Chinese Journal of Chemical Physics  2019, Vol. 32 Issue (4): 457-466

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Sai-nan Wang, Run-run Wu, Li-ming Wang

Role of Hydrogen Migrations in Carbonyl Peroxy Radicals in the Atmosphere

Chinese Journal of Chemical Physics, 2019, 32(4): 457-466

http://dx.doi.org/10.1063/1674-0068/cjcp1811265

### Article history

Accepted on: February 20, 2019
Role of Hydrogen Migrations in Carbonyl Peroxy Radicals in the Atmosphere
Sai-nan Wanga,b , Run-run Wua , Li-ming Wanga,c
Dated: Received on November 22, 2018; Accepted on February 20, 2019
a. School of Chemistry & Chemical Engineering, South China University of Technology, Guangzhou 510640, China;
b. State Key Laboratory of Organic Geochemistry and Guangdong Key Laboratory of Environmental Protection and Resources Utilization, Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, Guangzhou 510640, China;
c. Guangdong Provincial Key Laboratory of Atmospheric Environment and Pollution Control, South China University of Technology, Guangzhou 510006, China
Abstract: Carbonyl peroxy radicals (RC(O)O$_2$) are the ubiquitous radical intermediates in the atmospheric oxidation of volatile organic compounds. In this work, theoretical studies are carried out to explore the role of the unimolecular H-migration in the carbonyl peroxy radicals by using quantum chemistry and kinetics calculations. The results showed that H-migration could be significant in the atmosphere at least in CH$_3$CH$_2$CH$_2$C(O)O$_2$ and (CH$_3$)$_2$CHCH$_2$C(O)O$_2$ with rates of ~0.012 and ~0.58 s$^{-1}$ at 298 K. Subsequent reactions of CH$_3$CHCH$_2$C(O)OOH would lead to the products with multi-functional groups, which might affect the aerosol formation process; while (CH$_3$)$_2$CCH$_2$C(O)OOH would transform to formaldehyde and acetone in a few steps. These processes would be important for the atmospheric modelling of volatile organic compounds under low-NO$_x$ conditions.
Key words: Carbonyl peroxy radical    H-migration    Atmospheric oxidation
Ⅰ. INTRODUCTION

Carbonyl compounds are ubiquitous components in the atmosphere, such as aldehydes and ketones, which are key intermediates in the atmospheric oxidation of volatile organic compounds (VOCs) and play important roles in atmospheric chemistry [1, 2]. The ambient sources of carbonyl compounds include the primary emission from exhausts of motor vehicles, incomplete combustion of hydrocarbons, and particularly the secondary formation in the atmospheric oxidation of hydrocarbons. Photo-oxidation of carbonyl compounds produces intermediate carbonyl radicals (RCO) in the reactions of aldehydes with free radicals such as OH, NO$_3$, Cl, and Br, $etc.$ or in photolysis of carbonyl compounds:

 $\begin{eqnarray*} & & \rm{CH}{_3}\rm{CHO}+\rm{OH} \rightarrow \rm{CH}{_3}\rm{CO}+\rm{H}{_2}\rm{O} \\ & & \rm{CH}{_3}\rm{C(O)CH}{_3} + {h\nu} \rightarrow \rm{CH}{_3}\rm{CO}+\rm{CH}{_3} \end{eqnarray*}$

In the reaction of CH3CHO, the formation of CH3CO radical accounts for ~97% of the branching ratio; while in the photolysis of acetone, the quantum yield of CH3CO is ~20% (the rest ~80% is deactivated by collision) at atmospheric pressure at 300 nm [3, 4]. In the atmosphere, RCO radical would recombine with O$_2$ rapidly to form carbonyl peroxy radicals RC(O)O$_2$:

 $\begin{eqnarray*} \rm{CH}{_3}\rm{CO}+\rm{O}{_2}+\rm{M} \rightarrow \rm{CH}{_3}\rm{C(O)OO}+\rm{M} \end{eqnarray*}$

The peroxy radical CH$_3$C(O)O$_2$ is also an important intermediate in the low-temperature combustion of fossil fuels where the energetic RO$_2 $$^* could undergo a consecutive unimolecular isomerization and decomposition as RO _2$$ \rightarrow$QOOH$\rightarrow$product$+$OH [5, 6]. OH radical is recycled in this process.

