
+
('CH23Q,)2.3
(Aobsd = 1013*0sec-' (trans); Aobsd = ioi3*'Sec-l (cis))
5.6
= -A#"z (633) So[-(.CH2-+m)z.3
+
R In 2 = -1.6 gibbs/mol
E~,a-irans =
Aso4b
C)rc-
(Pge),
2. 1,d-Pentadiene (IJ4-P). It is difficult to estimate the stabilization energy in the transition state. A plausible electronic model is H
/\
(Et-vn-Pr)z.a
(Aobsd = 1018-6 and 10i3.*sec-l)
E,,t = AH"1
= [-(H
parable (all in units of second-I). Transition-state estimates of the A factors have been made8 and are in good agreement with observation. A simple comparison of either the rate constants or the temperature ranges of study for the two 1-methyl-2-vinylcyclopropanes (cis, T = 457 A 28OK; trans, T = 585 A 16°K) shows that the concerted isomerization of the cis isomer is a much faster process. I n all the cyclopropane isomerizations, the fastest reaction from the biradical is C3 ring closing. Thus in the trans isomer, ring opening will lead almost exclusively to the cis isomer, which, (13) K. Egger andS.W. Benson, J . Amer. Chem. SOC.,87,3314 (1966).
1877
THEBIRADICAL n4ECHANISM I N SMALL RINGCOMPOUND REACTIONS as we have seen, will react rapidly t o give cis-hexa-1,4diene. The rate of formation of the hexadiene, then, will be control.led by the rates of the ring-opening reactions a and or a'. Mechanism.
substitution at the a carbons from the rotational axis increased. Both criteria would support a higher rotational barrier in d' than in d. The high activation energy observed for l-cyclopropyl-2-methylpropene, which has a biradical with a fairly analogous structure
-0 fast
-
L
fast
__
~
I n contrast to vinylcyclopropane, cyclopentenes are a minor producl, of the pyrolysis. Of the two expected, 3- and 4-methylcyclopentenes, only the 3-methyl is observed. The symmetrical 4-methylcyclopentene1which a t first glance would be favored by an initial a(C-C)
steps
1
2
bond split, is absent. This surprising and paradoxical result is, however, understandable in terms of the conformations of the cis biradicals arising from the a(C-C) and P(C-C) bond fissions, The former, nonbranched biradical has as a competing step t o c6 ring closure, the much faster rotation of the -&ICHa group to cis position followed by Ca ring closure. However, the latter branched biradical is formed in a conformation where such isomerization is only possible if either a -cH2 or a -CH3 group is rotated past the allyl group and must have a very high activation energy. Thus only Cg ring closure is available for this path (d'). There is very little information regarding the barriers to rotation of groups larger than methyl in normal and branched alkanes. Zirnitt and S u ~ h c h i n s k ihave i~~ calculated the rotational barriers about the central bonds in substituted propanea from low frequencies observed in their Raman spectra. Some very sizable barriers, (i.e., from 5 to 12 kcal/mol) were obtained. Highest barriers seemed t o result when the reduced moments of inertia were large and more importantly, when
~~
~~
to d, also suggests high rotational barriers in a system of cis, cis, cis conformation. Transition-Slate Estimates, T = 585°K. Calculations have been made on the basis of a a(C-C) split only.
3
4b
For the above Ku,n(1,4-H) = 1; KU,,(3-MeC6) = 1 (ACp0)l+2 = 1.9 gibbs/mol (3-MC5)A = 1 cis; A(o1efins) = 1 gauche (0) (1,4-H)A = 0 AXOI
=
same as vinylcyclopropane
AS"2 = same as vinylcyclopropane
C
AS",, = -So(C
/\
C)350 cm-l
AS"(b = -So [(i-Pr+n-Pr)g.a] 1. cis-Hexa-1 ,&-diene Formation (I ,4-H) or cis trans Isomerization.
AS*(l,4-H) = 11.6 - 5.0
4
+ 1.5 - 2.3 = 5.8 gibbs/mol
(14) U. A. Zirnitt and M. M. Sushchinskii, Of. Spectry., 16, 489 (1964).
Volume 72, Number 6 June 1068
H. E. O'NEAL AND S. W. BENSON
1878
A *(1,4-H),,td
=
ekt h
= 1014Jsec-1
l/2--eAS*/R
Aoba = E(1,4-H)e,td = 51.9
sec-l
- 12.6 + 0.5 f 9.3
49.7 kcal/mole
=
= 48.6 kcal/mol)
d . 3-Meihylcyclopentene Formation (S-MCs).
