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groups of the ligand in a cyclic-like conformation of the Li' complex, as well as a high solvation energy of the Li' cation. As mentioned above, tetraglyme may transform its conformation from a flexible linear chain in the uncomplexed state to a fairly rigid quasi-cyclic conformations.*lain the complexed state. This would lead to a significant loss in entropy upon complexation. However, this loss may also be, partly, compensated by an increase in entropy resulting from solvent release on desolvation of the cation on complexation. This increase will be largest for the smallest cation. Thus the negative entropy of cation complexation in both solvents may primarily be due to a conformational change could hence result from significant ion pairing in this system. of tetraglyme, except with the small Li' ion, in which the entropic However, in the polar protic solvent methanol, capable of gain on desolvation of the cation should effectively compensate solvating both cations and anions, such a difference in association the loss in entropy from a conformational change of tetraglyme, between a given cation and various anions would be d i m i n i ~ h e d , ~ ~ . ~since ~ the value of TAS, is positive in both solvents. which is in accord with the present results. The TAS, values for a given complex is found to be more 5 . Thermodynamics of Complex Formation. In Table IV are negative in methanol than in acetonitrile. This suggests that the listed the thermodynamic parameters for alkali-metal complexation metal ion and tetraglyme may not be completely desolvated in by tetraglyme in methanol and acetonitrile at 25 OC. The T U , methanol, and hydrogen bonding between methanol molecules and values are calculated from experimental values of AG, and AH, the cation complexes may still exist. On the other hand, the origin by means of the relationship AG, = -RT log K, = AH,- TU,. of the more negative values of AH, in methanol is not clear at The free energy of complexation, AG,, results from contributions present. Recently Takeda and his c o - ~ o r k e r shave ~ ~ also found of both enthalpy and entropy terms, generally including the binding that the values of AHc and TAS, for alkali-metal complexes of energy between complexone and cation, the energy of conforthe flexible dibenzo-18-C-6 are more negative in methanol than mational change of the ligand as a consequence of complex forin acetonitrile and propylene carbonate. mation, and the energies of desolvating the ligand and the cation. The AH,values for alkali-metal complexes of tetraglyme are The main energy contribution to stability varies from one comcomparable: to those of 15-C-5,14a,20,29 but the TAS, values for the plexone to another depending on the solvent, the cation, and the tetraglyme complexes are much lower. Thus the high selectivity flexibility of the complexone, as well as on the nature of binding between 1542-5 and tetraglyme toward a given cation, Ks(15-Csites on the complexone, etc. Nevertheless, the experimental data 5)/Ks(TG) >> 1, results mainly from a loss in entropy in preomay indicate whether the complexation is enthalpic or entropic rientation of the open-chain tetraglyme on complexation. This in origin. result is in accord with previous findings on the origin of the The results in Table IV show that the stability of the TG-M+ macrocyclic e f f e ~ t . ~ ~ , ~ ~ complexes is enthalpy dominated, accompanied by an unfavorable Acknowledgment. This research was supported by Supply and decrease of entropy (TAS, < 0), except for the Li' complex in Services Canada, Department of National Defence. We thank both solvents, for which the stability constant has contributions Dr. B. G. Cox for helpful discussions and Dr. M. H. Abraham from both enthalpic and entropic terms ( A H , < 0, TAS, > 0 ) . and Dr. H. C. Ling for provision of computer programs for In both solvents, the values of AH,are rather similar for Na', calculation of stability constants. K+, Rb', and Cs' cations, and more negative than that for the Li' cation. The less favorable complexation enthalpy of Li' Registry No. AN, 75-05-8; MeOH, 67-56-1. suggests that tetraglyme does not bind optimally with this small cation, probably because of a steric effect between the two terminal TABLE I V Thermodynamic Data for Alkali-Metal (as Perchlorate Salts) Complex Formation by Tetraglyme in Methanol and Acetonitrile at 25 O C (in kJ/mol) solvent Li+ Na' K+ Rb' Cs+ methanol AG, -5.1 -6.3 -9.6 -8.7 -8.3 -30.5 -25.0 -32.4 -27.3 AH, -2.8 -21.8 -16.7 -26.1 -17.7 TAS, +2.3 acetonitrile AG, -12.4 -13.7 -11.5 -10.9 -8.7 -20.3 -19.7 -21.5 -21.1 AHc -5.7 -9.4 -11.0 -7.8 -9.6 TAS, +6.7
(32) Tusek-Boric, L. J.; Danesi, P. R. J. Inorg. Nucl. Chem. 1979, 41, 833. (33) Jackman, L. M.; Lange, B. C. Tetrahedron 1977. 33, 2737.