The reaction of CH$_3$CO with O$_2$ has been the subject of a few studies, covering a range of temperature, pressure, and bath gas [7-15]. These studies have focused on the formation of OH radical at reduced pressures (up to 500 mbar in helium) and elevated temperatures in the interest of fuel combustion. Generally, the OH production increases as temperature increases because of the high barrier for isomerization CH$_3$C(O)O$_2$$\rightarrowCH_2C(O)OOH. At room temperatures, the yield of OH radical is well below 1% when extrapolated to the atmospheric pressures [11, 12, 16, 17]. Under the tropospheric conditions, CH_3C(O)O_2$$^*$ is stabilized by collision and would have significant bimolecular reactions with other trace radicals such as NO, NO$_2$, and HO$_2$/RO$_2$ with rate coefficients of $\sim$2.0$\times$10$^{-11}$, $\sim$1.1$\times$10$^{-11}$, and (2.1$\pm$0.4)$\times$10$^{-11}$ cm$^3$$\cdotmolecule^{-1}$$\cdot$s$^{-1}$ for NO, NO$_2$, and HO$_2$, respectively [18]. The reaction with NO$_2$ is particularly important because of the formation of peroxyacetyl nitrate (PAN), which is stable enough to transport from NO$_x$-emission sites to downwind areas, representing a transport of pollution from polluted urban regions to relatively clean suburban regions. Under the low-NO$_x$ conditions, reaction with HO$_2$ radical becomes more important, resulting in the formation of CH$_3$C(O)OOH or CH$_3$C(O)O$+$OH, of which the former would also lead to OH formation upon its photolysis in the atmosphere [19].

The unimolecular H-migration RO$_2$$\rightarrowQOOH, while being important in combustion, is usually ignored in the atmospheric oxidation of VOCs because of its endothermicity and high barriers, e.g., for CH_3C(O)O_2$$\rightarrow$CH$_2$C(O)OOH, the reaction energy ($\Delta$$E$$_\rm{0\hspace{0.05cm}K}$) and barrier height (${{{\Delta}E}_\rm{0\hspace{0.05cm}K}}^{\neq}$) were predicted as 11.8 and 125.1 kJ/mol at G3X level [9]. However, the barrier heights for H-migration could be reduced for larger R-groups. In CH$_3$CH$_2$C(O)OO, the barrier height reduces to 113 kJ/mol for the similar H-migration to CH$_3$CHC(O)OOH via a five-membered-ring transition state, and the barrier height of 99 kJ/mol for H-migration to CH$_2$CH$_2$C(O)OOH via a six-membered-ring transition state is even lower [17]. Hou and Wang [20] found similar trend in CH$_3$CH$_2$C(O)OO. H-migration via six-membered-ring transition state has a lower barrier because the ring is less constrained. We would reasonably expect the even lower barriers for H-migrations via six-membered-ring transition state with more alkyl substitution in RC(O)O$_2$ radicals, allowing the H-migration to compete with their bimolecular reactions in the atmosphere. Recent laboratory studies have shown that the H-migration in the peroxy radicals could be important in the atmospheric autoxidation of a few important VOCs [21-26]. Field study also suggested the importance of autoxidation via H-migration in urban and suburban atmosphere [26], especially when the concentrations of NO/HO$_2$ are low and the bimolecular reactions no longer dominate the fate of RO$_2$ radicals. The elusive QOOH radical was also detected experimentally under low oxygen concentrations when the Q-group was resonance-stabilized in QOOH radical [27]. However, no information is available so far on the role of H-migration in RC(O)O$_2$ radicals in the atmosphere. A recent study showed that the hydrogen shift (H-shift) reactions could occur in hydroperoxy acylperoxy radicals as HOOCH$_2$C(O)OO$\rightarrow$OOCH$_2$C(O)OOH, which would be an important reaction pathway in competition with bimolecular reactions [28].

