On the Importance of Prereactive Complexes in Molecule-Radical Reactions: Hydrogen Abstraction from Aldehydes by OH

Transcription

1 2018 J. Am. Chem. Soc. 2001, 123, On the Importnce of Prerective Complexes in Molecule-Rdicl Rections: Hydrogen Abstrction from Aldehydes by OH J. Rúl Alvrez-Idboy,, Neline Mor-Diez,, Russell J. Boyd, nd Annik Vivier-Bunge*, Contribution from the Lbortorio de Químic Computcionl y Teóric, Fcultd de Químic, UniVersidd de L Hbn, Hbn 10400, Cub, Instituto Mexicno del Petróleo, México, D.F., México, Deprtment of Chemistry, Dlhousie UniVersity, Hlifx, NoV Scoti, Cnd B3H 4J3, nd Deprtmento de Químic, UniVersidd Autónom Metropolitn, Iztplp, México, D.F., México ReceiVed September 13, ReVised Mnuscript ReceiVed NoVember 27, 2000 Abstrct: In this work, the OH + formldehyde nd OH + cetldehyde rections hve been chrcterized using ccurte b initio methods with lrge bsis sets. The results clerly indicte tht the rection occurs by hydrogen bstrction, nd tht the OH ddition chnnel is unfvorble. Close to zero (for formldehyde) nd negtive (for cetldehyde) ctivtion energy vlues re obtined, which re in excellent greement with the experimentlly observed vlues. The rection rte constnts, clculted using the clssicl trnsition-stte theory s pplied to complex mechnism involving the formtion of prerective complex, reproduce very well the reported experimentl results. Considertion of the prerective complex is shown to be essentil for the determintion of the height of the energy brrier nd thus for the correct clcultion of the tunneling fctor. 1. Introduction Crbonyl compounds re directly emitted into the troposphere from biogenic nd nthropogenic sources, 1 nd they re lso formed in lrge concentrtions s end products in the oxidtion rections of hydrocrbons. They re known to enter the tropospheric rectnts pool minly through one rection, 2 tht is, the rection with the OH rdicl, ccording to the following overll eqution: RHC ) O + OH f [RC ) O] + H 2 O (1) Bimoleculr rte constnts for the OH rection with vriety of ldehydes hve been mesured, nd their Arrhenius prmeters hve been reported, 2,3 but there re serious uncertinties s to the rection mechnism. The negtive temperture dependence of the rte constnt is well estblished, except in formldehyde, for which the ctivtion energy is known to be lmost zero, most experimentl results vrying between +0.4 nd -0.4 kcl/mol. 3 It suggests the possibility tht the rections of ldehydes with the hydroxyl rdicl, in generl, occur by n ddition-elimintion mode, 4,5 since mny ddition rections of OH show overll negtive temperture dependence. Niki et l. 7 * Corresponding uthor. E-mil: nnik@xnum.um.mx. Universidd de L Hbn. Instituto Mexicno del Petróleo, México, D.F., México. Deprtment of Chemistry, Dlhousie University, Hlifx, Nov Scoti, Cnd B3H 4J3. Deprtmento de Químic, Universidd Autónom Metropolitn, Iztplp, México, D.F., México. (1) Ppgni, C.; Arey, J.; Atkinson, R. Int. J. Chem. Kinet. 2000, 32, 79. (2) Finlyson-Pitts, B. J.; Pitts, N. Atmospheric Chemistry: Fundmentls nd Experimentl Techniques; Wiley-Interscience: New York, (3) The NIST Chemicl Kinetics Dt Bse, NIST Stndrd Reference Dtbse; U.S. Dept. of Commerce, Technology Administrtion, Ntionl Institute of Stndrds nd Technology: Githersburg, MD, 17-2Q98. (4) Michel, J. V.; Keil, D. G.; Klemm, R. B. J. Chem. Phys. 1985, 83, (5) Tylor, P. H.; Rhmn, M. S.; Arif, M.; Dellinger, B.; Mrshll, P. Symp. Int. Comb. Proc. 1996, 26, 497. ruled out the formtion of HC(O)OH + H but not the rection H 2 C ) O + OH f [H 2 C ) O(OH)] f [HC ) O] + H 2 O (2) However, for formldehyde it is believed tht only hydrogen bstrction occurs. Recent experimentl work by Butkovsky nd Setser 8 using infrred chemiluminescence confirms tht the results re consistent with mny polytomic rections in which H tom is directly bstrcted. For cetldehyde, Michel et l. 4 hve presented very complete mechnistic discussion of their experimentl dt of the