(34) (a) Kodama, M.; Kimura, E. J. Chem. Soc., Dalton Trans. 1976, 116. (b) Kodama, M.; Kinura, E. Bull. Chem. SOC.Jpn. 1976, 49, 2465. (35) Takeda, T.; Kudo, Y.;Fujiwara, S. Bull. Chem. Soc. Jpn. 1985, 58, 1315.
Reactions of Singlet and Triplet Methylene with a C-H Bond of Ethylene. An ab Initio Study Miquel Moreno, Jose M. Lluch, Antonio Oliva, and Juan BertrPn* Departament de Quimica, Universitat Autbnoma de Barcelona, 08193 Bellaterra, Barcelona, Spain (Received: August 13, 1987)
The insertion reaction of singlet methylene into a C-H bond of ethylene and the hydrogen abstraction from ethylene by triplet methylene have been theoretically studied by using the 3-21G and 6-31G* basis sets and introducing electron correlation and thermodynamic corrections. The obtained results have permitted us to analyze the mechanistic differences between both processes. The competition between them and the well-known addition reactions to olefinic double bonds is also discussed.
Introduction Methylene reactions have become the topic of an increasing number of experimental and theoretical studies in recent years. 1*2 It has been found that the product composition of many systems (1) Baird, M. S. Annu. Rep. Prog. Chem., Sect. B 1984, 81, 79. (2) Skell, P.S. Tetrahedron 1985, 41, 1427.
0022-3654/88/2092-4180$01.50/0
involving methylene is profoundly influenced by the presence of hydrogen atoms3f4 It is now firmly established that triplet methylene abstracts hydrogen atoms from hydrocarbons while the analogous reactions with singlet methylene yield very fast insertions (3) Buehler, C. A. J. Chem. Educ. 1972, 49, 239. (4) Isaacs, N. S. Reactiue Intermediates; Wiley: London, 1974; p 375.
0 1988 American Chemical Society
Reactions of Methylene with a C-H Bond of Ethylene into C-H bond^.^^^ Whereas the triplet abstractions have high-energy barrier^,^,^ the singlet methylene insertions are predicted to occur with no energy barrier.9 For the latter process, which is one of the most characteristic reactions of singlet methylene, two mechanisms have been considered. Skell'O proposed that the reaction proceeds by a cyclic three-center concerted mechanism. On the contrary, Benson1'q12postulated a two-step process in which the singlet methylene initially abstracts the hydrogen atom, leading to a radical pair that subsequently combines together. The most recent experimental e v i d e n ~ e ' ~sug-'~ gests that the former mechanism is the correct one. From the theoretical point of view, the prototype methylene reaction is CH2 H2, hydrogen being the simplest partner molecule for which both abstraction and insertion reactions might occur. Schaefer et al.16317suggested that the abstraction and insertion reactions of triplet and singlet methylene with H2 may be representative of the analogous reactions of CH2 with saturated hydrocarbons. On this basis the insertion would occur in a concerted, non-least-motion manner, with little or no energy barrier, but in two phases: an electrophilic phase in which the empty p orbital on singlet methylene carbon atom interacts with the X-H bond followed by a nucleophilic phase corresponding to the interaction between the methylene lone pair (a) and the X-H antibonding molecular orbital.18 In contrast, the transfer of one hydrogen atom to triplet methylene is assumed to take place through a linear transition state, this mechanism imposing an important energy barrier.I9 These predictions have been confirmed by a large number of theoretical calculations carried out for the reactions of CH2 with the hydrogen m o l e c ~ l e , ~methane,25-28 ~-~~ and ethane.29,30 However, to our knowledge no theoretical studies have been performed until now on the reaction of methylene with vinylic hydrogen atoms. This case is quite interesting due to the fact that addition of CHI to the C-C double bond is a competitive reaction. The main object of this paper is to determine whether the above-mentioned models are also valid for the reactions of CH2 with vinylic hydrogens. For this purpose we have studied the simplest reaction of this type: the attack of singlet and triplet methylene on the C-H bonds of ethylene.
