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Computational study of the reaction mechanism of benzylperoxy radical with HO2 in the gas phase
Chemical Physics Letters 445 (2007) 17–21 www.elsevier.com/locate/cplett
Computational study of the reaction mechanism of benzylperoxy radical with HO2 in the gas phase Benni Du, Weichao Zhang *, Lailong Mu, Changjun Feng, Zhenglong Qin College of Chemistry and Chemical Engineering, Xuzhou Normal University, Xuzhou, Jiangsu 221116, People’s Republic of China Received 20 May 2007; in final form 8 July 2007 Available online 21 July 2007
Abstract The triplet and singlet potential energy surfaces for the reaction of C6H5CH2O2 with HO2 have been explored by ab initio molecular orbital calculations. The mechanisms for formation of possible product channels involved in both triplet and singlet potential energy surfaces have been predicted using a dual-level approach to density functional theory (B3LYP/6-311++G(3df,3pd)//B3LYP/6311G(d,p)). Our results show that the products C6H5CH2OOH + 3O2 are the major products, while the products C6H5C(O)H + OH + HO2 are the secondary products. The other products may be minor or negligible in the overall reaction of C6H5CH2O2 + HO2. Ó 2007 Elsevier B.V. All rights reserved.
1. Introduction Toluene is emitted into the troposphere from a number of processes such as internal-combustion engine exhausts, paint solvents and cigarette smoke [1,2]. Toluene can react with OH or NO3 radicals or Cl or atoms in the troposphere to produce a benzyl radical which is rapidly converted into benzylperoxy radical (C6H5CH2O2) by combination with molecular oxygen [3,4]. The kinetics of reactions for the peroxy radicals (RO2) with HO2 are of atmospheric interest, because these reactions represent the predominant loss process of the RO2 radicals in the troposphere under low NOx conditions in the global or regional environment [5]. Knowledge of the kinetics of aromatic peroxy radicals is currently limited to a few reactions. The reaction rate constant of C6H5CH2O2 with HO2 has been studied by two research groups. Nozie`re et al. [6] have investigated the kinetics and mechanism by using two complementary techniques: flash photolysis/UV absorption and photolysis/FTIR spectroscopy. Quite recently, El Dib et al. [7] have measured the rate constant by using the laser photolysis technique with *
Corresponding author. Fax: +86 516 83403164. E-mail address: [email protected] (W. Zhang).
0009-2614/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.07.047
time-resolved UV–visible absorption spectroscopy over the temperature range 298–353 K and the pressure range 50– 200 Torr. In addition, the rate constants for the title reaction obtained by El Dib et al. are close to those determined by Nozie`re et al. (the discrepancy does not exceed 20%). To date, there are no previous quantum chemical calculations on the C6H5CH2O2 + HO2 system. To reveal the detailed reaction mechanism and to enrich data concerning the vapor phase reaction of C6H5CH2O2 + HO2, here we report the reaction mechanism of the C6H5CH2O2 + HO2 reaction by calculating the potential energy surfaces (PESs) including all possible product channels. 2. Calculation methods The geometries and harmonic vibrational frequencies of all the stationary points (the reactants, intermediates (IMs), transition states (TSs) and products) were calculated with the hybrid density functional B3LYP method, i.e., using Becke’s three-parameter nonlocal-exchange functional [8] with the nonlocal correlation functional of Lee et al. [9] with the 6-311G(d,p) basis set. The number of imaginary frequencies (0 or 1) indicates whether the obtained structure is a minimum or a saddle point. The intrinsic reaction coordinate (IRC) [10,11] calculations were carried out at
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B. Du et al. / Chemical Physics Letters 445 (2007) 17–21