product observed was cyclohexene, although a total of at least 17 products were found in the glpc analysis. Those identified were 1,3-butadiene, isopropenylcyclopropane, and cis- and trans-l-cyclopropyl-l-propene. The biradical mechanism of this reaction is shown below along with the 5 primary and 12 secondary (or 17 total) products expected. Mechanism. ,
+
P-a = 1
J
1
dJ
1'
r
-5 6
M I
It 6
AS*(3-n/ICs) = 11.6 - 5.0
+ 1.5 - 8.1 = 0.0 gibbs/mol
A *(3-R!tCs) = 1013.6sec-1
(Aobsd = 1013J sec-1)
+
+
E(3-MCs) = 52.9 - 12.6 0.5 8.3 = 49.1 kcal/mol (Bobsd = 48.6 kcal/mol) 3. Relative Rates of Compeling Processes f r o m the Biradical. For the following activation energies, E-. = E-,( = 9.3, E d ' = E d = 8.3, E b t = 12.0, and Ed > 12.0, one obtains log IC-,= log log kd,
=
- 9.3/e
log k b = 12.0 - 8.o/e
log kbJ log
= 13.0
L)
kd
=
11.3 - 12/8
= 11.7
- i2.0/0
V . Bicyclopropyl. Bicyclopropyl is a particularly interesting system because it illustrates the predictive capabilities of the biradical mechanism. The principal The JOUTnd of Physical Chemistry
Since so many products are formed, steps 2-6 must all be competitive. Steps 2-6 are H migrations. Products from these reactions account for about 98% of the reaction. One would, therefore, expect the over-all Arrhenius parameters to be twice those of the over-all methylcyclopropane reactions (the factor of 2 comes from the reaction path degeneracy ratio). Thus sec-l ,* kobsd = k(al1 prodUCtS)estd = 1016*7-64*2/8 1016.36-60.7/e sec-l. The differences in activation energy may be significant. Since cyclopropane is believed to have some ?r-bond character,15 conjugation in the biradical with the ring is possible. A resonance stabilization of about 3.5 kcal/mol, similar to that of 1,3butadiene, is suggested. Decomposilion Parameters of Cyclopropylmethyl Radicals. The rate of production of cyclohexene is about 50-fold slower than the rate of production of all other products. If one makes the justifiable assumption that products of reaction 6 are small, then (16)W. A. Benett, J . Chew. Educ., 44, 17 (1967).
1879
THE BIRADICAL MECHANISM IN SMALL RINGCOMPOUND REACTIONS kz
+ ks + k5
k4
=
' / hmig(cyclopropane) ~ = lol,, ks
The over-all reaction entropy for cyclohexene formation, with reaction 5 as rate determining, is given by AS *( ~ycl0heXene)~b~ d ( 7 14"K) = 14.7 gibbs/mol = AS"1
C ASo4 = -So(C
The 1kcal reduction in E5 allows for the A(AH,O) of the cis biradical compared to the simple unhindered monoradical. Other data1* lead to an estimated lifetime for the cyclopropylmethyl radical a t 400°K of between and sec. Our parameters give a lifetime of 10-s.5 sec at 400°K. Considering the approximations required in the former estimate and the limitations of the transition-state results, the order-of-magnitude agreement in the lifetime estimates is acceptable." The activation energy for cyclohexene formation
C)350 cm-l
(with a probability of
+ AS*s
By group additivities, ASol = 10.6 gibbs/mol; theresec-'. fore, AS*5 = 4.0 gibbs/mol and A6,estd = 10i4*6 into the Substitution of A5 and k~ mig = 1012*T-10*7/e rate-constant ratio above, with 67000K = 3.2 kcal/ mol, gives E5 = 21.3 kcal/mol. Estimated Arrhenius parameters for the cyclopropylmethyl radical decomposition are, therefore IC5 = 1014.5-20.S/0 see-1
/\
isomerization ring closing of 0.5) = 8.6
- 3.9 + 1.9 - 2.1 = 4.5 gibbs/niol
ek T h
=
1/2---eAS*/R
1014.1 set-1 (&,bad= 10'4*0Sf3C-l)
Eestd
= 41.8
- 12.6 + 0.8 + 9.3 39.3 kcal/mol
(Eobsd
=
40.3 kcal/mol)
This reaction is interesting because the activation energy indicates that almost all of the allylic resonance is developed in the transition state, despite an apparent steric inhibition. Other experimental and calculated Arrhenius parameters for three-membered ring reactions are summarized in Table IV. Four-Membered Ring Compounds. The "standard" reactions for cyclobutene isomerizations and decompositions are those of cis- and trans-1,2-dimethylcyclobutane. A partial mechanism is
a biradical
p(C-C)split
+
+
sne
P
should be just E5 - Ez = 10.6 kcal/mole higher than that for the over-all reaction, Thus E(cyclohexene)estd = 71.3 kcal/mol
70*8kcal/mol) = 600°K. Mechanism and Transition-State Estimates. =
V I . Ethylidenecyclopropane (Type 11),T
Steps
1
2
Comparison of the experimental results of the cis and trans dimethylcyclobutane reactions indicates that all of the rate processes in the mechanism are important. First, the cis :trans-but-2-ene ratios are significantly different in the two systems (Le., -c/t = 1.8 from cis, t/c = 9.0 from trans). A decided preference for the original geometric conformation is evident. This