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( 5 ) Kirmse, W. Carbene Chemistry; Academic: New York, 1971. (6) Jones, M.; Moss, R. A. Carbenes; Wiley-Interscience: New York, 1972; Vol. I. (7) Hadel, L. M.; Platz, M. S . ; Scaiano, J. C. J . A m . Chem. SOC.1984, 106, 283. (8) Wright, B. B.; Kanakarajan, K.; Platz, M. S. J . Phys. Chem. 1985,89, 3574. (9) Herzog, B. M.; Carr, R. W., Jr. J . Phys. Chem. 1967, 71, 2688. (10) Skell, P. S.; Woodworth, R. C. J . A m . Chem. SOC.1956, 78,4496. (11) de Moore, W. B.; Benson, S . V. Adu. Photochem. 1964, 2, 1. (12) Benson, S . V. Adv. Photochem. 1964, 2, 219. (13) Berdick, T. E.; Levin, R. H.; Wolf, A. D.; Jones, M., Jr. J . Am. Chem. SOC.1973, 95, 5087. (14) Jackson, J. E.; Mock, G. B.; Tetef, M. L.; Theng, G. X.;Jones, M., Jr. Tetrahedron 1985, 41, 1453. (15) Harada, T.; Akiba, E.; Tsujimoto, K.; Oku, A. Tetrahedron Lett. 1985, 26, 4483. (16) Baskin, C. P.; Bender, C. F.; Bauschlicher, C. W., Jr.; Schaefer, H. F., I11 J. Am. Chem. SOC.1973, 96, 2709. (17) Bauschlicher, C. W., Jr.; Haber, K.; Schaefer, H. F., 111; Bender, C. F. J . Am. Chem. SOC.1977, 99, 3610. (18) Kollmar, H. Tetrahedron 1972, 28, 5893. (19) Bauschlicher, C. W., Jr.; Bender, C. F.; Schaefer, H. F., I11 J . Am. Chem. SOC.1976, 98, 3072. (20) Murrell, J. N.; Pedley, J. B.; Darmaz, S . J . Chem. SOC.,Faraday Trans. 2 1973, 69, 1370. (21) Cremaschi, P.; Simonetta, M. J . Chem. SOC., Faraday Tram. 2 1974, 70, 1801. (22) Jeziorek, D.; Zurawski, B. Int. J . Quantum Chem. 1979, 16, 277. (23) Kollmar, H.; Staemmler, V. Theoret. Chim. Acta 1979, 51, 207. (24) Sosa, C.; Schlegel, H. B. J . A m . Chem. SOC.1984, 106, 5847. (25) Bodor, N.; Dewar, M. J. S.; Wasson, J. S . J . Am. Chem. SOC.1972, 94, 9095. (26) Nagase, S.; Fueno, T.Bull. Chem. SOC.Jpn. 1976, 49, 2920. (27) Gordon, M. S. J . Am. Chem. SOC.1984, 106, 4054. (28) Gordon, M. S.; Gano, D. R. J . A m . Chem. SOC.1984, 106, 5421. (29) Jug, K.; Mishra, P. C. Inr. J . Quantum Chem. 1983, 23, 887. (30) Gordon, M. S.; Boatz, J. A,; Gano, D. R.; Friederichs, M. G. J . Am. Chem. SOC.1987, 109, 1323.
