J. Phys. Chem. 1996, 100, 17087-17089
17087
Hydrogen Transfer between Ethyl Radical and Ethylene: An Example Where Kinetics Does Not Follow Thermodynamics Johan P. A. Heuts,1a,b Addy Pross,1c and Leo Radom*,1a Research School of Chemistry, Australian National UniVersity, Canberra, ACT 0200, Australia, and Department of Chemistry, Ben-Gurion UniVersity of the NegeV, Beer SheVa, Israel ReceiVed: August 6, 1996X
Ab initio molecular orbital calculations and transition-state theory have been used to study reactions between ethyl radical and ethylene that model chain transfer in the polymerization of ethylene, and the results rationalized with the aid of the curve-crossing model. It is found that the endothermic transfer of hydrogen from ethylene (abstraction) is kinetically favored over the thermoneutral transfer of hydrogen to ethylene (transfer). A possible explanation lies in the fact that only one bond needs to be broken in the abstraction reaction, in contrast to the two bonds that need to be broken in the transfer reaction.
Hydrogen-transfer and hydrogen-abstraction reactions play an important role in free-radical polymerization because they are involved in many chain-transfer reactions, including chain transfer to monomer.2 The chain-transfer processes are of major importance because they directly affect the molecular weight distribution of the polymer formed and, through this, its mechanical properties.3 It is clear that a better understanding of the mechanisms involved might lead to better process and product control. Although many experimental studies have been performed and chain-transfer rate coefficients have been measured, one of the most basic questions to be asked in unravelling the mechanism has remained unanswered: In which direction does the transfer of the hydrogen atom take place - from the radical to the monomer (i.e., to the alkene) or from the monomer to the radical (i.e., from the alkene)? In the latter case, a strong vinylic C-H bond needs to be broken, which will often mean that the reaction is endothermic. It has generally been assumed that, in cases where there are no labile hydrogens present in substituents of the monomer, it is unlikely that hydrogen transfer from monomer to radical is responsible for the chain-transfer reaction.4 We report here results of a theoretical study on the two possible hydrogen-transfer reactions in the ethyl radical + ethylene system, the system that we have chosen as a model for the free-radical polymerization of ethylene. These are the hydrogen-transfer reaction, modeling transfer to the monomer:
CH3-CH2• + CH2dCH2 f CH2dCH2 + CH3-CH2•
(1)
and the hydrogen-abstraction reaction, modeling transfer from the monomer:
CH3-CH2• + CH2dCH2 f CH3-CH3 + CH2dCH•
(2)
These two reactions have been studied using ab initio molecular orbital calculations5 and transition-state theory,6 and the results rationalized using the curve-crossing model.7,8 We reach the interesting conclusion that the endothermic abstraction reaction is the kinetically faVored process and that a possible explanation lies in the fact that only one bond needs to be broken in the abstraction reaction, in contrast to the two bonds that need to be broken in the thermoneutral transfer reaction. X
Abstract published in AdVance ACS Abstracts, October 1, 1996.
S0022-3654(96)02379-9 CCC: $12.00
High-level ab initio molecular orbital5 and density functional theory9 calculations have been carried out using the GAUSSIAN 94 series of programs.10 Reaction barriers and energies were obtained at a modified G2(MP2) level of theory.11,12 Arrhenius activation energies and frequency factors were obtained as described in an earlier paper,13 replacing the lowest real frequency in the transition structure by a free internal rotation,14 and the importance of tunneling effects was estimated by using the Wigner tunneling correction factor.15 Full details of these calculations will be reported elsewhere.16 The optimized geometrical parameters of the transition states for the two reactions (Figure 1) show similar features. In addition, normal-mode analyses indicate that the low-frequency modes present in the two transition states are also similar, which leads to quite similar Arrhenius frequency factors (Table 1). Finally, the imaginary frequencies in both cases are similar, which leads to similar tunneling corrections for the two reactions. However, the calculated barriers at 0 K (and hence the activation energies) for the two reactions differ significantly: 128.1 kJ mol-1 for the hydrogen-transfer reaction (eq 1) and 80.2 kJ mol-1 for the hydrogen-abstraction reaction (eq 2; see Table 1). The calculated reaction enthalpies are as expected: the transfer reaction is of course thermoneutral, while the abstraction reaction is endothermic. Our results are consistent with recent theoretical results reported in the literature.17-19 In particular, recent high-level calculations18 give a classical barrier (i.e., without zero-point energy corrections) of 135.0 kJ mol-1 for the hydrogen-transfer reaction (eq 1), which agrees well with our classical barrier of 132.5 kJ mol-1. We are not aware of any relevant experimental data for this reaction. For the hydrogen-abstraction reaction, however, our calculated values for the frequency factor (A) and activation energy (Eact) of 1010.4 dm3 mol-1 s-1 and 98.6 kJ mol-1, respectively, at 900 K (before tunneling corrections) are in reasonable agreement with data reported for eq 2 by Halstead and Quinn (i.e., 109.8(0.4 dm3 mol-1 s-1 and 81.2 ( 5.9 kJ mol-1 for A and Eact, respectively)20 and are consistent with the activation energy of 74.3 ( 8 kJ mol-1 (at 523 K) found experimentally by Buback et al.21,22 for the transfer to monomer reaction in the free-radical polymerization of ethylene. They are in less good agreement with more recent values for A and Eact of 108.2(0.2 dm3 mol-1 s-1 and 62.2 ( 3.0 kJ mol-1, respectively, in the temperature range of about 650900 K.23 © 1996 American Chemical Society
17088 J. Phys. Chem., Vol. 100, No. 43, 1996
Letters abstraction
CH3-CH2•v H••vV CHdCH2 98 CH3-CH2••vV H •V CHdCH2 (4)
Figure 1. Selected geometrical parameters (bond lengths in angstroms and bond angles in degrees, B3-LYP/6-31G*) in the optimized transition structures for (a) the hydrogen transfer from ethyl radical to ethylene (C2V symmetry), and (b) the hydrogen abstraction from ethylene by ethyl radical (C1 symmetry).