OH-cetldehyde rection in the rnge K. They conclude tht the preferred process ppers to be the bstrction of the ldehydic hydrogen tom. Tylor et l. 5 fvor n ddition-elimintion mechnism t low tempertures. Atkinson 9 postulted tht the rection proceeds vi overll H-tom bstrction, lthough the initil rection possibly involves the OH rdicl ddition to the >CdO bond system However, it is not cler why hydrogen bstrction rection presents negtive ctivtion energy nd why the overll OH ddition to the double bond does not occur. It is interesting to know the energetics of the trget rections. These cn be clculted using the vlues of the bond energies given by Berkowitz et l., 6 wherein ll originl references cn be found. The bond enthlpies (in kcl/mol) re H 298 (HO- H) ) ( 0.05, H 298 (H-CHO) ) ( 0.16, H 298 (H-CH 2 CHO) ) 94.3 ( 2.2, nd H 298 (CH 3 CO-H) ) 89.4 ( 0.3. Consequently, the hets of rection t 298 K in kcl/ mol re estimted to be: H 2 C ) O + OH f [HC ) O] + H 2 O H ( 0.2 (3) (6) Berkowitz, J.; Ellison, G. B.; Gutmn, D. J. Phys. Chem. 1994, 98, (7) Niki, H.; Mker, P. D.; Svge, C. M.; Breitenbch, L. P. J. Phys. Chem. 1984, 88, (8) Butkovsky, N. I.; Setser, D. W. J. Phys. Chem. A 1998, 102, (9) Atkinson, R. J. Phys. Chem. Ref. Dt 1994, Monogrph 2, /j003372g CCC: $ Americn Chemicl Society Published on Web 02/10/2001

2 Hydrogen Abstrction from Aldehydes by OH J. Am. Chem. Soc., Vol. 123, No. 9, CH 3 CH ) O + OH f [CH 3 C ) O] + H 2 O H ( 0.23 (4) CH 3 CH ) O + OH f [CH 2 CH ) O] + H 2 O H ( 2 (5) The behvior of rections hving negtive temperture dependence hs been successfully described, for systems t low pressures, by Mozurkewich nd Benson, 10 nd for systems t high pressures, by Singleton nd Cvetnovic. 11 In this cse, severl explntions hve been proposed, which re summrized in ref 2. Three of them mintin the ide of n elementry rection but suggest modifiction of the preexponentil fctor in the Arrhenius eqution to llow for term T Singleton nd Cvetnovic 11 propose complex mechnism nd explin the occurrence of these negtive ctivtion energies s being due to the reversible formtion of loosely bound prerective complex which is formed without ctivtion energy, followed by second rection, which is irreversible, nd whose trnsitionstte energy is lower thn the energy of the seprted rectnts. A prerective complex hs, in fct, been identified in severl OH-ddition rections to lkenes, 12-15,19 hloethnes 16 nd romtic hydrocrbons (toluene nd xylenes). 17,18 In recent study on the OH ddition to substituted lkenes, 19 we hve shown, by clculting the rte constnts for the individul steps, tht the mechnism proposed by Singleton nd Cvetnovic 11 provides cler explntion of the experimentl dt. Prerective complexes seem to be common in ll rdiclmolecule rections, nd they re due minly to the long-rnge Coulombic interctions between the rectnt molecules. In fct, in the prerective complex formed between the OH rdicl nd n unsturted hydrocrbon, it is the H tom of the OH rdicl which points towrd the π electrons of the double bond, even though the OH group hs to flip over in order to form the C-O bond in the dduct ,17-19 If the rection occurs t pressures high enough for these complexes to be collisionlly stbilized, nd if the energy brriers re smll, they re likely to ply n importnt role. Sekušk nd Sbljić hve lso found tht such intermedite complexes ply key role in hydrogen bstrction rections from hloethnes. 16 Considering the OH + ldehyde rections, if rection 1 were elementl with negligible energy brrier, the rte constnt should depend essentilly on the preexponentil fctor. Thus, becuse formldehyde hs two bstrctble hydrogen toms, one would expect its rection to be bout twice s fst s the one of cetldehyde. This disgrees with the observed experimentl results, the reported rte constnts t 298 K for OH-ldehyde (10) Mozurkewich, M.; Benson, S. W. J. Phys. Chem. 1984, 88, 6249; Mozurkewich, M.; Lmb, J. J.; Benson, S. W. J. Phys. Chem. 1984, 88, (11) Singleton, D. L.; Cvetnovic, R. J. J. Am. Chem. Soc. 1976, 98, (12) Sos, C.; Schlegel, H. B. J. Am. Chem. Soc. 1987, 109, (13) Díz-Acost, I.; Alvrez-Idboy, J. R.; Vivier-Bunge, A. Int. J. Chem. Kinet. 