Figure 1. Geometrical structure of the transition state for the insertion reaction of singlet methylene into a C-H bond of ethylene. Bond lengths are in angstroms, and angles in degrees. Arrows indicate the main components of the transition vector, closed when directed upward and open when directed downward. TABLE I: Energy Barriers4 for the Insertion Reaction of Singlet Methylene into a C-H Bond of Ethylene and for the Abstraction Reaction from Ethylene by Triplet Methylene insertion abstraction of CH2 by CH2 AE' (3-21G//3-21G) 6.4 24.2 AE' (6-31G*//3-21G) 8.6 26.0 AE' (MP2/6-31G*//3-21G) -13.1 25.1 AE' (MP3/6-31G*//3-21G) -8.5 24.4 AH' (3-21G) 8.0 20.5 AG' (3-21G) 17.8 28.2 AG' (MP3/6-31G*)b 2.9 28.4 " I n kcal/mol. bObtained by adding the 3-21G thermodynamic corrections to the MP3/6-31G*//3-21G energy barrier.
Method Ab initio self-consistent field (SCF) calculations have been carried out with the GAUSSIAN 80 and GAUSSIAN 82 series of programs31 using extended 3-21G32and polarization 6-31G* 33 basis sets. To study the insertion reaction of singlet methylene, we have used the restricted Hartree-Fock formalism (RHF),34 whereas the unrestricted Hartree-Fock formalism (UHF)35has been used to deal with the hydrogen abstraction reaction that occurs when triplet methylene is considered. Geometry optimization and direct location of stationary points have been done with the Schlegel gradient optimization algorithm.36 Analytical second derivatives of the energy with respect to the Cartesian coordinates3' were computed to test the nature of each stationary point: no negative eigenvalue for an equilibrium structure and one negative eigenvalue for a transition state. The influence of correlation energy on the different species of the reaction was determined by using the Merller-Plesset perturbation theory up to third order,38the 3-21G geometries being kept frozen in these calculations. Thermodynamic magnitudes were also computed by using the partition functions as provided by the statistical thermodynamic (31) Binkley, J. S.; Whiteside, R. A.; Krishnan, R.; Seeger, R.; DeFrees, D. J.; Schlegel, H. B.; Topiol, S.; Kahn, L. R.; Pople, J. A. QCPE 1980, 13, 406. Binkley, J. S.; Frisch, M. J.; DeFrees, D. J.; Krishnan, R.; Whiteside, R. A.; Schlegel, H. B.; Fluder, E. M.; Pople, J. A. GAUSSIAN 82; Carnegie Mellon University, Pittsburgh, PA. (32) Binkley, J. S.; Pople, J. A,; Hehre, W. J. J . A m . Chem. SOC.1980, 102, 939. (33) Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M. S.; DeFrees, D. J.; Pople, J. A. J . Chem. Phys. 1982, 77, 3654. (34) Roothaan, C. C. J. Rev. Mod. Phys. 1951, 23, 69. (35) Pople, J. A,; Nesbet, R. K. J . Chem. Phys. 1974, 22, 571. (36) Schlegel, H. B. J . Comput. Chem. 1982, 3, 214. (37) Pople, J. A,; Krishnan, R. A,; Schlegel, H. B.; Binkley, J. S. Int. J. Quantum Chem., Quantum Chem. Symp. 1979, 13, 225. (38) Pople, J. A.; Binkley, J. S.; Seeger, R. In?. J . Quantum Chem., Quantum Chem. Symp. 1976, 10, 1.
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formulas within the ideal gas, rigid rotor, and harmonic oscillator modelsj9as implemented in the GAUSSIAN 82 package. A pressure of 1 atm and a temperature of 298.15 K were assumed in the calculations. The second derivatives of the energy were used for the determination of vibrational frequencies. For transition states the imaginary frequency is neglected in the thermodynamic evaluation.