In this work, we carried out a systematic theoretical study on carbonyl peroxy chemistry using quantum chemistry and kinetics calculations. H-migrations in a few short-chain RC(O)O$_2$ radicals were investigated to examine the effect of alkyl substitution. An additional reaction pathway was suggested for RC(O)O$_2$ radicals in the atmosphere.

Ⅱ. THEORETICAL METHODS

All the molecular structures were optimized at the DFT-M06-2X/6-311++G(2df, 2p) level, which was found to be adequate for thermochemical and kinetics study [29]. Each transition state has one imaginary frequency associating with the reaction coordinate. The optimized structures were submitted to single-point energy calculation using the complete basis set model chemistry with restricted (ROCBS-QB3) [30] and unrestricted (UCBS-QB3) [31] wave functions and explicitly correlated coupled-cluster theory at RHF-RCCSD(T)/F-12a/cc-pVDZ-F12 level (F12) [32, 33]. The calculations based on RHF-wavefunction in ROCBS-QB3 eliminate the empirical correction term due to spin contamination appearing in UCBS-QB3 calculations for open-shell species. This is important for the calculations of a few transition states. The quality of electron correlation of F12 here is better than that in standard CCSD(T)/cc-pVQZ [34]. The values of $T_1$-diagnostic in CCSD calculations were checked for the multi-reference nature of the wavefunction and for the validity of CCSD(T) calculations using single-reference wavefunctions [35]. The M06-2X and CBS calculations were carried out using the Gaussian 09 package [36] and F12 ones using Molpro 2015 package [37, 38].

The reaction kinetics and pressure dependence of rate coefficients were obtained by calculations coupling the unimolecular rate theory and collisional energy transfer through the master equation (RRKM-ME) [39]. The calculations were carried out using the MESMER code [40], in which the RRKM theory was used for $E$-resolved microcanonical rate $k$($E$) for processes with 'well-defined' transition states, and the inverse Laplace transform (ILT) method was used for the microcanonical rate $k$($E$) for the barrierless dissociation of RC(O)O$_2$ to RCO$+$O$_2$ with a fixed recombination rate coefficient [39, 41]. A high-pressure limit rate coefficient of 6$\times$10$^{-12}$ cm$^3$$\cdotmolecule^{-1}$$\cdot$s$^{-1}$ was used for all RCO$+$O$_2$ reactions. The single exponential-down model was used to approximate the collisional energy transfer. The collisional parameters of radicals were estimated by the method of Gilbert and Smith [42] and the tunneling correction factors were included to $k$($E$) by the method of Miller [43]. Collisional parameters $\sigma$ and $\varepsilon$ were: 2.55 Å and 10.2 cm$^{-1}$ for helium, 3.9 Å and 48.0 cm$^{-1}$ for N$_2$, 5.6 Å and 500 cm$^{-1}$ for C$_2$H$_5$C(O)O$_2$ and QOOHs, 6.0 Å and 530 cm$^{-1}$ for C$_3$H$_7$C(O)O$_2$ and QOOHs, and 6.33 Å and 545 cm$^{-1}$ for C$_4$H$_9$C(O)O$_2$ and QOOHs. Internal rotations, when free in reactant and frozen in transition state, were treated as hindered rotors. Potential energy profiles for the internal rotations were fitted to truncated cosine and sine functions. As being implemented in MESMER, the energy levels of the internal rotations were obtained by numerically solving their Schrödinger equations using the Fourier Grid Hamiltonian (FGH) method [44], and were then used for the calculation of density/sum of state of the species in RRKM calculations.