3
4
IA
+I
47 Volume 76,Number 6 June 1968
1880
H.E.O'NEALAND S. W. BENSON
can only happen if internal rotation and decomposition rates from the biradical are comparable, since fast internal rotations would give equivalent cis :trans ratios from the two starting isomers. I n addition, activation energies observed for the various products strongly sug-
constants. Empirically, eight rate constants have been measured and the thermochemistry of cis-trans isomerization provides two further relations. We thus need three assumptions to derive step rate constants from the data. We have assumed that kz = 2k2' (from symmetry considerations) and that I C 4 ks' and kl = k-1'. With the justifiable approximation that most of the isomerization goes via the a split, we can show that
-
Table VI Eaot
Process
(from cis), kcal/mol
Geometric isomer Propylene Ethylene
60.1 60.4 63.4
Lot
(from t ~ a n s ) , kcal/mol
Keq
1
.-
Activation energies for geometric isomerization and propylene formation from the same starting isomer are identical and, in addition, are lower in the cis isomer by about 1 cis effect (Le,, (1-1.3 kcal/mol). Also, activation energies of ethylene formation via B(C-C) cleavage (which will not relieve significantly the methyl-methyl steric repulsion) are insensitive to the starting isomer. They are also about 2 kcal higher than the activation energies for propylene via the weaker a(C-C) bond cleavage. I n carrying out the steady-state treatment, we have omitted completely an initial y split. This split cannot produce isomerization and can only contribute very little to the propylene formation. We have also omitted the trans rotomeric forms of the biradicals in which rotation has occurred about the C-C bond opposite the radical atoms (e.g., about the y bond in the a biradical). This is probably not too serious in the a biradical, but it could enhance by possibly a factor of 2 the olefin-forming reactions for the /3 biradical. The reason for this enhancement is that rotation about the a(C-C) bond in the p biradical to form trans from cis (step 2') has about the same rate as rotation about the ,f3(C-C) bond. The trans-rotomeric form produced from the p biradical by the latter rotation can only split into olefin or rotate to a trans-Me configuration. It cannot ring close. Finally, we have made the assumption that all bond cleavages (step 4) to form olefins have the same rate constants, k4. Even this partial scheme has 13 rate The Journal of Phgsical Chemistry
X K2 X K-3 =
K1'
X K2' X K-3'
w
4
0.7 kl'/ka' = 2.0; k-l'/k-2' = 4.3; k-a/k-1' 0.7 k-z/k-z' 3.0; k4/k-z' = 4.0; k-3/kz = 0.5
Kz = 2.0; K2' = 3.0;
61.3 61.6 63.4
ki/k3
= 2.6; k-3/k-i
N
N
The data yield absolute values for kl and kl' and, from the above ratios, 1ca and ha'. From the cis isomer, kc-t N '/del, k(propylene)(cis) * l/$cl, and k(cisbutene) (cis) N '/3k1'. I. Transition-State Estimates for cis-1 ,&Dimethylcyclobutane, T = 688'8. a(C-C) Split.
gests that decomposition, internal rotation, and ringclosing reactions all have very similar activation energies. This follows from the fact that the activation energies seem to parallel the bond dissociation energies of the initial bond (see Table VI).
steps
K1
3
-
4
For the above (AC,')W-W = 2.9 gibbs/mol AX'i = 2[*C-(Cz)(H)]- 2[C-(Ca)(H)] -
1 cis
-
0 correction (calculated for the most stable conformation)
AS'a = -S0(n-Pr+n-Pr)7.4 (rc) 1. Isomerization (c --t t), lecvt
AS* = 13.8
* '/7k1.
+ 2.5 - 7.5 = 8.8 gibbs/mol
A1 = 1016-b sec-';
= 1014.7 sec-' (Aobsd
E,-,, obsd
= 60.1 = 51.5
Eo, ring oloaing
=
SeC-')
+ 1.1 + Ecr + 2 gauche
+ 2 gauche = 7.4 lical/mol
It should be noted that ring closing from the most stable conformation of the biradical involves rotating to a conformation with about 2 gauche repulsions. Thus the activation energy for C4 ring closing is really only 5.9 kcal/mol. Since the thermodynamic properties for the most stable radical conformation are most readily calculated, the activation energy in general fcr C4 (16) L. K. Montgomery, J. W. Matt, and J. R. Webster, J . Amer. Chem. SOC.,89, 923 (1967). The estimate is based on an assumed rate of H abstraction from a methyl-substituted pentenal by secondary alkyl radicals of log k (l./mol sec) .V 8.5 - lO/O. (f7) A change in energy estimates of 2 kcal would account for the
discrepancy.