B3LYP/6-311G(d,p) level to test whether the transition state connects the right reactants and products or not along the reaction paths. To gain reliable relative energies of each stationary point on the PES, the single-point electronic energy of each optimized geometry was recalculated using a dual-level approach (X//Y) to density functional theory (DFT) [12,13]. In this methodology, the potential information, including geometries, and frequencies of some points along the reaction path, is obtained at lower-level Y from electronic structure calculations, and the energies of a few selected points are calculated at higher-level X. For this large system, we carried out the single-point calculations for the stationary points at the DFT/B3LYP level with the 6-311++G(3df,3pd) basis set. In this Letter, we have chosen the B3LYP/6-311++G(3df,3pd)//B3LYP/6311G(d,p) values for the following discussion, unless mentioned otherwise. All ab initio calculations were performed with GAUSSIAN 03 package of program Version B.01 [14] at HPxw9400 workstation. 3. Results and discussion The geometries of the reactants, intermediates, transition states and products involved in the C6H5CH2O2 + HO2 reaction are shown in Figs. 1 and 2. The unpaired spin also has been localized at the species on the triplet surface according to the atomic–atomic spin densities calculation and shown in Fig. 1. The relative energies (relative to reactants of C6H5CH2O2 + HO2) of all the species calculated at the DFT/B3LYP/6-311G(d,p) and B3LYP/6-311++G(3df, 3pd)//B3LYP/6-311G(d,p) levels are summarized in Table
1. Finally, the schematic potential energy surface on the B3LYP/6-311++G(3df,3pd)//B3LYP/6-311G(d,p) energies for C6H5CH2O2 + HO2 reaction pathways is shown in Fig. 3. As shown in Fig. 3, the reaction occurs on both triplet and singlet energy surfaces. The reaction pathways proceed on both triplet and singlet energy surfaces corresponding to the spin-conservation rule. 3.1. The triplet surface As the reactants C6H5CH2O2 and HO2 approach, they form a seven-membered-ring complex, where the O5–H8 ˚ and the O6–H3 distance is 2.361 A ˚. distance is 1.804 A 3 The loose adduct, IM1, at the entrance of the valley, most likely reflects the long-range dipole interaction forces between reactants. The 3IM1 is 31.72 kJ/mol below the initial reactants and has a C1 point group. Starting from the adduct 3IM1, there is only one possible pathway. The most favorable path is 3IM1 ! C6H5 CH2OOH + 3O2 via a direct hydrogen abstraction transition state (3TS1). The barrier height of 3TS1 relative to 3 IM1 is 7.34 kJ/mol. It should be mentioned that the energy of 3TS1 is calculated to be 3.71 kJ/mol lower than that of 3IM1 at the B3LYP/6-311G(d,p) level. However, at the B3LYP/6-311++G(3df,3pd)//B3LYP/6-311G(d,p) level, the energy of 3TS1 becomes about 7.34 kJ/mol higher than that of 3IM1. TS1 is characterized by a near linear O5–H8–O7 geometry, since this bond angle is equal to 166.0°. In TS1, the O7–H8 bond has elongated to ˚ , the O5–H8 bond length is reduced to 1.439 A ˚ 1.048 A ˚ from and the O6–O7 bond length is reduced to 1.296 A ˚ of 3IM1, the corresponding 0.991, 1.804 and 1.326 A respectively.
Fig. 1. The optimized geometries of the reactants, intermediate, transition states, and products in the triplet state at the B3LYP/6-311G(d,p) level. Bond lengths are given in angstrom. The unpaired spin is represented by solid circles (d).
B. Du et al. / Chemical Physics Letters 445 (2007) 17–21
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Fig. 2. The optimized geometries of the intermediate, transition states, and products in the singlet state at the B3LYP/6-311G(d,p) level. Bond lengths are given in angstrom.
The reactions of C6H5CH2O2 with HO2 can be divided into C6H5CH2OOH + 3O2 through bimolecular nucleophilic substitution pathway (SN2) via 3TS2, which involves the end O6 atom of HO2 attack at carbon (C1), and which results in the C1–O4 bond rupture. This step is prohibited by a large barrier, up to 73.26 kJ/mol. It is evident that the direct hydrogen abstraction on the triplet surface is a feasible path both thermodynamically and kinetically. The energy of 3TS1 is even 24.38 kJ/mol lower than the total energy of the reactants. This indicates that most likely the title reaction should exhibit a negative temperature dependence of its rate constant. It explains that the negative temperature dependence of the total rate constants has been observed in the reactions of C6H5CH2O2 with HO2 [6,7].
3.2. The singlet surface As shown in Fig. 3, the singlet surface is more complicated than the triplet one. For the initial reaction of C6H5CH2O2 + HO2, three possible processes have been identified. As a first reaction step, the terminal oxygen atom of C6H5CH2O2 may either add onto the terminal oxygen atom or abstract a H atom of HO2 molecule or the terminal oxygen atom of HO2 abstract a H atom of C6H5CH2O2 molecule. These reaction mechanisms will be discussed separately as follows in terms of their structural and energetic characteristics. The addition between the terminal oxygen atom of the C6H5CH2O2 and HO2 radicals leads to the intermediate 1 IM1. This process is found to be a barrierless association.