Ⅲ. RESULTS AND DISCUSSION A. Potential energy surfaces and prompt OH formation

The reaction of CH$_3$CO and O$_2$ has been studied extensively for the interest of fuel combustion. The reaction proceeds by addition and H-migration from C$_\alpha$ through a five-membered-ring transition state (TS5-A) to form Q5OOH-A, and then decomposition through a transition state TSQ5-A to a lactone-3-A product (3 is the number of the lactone ring members) and an OH radical as:

Under low pressures and high temperatures, RC(O)O$_2$ from the recombination contains high enough energy to isomerize and decompose promptly before being thermalized by collisions. For larger RC(O)O$_2$, the –OO group might also take an H-atom from the C$_\beta$/C$_\gamma$-position through a six/seven-membered-ring transition state (TS6/TS7), forming a radical denoted as Q6OOH/Q7OOH. The Q6OOH/Q7OOH would further isomerize and decompose to (substituted) propio-/butyro-lactone (lactone-4/-5) and an OH radical through transition states TSQ6/TSQ7,

The yields of prompt OH formation in reactions of CH$_3$CO and CH$_3$CH$_2$CO with O$_2$ under reduced pressures (up to $\sim$0.5 bar in helium) and elevated temperatures have been measured in previous studies [7-16]; however, it was also found that the OH yields approached zero at room temperature and atmospheric pressure for both CH$_3$CO and CH$_3$CH$_2$CO radicals. No previous information is available for the OH formation in the reaction of other RCO radicals. Here we examined several RCO radicals using theoretical calculations. Table S1 (see supplementary materials) lists the relative energies of intermediates, transition states, and products at UCBS-QB3, ROCBS-QB3, and F12 levels for the reactions. Generally, UCBS-QB3 and F12 agreed within 4 kJ/mol, while ROCBS-QB3 predicted lower barrier heights. In this study, we used energies at F12 level for discussion and for kinetics calculations if not otherwise stated, because the CCSD calculations in F12 usually have their values of $T_1$-diagnostic less than 0.025 for the transition states (Table S1 in supplementary materials). Conversely, the values of $T_1$-diagnostic in those of U/ROCBS-QB3 were usually higher than 0.03 for TSQ5 and TSQ6. FIG. 1 shows the potential energy surfaces for H-migrations and subsequent decomposition to lactone and OH radical for the reactions of CH$_3$CO, CH$_3$CH$_2$CO, CH$_3$CH$_2$CH$_2$CO, and (CH$_3$)$_2$CHCH$_2$CO with O$_2$ at F12 level.

 FIG. 1 Potential energy surfaces at RHF-RCCSD(T)-F12a/cc-pVDZ-F12 level for reactions of O$_2$ with RCO radical for CH$_3$CO (A), CH$_3$CH$_2$CO (B), CH$_3$CH$_2$CH$_2$CO (C), and (CH$_3$)$_2$CHCH$_2$CO (D).

The alkyl substitution in R-group might affect the kinetics of reactions between RCO radicals and O$_2$ by lowering the barrier heights for the intramolecular H-migrations. Upon successive methyl substitution, the barrier height for H-migrations in RC(O)O$_2$ radicals decreases gradually, $e.g.$, from 122.2 kJ/mol via 108.7 kJ/mol to 93.2 kJ/mol for H-migration from C$_\alpha$ in CH$_3$C(O)O$_2$, CH$_3$CH$_2$C(O)O$_2$, and (CH$_3$)$_2$CHC(O)O$_2$, or from 99.6 kJ/mol via 84.6 kJ/mol to 73.4 kJ/mol for H-migration from C$_\beta$ in CH$_3$CH$_2$C(O)O$_2$, CH$_3$CH$_2$CH$_2$C(O)O$_2$, and (CH$_3$)$_2$CHCH$_2$C(O)O$_2$. For H-migrations from C$_\alpha$ via C$_\beta$ to C$_\gamma$ through five-, six- and seven-membered-ring transition states, their barrier heights decrease gradually due to the decreased ring strain energy, $e.g.$, from 109.2 kJ/mol via 86.7 kJ/mol to 79.8 kJ/mol in CH$_3$CH$_2$CH$_2$CH$_2$C(O)O$_2$ for H-abstractions from C$_\alpha$, C$_\beta$, and C$_\gamma$ which are all secondary carbons, even though the Q5OOH radicals are resonance stabilized (Table S1 in supplementary materials). For the decompositions Q$n$OOH$\rightarrow$lactone$+$OH, alkyl substitution to the carbon radical center also reduces the barrier height (TSQ$n$, relative to Q$n$OOH), $e.g.$, from 95.4 kJ/mol via 89.7 kJ/mol to 82.5 kJ/mol in Q5OOH for Q5$=$ –CH$_2$C(O), –CH(CH$_3$)C(O), and –C(CH$_3$)$_2$C(O), and from 81.9 kJ/mol via 69.5 kJ/mol to 59.7 kJ/mol in Q6OOH for Q6$=$–CH$_2$CH$_2$C(O), –CH(CH$_3$)CH$_2$C(O), and –C(CH$_3$)$_2$CH$_2$C(O), respectively.