1999, 31, 29. (14) Alvrez-Idboy, J. R.; Díz-Acost, I.; Vivier-Bunge, A. J. Comput. Chem. 1998, 88, 811. (15) Sekuśk, S.; Liedl, K. R.; Sbljić, A. J. Phys. Chem. A 1998, 102, (16) Sekuśk, S.; Sbljić, A. Chem. Phys. Lett. 1997, 272, 353. (17) Uc. V. H.; Grcí-Cruz, I.; Hernández-Lgun, A.; Vivier-Bunge, A. J. Phys. Chem. 2000, 104, (18) Uc. V. H.; Grcí-Cruz, I.; Vivier-Bunge, A. In Quntum Systems in Chemistry nd Physics; Advnced Problems nd Complex Systems, Vol. 2; Kluwer Acdemic Publishers: Gret Britin, 2000; p 241. (19) Alvrez-Idboy, J. R.; Mor-Díez, N.; Vivier-Bunge, A. J. Am. Chem. Soc. 2000, 122, Tble 1. Selected Experimentl Dt for the Rections: XCHO + OH ) H 2 O + XCO X T(K) A E (kcl/mol) k (L/mol s) ref H CH Rte constnts in column 5 re t 298 K. rections being L mol -1 s -120 nd L mol -1 s -121 for formldehyde, nd L mol -1 s -120 for cetldehyde. The experimentlly determined Arrhenius prmeters, 20,21 however, do indicte very smll negtive ctivtion energy nd preexponentil fctor which is lrger for formldehyde thn for cetldehyde (see Tble 1). On the other hnd, higher rectivity of cetldehyde is in line with the fct tht the inductive effect of the methyl group should help stbilize the corresponding trnsition stte. Using quntum chemicl methods, it is possible to clculte energies of intermedite structures nd trnsitions sttes with resonble degree of precision, nd thus to model the rection pth of rection. Indeed, correltion fctor ws recently obtined 19 between our b initio clculted effective ctivtion energies nd the experimentl rte constnts, for the OH rdicl ddition to series of substituted ethenes. Previous theoreticl work on the formldehyde + OH rection hs been reported by Dupuis nd Lester 22 using multiconfigurtion self-consistent-field Hrtree-Fock (MCSCF) nd configurtion interction (CI) wve functions. They predicted positive ctivtion brrier for the ldehydic hydrogen OH bstrction rection, of 5.5 kcl/mol. Frncisco 23 used the b initio Møller-Plesset method up to fourth order (MP4) to determine the brriers nd energetics. He obtined smll positive brrier of 1.2 kcl/mol nd rte constnt in very good greement with experiment. The formtion of prerective complex ws not considered in this pper. In the present work, his results will be discussed nd compred with ours. The wekly bound complexes of the hydroxyl rdicl with formldehyde nd cetldehyde were clculted recently by Aloisio nd Frncisco 24 using density functionl pproch. Tylor et l. 5 hve investigted the rection of hydroxyl rdicls with cetldehyde in wide temperture rnge using quntum RRK model to describe the competition between ddition nd bstrction. They conclude tht different rection mechnisms occur, depending on the temperture, nd tht OH ddition followed by CH 3 elimintion is the dominnt rection pthwy between 295 nd 600 K. Moreover, they clim tht the H-tom elimintion pthwy is lrgely insignificnt, except possibly t the lowest tempertures. Their clculted rte constnt, t 298 K, however, is bout fctor of 10 too low. In this work, the OH + formldehyde nd the OH + cetldehyde rections shll be chrcterized using severl methods nd lrge bsis sets to obtin n ccurte rection profile nd to reproduce the experimentlly observed vlues of the ctivtion energy (pproximtely zero 8,20 for formldehyde, (20) Atkinson, R.; Bulch, D. L.; Cox, R. A.; Hmpson, R. F., Jr.; Kerr, J. A.; Rossi, M. J.; Troe, J. J. Phys. Chem. Ref. Dt 1997, 26, 521. (21) DeMore, W. B.; Snder, S. P.; Golden, D. M.; Hmpson, R. F.; Kurylo, M. J.; Howrd, C. J.; Rvishnkr, A. R.; Kolb, C. E.; Molin, M. J. JPL Publiction 97-4, (22) Dupuis, M.; Lester Jr., W. A. J. Chem. Phys. 1984, 81, 847. (23) Frncisco, J. S. J. Chem. Phys. 1992, 96, (24) Aloisio, S.; Frncisco, J. S. J. Phys. Chem. 2000, 104, 3211.