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B. Du et al. / Chemical Physics Letters 445 (2007) 17–21
Table 1 Total energies and relative energies of various species involved in the reaction of C6H5CH2O2 with HO2 using different levels of theory Species
ZPEa
E[B3LYP/6-311G(d,p)]a
DEb
E[B3LYP/6-311++G(3df,3pd)//B3LYP/6-311G(d,p)]a
DEb
C6H5CH2O2 + HO2 3 IM1 3 TS1 3 TS2 1 IM1 1 TS3 1 TS4 1 TS5 1 TS6 1 TS7 1 TS8 1 TS9 C6H5CH2OOH + 3O2 C6H5C(O)H + HOOOH C6H5CH2OOH + 1O2 C6H5C(O)H + OH + HO2 C6H5CH2OH + 1O3 C6H5C(O)H + H2 + 1O3 C6H5CHOO + H2O2
0.138325 0.141013 0.137949 0.136713 0.142524 0.136780 0.136419 0.138637 0.136874 0.131368 0.139839 0.140351 0.139568 0.139844 0.139535 0.132079 0.139804 0.126843 0.139274
572.180857 572.193248 572.194660 572.155602 572.189348 572.150368 572.167373 572.128538 572.157596 572.116231 572.142121 572.141458 572.232322 572.269923 572.170172 572.224254 572.186475 572.174816 572.202866
0.00 32.53 36.24 66.31 22.29 80.05 35.40 137.36 61.07 169.68 101.70 103.44 135.12 233.84 28.05 113.94 14.75 15.86 57.78
572.387941 572.4000201 572.3972253 572.3600384 572.3988059 572.3526999 572.3697324 572.3237657 572.3590901 572.3134204 572.3473454 572.3455038 572.439699 572.479297 572.378355 572.429027 572.398323 572.372422 572.416893
0.00 31.72 24.38 73.26 28.53 92.52 47.81 168.49 75.75 195.65 106.58 111.42 135.89 239.86 25.17 107.87 27.26 40.74 76.01
a b
Total energies and ZPE are in hartree. Relative energies are in kJ/mol.
Fig. 3. Energetic profile (kJ/mol, T = 298.15 K) for the potential energy surface of the C6H5CH2O2 + HO2 reaction at the B3LYP/6-311++G(3df,3pd)// B3LYP/6-311G(d,p) level of theory.
The binding energy is only 28.53 kJ/mol. H-abstraction from HO2 by O5 atom proceeds via 1TS8, which directly correlate to products C6H5CH2OOH + 1O2 (a mixture of the 1Rg and 1Dg states). The next direct H-abstraction chan-
nel is the terminal oxygen atom of HO2 abstract a H2 atom of C6H5CH2O2 molecule to produce C6H5CHOO + H2O2 via transition state 1TS9. The barrier heights of 1TS8 and 1 TS9 are 106.58 and 111.42 kJ/mol above the initial reac-
B. Du et al. / Chemical Physics Letters 445 (2007) 17–21
tants calculated at the B3LYP/6-311++G(3df,3pd)// B3LYP/6-311G(d,p) level of theory, such that abstraction cannot compete with addition at low to fairly high temperatures. It can be seen from Fig. 3 that 1IM1 is 28.53 kJ/mol lower than that of the initial reactants, i.e., IM1 adduct is an energy-rich intermediate. Many decomposition or isomerization channels of 1IM1 would be open. Starting from 1 IM1, there are five possible reaction pathways. The first pathway is that 1IM1 undergoes a 1,3-H migration (H3 atom shifts from C1 to O5 atom), followed by dissociation of O4–O5 bond to produce C6H5C(O)H + HOOOH via a four-center transition state 1TS3. At the B3LYP/6-311++G(3df,3pd)//B3LYP/6-311G(d,p) level of theory, the barrier height is 121.05kJ/mol with respect to 1 IM1. The production of C6H5C(O)H + HOOOH is exothermic by 239.86 kJ/mol. The second pathway is that the hydrogen atom (H3) of 1 IM1 shifts to the oxygen atom (O6) and the O4–O5 and O6–O7 bonds are broken simultaneously to form C6H5C(O)H + OH + HO2 via a five-membered-ring transition state 1TS4, facing a barrier of 76.34 kJ/mol. The last three pathways are 1IM1 can dissociate into the products C6H5CH2OOH + 1O2, C6H5CH2OH + 1O3, and C6H5C(O)H + H2 + 1O3 via four-membered-ring transition state 1TS5, five-center transition state 1TS6, and seven-membered-ring transition state 1TS7, respectively. These steps face barriers of 197.02, 104.28, and 224.18 kJ/mol, respectively. As can