Results and Discussion We will successively present the results corresponding to the insertion reaction of singlet methylene into a C-H bond of ethylene and to the hydrogen abstraction process that takes place when triplet methylene is considered. Afterward, a comparative analysis of the mechanism of both processes will be carried out. This will permit us to underline the similarities and differences that appear in the reactivity of singlet and triplet methylene. For the insertion reaction of singlet methylene into a C-H bond of ethylene, we have found one first-order saddle point on the 3-21G potential energy hypersurface. The geometrical parameters of this transition state are presented in Figure 1. It has to be remarked that the ethylenic fragment is almost unchanged, except the hydrogen atom to which methylene approaches, this atom being 0.33 A below the ethylenic plane. Regarding the methylenic fragment, it approaches ethylene from above, the distances of the carbon and of the two hydrogen atoms to the plane being 0.72, 1.18, and 1.42 A, respectively. Figure 1 also shows the main components of the transition vector. One can observe that the greatest component corresponds to the transfer of one hydrogen atom from ethylene to methylene. Table I presents the energy barriers obtained at different levels of calculation for the insertion process of singlet methylene into a C-H bond of ethylene. The values corresponding to the hydrogen abstraction reaction from ethylene by triplet methylene are also collected in Table I, but they will be discussed later on. The first row shows the energy barriers calculated at the Hartree-Fock level with direct location of the transition states on the 3-21G potential energy hypersurface. The second row presents the values of the energy barriers recalculated with the 6-31G* basis set, the 3-21G geometry being kept unchanged. In the third and fourth rows the electron correlation is introduced at the 6-3 1G* level by using the Maller-Plesset perturbational formalism up to second and third order, respectively. Finally, the last three rows present the enthalpy and free-enthalpy barriers that have been calculated by adding the 3-21G thermodynamic corrections to the previously obtained values of AE*. The first thing one can observe in Table I is that the use of the 6-31G* basis set slightly increases the energy barrier obtained with the smaller 3-21G basis set. Another interesting fact is that the energy barrier disappears when electron correlation is introduced, the AE* value at the MP3 level being noticeably greater than the one obtained at the MP2 level. This was to be expected, since it is well-known that the MP2 level tends to overestimate the effect of electron correlation. It is interesting to underline that our results are in good agreement with the ones obtained for the analogous insertion into methane and ethane25-30and with the experimental works mentioned in the I n t r o d u ~ t i o nsince , ~ ~ ~in all the cases the insertion of singlet methylene to C-H bonds is predicted to occur with a very small energy barrier or with no energy barrier at all. Regarding the introduction of the thermal and entropic corrections, the values in the fifth and sixth rows of Table I show that these corrections lead to a noticeable increase in the value of the 3-21G energy barrier. This increase is especially important in the case of AG* due to the magnitude of the entropic term, - T U * , which is about 10 kcal/mol. Indeed, the large enthalpy and free-enthalpy barriers at the 3-21G level of calculation, as is the 3-21G AE* value itself, are exaggerated. So, it would be necessary to calculate the AG' value at a higher level of calculation. We have estimated the MP3/6-31G* A c t value (last row (39) McQuarrie, D. A. Statistical Mechanics; Harper and Row: New York, 1976.
Figure 2. Isodensity contour plots in the plane that contains the carbon atom of singlet methylene and the C-H bond of ethylene to which the insertion is produced. Numbers indicate the electronic charge density at the bond critical points.
of Table I) by adding the 3-21G thermodynamic corrections to the most accurate value of AE*calculated in this work. The value obtained in this way indicates that although the insertion reaction of singlet methylene into a C-H bond might occur with no energy barrier, it probably proceeds with a certain free-enthalpy barrier as a direct consequence of the important entropic term. Let us now analyze the electronic structure of the transition state shown in Figure 1. A first aspect of this analysis is the charge transfer between the ethylenic and methylenic fragments. We have found an important electronic transfer from ethylene to methylene, the value of this charge transfer being 0.162 au. The sense of the charge transfer agrees with the one observed for the addition of singlet methylene to olefin^.