TABLE 1: Calculated Barriers, Activation Energies, and Frequency Factors (with and without Tunneling Corrections), and Reaction Enthalpies for Hydrogen Transfer from Ethyl Radical to Ethylene (Eq 1) and Hydrogen Abstraction from Ethylene by Ethyl Radical (Eq 2) hyrogen transfer
hydrogen abstraction
128.1 129.8 3.2 × 108 125.7 3.7 × 108 0
80.2 81.8 7.6 × 108 77.6 8.5 × 108 40.1
a
E0 Eactb without tunneling Ac without tunneling Eactb with tunnelingd Ac with tunnelingd ∆Hre a
-1
Barrier at 0 K (kJ mol ) calculated at a modified G2(MP2) level. Activation energy at 298.15 K (kJ mol-1). c Arrhenius frequency factor at 298.15 K (dm3 mol-1 s-1). d Calculated using the Wigner tunneling correction factor. e Reaction enthalpy at 298.15 K (kJ mol-1) calculated at a modified G2(MP2) level.12
Why is the endothermic hydrogen-abstraction reaction kinetically favored over the thermoneutral hydrogen transfer? A rationalization for this, at first sight unlikely, result can be found by applying the curve-crossing model7,8 to the two reactions. In this model, the reaction barrier is considered to arise from an avoided crossing of electronic configurations that correspond to reactants and products, respectively. For the hydrogen-transfer reaction, the important aspects of the reactant configuration are the singlet couplings in the two bonds that need to be broken, i.e., the C-H bond of ethyl radical and the π-bond of ethylene. To break these two bonds, these two singlet configurations need to be converted to the corresponding triplet configurations, i.e., to configurations in which bonding is absent: v V transfer •CH2-CH2• 98 V v •CH2-CH2•
Acknowledgment. Useful discussions with Professor Robert Gilbert, Dr. Athanassios Nicolaides, and Dr. Harold Schoonbrood, the provision by Dr. James Franz of manuscripts prior to publication, a generous allocation of time on the Fujitsu VP2200 of the Australian National University Supercomputer Facility, support by the Australian Research Council, and the provision of an Overseas Postgraduate Research Scholarship to J.P.A.H. are all gratefully acknowledged. References and Notes
12
b
V Vv •CH2-CH2••H
Accordingly, the initial energy gap for the abstraction reaction is proportional to the strength of a single Csp2-H bond, i.e., the initial gap is expected to be significantly less than for the transfer reaction. Since a larger initial energy gap is considered to contribute to the generation of a larger activation barrier, the barrier to abstraction is likely to be less than the barrier to transfer, despite the endothermicity of the abstraction reaction.24 In summary, we find that the endothermic hydrogen abstraction from ethylene by ethyl radical is kinetically favored over the thermoneutral hydrogen transfer from ethyl radical to ethylene by approximately 50 kJ mol-1. This result may be rationalized by noting that only one bond needs to be broken in the abstraction reaction, in contrast to the two bonds that need to be broken in the thermoneutral transfer reaction. Our results suggest that the transfer to monomer reaction in the freeradical polymerization of ethylene21 involves hydrogen abstraction from ethylene.