be seen from the discussion above and from Fig. 3, singlet 1IM1 can decompose via different channels, of which the channel via 1TS4 leading to C6H5C(O)H + OH + HO2 is predominant on the singlet energy surface because of its lowest barrier height of 76.34 kJ/mol, whereas C6H5CH2OH + 1O3 are expected to be secondary products. The other paths may play a minor or negligible role in the overall reaction of C6H5CH2O2 with HO2. In summary, all reaction channels involve significant barriers, ranging from 76.34 to 224.18 kJ/mol on the singlet surface. The energy differences in the adducts of 1 IM1 and 3IM1 and in the transition states of 1TS4 and 3 TS1 are calculated to be 3.19 and 72.19 kJ/mol, respectively. This indicates that the formation of 3IM1 should be slightly favorable thermodynamically and that the formation of C6H5CH2OOH + 3O2 should be more favorable kinetically. Thus, the reaction prefers to occur on the triplet surface because the hydrogen abstraction pathway to produce C6H5CH2OOH + 3O2 via 3TS1 faces the lowest barrier, and apparently, this step should predominate in the overall reaction. Therefore, it should be clear to
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deduce that the formation of C6H5CH2 OOH + 3O2 is the dominant product channel in the title reaction, whereas C6H5C(O)H + OH + HO2 are expected to be minor products. This result is in agreement with the experimental observations that the major product appears as the C6H5CH2OOH estimated by Nozie`re et al. [6] and El Dib et al. [7]. 4. Conclusions Potential energy surfaces for the reactions of C6H5CH2O2 with HO2 have been constructed at the B3LYP/6-311++G(3df,3pd)//B3LYP/6-311G(d,p) level of theory. Our results show that all the reactions take place on both triplet and singlet potential energy surfaces. The reaction mechanism on the singlet surface is more complicated. On the singlet surface, all reaction channels involve significant barriers. These pathways may play a minor or negligible role in the overall reaction of C6H5CH2O2 with HO2. The reaction mechanism on the triplet surface is simple, including hydrogen abstraction and SN2-type displacement. The pathway of 3IM1 ! 3TS1 ! C6H5CH2OOH + 3 O2 faces the lowest barrier in the overall reaction of C6H5CH2O2 with HO2, and accordingly, this pathway can be expected as the dominant channel. More importantly, the calculated results indicate that the title reaction should exhibit a negative temperature dependence of its rate constant. References [1] R.P. Wayne, Chemistry of AtmospheresOxford Science, Clarendon Press, Oxford, UK, 1985. [2] J.H. Seinfeld, Atmospheric Chemistry and Physics of Air Pollution, John Wiley and Sons, New York, 1986. [3] L. Elmaimouni, R. Minetti, J.P. Sawerysyn, P. Devolder, Int. J. Chem. Kinet. 25 (1993) 399. [4] F.F. Fenter, B. Nozie`re, F. Caralp, R. Lesclaux, Int. J. Chem. Kinet. 26 (1994) 171. [5] J.J. Orlando, G.S. Tyndall, T.J. Wallington, Chem. Rev. 103 (2003) 4657. [6] B. Nozie`re, R. Lesclaux, M.D. Hurley, M.A. Dearth, T.J. Wallington, J. Phys. Chem. 98 (1994) 2864. [7] G. El Dib, A. Chakir, E. Roth, J. Brion, D. Daumont, J. Phys. Chem. A 110 (2006) 7848. [8] A.D. Becke, J. Chem. Phys. 98 (1993) 1372. [9] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [10] C. Gonzalez, H.B. Schlegel, J. Chem. Phys. 90 (1989) 2154. [11] C. Gonzalez, H.B. Schlegel, J. Phys. Chem. 94 (1990) 5523. [12] R.L. Bell, T.N. Truong, J. Chem. Phys. 101 (1994) 442. [13] W.P. Hu, D.G. Truhlar, J. Am. Chem. Soc. 118 (1996) 860. [14] M.J. Frisch et al., Gaussian 03, revision B.01, Gaussian, Inc., Pittsburgh, PA, 2003.