3 2020 J. Am. Chem. Soc., Vol. 123, No. 9, 2001 AlVrez-Idboy et l kcl/mol for cetldehyde. 5,20 With the corresponding prtition functions, the effective rte constnts will then be clculted, using clssicl trnsition-stte theory nd the proposed hydrogen bstrction mechnism. The results will be compred with the experimentl dt nd with the results of previous clcultions. Our im is the following: (i) to show tht the sme complex mechnism cn be pplied to both the formldehyde nd the cetldehyde rections, (ii) to show tht considertion of the prerective complex is essentil for the correct clcultion of the rte constnt, when the tunneling fctor is significnt, s is the cse in hydrogen bstrction rections, nd (iii) to define theoreticl methodology which is ble to reproduce theoreticlly the rte constnts of the two rections. 2. Computtionl Methodology Electronic structure clcultions hve been performed with the system of progrms Gussin Unrestricted b initio methods were used to clculte the energies of the rdicls. The correltion energy corrections were introduced with Møller-Plesset perturbtion theory nd with the coupled cluster method t the CCSD(T) level. All geometries were fully optimized t the MP2(FC)/ G- (d,p) level, nd the chrcter of the trnsition sttes ws confirmed by frequency clcultion, performed t the sme level, nd presenting only one imginry frequency corresponding to the expected trnsition vector. We ssume tht the rection occurs ccording to the following twostep mechnism: Step 1: RHC ) O + OH h [RHC ) O HO ] (6) Step 2: [RHC ) O HO ] f RC ) O + H 2 O (7) involving fst preequilibrium between the rectnts nd the prerective complex followed by n internl rerrngement leding to the elimintion of wter molecule. If k 1 nd k -1 re the rte constnts for the first step nd k 2 corresponds to the second step, stedy-stte nlysis leds to rte constnt for the overll rection which cn be written s: k ) k 1 k 2 ) k -1 ( A 1 A 2 A -1 ) exp[-(e 1 + E 2 - E -1)/RT] (8) Since E 1 is zero, the net ctivtion energy for the overll rection is: E ) E 2 - E -1 ) (E TS - E P-R ) - (E R - E P-R ) ) E TS - E R (9) where E R, E P-R, nd E TS re the totl enegies of the rectnts, the prerective complex, nd the trnsition stte, respectively. Thus, the ctivtion energy t high pressures cn be clculted s the difference between the energy of the TS nd tht of the rectnts, without hving to obtin the prerective complex. Applying bsic sttisticl thermodynmic principles, the equilibrium constnt of the fst preequilibrium between the rectnts nd the prerective complex my be obtined s: (25) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseri, G. E., Robb, M. A.; Cheesemn, J. R.; Zkrzewski, V. G.; Montgomery, J. A., Jr.; Strtmnn, R. E.; Burnt, J. C.; Dpprich, S.; Millm, J. M.; Dniels, A. D.; Kudin, K. N.; Strin, M. C.; Krks, O.; Tomsi, J.; Brone, V.; Cossi, M.; Cmmi, R.; Mennucci, B.; Pomelli, C.; Admo, C.; Clifford, S.; Ochterski, G.; Petersson, G. A., Ayl, P. Y., Cui, Q.; Morokum, K.; Mlick, D. K.; Rbuck, A. D.; Rghvchri, K.; Foresmn, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefnov, B. B.; Liu, G.; Lishenko, A.; Piskorz, P.; Komromi, I.; Gomperts, R.; Mrtin, R. L.; Fox, D. J.; Keith, T. A.; Al-Lhm, M. A.; Peng, C. Y.; Nnykkr, A.; Gonzlez, V.; Chllcombe, M.; Gill, P. M. W.; Johnson, B. G.; Chen, W.; Wong, M. W.; Andres, J. L.; Hed-Gordon, M.; Replogle, E. S.; Pople, J. A., Gussin 98, Revision A.1; Gussin, Inc.: Pittsburgh, PA, K eq ) Q P-R Q R exp[(e R - E P-R )/RT] (10) Under high-pressure conditions, n equilibrium distribution of rectnts is mntined in unimoleculr process, nd the clssicl TST formul cn be pplied 26 to clculte k 2: k 2 ) κ k B T h Q TS Q P-R exp[(e P-R - E TS )/RT] (11) where κ is the tunneling fctor. The rection pth degenercy is not included in this expression since the rottionl symmetry numbers re lredy introduced in the clcultion of the prtition functions. The prtition functions re obtined from the rottionl constnts nd the vibrtionl frequencies of the b initio clcultions. The energy differences include the zero-point corrections. The rte constnts of the hydrogen bstrction rections hve been clculted in two different wys, for comprison. In the first one, the two-step mechnism described bove is ssumed to hold, nd the effective rte constnt is obtined ccording to the following eqution: k ) K eq k 2 (12) In the second one, it is ssumed tht the rection is elementl, the formtion of the prerective complex is ignored, nd the rte constnt is clculted s: k ) κ k B T Q TS exp[(e h Q R - E TS )/RT] (13) R It is importnt to note tht these two expressions turn out to be identicl except for the vlue of the tunneling fctor κ, which depends on the ctivtion brrier of the elementl process in which the hydrogen tom is bstrcted. The tunneling correction is defined s the rtio of the quntummechnicl to the clssicl brrier crossing rte, nd it is clculted ssuming n unsymmetricl, one-dimensionl Eckrt function brrier. 