1881
THEBIRADICAL MECHANISM IN SMALL RING COMPOUND REACTIONS C4 ring closing AS'rc = -S"(n-Pr+n-Pr).r.*
ring closing from the most stable conformation is given by Ec, = 5.9 -I- An(gauche),where A n is the differencein the number of gauche interactions between the biradical conformation formed in the ring-opening process and the most stable biradical conformation. 2. Propylene Formation, k(propy1ene) = l/2k1.
A1 = 1016Jsec-l;
Edeoomp
=
decomposition
(C-C)
2(C
A1t = 10'6J sec-l;
Aint
A(CB2)est = 10'6.' sec-1
62'2 kcal'mol
=
63*4kcal/mol)
In the above A X o , = [*C-(C)(Hz)]
+
[ * (=-(C2) (H) I - [C-(Cz) (H2) ] [C-(Ca)(H)] - cis 2 gauche - 0 correction
+
+ (cy t-B3e)t + (c, t-B4e)t +
C)
+ (Sr -
=
1012.asec-'
Adecomp=
-
=
-6.8 gibbs/mol
1012*o Sec-l all within a factor of 2
Ac, = 10l2.lsec-l
3
+ 2.9 - 7.5 + R In 2 = 9.2 gibbs/mol
C)
C
/
Again, decomposition from the biradical immediately formed should probably occur with the lower activation energy of 5.9 kcal/mol. 3. cis-But-9-ene Formation (p(C-C) split),k (c-B2) = '/&I' Cfrom cis)
AS*lt = 12.4
=
/"\
+ 2 gauche = 7.4 kcal/mol
steps
-7.5 gibbs/mol
SO1-2(.Et-tn-B~)~.~ - 2(C
A(propylene),,td = 1015a2sec-' (Aobsd = 10'6.5 sec-l)
Ec,
AS'decomp
=
4
The relative rate constants from the steady-state treatment show that the rate constants are comparable
Thus activation energies should also be comparable and lie in the range of about 6.5 i 1.5 kcal/mol. II. The Second Class of Cyclobutane Reactions Is Those of the Vinyl- and CarbonyESubslituled Cyclobutanes. The mechanism for isopropenylcyclobutane is shown as
+I (AC,o)aoo-l~~ = 3.5 gibbs/mol
A S o , = -So [Et+t-Bu]7.4
4. Frequency Factors for Internal Rotation, Ring Closing, and Decomposition fyom 1,4 Biradicals. The factors are shown below using the empirical barriers of 7.4 kcal/mol in the biradical internal rotation
AS*int
rot
=
+
- - X " ( . E ~ + ~ - B U ) ~ . ~R In 2 = -5.9 gibbs/mol
Arrhenius parameters for the formations of the cyclohexene and ethylene are almost identical. The transition-state estimates (see below) are consistent with this observation and suggest that the three processes proceeding from the biradical have comparable rates. From the steady state, assuming k-1 'v kz 'v kI, one obtains k(methylcyc1ohexene) = Ic(ethy1ene) = l/akl
Transilion-8tate Estimates, T = 600'K. Volume 7.2, Number 6 June 1068
1882
H. E. 0 NEALAND S. W. BENSON
ASo
-'z, 13.4 686
AH'
steps
J
1
-421
-l26
08
2
8
+ (2-MBae)t
AS"z = -(i-Pr-~n-Bu)o.e (Cp0)1+z
-7.0
+ 1 cis = 3.1 gibbs/mol
been obtained from the observed activation energies by assigning Edecomp fsi 7.4 kcal/mol. It is possible that a slightly higher value, say Edeoomp s 8.7 kcal/mol, should have been used since the calculated value for isopropenylcyclobutane was low by 1.7 kcal/mol. This would raise the calculated resonance energies (Table VII) by 1.7 kcal/mol.
(Kr,n(all processes) = 2 )
1. Rate Constant Estimates for Reactions 2, 3, and
Table VI1
-1.
Resonance Radical
o-=G
7.7
O5CH
8.7
L(
U
This gives A-1 N 2Az (cis only) 'v 1.3A3. Since E-1 L L ~E3 = 7.4 kcal/mol and Ez 'V Ec, ring olosing 3 8.3 kcal/mol, within our experimental error, k-2 = ka = kl. 2. Methylcyclohexene and Ethylene, IC = '/3k1.