Computational study of the reaction mechanism of benzylperoxy radical with HO2 in the gas phase Benni Du, Weichao Zhang *, Lailong Mu, Changjun Feng, Zhenglong Qin College of Chemistry and Chemical Engineering, Xuzhou Normal University, Xuzhou, Jiangsu 221116, People’s Republic of China Received 20 May 2007; in final form 8 July 2007 Available online 21 July 2007
Abstract The triplet and singlet potential energy surfaces for the reaction of C6H5CH2O2 with HO2 have been explored by ab initio molecular orbital calculations. The mechanisms for formation of possible product channels involved in both triplet and singlet potential energy surfaces have been predicted using a dual-level approach to density functional theory (B3LYP/6-311++G(3df,3pd)//B3LYP/6311G(d,p)). Our results show that the products C6H5CH2OOH + 3O2 are the major products, while the products C6H5C(O)H + OH + HO2 are the secondary products. The other products may be minor or negligible in the overall reaction of C6H5CH2O2 + HO2. Ó 2007 Elsevier B.V. All rights reserved.
1. Introduction Toluene is emitted into the troposphere from a number of processes such as internal-combustion engine exhausts, paint solvents and cigarette smoke [1,2]. Toluene can react with OH or NO3 radicals or Cl or atoms in the troposphere to produce a benzyl radical which is rapidly converted into benzylperoxy radical (C6H5CH2O2) by combination with molecular oxygen [3,4]. The kinetics of reactions for the peroxy radicals (RO2) with HO2 are of atmospheric interest, because these reactions represent the predominant loss process of the RO2 radicals in the troposphere under low NOx conditions in the global or regional environment [5]. Knowledge of the kinetics of aromatic peroxy radicals is currently limited to a few reactions. The reaction rate constant of C6H5CH2O2 with HO2 has been studied by two research groups. Nozie`re et al. [6] have investigated the kinetics and mechanism by using two complementary techniques: flash photolysis/UV absorption and photolysis/FTIR spectroscopy. Quite recently, El Dib et al. [7] have measured the rate constant by using the laser photolysis technique with *
Corresponding author. Fax: +86 516 83403164. E-mail address: [email protected] (W. Zhang).
0009-2614/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.07.047
time-resolved UV–visible absorption spectroscopy over the temperature range 298–353 K and the pressure range 50– 200 Torr. In addition, the rate constants for the title reaction obtained by El Dib et al. are close to those determined by Nozie`re et al. (the discrepancy does not exceed 20%). To date, there are no previous quantum chemical calculations on the C6H5CH2O2 + HO2 system. To reveal the detailed reaction mechanism and to enrich data concerning the vapor phase reaction of C6H5CH2O2 + HO2, here we report the reaction mechanism of the C6H5CH2O2 + HO2 reaction by calculating the potential energy surfaces (PESs) including all possible product channels. 2. Calculation methods The geometries and harmonic vibrational frequencies of all the stationary points (the reactants, intermediates (IMs), transition states (TSs) and products) were calculated with the hybrid density functional B3LYP method, i.e., using Becke’s three-parameter nonlocal-exchange functional [8] with the nonlocal correlation functional of Lee et al. [9] with the 6-311G(d,p) basis set. The number of imaginary frequencies (0 or 1) indicates whether the obtained structure is a minimum or a saddle point. The intrinsic reaction coordinate (IRC) [10,11] calculations were carried out at
18
B. Du et al. / Chemical Physics Letters 445 (2007) 17–21
B3LYP/6-311G(d,p) level to test whether the transition state connects the right reactants and products or not along the reaction paths. To gain reliable relative energies of each stationary point on the PES, the single-point electronic energy of each optimized geometry was recalculated using a dual-level approach (X//Y) to density functional theory (DFT) [12,13]. In this methodology, the potential information, including geometries, and frequencies of some points along the reaction path, is obtained at lower-level Y from electronic structure calculations, and the energies of a few selected points are calculated at higher-level X. For this large system, we carried out the single-point calculations for the stationary points at the DFT/B3LYP level with the 6-311++G(3df,3pd) basis set. In this Letter, we have chosen the B3LYP/6-311++G(3df,3pd)//B3LYP/6311G(d,p) values for the following discussion, unless mentioned otherwise. All ab initio calculations were performed with GAUSSIAN 03 package of program Version B.01 [14] at HPxw9400 workstation. 