Prompt OH formation depends obviously on some parameters including reaction energies and barrier heights, the $\langle $${\Delta}E$$ \rangle $$_\rm{Down} in modeling of collisional energy transfer, and the internal rotations etc . FIG. S1 (see supplementary materials) shows the OH formation yield in the reaction of CH _3 CH _2 CO and O _2 at 298 K and at low pressures using helium or N _2 as buffer gas from RRKM-ME calculations with different values for \langle$$ {\Delta}E $$\rangle$$ _\rm{Down}$, along with the available experimental values. The predicted OH yields, in helium buffer with $\langle $${\Delta}E$$ \rangle $$_\rm{Down} = 0 cm ^{-1} , agree excellently with the experimental values by Zügner et al. [11] while being much lower than the values by Baeza-Romero et al . [16]. Increasing \langle$$ {\Delta}E $$\rangle$$ _\rm{Down}$ to 200 cm$^{-1}$ for helium buffer gas resulted in underestimation of OH yields. A $\langle $${\Delta}E$$ \rangle $$_\rm{Down} of 100 cm ^{-1} for helium is likely an optimal value for reaction C _2 H _5 CO + O _2 in fitting the OH yields. However, obtaining an 'exact' value for \langle$$ {\Delta}E $$\rangle$$ _\rm{Down}$ is difficult both experimentally and theoretically. Generally, $\langle $${\Delta}E$$ \rangle $$_\rm{Down} depends on energy, density of states, and temperature (average collisional energy), etc . Collision with larger colliders usually has larger energy transfer. For simplicity, we adopted \langle$$ {\Delta}E $$\rangle$$ _\rm{Down}$ values of 250 cm$^{-1}$ for reactions of RCO$+$O$_2$ in N$_2$ buffer gas in current study. It is also necessary to treat the internal rotations as hindered rotors (see FIG. S2 in supplementary materials for potential energy profiles) because treating the internal rotations as harmonic oscillators would over-estimate the OH yield (FIG. S1 in supplementary materials). Treating the internal rotations as harmonic oscillator, Zügner $et$ $al.$ fitted their experimental results in helium buffer gas and obtained a $\langle $${\Delta}E$$ \rangle $$_\rm{Down} value of 20 cm ^{-1} , which is obviously too small. FIG. 2 shows the typical yield profiles of intermediate radical RC(O)O_2 and the product channels via Q5OOH and Q6OOH at two different pressures for R=CH_3CH_2 and (CH_3)_2CHCH_2. With increased pressure, fraction of the collisionally stabilized CH_3CH_2C(O)O_2 increases drastically and OH formation yield decreases drastically. Note that OH formation via Q5OOH-B for R=CH_3CH_2 is higher than that via Q6OOH-B because of the high barriers of TSQ6 for Q6OOH decomposition (FIG. 1(B)); while for R=(CH_3)_2CHCH_2, OH formation via Q6OOH-D is virtually the sole channel. Clearly, the OH radical is formed promptly at both pressures, e.g., within \sim400 collisions (\sim5\times10^{-6} s of the reaction time at 3.8 torr or within 5\times10^{-7} s of the reaction time at 38 torr). The decay rates of CH_3CH_2C(O)O_2$$^*$ or the equivalent rates of OH formation from Q5OOH-B/Q6OOH-B$^*$, obtained by fitting its profiles within the first reaction time of 10$^{-5 }$ s, are all higher than 10$^6$ s$^{-1}$ at both pressures. Therefore we could ignore the recombination of QOOH with O$_2$ in the RRKM-ME calculations when comparing the OH yields from theoretical prediction to the experimental measurements. In those experiments, with low [O$_2$] (usually less than 10$^{15}$ molecule/cm$^{3}$) and low pressures, the effective rates of recombination were usually less than 10$^4$ s$^{-1}$ in previous measurements if assuming a rate coefficient of $<$5$\times$10$^{-12}$ cm$^3$$\cdotmolecule^{-1}$$\cdot$s$^{-1}$. In the atmosphere, OH formation would become negligible due to the relatively high reaction pressure and high concentration of O$_2$. High reaction pressure would result in the deactivation of RCO$^*$ by collision, and high [O$_2$] would rapidly deplete Q5OOH and Q6OOH by recombining to OOQ5OOH and OOQ6OOH.

