The reaction of methyl peroxy and hydroxyl radicals as a major source of atmospheric methanol

Methyl peroxy, a key radical in tropospheric chemistry, was recently shown to react with the hydroxyl radical at an unexpectedly high rate. Here, the molecular reaction mechanisms are elucidated using high-level quantum chemical methodologies and statistical rate theory. Formation of activated methylhydrotrioxide, followed by dissociation into methoxy and hydroperoxy radicals, is found to be the main reaction pathway, whereas methylhydrotrioxide stabilization and methanol formation (from activated and stabilized methylhydrotrioxide) are viable minor channels. Criegee intermediate formation is found to be negligible. Given the theoretical uncertainties, useful constraints on the yields are provided by atmospheric methanol measurements. Using a global chemistry-transport model, we show that the only explanation for the high observed methanol abundances over remote oceans is the title reaction with an overall methanol yield of ∼30%, consistent with the theoretical estimates given their uncertainties. This makes the title reaction a major methanol source (115 Tg per year), comparable to global terrestrial emissions.

Oct./Nov. 1996 6 (diamonds). Itinerary used for sampling model results ( Supplementary Fig. 9) is from Figure 1 in Weller et al. 6 (adopting the 1994 itinerary leads to similar results). The HPLC measurements from the 1996 cruise were excluded since those data showed very high sample-to-sample variability. Inclusion of the HPLC data would not alter the conclusions from these comparisons. Model results for simulations A (dark blue), B (green), and C (red) defined in Table 4 of main article. For CH 3 OOH, the dashed red line corresponds to simulation C_VR, similar to C, adopting the lower measured rate constant for CH 3 OOH+OH (see text). The measurements averaged on 2° latitude bins are shown as the dashed black line.   Figure 14 for information on the aircraft campaigns. The measured and modelled HCOOH (pptv) are averaged in 1-km altitude bins. Formic acid was measured by ion chromatography 15 with estimated precision and accuracy of 15% and a detection limit of 10-31 pptv 16 . The model includes HCOOH formation from the OH-reaction of vinyl alcohol, the latter being formed from the photo-tautomerization of acetaldehyde as implemented in Peeters et al. 17 The number of measurements at each altitude bin is indicated on the right of each plot. Error bars represent the standard deviations of the measurements. The average biases are also indicated inset.  150  853  843  820  791  801  789  755  306  608  686  1029  1027  1024  1022  1013  1009  1007  1053  1036  1016  1149  1149  1149  1150  1146  1145  1145  1178  1159  1148  1293  1290  1287  1284  1282  1279  1277  1275  1274  1273  1364  1366  1367  1368  1371  1373  1372  1363  1367  1369  1395  1396  1397  1398  1395  1395  1396  1420  1409  1401  1513  1509  1486  1472  1471  1475  1473  1473  1471  1469  1548  1515  1513  1513  1516  1519  1517  1507  1514  1517  2952  2956  2959  2960  2960  2959  2959  2964  2960  2957  3033  3039  3038  3037  3035  3034  3034  3023  3029  3030  3096  3103  3098  3094  3090  3086  3084  3086  3083  3081  3661  3594  3641  3662  3674  3687  3691  3693  3693  3693 CCSD(T)-F12 relative energies with inclusion of ZPE ( kcal mol -1 ) -10.5 -10.  Table 4. Only measurements over oceans were considered. See Supplementary Figure 9 for more information on the measurements. n is the number of measurements per campaign. The mean bias factor is the geometrically averaged ratio of modelled to observed averages, and the discrepancy factor is the geometrically averaged ratio of the higher to the lower among the modelled and observed averages, as also defined as in Table 5 Figure 9 for more information on the measurements. n is the number of measurements per campaign. The mean bias factor is the geometrically averaged ratio of modelled to observed averages, and the discrepancy factor is the geometrically averaged ratio of the higher to the lower among the modelled and observed averages, as also defined as in Table 5  With careful exploration, we located two transition states for TS1 at M062x-D3/6- in each case the first two states correspond to the two Jahn-Teller states within the CH 3 O moiety, with HO 2 in its ground state, and the two others correspond to the two Jahn-Teller states of CH 3 O, with HO 2 in its excited state. Since these two higher states are much higher in energy, it is reasonable to consider the spin-orbit coupling of these two lower states of each multiplicity. Here we assume that the lowest singlet and second-lowest singlet as well as the lowest triplet and second-lowest triplet can interconvert readily due to the Jahn-Teller effects.