3. Results and discussion The geometries of the reactants, intermediates, transition states and products involved in the C6H5CH2O2 + HO2 reaction are shown in Figs. 1 and 2. The unpaired spin also has been localized at the species on the triplet surface according to the atomic–atomic spin densities calculation and shown in Fig. 1. The relative energies (relative to reactants of C6H5CH2O2 + HO2) of all the species calculated at the DFT/B3LYP/6-311G(d,p) and B3LYP/6-311++G(3df, 3pd)//B3LYP/6-311G(d,p) levels are summarized in Table
1. Finally, the schematic potential energy surface on the B3LYP/6-311++G(3df,3pd)//B3LYP/6-311G(d,p) energies for C6H5CH2O2 + HO2 reaction pathways is shown in Fig. 3. As shown in Fig. 3, the reaction occurs on both triplet and singlet energy surfaces. The reaction pathways proceed on both triplet and singlet energy surfaces corresponding to the spin-conservation rule. 3.1. The triplet surface As the reactants C6H5CH2O2 and HO2 approach, they form a seven-membered-ring complex, where the O5–H8 ˚ and the O6–H3 distance is 2.361 A ˚. distance is 1.804 A 3 The loose adduct, IM1, at the entrance of the valley, most likely reflects the long-range dipole interaction forces between reactants. The 3IM1 is 31.72 kJ/mol below the initial reactants and has a C1 point group. Starting from the adduct 3IM1, there is only one possible pathway. The most favorable path is 3IM1 ! C6H5 CH2OOH + 3O2 via a direct hydrogen abstraction transition state (3TS1). The barrier height of 3TS1 relative to 3 IM1 is 7.34 kJ/mol. It should be mentioned that the energy of 3TS1 is calculated to be 3.71 kJ/mol lower than that of 3IM1 at the B3LYP/6-311G(d,p) level. However, at the B3LYP/6-311++G(3df,3pd)//B3LYP/6-311G(d,p) level, the energy of 3TS1 becomes about 7.34 kJ/mol higher than that of 3IM1. TS1 is characterized by a near linear O5–H8–O7 geometry, since this bond angle is equal to 166.0°. In TS1, the O7–H8 bond has elongated to ˚ , the O5–H8 bond length is reduced to 1.439 A ˚ 1.048 A ˚ from and the O6–O7 bond length is reduced to 1.296 A ˚ of 3IM1, the corresponding 0.991, 1.804 and 1.326 A respectively.
Fig. 1. The optimized geometries of the reactants, intermediate, transition states, and products in the triplet state at the B3LYP/6-311G(d,p) level. Bond lengths are given in angstrom. The unpaired spin is represented by solid circles (d).
B. Du et al. / Chemical Physics Letters 445 (2007) 17–21
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Fig. 2. The optimized geometries of the intermediate, transition states, and products in the singlet state at the B3LYP/6-311G(d,p) level. Bond lengths are given in angstrom.
The reactions of C6H5CH2O2 with HO2 can be divided into C6H5CH2OOH + 3O2 through bimolecular nucleophilic substitution pathway (SN2) via 3TS2, which involves the end O6 atom of HO2 attack at carbon (C1), and which results in the C1–O4 bond rupture. This step is prohibited by a large barrier, up to 73.26 kJ/mol. It is evident that the direct hydrogen abstraction on the triplet surface is a feasible path both thermodynamically and kinetically. The energy of 3TS1 is even 24.38 kJ/mol lower than the total energy of the reactants. This indicates that most likely the title reaction should exhibit a negative temperature dependence of its rate constant. It explains that the negative temperature dependence of the total rate constants has been observed in the reactions of C6H5CH2O2 with HO2 [6,7].
3.2. The singlet surface As shown in Fig. 3, the singlet surface is more complicated than the triplet one. For the initial reaction of C6H5CH2O2 + HO2, three possible processes have been identified. As a first reaction step, the terminal oxygen atom of C6H5CH2O2 may either add onto the terminal oxygen atom or abstract a H atom of HO2 molecule or the terminal oxygen atom of HO2 abstract a H atom of C6H5CH2O2 molecule. These reaction mechanisms will be discussed separately as follows in terms of their structural and energetic characteristics. The addition between the terminal oxygen atom of the C6H5CH2O2 and HO2 radicals leads to the intermediate 1 IM1. This process is found to be a barrierless association.