 FIG. 2 Fractional yield profiles of intermediate radicals and end products from RRKM-ME calculations at 298 K and different pressures based on potential energy surfaces at RHF-RCCSD(T)-F12a/cc-pVDZ-F12 level.

Prompt OH formation is also expected in the reactions of CH$_3$CH$_2$CH$_2$CO and (CH$_3$)$_2$CHCH$_2$CO with O$_2$. FIG. 3 shows the predicted OH yields from RRKM-ME calculations. The prompt OH formation within 10$^{-4 }$ s of reaction time is significant at low pressures but decreases rapidly with the increased pressure to about zero at atmospheric pressure and temperatures up to 343 K, $e.g.$, $\sim$0.005 only at 380 torr and 343 K. Values with N$_2$ buffer gas and of 250 cm$^{-1}$ are recommended for the scenarios in the troposphere. Prompt formation of Q$n$OOH radical is also negligible ($<$0.01 of fractional yield) at atmospheric pressure. Therefore, the reaction of RCO and O$_2$ in the atmosphere would form RC(O)O$_2$ as the sole first-generation intermediate radicals.

 FIG. 3 Prompt formation of OH from RRKM-ME calculations based on electronic energies at RHF-RCCSD(T)-F12a/cc-pVDZ-F12 level in the reactions of O$_2$ with RCO radical for CH$_3$CH$_2$CO, CH$_3$CH$_2$CH$_2$CO, and (CH$_3$)$_2$CHCH$_2$CO using different $\langle$${\Delta}E$$\rangle$$_\rm{Down} for collisional energy transfer. Prompt OH formation in reactions of RCO with O_2 is different from those in alkyl peroxy radicals, in which isomerizations from ROO to QOOH are much more endothermic and therefore highly reversible, resulting in negligible OH formation at room temperatures [5, 6]. Savee et al. [27] also directly observed resonance stabilized QOOH radical intermediate in oxidation of 1, 3-cycloheptadiene, in which the resonance stabilized QOOH radical is formed from its corresponding RO_2 radical with a low barrier of \sim50 kJ/mol but is confined by a high barrier of \sim104 kJ/mol for its decomposition. In reactions of RCO+O_2, all Q5OOH intermediates are also resonance stabilized but the kinetics is much different. The Q5OOH radicals could be unlikely captured due to the high barriers (>100 kJ/mol) from RC(O)O_2 to Q5OOH and relatively low {barriers} ( < 95 kJ/mol) fordecompositions of Q5OOH to 3-lactone+OH. B. Thermal H-migrations in RC(O)O _\textbf{2} radicals In the atmosphere, the prompt OH formation in RCO + O _2 is quenched by collisional deactivation of RC(O)O _2$$ ^*$ radicals. However, the thermalized RC(O)O$_2$ radicals might be able to undergo the unimolecular isomerizations shown above. Such H-migrations in RC(O)O$_2$ radicals was usually ignored in the atmospheric oxidation of VOCs. However, with low barrier heights for substituted R-groups, the H-migration in RC(O)O$_2$ could become fast enough to compete with or even dominate over their bimolecular reactions in the atmosphere. Instead of decomposing to lactone and OH radical, the QOOH radicals would recombine rapidly with O$_2$ such as for (CH$_3$)$_2$CHCH$_2$C(O)O$_2$,