Supplementary
Now, the first singlet and triplet are degenerate, so the 1 PC minimum is effectively also the 3 PC minimum. So they can interconvert without a barrier. One very rough estimate of the rate constant for interconversion is to simply calculate the frequency associated with the coupling matrix element, as this corresponds to the frequency of Rabi cycling oscillation between the two states. However, because these two states both correspond to the same Jahn-Teller state of the CH 3 O fragment (and the same state of the HO 2 system), then there is almost no spin-orbit coupling (SOC) between them, it comes out as about 0.4 cm -1 . There will also be some contribution from spin-spin coupling, but that will be also small.
However, the spin-orbit coupling between the lowest singlet state and the second-lowest triplet state (or between the second-lowest singlet and the lowest triplet) is expected to be much larger, as there is now an orbital angular momentum difference. Indeed, we find a coupling matrix element of 58 cm -1 in both cases. In reality, there will be some kind of barrier needing to be crossed to go from the minimum of the lowest singlet state in 1 PC to a region where the second triplet state is degenerate with it.
 We can estimate the rate for the interconversion of 1 PC and 3 PC in several ways: (a) The MECP was optimized between 1 PC and 3 PC at the M06-2X-D3 level. This lies about 0.5 kcal mol -1 above 1 PC. However, this is the MECP between the lowest singlet and the lowest triplet. This is not exactly what we want to couple the lowest singlet state and the secondlowest triplet state (or between the second-lowest singlet and the lowest triplet).
(b) The second-lowest triplet and the second-lowest singlet lies 6.9 kcal mol -1 and 7.1 kcal mol -1 above the lowest singlet, respectively. Assuming harmonic potential energy surfaces, and knowing that all these states in fact correlate to the lowest singlet or triplet, we can guesstimate that the structure where the two lowest singlets and two lowest triplets are roughly degenerate will lie at about a quarter of the splitting, so at about 1.7 kcal mol -1 .
(c) The energy of the conical intersection between 2 A' and 2 Aʺ states in methoxy is about 0.5 kcal mol -1 above the minima with a spin-orbit coupling constant of 160 cm -1 20 . But in this case, there is a hydrogen bond (donated by HO 2 ) that splits the states a bit more.
Using a conservative relative energy for the 'true' MECP of 3 kcal mol -1 above the 1 PC minimum, using the slopes of the singlet and triplet PESs at the 1 PC/ 3 PC MECP, and the SOC of 58 cm -1 between the lowest singlet/second-lowest triplet, and an internal energy above the minimum of 1 PC of 4400 cm -1 , corresponding to 12.5 kcal mol -1 above 1 PC, corresponding to the relative energy of this point at the CCSD(T)-F12 level (-10.5 kcal mol -1 ) + the ~2 kcal mol -1 of thermal energy in reactants, we can estimate the rate constant for 1 PC → 3 PC conversion, using the non-adiabatic RRKM theory method developed by J. N. Harvey [21][22][23] . We get 3.4 x 10 12 s -1 , which is very close to the value given by Rabi-cycling method.
 Now, this value is subject to many approximations and assumptions. Some of these we can test, some we cannot: (a) We assume that the NA-RRKM works (and that e.g. centrifugal effects are unimportant, the NA-RRKM is not J-resolved).
(b) We assume that the 'true' MECP lies about 3 kcal mol -1 above 1 PC. Here we can test this by changing the energy: raising the MECP or lowering it by 1 kcal mol -1 (keeping other parameters the same) decreases/increases the rate by about a factor of 2.
(c) We assume that the slopes on the potential energy surfaces at the correct MECP are similar to those at the incorrect, lowest-singlet-lowest-triplet MECP. The calculated rate constant obtained by making quite drastic changes to these slopes (factor of four change in slopes) also changes by about a factor of 2-3.
(d) We assume that the frequencies for the correct MECP are about the same as we get for the incorrect MECP.
On the basis of the convergence of the simple Rabi-cycling model, and NA-RRKM calculations, and their relative insensitivity to input parameters, we can be fairly confident that the rate-constant 1 PC → 3 PC at the internal energy for the reaction conditions is about 3 × 10 12 s -1 with uncertainty by a factor of 2~3.

