New Measurements and Calculations on the Kinetics of an Old Reaction: OH + HO2 → H2O + O2

Literature rate coefficients for the prototypical radical–radical reaction at 298 K vary by close to an order of magnitude; such variations challenge our understanding of fundamental reaction kinetics. We have studied the title reaction at room temperature via the use of laser flash photolysis to generate OH and HO2 radicals, monitoring OH by laser-induced fluorescence using two different approaches, looking at the direct reaction and also the perturbation of the slow OH + H2O2 reaction with radical concentration, and over a wide range of pressures. Both approaches give a consistent measurement of k1,298K ∼1 × 10–11 cm3 molecule–1 s–1, at the lowest limit of previous determinations. We observe, experimentally, for the first time, a significant enhancement in the rate coefficient in the presence of water, k1,H2O, 298K = (2.17 ± 0.09) × 10–28 cm6 molecule–2 s–1, where the error is statistical at the 1σ level. This result is consistent with previous theoretical calculations, and the effect goes some way to explaining some, but not all, of the variation in previous determinations of k1,298K. Supporting master equation calculations, using calculated potential energy surfaces at the RCCSD(T)-F12b/CBS//RCCSD/aug-cc-pVTZ and UCCSD(T)/CBS//UCCSD/aug-cc-pVTZ levels, are in agreement with our experimental observations. However, realistic variations in barrier heights and transition state frequencies give a wide range of calculated rate coefficients showing that the current precision and accuracy of calculations are insufficient to resolve the experimental discrepancies. The lower value of k1,298K is consistent with experimental observations of the rate coefficient of the related reaction, Cl + HO2 → HCl + O2. The implications of these results in atmospheric models are discussed.


S1 Instrument Schematics
Figure S1a shows a schematic of the high pressure cell and OH observation cell. Further details can be found in Stone et al. 1 and Speak et al. 2 Figure S1a. Schematic of high-pressure reactor. The photolysis laser illuminates the reactor (green, and which can be heated), where the reaction zone is defined by the volume within ~1-2 mm of the pinhole. The OH is detected in the low-pressure cell, blue, within 1-2 cm of the pinhole where the probed gas is jetting. Figure S1b. A schematic of the adapted FAGE cell that allows for simultaneous OH kinetic measurement on the first OH detection axis, PMT-1, and HO 2 yield detection after titration of HO 2 to OH following the breakdown of the 'jet' on a second detection axis, PMT-2.
S3 Figure S2 shows a schematic of the conventional flash photolysis cell. Further details can be found in Onel et al. 3 or Glowacki et al. 4 Figure S2. Schematic of low-pressure reactor: the laser beams cross in the centre of the heated, multi-axes cell and defines the reaction zone where the OH is formed and monitored in situ, via detecting the fluorescence at right angles to the laser beams.