AS *(methylcyclohexene) = AS *(ethylene) = 12.8 - 5.2 2.8 - 7.0 1.4 = 5.1 gibbs/mol
+
+
A (methylcyclohexene)
= A (ethylene),std = 1/31014.7set-1 = 1014.2 sec-1 (Aobsd
Eeatd
=
53.5
= 1Oi4*'SeC-')
- 12.6 + 0.9 + 7.4 49.3 kcal/mol
(Eobsd
= 51.0 kcal/mol)
III. Resonance Energies of ,&Carbonyl Radicals. The mechanisms for the decompositions of methylcyclobutyl ketone, ethylcyclobutyl ketone, cyclobutane carboxaldehyde, and methylcyclobutane carboxylate should be the same as that for isopropenylcyclobutane. The activation energies observed for these reactions should then differ principally by the resonance energies developed in their biradicals. Resonance energies have The Journal of Phgsical Chemistry
energy (=W, kcal/mole
4.7
I V . Methylenecyclobutane. The isomerization and decomposition of methylenecyclobutane constitute particularly interesting and forceful illustrations of the biradical mechanism. The activation energy for decomposition of methylenecyclobutane to ethylene and allene is about the same as that observed for the cyclobutane decomposition, in spite of the possibility of an allylic resonance assist for the reaction, There are two possible explanations. l8 First, that allylic resonance is not achieved in the ring-opening reaction because the u bonds of the ring are at right angles to the methylene T system (i.e,, steric inhibition of resonance), or second, that the allylic resonance of the biradical must be lost in the biradical decomposition because of the necessity of forming the second allenic T bond at right angles to the first, which in the biradical contains the allylic system. Doering has recently resolved the problem by showing that methylenecyclobutane-dz isomerizes to methylenecyclobutane-dz with an activation energy roughly one allylic resonance lower than the decomposition to allene and ethylene. Thus the second explanation is supported. Transiiion-StateEstimates. (18) P. S. Nangia, Ph.D. Thesis, University of Southern California, Berkeley, Calif., 1964.
1883
THEBIRADICAL MECHANISM IN SMALL RINGCOMPOUND REACTIONS
cyclobutane reaction. The activation energy is considerably lower, in fact, just about the value one would calculate if the carbonyl resonance is maintained in the transition state. It is possible that the nonbonding p orbitals on the oxygen are able to assist in the stabilization of the transition state as the second n bond is formed. The remaining class of reactions for four-membered rings is the cyclobutene isomerizations. These reactions all proceed with lower than normal A factors and with very low activation energies (Le., 30-36 kcal/mol). Products of substituted cyclobutenes are all stereospecific in a manner consistent with the conrotary mechanism postulated by Woodward and Hoffmann. Such data are not consistent with any normal type of biradical mechanism and certainly appear to be concerted processes. Observed and estimated Arrhenius parameters for four-membered ring reactions are summarized in Table
V. Thermochemistry and Kinetics of Fluorine Substituted Small-Ring Compounds The effect of fluorine substitution on the kinetics and thermodynamics of small-ring compounds is unusual, The activation energies for isomerization of the fluorocyclopropanes are all appreciably smaller than that for cyclopropane (see Table IV), while the activation energies for decomposition and isomerization of fluorinated cyclobutanes are appreciably larger than that for cyclobutane (see Table V). Considerations of the thermochemistry of fluorinated three- and four-membered rings, alkanes, alkenes, and biradicals provide a reasonable explanation for the observed activation energies, The effect of fluorine substitution in compounds can be illustrated by the thermochemistry of various reactions. For the effect in olefins, we consider19 1
CFzHCFzH e * CFzCFz2
AHo1,2
It is interesting to compare the parameters of the cyclobutanone decomposition to those of the methylene-
+ 2H
= 2DHo(C-H) = 2(103.5) = 207 kcal/mol
(19) J. W. Coomber and E. Whittle, Trans. Faraday Xoc., 63, 384
(1967).