^^^^* In fact, it is easy to interpret if one looks at the geometrical structure of the transition state (see Figure 1). One can observe that the methylenic fragment is oriented in such a way that a large interaction is produced between the unoccupied p orbital (LUMO) of methylene and the hydrogen atom that is being transferred. In other words, the transition state is situated in the electrophilic phase of the insertion reaction. Other interesting aspects in the study of the electronic structure of the transition state can be obtained through the analysis of the electronic charge density map. Figure 2 presents the isodensity contour plots for the transition state in the plane that contains the carbon atom of methylene and the C-H bond of ethylene to which the insertion occurs. Bond critical points and bond paths linking the atoms on this plane are also shown. According to Bader's t e r m i n ~ l o g ybond ~ ~ paths are the unique pair of gradient paths that originate at each bond critical point, Le., at the saddle point situated between two linked atoms. It is interesting to mention that the electronic charge density at the bond critical point that links the hydrogen atom that is being transferred and the carbon atom of ethylene is notably smaller than the value of 0.27 which corresponds to the remaining C-H bonds of ethylene. Furthermore, a bond critical point also exists between this hydrogen atom and the carbon atom of methylene. The comparison between the electronic charge densities at the two C-H bonds clearly shows that the hydrogen atom that is being transferred is more tightly bonded to the ethylenic carbon atom at the transition state. Another interesting fact in Figure 2 is the lack of any bond between the methylenic and ethylenic carbon (40) Moreno, M.; Lluch, J. M.; Oliva, A,; Bertrin, J. J . Mol. Struct. THEOCHEM 1984, 107, 227. (41) Moreno, M.; Lluch, J. M.; Oliva, A,; Bertrln, J. J . Chem. SOC., Perkin
Trans. 2 1985, 131. (42) Bader, R. F. W.; Tal, Y.; Anderson, S. G.; Nguyen-Dang, T. T. Isr. J . Chem. 1980, 19, 8, and references cited therein.
Reactions of Methylene with a C-H Bond of Ethylene
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Figure 3. Geometrical structure of the transition state corresponding to the hydrogen abstraction from ethylene by triplet methylene. Bond lengths are in angstroms, and angles in degrees. The arrow indicates the main component of the transition vector.
atoms. So, the possibility that the reaction takes place via a three-centered cyclic structure, as proposed by Skel1,'O is not confirmed by our calculations, although the early character of Figure 4. Isodensity contour plots in the plane that contains ethylene and the transition state that we have found does not allow us to reach the carbon atom of methylene for the transition state of the hydrogen a definite conclusion over this point. abstraction reaction from ethylene by triplet methylene. Numbers inLet us now consider the hydrogen abstraction reaction from dicate the electronic charge density a t the bond critical points. The ethylene by triplet methylene. The geometrical structure of the projection of the out-of-plane hydrogen atoms of methylene is indicated corresponding transition state on the 3-21G potential energy by an asterisk. hypersurface is presented in Figure 3. In contrast with the insertion reaction of singlet methylene, one can observe that triplet methylene attacks in the direction of a C-H bond of ethylene, in such a way that the two carbon atoms and the hydrogen atom that is transferred between them are situated in a straight line. Furthermore the hydrogen atom is almost equidistant from both carbon atoms. These results are in good agreement with those of previous works mentioned in the I n t r o d u c t i ~ n . ' ~Figure ~~~-~~ 3 also shows that the only significant component of the transition vector corresponds to the transfer of the hydrogen atom from ethylene to methylene. As mentioned above, the energy barriers for this process at different levels of calculation are collected in the last column of Table I. One can observe that the 3-21G and 6-31G* energy barriers at the Hartree-Fock level are considerably higher than the ones found for the insertion reaction of singlet methylene. The difference between the energy barriers of both processes is even Figure 5. Spin isodensity contour plots in the plane containing ethylene greater when electron correlation is introduced, since this introand the carbon atom of methylene for the transition state of the hydrogen duction leads to a slight decrease of the energy barrier for the abstraction reaction from ethylene by triplet methylene. Solid lines hydrogen abstraction by triplet methylene, whereas it leads to a indicate a positive (a)spin density, whereas dotted lines correspond to drastic