The self-reaction of hydroperoxyl radicals: ab initio characterization of dimer structures and reaction mechanisms

Rongshun Zhu and M. C. Lin* Paper Department of Chemistry, Emory University, Atlanta, GA 30322, USA. E-mail: [email protected]

Received 21st August 2001, Accepted 15th October 2001 Published on the Web 31st October 2001

The global potential energy surfaces of singlet and triplet H2O4 systems have been searched at the B3LYP/ 6-311G(d, p) level of theory; their relative energies have been calculated at the G2M(CC5)// B3LYP/6-311G (d, p) level. The results show that the most stable intermediate out of the 11 open-chain and cyclic dimers of 21 HO2 is the singlet HO4H chain-structure with C1 symmetry which lies 19.1 kcal mol below the reactants. The transition states for the production of H2O2 z O2 (singlet and triplet), H2O z O3 and H2 z 2O2 have been calculated at the same level of theory. The results show that the most favored product channel, producing 3 H2O2 z O2, occurs by the formation of a triplet six-member-ring intermediate through head-to-tail association 21 3 with a dual -bonding energy of 9.5 kcal mol . The intermediate fragments to give H2O2 z O2 via a transition state, which lies below the reactants by about 0.5 kcal mol21. There are four channels over the singlet 1 surface which can produce O2; all the transition states associated with these channels lie above the reactants by 21 2.8–5.6 kcal mol at the G2M level. Similarly, the O3 and H2 formation channels also occur over the singlet surface with high energy barriers, 5.2 and 74.2 kcal mol21, respectively; their formation is kinetically unimportant.

1. Introduction may potentially drive the process to occur, although it has not The hydroperoxyl , HO2, plays a pivotal role in the yet been observed experimentally to date. chemistry of Earth’s atmosphere, from troposphere to meso- Theoretically, one of the most interesting aspects of the sphere. It is one of the key oxidizers, which can react with reaction lies perhaps in the mechanisms responsible for the volatile organic compounds and efficiently convert NO to NO2 formation of these products and the pronounced effect of H2O while regenerating OH.1–2 There have been numerous kinetic on the overall rate constant.50,51 Do these products share a studies on the self-reaction of HO2 because of the significant common precursor, which is long-lived and responsible for the role it plays in the atmosphere and chemistry.3–54 observed pressure dependence? If there are many possible long- The existing kinetic data vary widely; for example, at room lived intermediates, four of which have been predicted to be temperature where most data have been determined, the values stable in a series of papers by Schaefer and co-workers,56–58 of the rate constant reported to date for the major product how are they connected in the potential energy surface (PES), channel, which predisposes the observed product branching ratios? In this work, we investigate the reaction system by system- HO2 z HO2 A H2O2 z O2 (1) atically characterizing its PES with high-level molecular orbital calculations. Hopefully the predicted energetics for the low- are scattered by more than an order of magnitude. Part of the energy paths will be employed in the future for prediction of reason for the scatter was concluded to result from the effect of their rate constants under varying experimental conditions so pressure,4,5,6,10,28,34,36,38,40,48 which had not been recognized as to reconcile the observed widely scattered data. earlier. The origin and the extent of the pressure effect on the reaction rate are still not clearly understood. Another interesting aspect of the reaction is the mechanism 2. Computational methods responsible for reaction (1) as well as the minor product Ab initio calculations channel, The geometry of the reactants, intermediates, transition states, z z HO2 HO2 A H2 2O2, (2) and products of the HO2 z HO2 reaction were optimized by the B3LYP method (Becke’s three-parameter nonlocal which has been shown to occur by as much as 9%.11 There has exchange functional59–61 with nonlocal correlation functional 62 been a report of the chemiluminescence from the excited O2 of Lee et al. ) using the standard Gaussian 6-311G(d,p) basis 1 ( D) state in an electrochemical reaction involving H2O2; the set. Vibrational frequencies and zero-point energies for all emission was assumed to result from the decomposition of an species were calculated at the same B3LYP/6-311G(d, p) level 55 excited H2O4 intermediate. In addition, the high exothermi- of theory. The energies of all species were calculated by the 63 city of the spin-allowed O3 producing reaction channel via an G2M method, which uses a series of calculations with the open chain HO4H intermediate, B3LYP/6-311G(d,p) optimized geometry to approximate the CCSD(T)/6-311zG(3df,2p) level of theory including a ‘‘higher HO2 z HO2 A H2O z O3, (3) level correction (HLC)’’ based on the number of paired and