Volume 79,Number 6 June 1968
1884
H. E.O'NIALAND S. W.BENSON = -218.0 kcal/mol 2AHto(H) = 104.2 kcal/mol
AHtO (CF2HCF2H)
for these compounds from the observed reaction kinetics and available thermochemistry (see Table VIII). A discussion of the entries of Table VI11 is in order. The decomposition of perfluorocyclopropane proceeds to tetrafluoroethylene as i n d i ~ a t e d ~ ~ r ~ ~
Therefore = - 115 kcal/mol AHgo(CF2CF2+) 3
also, CFZ = CF2
e .CF2 - CF2. with 4
dHto(CF2 =
CF2) = -155.0 kcal/mol and the above heat of formation of the biradical, one obtains a G C ?r-bond strength in perfluoroethylene of only 40.0 kcal/ mol. This is 20 kcal/mol weaker than the corresponding bond in ethylene. The fluorine substitution has, therefore, destabilized the olefin by about 5.0 kcal/F mol. For the effect in cyclobutanes, we consider the equilibriumaobetween perfluorobutane and perfluoroethylene
(AC,") % - 1.8 gibbs/mo121*22 Kes(683) = 108.8-49-9/8 mol/l.zo Thus the reaction enthalpy at 298°K is AH6,c0 (298) = 52.0 kcal, which gives AHt" (perfluorocyclobutane) = -362.0 kcal/mol. From group additivities,21[C-(C)$(Fz)] = -97.5 kcal/mol, a strain energy of 28.0 kcal/ mol is obtained. Comparing this to the strain energy in cyclobutane (26.1 kcal/mol), we see that fluorine substitution has not appreciably changed the strain of the four-membered ring. The effect of fluorine substitution at a radical center can be estimated from the reactions
n
CFiHCF2CF2CFzH (Fa) t 2H I I1 I11 AH'',.^ = 2DH' (C-H) = 207 kcal/mol AH'(I) = -413.0 kcal/mol21 AHO(II1) = 104.2 kcal/mol Therefore, AH' (11) = -310.2 kcal/mol
II
+
Thus, AHo9~lo = 362.0 - 310.2 0.8 (gauche) = 52.6 kcal/mol. Calculation of the ring-opening enthalpy in the usual way gives, AHog,io = DHO(GC)oyolobutane Estrain(perfluorobutane)= 81.6 = 28 = 53.6 kcal/mol. Thus within the experimental uncertainties, there appears to be no appreciable effect of stabilization or destabilization by fluorine substitution at a radical center. This is in good agreement with the DHo(C-H) bond dissociation energy data in fluorinated me thane^.^ The effect of fluorine substitution on the stability of cyclopropanes is more ambiguous. No heats of formation for fluorinated cyclopropanes are available; however, it is possible to obtain reasonable estimates
-
The Journal of Physica: Chemistry
2 ---T
CzF4
From the rate-constant ratio (,7~-~/k~"') observed at cd?6decomposition temperatures and from other available kinetic data (CF2:addition to C2F4at low temp e r a t u r e ~and ~ ~ CF2 dimerization26),rate constants for reactions 1 and -1 were obtained: log kl = 13.25 = 38.6/0 sec-1 and log IC-1 = 7.46 - 9.0/0 l./mol sec. I n view of the Arrhenius parameters reported for the perfluoroallylcyclopropane reaction and as a result of transition-state calculations, we feel the decomposition Arrhenius parameters are too low and prefer log kl = 14.5 - 41.7/0. Thus one obtains AHi"(perfluoroAHf"(CF2:) 27 cyclopropane) = AHtO (CzF4) 8 = Edeoomp f E s d d n = -155.0 - 39.7 - 41.7 -228.4 kcal/mol. It was also observedz4 that CF2: radicals produced in reaction 1 could be scavenged with added perfluoropropene to give perfluoromethylcyclopropose. Trapping of CF2 with ethylene was considerably slower, although detectable. If one assumes that the scavenging of CF2 by ethylene is slower because of a higher activation energy, one can guess this activation energy to be about 12 kcal/mol. The other addition activation energies of Table VI11 are interpolations between this activation energy for CFz addition to ethylene and the 8 kcal/mol activation energy for reaction -1 (for k-1, atm-l). Strain energies in the mono-, di-, tri-, and tetrafluorocyclopropanes were obtained by assuming that the observed activation energies of reaction may be identified with the isomerization (fluoropropene) formation processes (however, see below). An activation energy for 1,2-H migration from the biradical of 10.8 kcal/mol was also assumed, along with an average heat capacity correction of 0.7 kcal/mol. Thus for fluorocyclopropane
+
The following data are available.
IV -
2CFG
E,,,
=
Eiaom = 61.0 =
DH"(C-C) -
Estrain
=
+
+ (ACpo)AT + EH +
inig
81.6 - Eatrain 0.8
+ 10.8
(20) J. N. Butler, J. Amer. Chem. SOC.,84, 1393 (1962). (21) 8. W. Benson, et al., Chem. Rev., in press. (22) A. Lifshitz, H. F. Carrol, and S. H. Bauer, J . Chem. Pfiye., 39, 1661 (1963). (23) J. W. Coomberand E. Whittle, J. Phys. Chem., 70,593 (1966). (24) B. Atltinson and D. McKeagan, Chem. Commun., 189 (1966). (25) H. E. O'Neal and S. W. Benson, J . Phys. Chem., 71,2903 (1967). (26) F. W. Dalby, J. Chem. Phys., 41, 2297 (1964). (27) A H ~ ~ ( C F ~A. : ) :P. hlodica and J. E. LaGraff, J . Chem. Phys., 43, 3383 (1965).