27 For this, we hve used the numericl integrtion progrm of Brown. 28 The Gussin qudrture ws performed t 40 points, for incresed ccurcy. A useful mesure of the brrier width is the full width of the brrier t hlf its height in the forwrd direction, s 1/2. Its vlue will lso be reported. 3. Results nd Discussion The OH rdicl ttck on ldehydes ppers to occur in the following wy. At first, the positively chrged hydrogen tom of the OH rdicl pproches lone pir of the oxygen tom to form very stble prerective complex, whose energy is found to be more thn 3 kcl/mol lower thn the energy of the rectnts. Severl such prerective complexes were identified in the cse of the formldehyde OH rection, but in the most stble one, the OH rdicl lies in the plne of the CHO group (Figures 1 nd 2). From this structure, the oxygen of OH my flip, in the plne, towrd the hydrogen to be bstrcted s the energy increses to mximum t the trnsition stte. Another process my lso occur, which leds to OH ddition. Strting from the sme prerective complex, the OH group my flip in plne perpendiculr to the CHO plne, in such wy s to let the oxygen tom pproch the crbon tom of the ldehyde from bove. It will be shown tht the corresponding trnsition stte hs considerbly lrger energy thn in the bstrction chnnel. A third process could be considered, in which the OH rdicl would ttck cetldehyde t the methyl group nd produce the formylmethyl rdicl, CH 2 CHO. Indeed, this hydrogen bstrc- (26) Pilling, M. J. nd Sekins, P. W. Rection Kinetics; Oxford University Press: New York, (27) Eckrt, C. Phys. ReV. 1930, 35, (28) Brown, R. L. J. Res. Ntl. Bur. Stnd. (U. S.) 1981, 86, 357.

4 Hydrogen Abstrction from Aldehydes by OH J. Am. Chem. Soc., Vol. 123, No. 9, Figure 1. Optimized structures in the OH + formldehyde hydrogen bstrction rection, s obtined t the MP2(FC)/ G(d,p) level. Figure 2. Optimized structures in the OH + cetldehyde hydrogen bstrction rection, s obtined t the MP2(FC)/ G(d,p) level. tion is 25 kcl/mol exothermic. However, the position of the OH hydrogen tom in the prerective complex is very fr from the methyl hydrogens. In ddition, the energy of the methyl C-H bond is bout 5 kcl/mol lrger thn tht of the crbonyl C-H bond (eqs 4 nd 5). The proposed bstrction mechnism resembles closely the one described by Sekušk nd Sbljić 16 in the cse of the hydrogen bstrction rection from hloethnes. These uthors hve stressed the importnce of the prerective complex nd the role of strongly electronegtive tom in guiding the rection from the very beginning nd in lowering the trnsitionstte energy. The MP2 optimum geometries of the intermedite structures long the hydrogen bstrction rection pths re shown in Figures 1 nd 2, nd the relevnt prmeters hve been indicted on the figures. The geometries of the prerective complexes obtined for OH + formldehyde nd OH + cetldehyde re very similr to those obtined by Aloisio nd Frncisco 24 using density functionl method. Both the hydrogen bstrction nd the OH ddition chnnels hve been investigted in the cse of the formldehyde rection. For cetldehyde, however, we hve studied only the bstrction chnnel. The trnsition sttes corresponding to the ddition nd bstrction chnnels in formldehyde + OH re shown in Figure 3. Compring their structures with the ones for similr rections, it is possible to explin why the bstrction trnsition stte is the one with the lowest energy. The trnsition stte for hydrogen bstrction from ethne 29 clculted t the sme level, occurs considerbly lter, when the O H distnce between the oxygen tom of the OH rdicl nd the hydrogen tom which is bstrcted is 1.33 Å, s compred to 1.41 Å for formldehyde, indicting tht the hydrogen tom in formldehyde is less tightly bound. On the contrry, the trnsition stte for ddition to formldehyde occurs much lter thn, for exmple, the one in the ethene + OH rection 13 (the C O distnce in this rection is 2.06 Å, s compred to 1.83 Å). It cn lso be observed tht, in the bstrction trnsitionstte structures, the C H nd O H distnces in the cse of (29) Grcí-Cruz, I., Ruíz-Sntoyo, M. E., Alvrez-Idboy, R.; Vivier- Bunge, A. J. Comput. Chem. 1999, 20, 845.