DOI: 10.1039/b107602g PhysChemComm, 2001, 23, 1–6 1 This journal is # The Royal Society of Chemistry 2001 unpaired electrons. The total G2M energy given in units of Eh different products. The detailed mechanisms for these processes (hartrees) with zero-point energy (ZPE) correction is calculated are discussed in the following sections. as follows:

E[G2M(CC5)] ~ E[CCSD(T)/6-311G(d, p)] A. Stable isomers of HO4H z DE(z3df, 2p) z DE(HLC) Singlet. Due to the rotation of OH and HO groups in the z ZPE[B3LYP/6-311G(d, p)]. 2 HO4H chain , there are several isomers with similar DE(z3df, 2p) ~ E[MP2/6-311zG(3df, 2p)] stabilities. In the present calculation, six chemically bonded 2 E[MP2/6-311G(d, p)]. chain-structures have been identified. They are LM1a, LM1b, LM2a, LM2b, LM3a and LM3b as shown in Fig. 1. These DE(HLC) ~ 20.00530n 2 0.00019n ; isomers, LM1a and LM1b, LM2a and LM2b, and LM3a and b a LM3b, are mirror isomers of each other. LM1a, LM2a and their mirror-isomers have C2 symmetry, the apparent structure where na and nb are the numbers of valence electrons, na ¢ nb. All calculations were carried out with Gaussian 98.64 differences are that the bridging O–O bonds in LM2a and LM2b are 0.024 A˚ shorter than those in LM1a and LM1b; however, the O–O bonds in the HO2 groups of LM2a and ˚ 3. Results and discussion LM2b are 0.016 A longer than those in LM1a and LM1b. In addition, in LM2a and LM2b, there are intra-molecular The optimized geometries of the reactants and long-lived hydrogen bonds (2.824 A˚ ) which LM1a and LM1b lack. intermediates are shown in Fig. 1 and those of transition states LM3a and LM3b have C1 symmetry with slightly stronger are shown in Fig. 2. The potential energy diagrams of singlet intra-molecular hydrogen bonds (2.661 A˚ ) compared with and triplet species are presented separately for clarity in Figs. 3 those in LM2a and LM2b. From Fig. 1 and Table 1, one can and 4, respectively. The total and relative energies are compiled see that the most stable chain structure intermediates are LM3a in Table 1. As shown in Figs. 3 and 4 the HO2 z HO2 reaction and LM3b. The predicted HO2 dimerization energies (see can occur by both singlet and triplet potential surfaces Table 1) in LM1, LM2 and LM3 are 218.2, 218.5 and involving different intermediates shown in Fig. 1 to form 219.1 kcal mol21 at the G2M//B3LYP/6-311G (d, p) level. The

Fig. 1 The optimized geometries of the reactants, singlet and triplet intermediates, in the HO2 z HO2 reaction at the B3LYP/6-311G(d, p) level.

2 PhysChemComm, 2001, 23, 1–6 Fig. 2 The optimized geometries of the singlet and triplet transition states for HO2 z HO2 at the B3LYP/6-311G(d, p) level. most stable isomer is LM3 because of its relatively stronger oriented differently. The head-to-tail connected O–O bond intra-molecular hydrogen bond. Schaefer and co-workers57 lengths are 2.140 and 2.149 A˚ in LM4 and LM5, respectively; also observed a similar result for two of these isomers, LM1 other structural parameters are close to those in the HO2 and LM3. monomer (see Fig. 1). These two minima are sensitive to the Besides these chain isomers, we also found two four- methods employed; they are found to be endothermic with member-ring minima, LM4 and LM5. In these two loose respect to the reactants. They lie above the reactants by 10.1 21 intermediates, the O4-ring was formed by the anti-parallel and 12.0 kcal mol (without ZPE corrections) at the B3LYP/ association of the two HO2 radicals with the O–H bonds 6-311G (d, p) level. However, at the G2M level, which includes

Fig. 3 Schematic energy diagram of the singlet HO2–HO2 system Fig. 4 Schematic energy diagram of the triplet HO2–HO2 system computed at the G2M level. computed at the G2M level.