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B. Du et al. / Chemical Physics Letters 445 (2007) 17–21
Table 1 Total energies and relative energies of various species involved in the reaction of C6H5CH2O2 with HO2 using different levels of theory Species
ZPEa
E[B3LYP/6-311G(d,p)]a
DEb
E[B3LYP/6-311++G(3df,3pd)//B3LYP/6-311G(d,p)]a
DEb
C6H5CH2O2 + HO2 3 IM1 3 TS1 3 TS2 1 IM1 1 TS3 1 TS4 1 TS5 1 TS6 1 TS7 1 TS8 1 TS9 C6H5CH2OOH + 3O2 C6H5C(O)H + HOOOH C6H5CH2OOH + 1O2 C6H5C(O)H + OH + HO2 C6H5CH2OH + 1O3 C6H5C(O)H + H2 + 1O3 C6H5CHOO + H2O2
0.138325 0.141013 0.137949 0.136713 0.142524 0.136780 0.136419 0.138637 0.136874 0.131368 0.139839 0.140351 0.139568 0.139844 0.139535 0.132079 0.139804 0.126843 0.139274
572.180857 572.193248 572.194660 572.155602 572.189348 572.150368 572.167373 572.128538 572.157596 572.116231 572.142121 572.141458 572.232322 572.269923 572.170172 572.224254 572.186475 572.174816 572.202866
0.00 32.53 36.24 66.31 22.29 80.05 35.40 137.36 61.07 169.68 101.70 103.44 135.12 233.84 28.05 113.94 14.75 15.86 57.78
572.387941 572.4000201 572.3972253 572.3600384 572.3988059 572.3526999 572.3697324 572.3237657 572.3590901 572.3134204 572.3473454 572.3455038 572.439699 572.479297 572.378355 572.429027 572.398323 572.372422 572.416893
0.00 31.72 24.38 73.26 28.53 92.52 47.81 168.49 75.75 195.65 106.58 111.42 135.89 239.86 25.17 107.87 27.26 40.74 76.01
a b
Total energies and ZPE are in hartree. Relative energies are in kJ/mol.
Fig. 3. Energetic profile (kJ/mol, T = 298.15 K) for the potential energy surface of the C6H5CH2O2 + HO2 reaction at the B3LYP/6-311++G(3df,3pd)// B3LYP/6-311G(d,p) level of theory.
The binding energy is only 28.53 kJ/mol. H-abstraction from HO2 by O5 atom proceeds via 1TS8, which directly correlate to products C6H5CH2OOH + 1O2 (a mixture of the 1Rg and 1Dg states). The next direct H-abstraction chan-
nel is the terminal oxygen atom of HO2 abstract a H2 atom of C6H5CH2O2 molecule to produce C6H5CHOO + H2O2 via transition state 1TS9. The barrier heights of 1TS8 and 1 TS9 are 106.58 and 111.42 kJ/mol above the initial reac-
B. Du et al. / Chemical Physics Letters 445 (2007) 17–21
tants calculated at the B3LYP/6-311++G(3df,3pd)// B3LYP/6-311G(d,p) level of theory, such that abstraction cannot compete with addition at low to fairly high temperatures. It can be seen from Fig. 3 that 1IM1 is 28.53 kJ/mol lower than that of the initial reactants, i.e., IM1 adduct is an energy-rich intermediate. Many decomposition or isomerization channels of 1IM1 would be open. Starting from 1 IM1, there are five possible reaction pathways. The first pathway is that 1IM1 undergoes a 1,3-H migration (H3 atom shifts from C1 to O5 atom), followed by dissociation of O4–O5 bond to produce C6H5C(O)H + HOOOH via a four-center transition state 1TS3. At the B3LYP/6-311++G(3df,3pd)//B3LYP/6-311G(d,p) level of theory, the barrier height is 121.05kJ/mol with respect to 1 IM1. The production of C6H5C(O)H + HOOOH is exothermic by 239.86 kJ/mol. The second pathway is that the hydrogen atom (H3) of 1 IM1 shifts to the oxygen atom (O6) and the O4–O5 and O6–O7 bonds are broken simultaneously to form C6H5C(O)H + OH + HO2 via a five-membered-ring transition state 1TS4, facing a barrier of 76.34 kJ/mol. The last three pathways are 1IM1 can dissociate into the products C6H5CH2OOH + 1O2, C6H5CH2OH + 1O3, and C6H5C(O)H + H2 + 1O3 via four-membered-ring transition state 1TS5, five-center transition state 1TS6, and seven-membered-ring transition state 1TS7, respectively. These steps face barriers of 197.02, 104.28, and 224.18 kJ/mol, respectively. As can