where the intermediate Q6OOH radical is depleted by reversed H-migration and rapid recombination with O$_2$. Table Ⅰ lists the reaction energies, barrier heights, and the rates for the forward processes. Under the atmospheric conditions, values of $k_\rm{Bi}$[O$_2$], at $\sim$5$\times$10$^7$ s$^{-1}$, are orders of magnitude larger than those of $k_\rm{F}$ or $k_\rm{R}$ for all RC(O)O$_2$ radicals examined here (Table Ⅰ). Assuming steady-state for QOOH, the effective rate from RC(O)O$_2$ to O$_2$QOOH is $k_\rm{eff}$$=$$k_\rm{F}$$k_\rm{Bi}[O_2]/(k_\rm{R}$$+$$k_\rm{Bi}[O_2])\approx$$k_\rm{F}$.

Table Ⅰ Reaction energies and barrier heights ($\Delta$$E$$_\rm{0\hspace{0.05cm}K}$ and ${{{\Delta}E}_\rm{0\hspace{0.05cm}K}}^{\neq}$, in kJ/mol) at F12 level, the rates at 298 K ($k_\rm{F, 298 K}$, in s$^{-1}$) and temperature dependent rate coefficients of unimolecular reactions$^\rm{a}$.

We have carried out RRKM-ME calculations and obtained $k_\rm{F}$ values of 1.38$\times$10$^{-4}$, 1.20$\times$10$^{-2}$, and 0.58 s$^{-1}$ for H-migrations via six-membered-ring transition state in ${\textbf{C}}{\rm{H}}_3$CH$_2$C(O)O$_2$, CH$_3$${\textbf{C}}{\rm{H}}_2CH_2C(O)O_2, and (CH_3)_2$${\textbf{C}}{\rm{H}}$CH$_2$C(O)O$_2$, respectively, at 298 K and atmospheric pressure. The overall tunneling correction factors for the thermal distribution of RC(O)O$_2$ radicals were 131, 75, and 33, respectively. The rates from CH$_3$${\textbf{C}}{\rm{H}}_2CH_2C(O)O_2 and (CH_3)_2$${\textbf{C}}{\rm{H}}$CH$_2$C(O)O$_2$ to their Q6OOHs are comparable to the effective bimolecular rates from 10$^{-2}$ s$^{-1}$ to 10 s$^{-1}$ in the atmosphere with NO in the range of 40 pptv to 40 ppbv if assuming rate coefficients of 10$^{-11}$ cm$^3$$\cdotmolecule^{-1}$$\cdot$s$^{-1}$ for reactions between RC(O)O$_2$ and NO [18]. Isomerizations via five- or seven-membered-ring transition states are comparatively too slow for all RC(O)O$_2$ radicals. Obviously, the H-migration would be faster and therefore more important with the increase of reaction temperature. Table Ⅰ lists the temperature dependences for several H-migration processes. In CH$_3$CH$_2$C(O)O$_2$, the transition state to CH$_3$CHC(O)OOH is tighter than the six-membered-ring one to CH$_2$CH$_2$C(O)OOH, resulting a larger pre-exponential $A$ factor but with a higher barrier.