1885
THEBIRADICAL MECHANISM IN SMALL RINGCOMPOUND REACTIONS Table VI11 Reaction
AHf'(v)~x
Eatrain
61.0
-26.2
32.1
4.5
56.4
-71.3
35.7
4.1
Eexptl
Eatrain/F
Eaddn
Edeoomp
12
56.1
11
47.7
10
48.5
F P
-
F AHP
d
-71.3
F F
k/
CF2
+
-39.7
cZH4 12.5
F 50.5
(A)F3
d ---t
AHf"'
(&IF2
-107.8
CF2
+
-39.7
bHroC
-154.4
AHr°C
(-227.4)
-39.7
-154.4
44.6
4.3
(-76.2)"
-39.7
CF2
5.0
-31.4
-39.7
(-190.1)
42.6
CHZ-CHF 48.5
AH^^^
-107.8
(-190.1)
51.9
4.9
9
44.3
(-227.4)
63.6
6.0
8
41.7
-115.1
+
CF~SCFB 38.6 -155.0
Group additivity gives - 71.5 kcal/mol. An a The experimental value, subject to considerable uncertainty, is -80.8 kcal/mol. average of these two has been used here. * The activation energy for the decomposition of perfluoroalkylcyclopropane is 42.7 kcal/mol Thermochemistry of the decomposition reaction giving heats of formation in kcal/mol. (see text).
Estrain = 32.1 ltcal/mol; Estrain = 4.5 kcal/(mol Fatom) The heats of formation of the fluorocyclopropanes were then calculated from group additivities and the strain energies. For the di-, tri-, and tetrafluorocyclopropanes, activation energies for decomposition to CF2 and the corresponding fluoroethenes were calculated from the reaction thermodynamics and the indicated activation energies of CF2 addition to the olefins. Thus for difluorocyclopropane Edecornp-Eaddn-k
AH'f(CF2)
+ A H o & H 4 ) - ~ H o f rh7)
-
-12 - 39.7 + 12.5f71.3 561 kcal/hole It is particularly interesting and important to note that the activation energies so calculated are equal to the
experimental activation energies within the experimental errors. Thus in obtaining the strain energies of Table VI11 it was immaterial whether the experimental activation energies were identified with the isomerization reactions or the decomposition reactions. The results suggest that for cyclopropanes with two or more geminal fluorine atom substitutions, the decomposition into :CF2 olefin should be competitive with,
and in some cases possibly preferred to, the usual cyclopropane-type isomerization reactions. This could well be the reason why extensive polymerization of products was observed in all but the monofluorocyclopropane reaction, thus discouraging detailed product analysis. The pentafluorocyclopropane reaction has not been studied. However, if the activation energy for perfluoroallylcyclopropane (raised by 1.6 kcal/mol to account for the effect of the perfluoroallyl substitution for H) is adopted, the values listed are obtained. Strain (or destabilization) energies per F atom substitution seem to center around 5 kcal/F. This is very analogous to the effect of fluorine on the ?r-bond strength in olefins and may be considered as additional evidence for ?r-bond character in cyclopropane bonding. Energetics of the Reactions of 1 ,W-DichlorohexaJluorocyclobutane. Mechanism.
+
Volume 78,Number 6 June 1968
1886
H. E. O'NEALAND S. W. BENSON
The isomerization reaction is probably rotationally controlled Eiaom
= DH"(C-C)
- Estrain
+ E , (as in cyclobutane)
Eobsd
= 60.2 kcal/mol
W. H Migration in 1,s Biradicals. H migration, accompanied by partial double bond formation, restricts two internal rotations of the biradical. Since both the H bridge and double bond involve four electrons, the internal rotations have been replaced by "normal" double bond torsions
The decomposition activation energy would be expected to be less than the decomposition activation energy of the analogous perfluorocyclobutane reaction by about 11 kcal/mol. The reasons for the lower value are as follows. 1. Ring opening should be very nearly the same since fluorine (and we assume chlorine) substitution does not appreciably effect the stability of cyclobutane systems. 2. The product olefin ( C F F C F C l ) should have a (C-C) ir bond more stable by about 5 kcal/mol than does CzF4 (Le., one less F atom substitution). 3. The back-reaction activation energies for the two systems differ by only 1 kcal/mol.
C) bond bend. 3. Ring Closing in 1 ,3 Biradicals. The ring-closing transition state has been placed close to the biradical, and the entropy of the transition state has been assumed to be equal to that of the biradical less the entropy of the reaction coordinate. The carbon skeletal
Thus
bend has been identified with the reaction coordinate.
Edecomp
= Edecomp(perflUOrObUtane)
74.1
- 11 =
- 11 = 63.1 kcal mol (Eobsd
of accounting for resonance on the thermodynamics of radicals is illustrated below for the 1-pentene-3,5 biradical
I n the nonresonance form of the biradical, the vinyl group can rotate almost freely around bond 2-3. Delocalization of the electron in the resonance form restricts this rotation and "freezes" the biradical into whatever geometry it has assumed when formed. The entropy of the restricted motion about bond 2-3 has been approximated by the entropy of a three-electron torsion, which in the above, should be like a trans-but-2-ene torsion. Thus from Tables I1 and 111, one estimates = So [ - (Et+n-Pr)o.s
+
(t-B3e)t]= -5.0 gibbs/mol
ACp03O0 = -1.2
+ 1.6 = 0.4gibbs/mol
The electron-dot picture is useful for bookkeeping purposes and indicates the number of three- and four-electron bonds assumed in the transition state. The Journal of Phyakal Chemistry
(H
115Ocm-1) C)
& -2(5.8)+ 2(130)-0.6-9.8gibb~mole
The reaction coordinate has been specified as the C
A
(H
A - (A)*
= 65.3 kcal/mol)
Appendix Calculational Methods. 1. Resonance. The method
As0300
-,q
IST-~(CH~ETf ) ~2(P4& ,~
4. Ring Closing in 1,4 Biradicals. The reaction coordinate for four-membered ring closing has been identified with an internal rotation. Ring closing involves a series of concerted events. In addition to the internal rotation which brings the radical ends into the proper cis conformation, the bonding orbitals must also be directed toward one another and the carbon bends must bring the orbitals together. Since the slowest of these processes will be the internal rotation about the central bond, this rotation has been taken as the reaction coordinate.