be seen from the discussion above and from Fig. 3, singlet 1IM1 can decompose via different channels, of which the channel via 1TS4 leading to C6H5C(O)H + OH + HO2 is predominant on the singlet energy surface because of its lowest barrier height of 76.34 kJ/mol, whereas C6H5CH2OH + 1O3 are expected to be secondary products. The other paths may play a minor or negligible role in the overall reaction of C6H5CH2O2 with HO2. In summary, all reaction channels involve significant barriers, ranging from 76.34 to 224.18 kJ/mol on the singlet surface. The energy differences in the adducts of 1 IM1 and 3IM1 and in the transition states of 1TS4 and 3 TS1 are calculated to be 3.19 and 72.19 kJ/mol, respectively. This indicates that the formation of 3IM1 should be slightly favorable thermodynamically and that the formation of C6H5CH2OOH + 3O2 should be more favorable kinetically. Thus, the reaction prefers to occur on the triplet surface because the hydrogen abstraction pathway to produce C6H5CH2OOH + 3O2 via 3TS1 faces the lowest barrier, and apparently, this step should predominate in the overall reaction. Therefore, it should be clear to
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deduce that the formation of C6H5CH2 OOH + 3O2 is the dominant product channel in the title reaction, whereas C6H5C(O)H + OH + HO2 are expected to be minor products. This result is in agreement with the experimental observations that the major product appears as the C6H5CH2OOH estimated by Nozie`re et al. [6] and El Dib et al. [7]. 4. Conclusions Potential energy surfaces for the reactions of C6H5CH2O2 with HO2 have been constructed at the B3LYP/6-311++G(3df,3pd)//B3LYP/6-311G(d,p) level of theory. Our results show that all the reactions take place on both triplet and singlet potential energy surfaces. The reaction mechanism on the singlet surface is more complicated. On the singlet surface, all reaction channels involve significant barriers. These pathways may play a minor or negligible role in the overall reaction of C6H5CH2O2 with HO2. The reaction mechanism on the triplet surface is simple, including hydrogen abstraction and SN2-type displacement. The pathway of 3IM1 ! 3TS1 ! C6H5CH2OOH + 3 O2 faces the lowest barrier in the overall reaction of C6H5CH2O2 with HO2, and accordingly, this pathway can be expected as the dominant channel. More importantly, the calculated results indicate that the title reaction should exhibit a negative temperature dependence of its rate constant. References [1] R.P. Wayne, Chemistry of AtmospheresOxford Science, Clarendon Press, Oxford, UK, 1985. [2] J.H. Seinfeld, Atmospheric Chemistry and Physics of Air Pollution, John Wiley and Sons, New York, 1986. [3] L. Elmaimouni, R. Minetti, J.P. Sawerysyn, P. Devolder, Int. J. Chem. Kinet. 25 (1993) 399. [4] F.F. Fenter, B. Nozie`re, F. Caralp, R. Lesclaux, Int. J. Chem. Kinet. 26 (1994) 171. [5] J.J. Orlando, G.S. Tyndall, T.J. Wallington, Chem. Rev. 103 (2003) 4657. [6] B. Nozie`re, R. Lesclaux, M.D. Hurley, M.A. Dearth, T.J. Wallington, J. Phys. Chem. 98 (1994) 2864. [7] G. El Dib, A. Chakir, E. Roth, J. Brion, D. Daumont, J. Phys. Chem. A 110 (2006) 7848. [8] A.D. Becke, J. Chem. Phys. 98 (1993) 1372. [9] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [10] C. Gonzalez, H.B. Schlegel, J. Chem. Phys. 90 (1989) 2154. [11] C. Gonzalez, H.B. Schlegel, J. Phys. Chem. 94 (1990) 5523. [12] R.L. Bell, T.N. Truong, J. Chem. Phys. 101 (1994) 442. [13] W.P. Hu, D.G. Truhlar, J. Am. Chem. Soc. 118 (1996) 860. [14] M.J. Frisch et al., Gaussian 03, revision B.01, Gaussian, Inc., Pittsburgh, PA, 2003.