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 hydrogen-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 radical, 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 combustion 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 molecules, 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 .