PhysChemComm, 2001, 23, 1–6 3 Table 1 Total and relative energies of reactants, intermediates, transition states and products for the self-reaction of HO2 calculated at different levels of theory with B3LYP/6-311G(d, p) optimized geometries

Energiesb

Species ZPEa B3LYP/6-311G (d, p) MP2/6-311G(d, p) MP2/6-311zG(3df, 2p) CCSD(T)/6-311G (d, p) G2M

HO2 z HO2 17.7 2301.900816 2301.1704524 2301.353157 2301.229014 2301.44973 LM1a 21.0 210.9 220.7 226.9 212.1 218.2 LM1b 21.0 210.9 220.7 226.9 212.1 218.2 LM2a 21.0 210.5 221.5 227.9 212.2 218.5 LM2b 21.0 210.5 221.5 227.9 212.2 218.5 LM3a 21.1 211.4 221.5 227.9 212.9 219.1 LM3b 21.1 211.4 221.5 227.9 212.9 219.1 LM4 21.4 10.1 223.9 231.9 3.5 24.1 LM5 21.3 12.0 222.1 230.6 5.3 22.8 LM6 20.5 214.8 211.5 211.3 212.5 29.49 LM7 19.6 27.4 26.4 25.9 26.6 24.3 LM8 20.5 214.6 211.4 211.3 212.4 29.5 TS1 19.2 27.0 21.1 24.9 11.2 5.6 TS2 19.4 23.7 24.3 27.9 9.1 3.9 TS3 18.4 32.8 6.5 6.3 5.7 2.9 TS4 19.3 13.7 210.1 215.0 9.3 2.8 TS5 14.8 75.4 68.8 67.4 81.7 74.2 TS6 18.2 15.6 5.9 20.2 13.9 5.2 TS7 21.1 21.7 211.1 217.2 22.7 28.6 TS8 20.5 27.3 217.1 223.4 28.8 215.3 TS9 21.2 25.2 214.7 220.3 26.0 211.4 TS10 17.7 25.5 2.5 2.6 1.6 1.7 TS11 18.9 26.7 23.3 23.1 23.9 22.6 TS12 17.4 27.8 2.3 2.1 20.06 20.5 3 H2O2 z O2 18.9 235.0 252.9 252.6 239.7 238.2 H2O z O3 17.9 210.9 244.2 252.1 221.9 232.8 1 H2O2 z O2 18.9 3.9 220.9 222.5 29.1 212.6 H2 z 2O2 11.0 25.2 223.1 216.0 29.2 25.6 a 21 b Values are in units of kcal mol . The total energies of the reactants (2 6 HO2) at different level are given in au (Eh) and the relative energies (relative to the reactants) of other species at the corresponding levels are given in units of kcal mol21, ZPE corrections are included only in the G2M energies. basis set expansion and high-level correlation, they lie below intermediate LM8 with two hydrogen bonds. The two equal the reactants by 4.1 and 2.8 kcal mol21 (with ZPE corrections), O–H bond lengths are 1.809 A˚ at the B3LYP/6-311G (d, p) respectively. It is apparent that the use of larger basis sets with level; they are shorter than those of 2.192, 2.242 and 1.967 A˚ high-level treatment of electronic correlation corrections is predicted at the HF/DZP, HF/DZ and TZ2P z diff-CISD necessary to properly describe these minima. levels, respectively, by Schaefer et al.56–58 We also examined As alluded to above, Schaefer and co-workers56–58 have this structure at the B3LYP/6-311zzG (d, p) and MP2/ reported two singlet chain-structure minima with C1 and C2 6-311G (d, p) levels; the corresponding O–H bond lengths are symmetry; they estimated the dissociation energies D0 for the 1.844 and 1.855 A˚ , respectively. From this comparison, we see lowest minima with chain structures to be y11 kcal mol21 that