diminution in the insertion reaction of singlet methylene. negative ( p ) spin density. The projection of the out-of-plane hydrogen The high-energy barrier found by us agrees with the results obatoms of methylene is indicated by an asterisk. tained by other authors16,25-27,43 for a series of hydrogen abstraction reactions involving triplet methylene. However, several recent au. This reduced electrophilic character of triplet methylene is papers4446 have shown that Mdler-Plesset perturbation theory easy to explain if one takes into account that its electronic structure tends to overestimate the barrier height for this kind of process is very different from that of singlet methylene, since now the u due to spin contamination of the unrestricted Hartree-Fock and p orbitals are both half-occupied. This leads to a different function. orientation of attack in such a way that now the greatest interThe last three rows of Table I present the enthalpy and freeaction corresponds to the u orbital. This change in the orientation enthalpy barriers that are obtained when thermal and entropic of the attack had already been observed by us47948in the addition corrections are taken into account. In contrast with the reaction of singlet and triplet carbenes to olefinic double bonds. of singlet methylene, the enthalpy barrier is now smaller than the Examination of the charge density map, which is presented in 3-21G energy barrier. On the contrary, the addition of the entropic Figure 4, shows that the bond between the hydrogen atom that term leads again to an important increase of the barrier. Anyway, is being transferred and the carbon atom of ethylene is notably the introduction of the thermodynamic corrections does not modify weakened at the transition state, whereas a new bond is being the above-stated qualitative trends. formed between this hydrogen atom and the carbon atom of Regarding the electronic structure of the transition state, we methylene. The most important difference between the maps of have found that the electronic charge transfer from ethylene to Figure 2 and of Figure 4 is that in the latter the electronic charge methylene is noticeably smaller than the one calculated for the densities at the bond critical points between the hydrogen atom insertion reaction of singlet methylene, its value now being 0.105 and the two carbon atoms are almost identical, a result that is (43) Cart, R. W., Jr. J . Phys. Chem. 1972, 76, 1581. (44) Schlegel, H. B.; Sosa, C. J . Phys. Chem. 1984, 88, 1141. (45) Schlegel, H. B. J . Chem. Phys. 1986, 84, 4530. (46) Sosa, C.; Schlegel, H. B. Int. J . Quunfum Chem. 1986, 29, 1 001.
(47) Moreno, M.; Lluch, J. M.; Oliva, A,; Bertrln, J. Chem. Phys. 1985, 100. 33.
(48) Moreno, M.; Lluch, J. M.; Oliva, A,; Bertrln, J. J . Mol. Sfruct. THEOCHEM 1988, 164, 17.
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a direct consequence of the fact that both C-H bond lengths are also very similar. For insight into the description of the electronic structure of the transition state, Figure 5 presents the spin density map. Obviously, in the reactants the spin density differs from zero only on triplet methylene, since ethylene is a closed-shell molecule. Figure 5 shows that the a spin density of triplet methylene has been delocalized over the whole system at the transition state. In ethylene the a spin density is concentrated on the carbon atom that is closest to methylene. Another interesting fact is the existence of a noticeable @ spin density at the hydrogen atom that is being transferred. This is due to an important phenomenon of spin polarization in the linear fragment C-H-C. Let us now compare the results obtained for the two studied processes. Undoubtedly, the most important difference between them lies in the values of the energy barriers. Thus, the energy barrier for the insertion reaction of singlet methylene is much smaller than the one corresponding to hydrogen abstraction by triplet methylene. This occurs at all levels of calculation considered by us. At the MP3/6-31G*//3-21G level, for instance, the hydrogen abstraction by triplet methylene requires a barrier of 24.4 kcal/mol while no energy barrier is found for the insertion reaction of singlet methylene. In fact this great difference between both energy barriers mainly arises from the energy gap between singlet and triplet methylene, this gap being 18.5 kcal/mol at the MP3/6-31G*//3-21G level of calculation. Regarding, the mechanism, it is generally accepted that the insertion of singlet methylene takes place in one step via formation of a cyclic tricentric bond, while triplet methylene abstracts one hydrogen atom in a first step, the subsequent formation of a C-C bond between the two generated radicals requiring a previous intersystem crossing. Our results seem to indicate that both processes are not very different at the beginning, since the structure of the transition state for the insertion of singlet methylene does not present such a cyclic tricentric bond, and the main component of the transition vector corresponds to the transfer of one hydrogen atom from ethylene to methylene. Finally, another aspect that is interesting to discuss is the competition between the studied processes and the addition of singlet and triplet methylene to the ethylenic double bond. It is well-known that the insertion of singlet methylene into vinylic C-H