H••vV CH2-CH2•V (3)
As a consequence, in a curve-crossing diagram, which models barrier formation in a chemical reaction, the initial energy gap between reactant and product configurations will be roughly proportional to the sum of the strengths of the Csp3-H bond and the CdC π bond. By contrast, in the abstraction reaction, to break the C-H bond in ethylene and create a C-H bond in ethane, only one bond needs to be broken so only one electronic reorganization from singlet coupling to triplet coupling is required:
(1) (a) Australian National University. (b) Present address: School of Chemical Engineering and Industrial Chemistry, University of New South Wales, Kensington, NSW 2052, Australia. (c) Ben-Gurion University. (2) See, for example: (a) Farina, M. Makromol. Chem., Macromol. Symp. 1987, 10/11, 255. (b) Moad, G.; Solomon, D. H. The Chemistry of Free Radical Polymerization; Pergamon: Oxford, 1995. (3) See, for example: Gilbert, R. G. Emulsion Polymerization; Academic Press: London, 1995. (4) See, for example: (a) Metzger, J. O. Angew. Chem., Int. Ed. Engl. 1986, 25, 80. (b) Reference 2b, p 251. (5) See, for example: Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. (6) See, for example: Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and Recombination Reactions; Blackwell Scientific: Oxford, 1990. (7) For reviews of the curve-crossing model, see: (a) Pross, A.; Shaik, S. S. Acc. Chem. Res. 1983, 16, 363. (b) Pross, A. AdV. Phys. Org. Chem. 1985, 21, 99. (c) Shaik, S. S. Prog. Phys. Org. Chem. 1985, 15, 197. (d) Shaik, S. S.; Schlegel, H. B.; Wolfe, S. Theoretical Aspects of Physical Organic Chemistry, The SN2 Transition State; Wiley: New York, 1992. (e) Pross, A. Theoretical and Physical Principles of Organic ReactiVity; Wiley: New York, 1995. (8) For an application of the curve-crossing model to hydrogenabstraction reactions, see: Pross, A.; Yamataka, H.; Nagase, S. J. Phys. Org. Chem. 1991, 4, 135. (9) See, for example: Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules; Oxford University Press: New York, 1989. (10) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; DeFrees, D. J.; Baker, J.; Stewart, J. P.; HeadGordon, M.; Gonzalez, C.; Pople, J. A. GAUSSIAN 94, Revision B.3; Gaussian, Inc.: Pittsburgh PA, 1995. (11) (a) Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. J. Chem. Phys. 1991, 94, 7221. (b) Curtiss, L. A.; Raghavachari, K.; Pople, J. A. J. Chem. Phys. 1993, 98, 1293. (c) Curtiss, L. A.; Raghavachari, K.; Pople, J. A. J. Chem. Phys. 1995, 103, 4192. (12) (a) The modification of G2(MP2) theory11b that was applied here is similar to that investigated by Bauschlicher and Partridge12b and consists of replacing MP2/6-31G* for geometry optimization and HF/6-31G* for frequency analysis by B3-LYP/6-31G*. A scale factor of 0.9826 (see ref
Letters 12c) was used for zero-point vibrational energy calculations. In the temperature correction of the reaction enthalpy to 298.15 K, a scale factor of 1.0013 was used for the harmonic frequencies (see ref 12c) and the methylene torsion in the ethyl radical was treated as a free rotation. (b) Bauschlicher, C. W.; Partridge, H. J. Chem. Phys. 1995, 103, 1788. (c) Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502. (13) Heuts, J. P. A.; Gilbert, R. G.; Radom, L. Macromolecules 1995, 28, 8771. (14) UHF/6-31G* optimized geometries and frequencies (scaled by 0.9061; see ref 12c) were used for the determination of the partition functions required for the evaluation of the rate coefficient with transition-state theory. (15) Wigner, E. Z. Phys. Chem. 1932, 19, 203. (16) Heuts, J. P. A.; Gilbert, R. G.; Radom, L., to be published. (17) Franz, J. A.; Ferris, K. F.; Camaioni, D. M.; Autry, S. T. Energy Fuels 1994, 8, 1016. (18) Watts, J. D.; Franz, J. A.; Bartlett, R. J. Chem. Phys. Lett. 1996, 249, 496. (19) Litwinowicz, J. A.; Ewing, D. W.; Jurisevic, S.; Manka, M. J. J. Phys. Chem. 1995, 99, 9709.
J. Phys. Chem., Vol. 100, No. 43, 1996 17089 (20) Halstead, M. P.; Quinn, C. P. Trans. Faraday Soc. 1968, 64, 103. (21) Buback, M.; Choe, C.-R.; Franck, E.-U. Makromol. Chem. 1984, 185, 1685. (22) Our calculated value for Eact at 523 K is 87.4 kJ mol-1 (without tunneling correction; including the Wigner correction yields a value of 82.0 kJ mol-1). (23) (a) Zhang, H. X.; Back, M. H. Int. J. Chem. Kinet. 1990, 22, 21. (b) Roscoe, J. M.; Jayaweera, I. S.; MacKenzie, A. L.; Pacey, P. D. Int. J. Chem. Kinet. 1996, 28, 181. (24) An interesting alternative (but somewhat related) argument to that presented here has been used by Franz et al.17 to explain the difference in their PMP2/6-31G** reaction barriers for hydrogen abstraction from ethane by ethyl radical (64.8 kJ mol-1) and the hydrogen transfer given by eq 1 (113.7 kJ mol-1), both being thermoneutral reactions. It was argued that the energy required to bend the methylene group at the reaction site in the abstraction is lower than the energy required to bend the methylene group at the vinylic carbon center involved in the transfer reaction.
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