the hydrogen bond length is sensitive to the methods (DZ z P CI).55 These two structures are similar to our employed. The O–O bond lengths also vary with different structures LM1a and LM3a as aforementioned. One six- methods; they are 1.309, 1.367 and 1.305 A˚ at the HF/DZP, member-ring singlet minimum was also located in their work HF/DZ and TZ2P z diff-CISD levels, respectively, in using the two-configuration DZ (TC) SCF method56 and found Schaefer’s calculations.56–58 The values obtained in our to be only 0.01 kcal mol21 above the analogous triplet minima calculation are 1.324, 1.324 and 1.298 A˚ at the B3LYP/ located with singlet DZ SCF method.56 In our calculation, the 6-311G (d, p), B3LYP/6-311zzG (d, p) and MP2/6-311G six-member-ring singlet minimum LM6 was located only when (d, p) levels, respectively (Fig. 1 only shows the structures the UHF wavefunctions were used. At the G2M level, the obtained at the B3LYP/6-311G (d, p) level). These values can energy is 0.1 kcal mol21 lower than that of the corresponding be compared with the predicted (1.328 A˚ ) and experimental triplet state to be described below. (1.314 A˚ ) O–O bond length in HOO.69 In LM8, the HOO bond angle of 103.9u predicted in our calculation can be compared z 56 Triplet intermediates. As depicted in Fig. 4, the products with 105.6, 107.3 and 104.6u predicted by HF/DZ P, HF/ 3 DZ56 and CISD/TZ2P z diff58 level calculations, respectively. H2O2 z O2 can be formed via two triplet channels which The O–H bond length has relatively minor changes by different involve different intermediates. First, HO2 and HO2 can form a 21 one-hydrogen-bond chain intermediate, LM7 (see Fig. 1) by methods. The bonding energy D0 of LM8 is 9.5 kcal mol at … the G2M level; this is slightly larger than that of y7 kcal mol21 head-to-tail association. The hydrogen bond length (O H) in 57 this is 1.861 A˚ which is shorter than the experimental estimated by Schaefer and co-workers. O…H distance, 2.02 A˚ , of a dimer.65 The OHO bond angle is 173.8u. It can be seen that the structures of the two HO fragments in LM7 are almost the same as that of the 2 B. Product formation HO2 monomer; the O–O bond length changes are 20.004 yz 0.001 A˚ and HOO bond angle changes are Although some of stable minima were discussed in the 56–58 20.8uyz 0.2u. The bonding energy D0 is predicted to be literature as cited above, to our knowledge, the full 4.3 kcal mol21 at the G2M level, which is close to the potential energy surfaces for the formation of different dimerization energy about 5 kcal mol21 found for water.66–68 products have not been reported. In this section, we will The two HO2 radicals can also form a planar six-member-ring discuss the mechanisms for product formation.