5 2022 J. Am. Chem. Soc., Vol. 123, No. 9, 2001 AlVrez-Idboy et l. Tble 2. Relevnt Brriers (including the ZPE) nd Het of Rection Energies ( H), (including the therml energy corrections, TCE), in kcl/mol, for the OH Hydrogen Abstrction Rection in Formldehyde nd Acetldehyde nd for the OH Addition to Formldehyde E -1 E 2 (bstrction) E eff (bstrction) H (bstrction) E 2 (ddition) E eff (ddition) H (ddition) Formldehyde PMP PMP CCSD(T) experimentl b ( 0.3 c Acetldehyde PMP CCSD(T) experimentl d -1.3 e Reference 20. b Clculted from dt in ref 20. c Reference 8. d Reference 21. e Reference 5. Figure 3. OH ddition nd hydrogen bstrction nd trnsition-stte structures of the OH + formldehyde rection, optimized t the MP2- (FC)/ G(d,p) level. cetldehyde indicte tht it is formed erlier thn for formldehyde. The effect is probbly due to the electronic effect of the methyl group, which increses the electronic density t the crbonyl crbon, fvoring the bstrction of the hydrogen tom. The symmetries of the prerective complexes nd of the trnsition sttes re 2 A, implying tht the rdicl electron is in the plne, where it cn ttck the ldehyde. In Tble 1, selected experimentl dt for the rte constnts nd the Arrhenius prmeters of the OH + ldehyde rections re reported. Considerble differences re observed mong the experimentl prmeters reported for the formldehyde rection. The clculted totl energies, the zero-point vibrtionl energy corrections (ZPE) of the rectnts, the prerective complex, the trnsition stte, the product complex, nd the seprted products long the rection pths for the OH rection with formldehyde nd cetldehyde re given s Supporting Informtion for the methods employed in this work. The therml corrections (TCE) re lso included for the min sttionry points. In these tbles, both corrections re given t the MP2 level, nd these vlues re used to obtin the CCSD(T) energy differences. For the bstrction rections, spin contmintion is only significnt (but smll) t the trnsition sttes: it is for the formldehyde rection nd for cetldehyde, nd in the MP2 clcultions it is completely eliminted by projection. Thus, for these prticulr rections, the CCSD(T) method pplied to n MP2 optimized geometry cn be expected to yield relible energies. In contrst, results obtined in the OH ddition chnnel indicte tht spin contmintion is much more importnt, 0.919, nd it is not eliminted completely by projection. This is not unusul. In fct, Sekušketl. 15 lso observed, in the cse of the OHlkene rections, tht the single-point coupled cluster method does not give stisfctory results, probbly due to the fct tht the geometry is not optimized t this level nd tht spin contmintion is not eliminted. Thus, for the ddition chnnel, the PMP2 results re expected to be more relible. The stbiliztion energy of the prerective complexes (which is equl to E -1 ), the effective ctivtion energies (E eff ) E 2 - E -1 ) t 0 K, nd the het of rection (E P - E R ), t 298 K, of the formldehyde + OH nd cetldehyde + OH rections re given in Tble 2 for the methods employed. The ZPE corrections hve been included in ll the energy differences, except in the cse of the hets of rection, which include the TCE. Concerning the stbiliztion energies of the prerective complexes, the sets of results obtined with the three different methods gree to within 3 kcl/mol for the formldehyde rection nd bout 4 kcl/mol for the cetldehyde rection. Aloisio nd Frncisco 24 obtined 8.9 kcl/mol for the former one, which is not surprising since density functionl methods in generl re known to emphsize positive interctions in wekly bound systems. It cn be seen tht the PMP2 effective ctivtion energies re overestimted nd tht, in these rections, the CCSD(T) seems to be the most pproprite method to use to obtin good ctivtion energies. Indeed, the CCSD(T) results gree remrkbly well with the experimentl vlues. On the bsis of the energy brriers for ddition nd bstrction in the cse of formldehyde, it is cler why the ddition pthwy is not fvored in these rections. The difference between the CCSD(T) energies of the trnsition sttes for these two chnnels is more thn 8 kcl/mol. It is interesting to note tht lmost hlf of this energy difference rises from the zero-point