Supplementary Note 3: Frequencies of the structures along the PC dissociation pathway
For the variational RRKM calculations, we used the raw frequencies obtained from diagonalization of the Hessian at the structures obtained from a relaxed scan by constraining the dissociative coordinate (the O-H hydrogen bond in product complex, see Fig. 2). This leads to a total of 24 eigenvalues and eigenvectors at each point. Along the scan, the structures do not correspond to stationary points, so the frequencies and eigenvectors are not necessarily meaningful. Careful inspection of the eigenvectors shows however that they follow the physically-expected behaviour: 3 eigenvectors clearly correspond to translation of the whole system, 3 others clearly correspond to overall rotation, and one corresponds to the reaction For this reason, we used the unprojected frequencies for calculating the ZPVE to avoid the artificial initial discontinuity of -2.5 kcal mol -1 relative to the equilibrium ZPVE of the PC when using the projected frequencies. Second, for this specific case, it is mainly the OO-H stretch mode in the HO 2 moiety that leads to changes between unprojected and projected frequencies, as this mode has an important component along the RC at the early stages but not anymore in the "TS" region itself, and that anyway, near the TS, the H-O 2 stretch mode with its 10 kcal mol -1 quantum cannot be active at our low total distributable energy of only 8 ~ 9 kcal mol -1 . For these reasons, we used the unprojected frequencies for both the G and ZPVE in the k diss calculations. Note that in the region of the variational TS, the unprojected and projected frequencies are in fact very similar to one another. We calculated the two k diss also using projected frequencies for ZPVE and G str (E v -E str ), finding k diss values only 12 +/-3 % higher and a direct methanol yield only about 10% lower compared to the values using unprojected frequencie.

Supplementary Note 4: Sinks of stabilized trioxide CH 3 OOOH
The important sinks for stabilized CH 3 OOOH in the troposphere are likely: (i) thermal decomposition, (ii) gas-phase reaction with OH, (iii) gas-phase reaction with water dimer, and (iv) uptake by wet aerosol and cloud droplets (not necessarily in that order): (i) Reaction (i) is the thermal analogue of conversion of TRIOX to 1 PC followed by 1 PC dissociation into CH 3 O + HO 2 or decomposition into CH 3 OH +O 2 , discussed in the Kinetics Results subsection. The thermal rate coefficient for the rate limiting step TRIOX → 1 PC was evaluated by TST theory in the harmonic oscillator approximation using the energy and vibration/rotation data computed in this work: k (i) (thermal) = 1. (ii) The CH 3 OOOH + OH reaction is expected to proceed through a very stable, doubly-Hbonded 6-ring pre-reaction complex and a submerged TS, the latter also in view of the ~38 kcal mol -1 exothermicity of the abstraction of the terminal H, and should result finally in CH 3 O + O 2 + H 2 O 25 . By analogy with CH 3 CHO + OH, with similar energetics and similar though less stable pre-reactive complex, the rate coefficient at 298 K can be roughly estimated at k (ii) (298 K) = 2×10 -11 cm 3 s -1 molecule -1 .
(iii) The reaction of CH 3 OOOH with water dimer, by analogy with HOOOH + (H 2 O) 2 , is expected to proceed likewise through a very stable pre-reactive complex followed by a double H-shift through a TS lying about 5 kcal mol -1 above the reactants, to result in formation of CH 3 OH + O 2 + 2 H 2 O 26 . Adopting a pre-factor equal to that for the analogous double-H-shift in the vinyl alcohol + formic acid reaction 16 , the rate coefficient can be roughly estimated at 3×10 -15 ×exp(-2500/T) cm 3 s -1 molecule -1 .
(iv) Given its ability to form stable, multiple H-bonded complexes with H 2 O and H 2 O clusters 26,27 , CH 3 OOOH should be highly hydrophilic and be readily taken up by aqueous aerosols and cloud droplets with an uptake coefficient of order 0.1, followed by its liquid-phase decomposition into CH 3 OH + O 2 26,27 .

Supplementary Note 6: The average thermal energy < E th,v > and the energy distribution of formation F(E th,v )
The thermal energy of the reactants at 298 K is made up of ~1.1 k B T vibration energy of