bonds can compete with the addition process, although the latter is f a ~ t e r . ~On , ~the ~ contrary, the hydrogen abstraction by triplet methylene is never observed when addition to a double bond is also possible.50 All these facts can be understood if one compares the energy barriers obtained in this work with those previously calculated for the addition of ~ i n g l e t ~and l . ~triplet4* ~ methylene to ethylene. Thus, the competition in the case of singlet methylene can be explained by the facts that no energy barrier is found for the addition process at all levels of calculation and the same occurs for insertion when electron correlation is introduced. On the contrary, the addition of triplet methylene has a much smaller energy barrier than the one corresponding to the hydrogen abstraction process. For instance, the energy barriers are 11.2 and 25.7 kcal/mol, respectively, at the MP2/3-21G//3-21G level of calculation. This large difference is the responsible for the fact that the hydrogen abstraction reaction is not observed when addition to a double bond is possible. In conclusion, we believe that this work has permitted us to gain insight into the different reactivity patterns that present singlet and triplet methylene when they react in front of a vinylic double bond. In the first stage both processes imply the transfer of a hydrogen atom from ethylene to methylene, this transfer being already important at the transition state. Given this similarity between the structures of both transition states, the difference in the energy barriers mainly arises from the energy gap between singlet and triplet methylene. Finally, the results obtained in this work have also permitted us to understand the different competitivity of the two studied processes when compared with the well-known addition reactions to olefinic double bonds. Acknowledgment. This work has been supported by the U. S.-Spain Joint Committee for Scientific and Technological Cooperation under Contract No. CCB-8509/016. Registry No. Methylene, 2465-56-7;ethylene, 74-85-1, (49) Tomioka, H.; Tabayashi, K.; Ozaki, Y.; Izawa, Y . Tetrahedron 1985, 41, 1435. (50) Ring, D. F.; Rabinovitch, B. S. Can. J . Chem. 1968, 46, 2435. (51) Zurawski, B.; Kutzelnigg, W. J . Am. Chem. SOC.1978, ZOO, 2654. (52) Rondan, N. G.; Houk, K. N.; Moss, R. A. J . Am. Chem. SOC.1980, 102, 1770.
Pressure and Temperature Dependence of the Gas-Phase Recombination of Hydroxyl Radicals R. Zellner,* F. Ewig, R. Paschke, and G. Wagner Institut fur Physikalische Chemie, Universitat Gottingen, Tammannstrasse 6, 3400 Gottingen, FRG (Received: August 28, 1987)
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Rate constants for the reaction OH + OH + M H202+ M (M = N2,H20) have been determined by using flash photolysis of H 2 0vapor in combination with quantitative OH resonance spectrometry. For M = N2 experiments were performed at 253,298, and 353 K and at pressures between 26 and 1100 mbar. Under these conditions the reaction is found to be primarily in the low-pressure limit with kl,N: ( T = 298 K) = (6.9!;,$) X low3'cm6/s and a temperature dependence of p , *Both . the absolute value of kl,N: and its temperature variation are in very satisfactory agreement with theoretical predictions and extrapolations from high-temperaturedissociation data. A pressure falloff of kl,Nzis also observed. On the basis of a theoretical analysis of the falloff behavior, a high-pressure limiting rate coefficient of k," = 1.5 X lo-" cm3/s, independent of temperature, is predicted. From experiments in N2/H20mixtures with xHZo= 0.11 at pressures up to 140 mbar a low-pressure limiting X rate coefficient for H 2 0 as a third body of kl,H200( T = 298 K) = (40.);: cm6/s is obtained.
I. Introduction Due to their importance in the chemistry of combustion proCeSSeS and in the atmosphere, reactions of O H radicals have received considerable attention. The range of interest covers the temperature region from around 250 K up to 2000 K and the 0022-3654/88/2092-4184$01.50/0
pressure scale from a few millibars to 1 bar. Although considerable progress has been made in recent years in measuring the rate coefficients for bimolecular reactions of the O H radical, comparatively little work has been devoted to a study of the -"t 1eCUlar process 0 1988 American Chemical Society