correction energies. This is clerly due to the fct tht the trnsition stte for ddition is expected to be much tighter thn the one for bstrction, nd thus its vibrtionl zero-point correction is lrger. Even considering tht the CCSD(T) method is not dequte for the ddition chnnel, the difference in energy between the trnsition sttes for ddition nd bstrction is lso lrge enough t the PMP2 nd PMP4 levels to gurntee tht only the bstrction chnnel occurs. The energy profiles obtined using the CCSD(T) energies re shown in Figures 4 nd 5. The formtion of stble prerective complex followed by trnsition stte whose energy is lower (or very slightly higher, in the cse of formldehyde) thn the energy of the rectnts is clerly observed. Product complexes re formed, which present hydrogen bonds between the wter molecule nd the ldehydic rdicls nd which re bout 2 kcl/mol more stble thn the corresponding seprted products. The best vlues for the hets of rection re the ones obtined from the PMP2 energies with TCE

6 Hydrogen Abstrction from Aldehydes by OH J. Am. Chem. Soc., Vol. 123, No. 9, Figure 4. Rection profile for OH ddition nd hydrogen bstrction in the OH + formldehyde rection. In this grph, the best energies were used in ech cse: CCSD(T), for bstrction, nd PMP2, for ddition. Figure 5. Rection profile for OH hydrogen bstrction in formldehyde nd cetldehyde using the clculted CCSD(T) energy vlues. Tble 3. Prtition Functions (Q), Preexponentil Fctors (A) (Not Including Tunneling Correction), nd Imginry Frequencies (νj i in cm -1 ) of the TS of the OH + Formldehyde nd OH + Acetldehyde Hydrogen Abstrction Rections, Clculted t the MP2(FC)/ G(d,p) Level rection HCHO + OH CH 3CHO + OH Q OH Q RCOH Q RCOH corr (*) Q P-R Q TS Q TS corr (*) A νj i The indicted prtition functions (*) hve been corrected for internl rottions (see text), the other vlues re those clculted by Gussin98. corrections. The CCSD(T) energies yield poorer results, s compred with the experimentl results, but ll of the theoreticl methods employed reproduce correctly the observed trends. All quntities necessry for the clcultion of the rte constnts of the bstrction rections re given in Tble 3. Three (for formldehyde) nd four (for cetldehyde) low frequencies re present in the hydrogen bstrction trnsition sttes, in ddition to the imginry frequency. Of these, two (for formldehyde) nd three (for cetldehyde) cn be viewed s internl rottions. Thus, in the prtition function of the trnsition stte, their hrmonic contributions hve been replced by those of free rotors. 30 The vibrtion corresponding to the free rotor motion of the methyl group in cetldehyde ws lso replced in the prtition function. The detils of the clcultion of the rte constnts re given in Tble 4. In the cse of the formldehyde hydrogen bstrction, Tble 4. Tunneling Prmeters nd Rte Constnts of the OH + Formldehyde nd OH + Acetldehyde Hydrogen Abstrction Rections Clculted Using CCSD(T)/ G(d,p)//MP2(FC)/ G(d,p) nd Both the Direct nd the Complex Mechnisms direct mechnism HCHO + OH CH 3CHO + OH κ b b s 1/2 (Å) b b k (L/mol s) complex mechnism HCHO + OH CH 3CHO + OH κ s 1/2 (Å) K eq (L/mol) k 2 (s -1 ) k eff (L/mol s) Energies include the zero point corrections t the MP2(FC)/ G(d,p) level. κ is the tunneling correction nd s 1/2 is the full width of the brrier t hlf its height. b κ < 1.0; therefore, tunneling is ignored. the best vlue of the effective ctivtion brrier, which is obtined with the CCSD(T) method using the MP2 optimized geometry, is clculted to be 0.03 kcl/mol. At the sme level, considering the formtion of the prerective complex, the ctul ctivtion energy of the second step in the complex mechnism of eq 2 is 3.19 kcl/mol. Thus, if the rte constnt is clculted ccording to the complex mechnism, tunneling fctor κ ) 5.69 is obtined, nd the rte constnt is L mol -1 s -1, in excellent greement with the experimentl vlues. If n elementry mechnism is ssumed, κ is 0.724, nd thus tunneling cn be neglected nd the clculted rte constnt is only L mol -1 s -1. In this context, we would like to suggest tht the excellent greement obtined by Frncisco 23 for the rte constnt of the OH-formldehyde rection, using the direct mechnism, is probbly due to cncelltion of errors. His best clculted vlue for the ctivtion energy ws found to be 1.2 kcl/mol, nd his tunneling fctor should hve been intermedite between the two κ vlues clculted bove. The importnce of considering the prerective complex when clculting the tunneling correction ws lredy mentioned by Sekušk nd Sbljić 16 in the cse of the hydrogen bstrction rection from hloethnes. However, these uthors clculted the rte constnts, ssuming direct rection mechnism, nd hence they found significnt discrepncies with the experimentl results. 