S2 Further details on ab initio calculations
The structures of the transition states found here were obtained using the same methodology for various levels of calculation, by first starting from structures far from the transition state and scanning the breaking and forming bonds. The peak in these scans was used as the input structure for the later transition state optimizations. In addition, transition state structures found with other methods were also used as the input guess structures. Any optimized transition state structures were assessed by IRC jobs to verify if they led to products and the pre reaction complex.
A range of DFT and post HF methods were used to calculate structures and high level single point energy calculations were performed on these structures (CCSD(T)/CBS(aug-cc-pvtz, aug-cc-pvqz, aug-cc-pv5z and jun-cc-pvtz, jun-cc-pvqz, jun-cc-pv5z). The results presented in this paper were for structures calculated with M06-2X using the triple zeta 6-311++g(3df,3pd) and aug-cc-pvtz basis sets carried out in Gaussian. Additional structures were found with UMP2 and the same triple zeta basis sets again in Gaussian and using restricted open shell MP2 in Molpro 2012 with the aug-cc-pvtz basis set. Differences between the structures for the transition states obtained with these different methods led us to evaluate the surface further with a series of further DFT functionals (B2PLYP-D3, BHandHLYP, wB97XD) and CCSD with the aug-cc-pvtz basis set. The CCSD calculations were performed in Gaussian for UCCSD and in Molpro 2012 for restricted open shell RCCSD. Again the structure and frequencies of the transition states differed with the pre reaction complex being well defined by all methods. Additional, CASSCF(14o,20e)/aug-ccpvtz calculations were performed in Molpro 2012 and the structure found by this was closest to the structure obtained at the RCCSD/aug-cc-pvtz than that found with UCCSD/aug-ccpvtz.
The resultant transition state structures could be broadly separated into two groups those with a shorter HO-H bond and more out of plane H-O-O-O dihedral and those with a longer HO-H bond and a flatter dihedral. Further exploration of the surface by using semi relaxed scans of both bond lengths and dihedrals to map out the surface showed that for each method evaluated the surface was not a smooth even surface as is common for many systems but had many troughs and peaks and discontinuities due to the methods utilised here not fully and accurately capturing the real behaviour of the system.
When the different structures were included in MESMER calculations QM rotors were utilised and QM tunnelling was accounted for in these calculations using the Eckhart model as described in the MESMER manual. The different rate coefficients derived from the differing surfaces varied by over an order of magnitude and covered the whole range of previous experimental measurements at 300 K. Table 2 in the main manuscript shows the variation in the low frequency vibrations in the PRC and TS that are significant in influencing the rate coefficient for the OH + HO 2 reaction as a function of the level of theory. Table S1 gives the complete set of vibrational frequencies. Table S1 -Full list of the vibrational frequencies of the TS and PRC for various levels of  theory   Vibration/cm -1  A  B  C  D  E  F  G  TS imaginary  -2658  -2020  -1387  -1524  -2441  -2521  -3162  TS ν1  251  110  205  101  397  395  292  TS ν2  520  195  388  164  503  493  566  TS ν3  742  458  551  475  693  694  736  TS ν4  775  656  857  640  770  773  765  TS ν5  1273  1113  1104  1133  1319  1336  1330  TS ν6  1410  1451  1310  1520  1387  1403 Figure S3 shows a series of traces in the high pressure system with increasing initial concentration of OH. The pseudo-first order rate coefficients from the individual fits to the traces show an increase of approximately 300 s -1 from the lowest to highest [OH] 0 in stark contrast to an increase of ~1000 s -1 in the fits to the simulated data based on the IUPAC data. Each photolysis pulse in the low pressure experiment should photolyse a fresh sample of gas and therefore there should be no secondary chemistry from the photolysis of any reaction products that could alter the observed rate coefficients. This is confirmed by the data shown below in Figure S4 where the reaction of OH with H 2 O 2 is followed under identical conditions, with the exception of the laser pulse repetition rates which were reduced from 10 to 2 Hz. The resulting two pseudo-first order rate coefficients are within experimental error, demonstrating a negligible influence of secondary chemistry from product photolysis. Figure S4. Variation in pseudo-first order rate coefficient as a function of laser repetition rate in the low pressure system. The red line shows the global fit to these particular traces based on the analysis of the full dataset of 47 traces, the yellow line is the exponential fit to the individual trace with the resulting pseudo-first order rate coefficient shown against each trace.

S4 HO 2 yield data
The high pressure system has the capability of observing HO 2 production via titration of HO 2 to OH by NO. The titration reaction occurs in the low pressure observation region following the break up of the jet; transport and titration time means that there is some loss of kinetic fidelity for pseudo-first-order kinetics greater than 3000 s -1 , however, the HO 2 yield should not be affected. Fitting the data gives identical HO 2 yields within experimental error, but Figure S5(b) show a Kintecus 5 simulation, where, with k 1 = 1.1 × 10 -10 cm 3 molecule -1 s -1 , the predicted HO 2 in the absence of methanol should be significantly lower.  Similar experiments were recorded over a range of conditions and the results are tabulated in Table S2.