--
A S " C ring ~ closing = ( E ~ + E ~ ) B . B The rotational barrier (6.6 kcal/mol in cyclobutane) can also be identified with the activation energy for C4 ring closing from the biradical. 6. Ring Closing in 1;5 Biradicals. Entropy estimates for C5ring closing are similar to those in C4 ring closing, since the reaction coordinate must also be an internal rotation. Thus for the allylic stabilized Cg cyclization of the 3,5-pent-l-ene biradical
PROTEIN AND AMINOACIDDENSITIES IN
THE
1887
DRYSTATE
AS0cs = -S"(Et-tn-Pr)S.r
The activation energy, or rotational barrier, for this process is 8.3 kcal/mol (from the kinetics). 6. Decomposition of 1,QBiradicals. The concerted process for decomposition of the 1,4-butanyl biradical into ethylene is depicted as
bond formations and replaced by a three-electron torsion and a four-electron torsion, The central internal rotation becomes a free rotation. I n addition, two skeletal bends involving the breaking bond are loosened and the carbon-carbon stretch has been equated with the reaction coordinate. Thus ASodeaomp = C So[-2(CH2-tn-Pr)6
+
The two end internal rotations are restricted by partial
+
-
/\
2(C C
/
c)420
-
+
(C-C)SOO
+
C)290 (Sf - 81J4.01. An (P8e)t (P4di 2(C explanation of the rotational barriers used is given in the text. For the frequency assignments, see ref 8
Densities of Several Proteins and L-Amino Acids in the Dry State by E. Berlin and M. J. Pallansch Dairy Products Laboratory, h'a8teTn Utilization Research and Development Division, Agrzcultural Research Service, U.S. Department of Agriculture, Washington, D . C. 80#50 (Received December 19,1967)
Densities were determined pycnometrically, by helium displacement, for the anhydrous forms of several proteins, 18 naturally occurring L-amino acids, glycine, and di- and tripeptides of glycine. Values observed for the proteins included 1.261 g/cma for p-lactoglobulin and 1.320 g/cm8 for bovine serum albumin. No correlation was observed between the experimentally determined densities of the proteins and the values calculated from their amino acid composition.
Introduction Early studies by Chick and Martin' on the density of proteins in solution or in anhydrous form showed that the proteins underwent a decided contraction upon solution. McMeekin, Groves, and Hipp2 have studied the density and water content of @-lactoglobulincrystals and showed that the density of the crystals is a linear function of their water content over the range of 1446% moisture. They reported the values of 0.802 ml/g for the specific volume of anhydrous P-lactoglobulin and 0.772 ml/g for the protein in crystals containing 14-46% water. This difference was attributed to either an apparent packing of the protein due to the high density of the water molecules or to the presence of molecular voids in the crystal which could not be entered by the organic solvent used in measuring the density of the dried crystals. Haurowitzla in discussing the problems encountered in determining the density of dry-protein or wet-protein preparations, pointed out the difficulties in choosing an appropriate displacing fluid when the density is to be
determined pycnometrically. These difficulties include selecting a fluid which enters all voids in the protein crystal and does not interact chemically with the protein. The technique of gas displacement will, however, circumvent many of these difficulties in density measurements. Helium is usually chosen as the displaced medium, as it is chemically inert, behaves as an ideal gas, does not adsorb on the surface to any appreciable extent at ambient temperatures, and is sufficiently small to enter all voids between as well as within the particles. We were, therefore, prompted to apply the technique of He displacement to measure the density of anhydrous /?-lactoglobulin to determine if any such molecular occlusions could be observed. The availability of (1) H.Chick and C. J. Martin, Biochcm. J . , 7 , 92 (1913). (2) T. L. McMeekin, M. Groves, and N. J. Hipp, J . Polyn. Sci., 12, 309 (1954). (3) F. Haurowitz, "The Chemistry and Function of Proteins," 2nd ed, Academic Press Inc., New York, N. Y., 1963,pp 113, 114.
Volume 78- Number 6 June 1968