4. Conclusions From the bove discussion we conclude tht, when the OHldehyde rection occurs t tmospheric pressure, the following hold: (i) The ddition of the OH rdicl to the double bond is excluded becuse its ctivtion energy is much higher thn the one for hydrogen bstrction. The ldehydic hydrogen tom hs reltively smll bonding energy (s compred with tht of lknes), while the ddition of OH to the crbon tom is unfvorble. This process resembles the OH hydrogen bstrction from hloethnes, lredy described by Sekušk nd Sbljić. 16 (ii) The rection is not elementl. (iii) The overll ddition of OH is irreversible, due to the lrge therml effect of rection 1 ( H is bout -30 kcl/mol). (iv) The overll rte depends on the rtes of two competitive rections (the reverse of the first step nd the second step in rection 1). If the ctivtion energy is negtive, the former is more ffected by temperture thn the ltter. (30) Benson, S. W. Thermochemicl Kinetics; Wiley & Sons: New York, 1976; p 43.

7 2024 J. Am. Chem. Soc., Vol. 123, No. 9, 2001 AlVrez-Idboy et l. The proposed mechnism provides cler explntion of the experimentl behvior. If E -1 is lrger thn E 2, the former will be reltively more fvored by n increse in temperture, nd the overll rte will decrese. In the OH + ldehyde rections, the effective negtive ctivtion energy is well founded nd cnnot be n rtifct of the experimentl method, s climed by Benson nd Dobis 31 for similr rdicl-molecule rections. We clim tht the results of the present work, together with those of Sekušk nd Sbljić 16 nd previous results obtined in our group 13,14,17-19 hve significnt implictions on the theory of trnsition sttes in generl. In fct, it is well-known tht the rection profile of ny bimoleculr rection presents minimum long the rection coordinte, previouis to the trnsition stte, which is commonly clled rectnts complex, vn der Wls complex, or prerective complex. This implies tht, strictly speking, in the gs phse there re no elementl bimoleculr rections, even though, in most cses, the possible formtion of the complex is irrelevnt. Nevertheless, the point corresponding to the prerective complex on the potentil energy surfce is especilly importnt in rdicl-molecule rections, mny of which re known to occur with n pprent negtive ctivtion energy. (31) Benson, S. W.; Dobis, O. J. Phys. Chem. A 1998, 102, (32) Yetter, R. A.; Rbitz, H.; Dryer, F. L.; Mki, R. G.; Klemm, R. B. J. Chem. Phys. 1989, 91, (33) Tsng, W.; Hmpson, R. F. J. Phys. Chem. Ref. Dt 1986, 15, (34) Tyndll, G. S.; Stffelbch, T. A.; Orlndo, J. J.; Clvert, J. G. Int. J. Chem. Kinet. 1995, 27, In the prticulr cse of rection involving the migrtion of hydrogen tom, if the prerective complex is not considered, the height of the ctul energy brrier is too smll, nd the tunneling fctor is underestimted, ffecting the clcultion of the rte constnt. In the rections studied in this work, both effects re present: negtive ctivtion brrier nd hydrogen tom migrtion. Acknowledgment. We grtefully cknowledge the finncil support from the Instituto Mexicno del Petróleo through progrm FIES VI, the Ministerio de Educción Superior de Cub nd the Nturl Sciences nd Engineering Reserch Council of Cnd (to R.J.B.). N. M. D. thnks Dlhousie University for Grdute Scholrship. Specil thnks re due to Professor P. D. Pcey t Dlhousie University for his vluble comments nd discussions nd for providing the progrms used to clculte tunneling fctors nd brrier thickness. Supporting Informtion Avilble: Tbles of totl energies, zero-point nd therml energy corrections, in hrtrees, tbles of optimized geometries in Crtesin coordintes (PDF). This mteril is vilble free of chrge vi the Internet t JA003372G