S5 The H 2 O:HO 2 Complex
Key to calculations on the water mediated reaction of OH + HO 2 is ensuring that the initial H 2 O:HO 2 complex is correctly calculated. Figure S7 shows the PES and the structure of the complex calculated at the CCSD(T)/CBS//CCSD/6-311++g(3df, 3dp) level of theory. 6 The equilibrium constants calculated from this PES are in excellent agreement with those from Kanno et al. 7 as shown in Table S3.  Figure S8 shows an analogous plot to Figure 3  S6 Further comparison with previous literature on k 1 The main reactions contributing to the IUPAC evaluation of reaction 1 have been considered in the main text, however, there have been a number of other studies of reaction 1 which are considered below. Cox et al., 1981 9 , k 1 = (9.9 ± 2.5) × 10 -11 cm 3 molecule -1 s -1 -Molecular modulation methods were used, monitoring the absorption of HO 2 over a 1 s timescale. OH and HO 2 were generated via the photolysis of O 3 in the presence of up to 10 Torr of water where Δk 1 , the change in the OH + HO 2 reaction due to gas phase complexation of HO 2 and H 2 O could be up to to 8 × 10 -11 cm 3 molecule -1 s -1 . The reported value of k 1 is again dependent on the HO 2 recombination rate coefficient, itself water dependent, and a complex kinetic model. reported to range from 5.8 × 10 -11 cm 3 molecule -1 s -1 at 75 Torr total pressure and 1 Torr of water to 1.2 × 10 -10 cm 3 molecule -1 s -1 at 730 Torr total pressure and 5 Torr of water. According to Figure 3 in the main text, the presence of 5 Torr of water should produce a significant enhancement (Δk 1 = 4 × 10 -11 cm 3 molecule -1 s -1 ) in the rate coefficient. Data were interpreted in terms of a potential pressure dependence for reaction 1, but it is likely that the data were influenced by the water dependence of both the OH + HO 2 and the HO 2 recombination reactions. Reactions were carried out over several seconds and hence there is also a potential for heterogeneous effects.
Braun et al., 1982 11 , k 1 = (11.0 ± 3.0) × 10 -11 cm 3 molecule -1 s -1 -Again in this study VUV photolysis of water was used to generate OH and HO 2 , however, in this case via a time resolved process. OH was detected via resonance fluorescence and k 1 was extracted from a complex analysis varying the amount of O 2 present and hence the amount of H from the initial photolysis which is converted to HO 2 . Concentrations of water vapour used are significantly lower than in the De More study, typically ~0.4 Torr and hence will have a limited enhancement (<1 × 10 -11 cm 3 molecule -1 s -1 ) on the observed value of k 1 .
Dransfeld and Wagner, 1987 12 , k 1 = (6.0 ± 1.5) × 10 -11 cm 3 molecule -1 s -1 -Dransfeld and Wagner generated 18 OH and monitored via laser magnetic resonance in a flow tube with excess H 16 O 2 . They saw a factor two enhancement in the rate coefficient in comparison to the 16 16 OH which is (6.0 ± 1.5) × 10 -11 cm 3 molecule -1 s -1 . As with all other studies, there is a careful analysis of potential errors. Water is used in the generation of OH, but at concentrations that will provide an insignificant enhancement of k 1 .
We have no explanation of the difference between this work and Dransfeld and Wagner, but we do note that pseudo-first-order rate coefficients are around 30 s -1 , so there is potential for heterogeneous chemistry to contribute to radical loss processes.
In summary the four previous studies discussed above provide results in stark contrast to the direct measurements of this work. Water dependence could account for the differences in the DeMore and Cox studies as water vapour concentrations were significant in these studies. Although water was used as a precursor in the studies of Dransfeld and Wagner and Braun et al., water was present at such low concentrations that it could not have contributed through gas phase complexation of HO 2 , but reactions were carried out under conditions where heterogeneous processes could have contributed. In all studies, k 1 has been extracted from complex and from relatively slow chemistry enhancing the potential for secondary chemistry or other systematic issues. Of course, as stated in the main text, we cannot rule out the potential for unknown systematic errors in our work. i) Grain size -in a master equation, energies of the species are divided into grains. The smaller the grain size, the more accurate, but also, more expensive the calculation is. Table  S4a shows the variation in k 1 with grain size. Our calculations typically use a 50 cm -1 grain size which is a good compromise between precision and computational cost.  iii) Low frequency vibrations in the transition state -Densities of states and state counts required for RRKM calculations are strongly influenced by the lowest frequency vibrations. Indeed, whether a motion is treated as a vibration or a hindered rotor, can have a significant effect. Table S4c shows the variation in k 1 as the lowest vibrational frequency for the transition state calculated by Burke et al. (121 cm -1 ) is either halved or doubled. As would be expected, decreasing the vibrational frequency increases the number of states accessible in the transition state and hence increases k 1. iv) -Imaginary frequency - Table S4d shows the variation in k 1 is the imaginary frequency. The range has been chosen deliberately to be so wide, reflecting the magnitude of the variation in the imaginary frequency as shown in Table 2. There is a significant effect, with the reaction being enhanced by a higher imaginary frequency. In summary, individually varying the barrier height, low frequency vibrations and imaginary frequency of the Burke et al. calculations input into MESMER can vary k 1 from 2.1 -10.5 x 10 -11 cm 3 molecule -1 s -1 . Figure S9 summarizes the impact of varying the lowest frequency vibration and imaginary frequency on k 1 . A similar variation is observed if we vary the parameters generated by the Method A in a similar fashion, although this variation will be centred around a lower value as our barrier is lower than that of Burke et al. Essentially, anything that increases the state count at the transition state (a lower barrier height or lower vibrational frequencies in the transition state) will increase k 1 . The sensitivity of the MESMER calculations to the barrier height and transition state frequencies mean the uncertainties in these parameters translate into calculated rate coefficients which can span all experimental determinations of k 1 .  Figure S10 shows the triplet potential energy surface for the reaction of Cl + HO 2 .

S8 Details on the Cl + HO 2 → HCl + O 2 reaction
Qualitatively the PES is similar to the OH + HO 2 reaction with the formation of a pre-reaction complex and a submerged barrier for abstraction. The reaction is known to also produce OH + ClO, but as can be seen from Figure S10, this will occur on the singlet surface via the formation of an HOOCl intermediate, analogous to the null reaction via HOOOH on the singlet surface for the OH + HO 2 system. Figure S10. Triplet potential energy surface for the Cl + HO 2 reaction carried out using Gaussian 09 at various levels of theory.
Examples of previous studies on the Cl + HO 2 reaction are given in the table below.