4 PhysChemComm, 2001, 23, 1–6 1 1 (a) Singlet product channels. H2O2 z O2 ( D). O2 ( D) can intermediate can also be formed via a rotational transition only be produced through a singlet surface, as shown in Fig. 3. state (TS11) with only 1.7 kcal mol21 barrier. LM8 can 3 2 There are four possible channels. Channels a and b are dissociate via TS12 to produce H2O2 z O2 ( Sg ) with a direct abstraction reactions via transition states TS1 and barrier of 9.0 kcal mol21. We should mention that TS12 has a TS2, respectively, corresponding to the trans–cis–trans and mirror structure TS12’ (see Fig. 1) with the same energy. This 3 trans–trans–trans structures as shown in Fig. 2. They lie 5.6 and process is apparently the major channel for H2O2 z O2 3.9 kcal mol21 above the reactants, respectively. The third formation. channel, c, occurring by the singlet chain intermediate LM1a, 1 can produce H2O2 z O2 ( D) via TS3 with a barrier of 3.0 kcal mol21 above the reactants. The structure of TS3 seems 4. Conclusion to be looser with an imaginary frequency of 489 cm21. IRC 21/2 Several singlet and triplet intermediates can be formed in the results with a smaller step size (0.01 u a0) along the reaction dimerization of HO2 radicals. They are: six singlet chain- path indicate that the TS3 directly connects with the structure intermediates with the dissociation energies z 1 H2O2 O2 ( D) products and the intermediate LM1a. The D ~ 18.2–19.1 kcal mol21, two loose singlet four-member- z 1 0 fourth channel occurs by LM4 producing H2O2 O2 ( D) via ~ 21 21 ring intermediates with D0 2.8 and 4.1 kcal mol , two TS4 with a 2.8 kcal mol barrier relative to the reactants. hydrogen-bonded six-member-ring intermediates (singlet and triplet) with D 9.5 kcal mol21 and one hydrogen-bonded z 8–11 z 0 # H2 2O2. There have been reports that H2 2O2 triplet open-structure intermediate with D # 4.3 kcal mol21. products were formed in experiments, but the product ratios 0 The chain-structure with C1 symmetry is the most stable one are uncertain, varying from 0 to 9%. In this calculation, the due to its intra-molecular hydrogen bonding. barrier for formation of H2 z 2O2 also predicted to be rather 21 Those intermediates can dissociate to produce different high, 74.2 kcal mol at the G2M level, and an IRC calculation products via several transition states. The transition states showed that the products are produced from LM2a via TS5. corresponding to the production of H2 z 2O2 and H2O z O3 The transition state TS5 (Fig. 2) has a six-member ring lie above the reactants at 74.2 and 5.2 kcal mol21 respectively. structure with C2v symmetry. This channel is exothermic The formation of the H O z 3O products is found to be the with an exothermicity of 5.6 kcal mol21. Apparently, this 2 2 2 most favorable channel in the self-reaction of HO2 with the channel is kinetically unimportant because of its higher barrier. transition state lying below the reactants by 0.5 kcal mol21. The rate constants for all the channels will be calculated and z H2O O3. In the intermediate LM3a, one of the terminal reported in the near future. H atom moves forward to the O atom attached to the other H atom to form a five-member-ring transition state TS6, followed by H2O elimination to form H2O and O3. The breaking O–O Acknowledgements and O–H bonds are 1.970 and 1.157 A˚ , which are 0.534 and 0.187 A˚ longer than those of in LM3a, respectively. The The authors are grateful for the support of this work by the relative energy of TS6 is 5.2 kcal mol21 above the reactants and Office of Naval Research, the US Navy, under the contract No. N00014-89-J-1494. the exothermicity for the production of O3 z H2Ois 32.8 kcal mol21 at the G2M level. The relatively high barrier for the formation O3 implies that this channel is unimportant at low temperatures. Our result is qualitatively consistent with References 70 experimental result of Niki et al. in which 2HO2 A 1 M. E. Jenkin, Proc. EUROTRAC Symp. 98: Transp. Chem. O3 z H2O channel was determined to be less than 0.1% of the Transform. Troposphere, ed. P. M. Borrell and P. Borrell, WIT total reaction. Press, Southampton, 1999, vol. 1, pp. 33–42. 2 A. Roger, Atmos. Environ., 2000, 34, 2063. 3 C. A. Taatjes and D. B. Oh, Appl. Opt., 1997, 36, 5817. Isomerization of the HO4H chain intermediates. The HO4H 4 M. J. Kurylo, P. A. Ouellette and A. H. Laufer, J. Phys. Chem., chain intermediates can isomerize to each other through the 1986, 90, 437. rotation of the HO2 group along the newly formed O–O bond. 5 R. Simonaitis and J. Heicklen, J. Phys. Chem., 1982, 86, 3416. TS7 is the isomerization transition state with Cs symmetry 6 S. P. Sander, M. Peterson and R. T. Watson, J. Phys. Chem., 1982, between LM1a and LM2a; the barrier of this process lies 86, 1236. 8.6 kcal mol21 below the reactants. In TS7, the noticeable 7 H. Niki, P. D. Maker, C. M. Savage and L. P. Breitenbach, Chem. Phys. Lett., 1980, 73, 43. changes are that the bridging O–O bond increases by about 8 S. L. Stephens, J. W. Birks and R. J. Glinski, J. Phys. Chem., 1989, 0.2 A˚ and the O–O bond in the HO2 group decreases by about 93, 8384. 0.08 A˚ compared with those in LM1a and LM2b. TS8 9 R. J. Glinski and J. W. Birks, J. Phys. Chem., 1985, 89, 3449. corresponds to the transition state for the isomerization of 10 R. R. Baldwin, C. E. Dean, M. R. Honeyman and R. W. Walker, 21 J. Chem. Soc., Faraday Trans., 1984, 80, 3187. LM2a and LM3a with C1 symmetry; it has only 3.2 kcal mol isomerization barrier. The final rotational transition state is 11 K. A. Sahetchian, A. Heiss and R. Rigny, J. Phys. Chem., 1987, 91, 2382. TS9 which connects LM1a and LM3a with an isomerization 21 12 J. Sehested, J. T. 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