The Q6OOH radicals formed from H-migration in RC(O)O$_2$ would either decompose as discussed above or recombine with O$_2$ as:

For both Q6OOH radicals, the decomposition, at rate of 7.8 s$^{-1}$ or 280 s$^{-1}$ at 298 K (Table Ⅰ), is too slow to compete with their recombination with the atmospheric O$_2$. Schemes 1 and 2 show further transformation of peroxy radicals OOQ6OOH formed from recombination with O$_2$. Unimolecular isomerization in the two OOQ6OOH radicals should be negligible due to their high barriers, $e.g.$, $\sim$139 kJ/mol for H-migration of OOCH$_2$CH$_2$C(O)OOH$\rightarrow$HOOCH$_2$CH$_2$C(O)O$_2$ at ROCBS-QB3 level. Therefore, they would react with other atmospheric trace radicals such as NO, HO$_2$, and RO$_2$ $etc$. Reaction of OOQ6OOH with NO/HO$_2$ would result in formation of nitrates, hydroperoxides, and alkoxy radical OQ6OOH$+$OH [18]. The alkoxy radical OQ6OOH would decompose or isomerize rapidly as:

 Scheme 1 New pathways of CH$_3$CH$_2$CH$_2$C(O)O$_2$ radical after H-migration.
 Scheme 2 New pathways of (CH$_3$)$_2$CHCH$_2$C(O)O$_2$ radical after H-migration.

The OQ6OOH radical could also react with O$_2$ at effective rates of 0.5$\times$10$^4$-5$\times$10$^4$ s$^{-1}$ with rate coefficients of 10$^{-15}$-10$^{-14}$ cm$^3$$\cdotmolecules^{-1}$$\cdot$s$^{-1}$ [45]. We have identified the transition states for the H-migration and C-C bond scission of OQ6OOH-C4 and OQ6OOH-C5 at M06-2X level, obtained their barrier heights at ROCBS-QB3 level, and predicted their rates using RRKM-ME calculations (Table Ⅰ). For both OQ6OOH radicals, the barriers for the H-migrations are slightly higher than those for the C-C bond scissions; however, the H-migrations are greatly enhanced by tunneling effect with imaginary vibrational frequency of $\sim$2200$i$ cm$^{-1}$ (M06-2X). Then, the main fate of OQ6OOH radical becomes the formation of HOQ6OO at rates of $\sim$10$^6$ s$^{-1}$ at 298 K. In the atmosphere, radical HOQ6OO-C5 would again react with NO, HO$_2$, and other RO$_2$ radicals as:

Reaction with NO would also form organic nitrates, and reactions with HO$_2$/R$'$O$_2$ would also form HOC(CH$_3$)$_2$CH$_2$C(O)OOH and HOC(CH$_3$)$_2$CH$_2$C(O)OH [18]. On the other hand, the HOQ6OO-C4 might undergo another intramolecular H-migration as:

A barrier height of 77.7 kJ/mol was obtained at F12 level, resulting in a rate of $\sim$0.9 s$^{-1}$ at 298 K. The process is expected to dominate under the atmospheric conditions when the slower H-migration in CH$_3$CH$_2$CH$_2$C(O)O$_2$, with a rate of 0.012 s$^{-1}$ only, is significant.

The CH$_2$C(O)O$_2$H radical, as a minor product from the decomposition of OQ6OOH-C4/C5, would recombine with O$_2$ to OOCH$_2$C(O)OOH in the atmosphere (see Schemes 1 and 2 for details):

The O$_2$ addition to CH$_2$C(O)OOH is exothermic with $\Delta$$E$$_\rm{0K}$ of $-$90.3 kJ/mol at F12 level ($\Delta$$G$$_\rm{298 K}$$=$$-$51.9 kJ/mol). In the atmosphere, with [O$_2$] of $\sim$5$\times$10$^{18}$ molecules/cm$^{3}$ and a rate coefficient of $\sim$1.9$\times$10$^{-13}$ cm$^3$$\cdotmolecule^{-1}$$\cdot$s$^{-1}$ as for O$_2$ addition to CH$_2$CHO or of $\sim$1.2$\times$10$^{-12}$ cm$^3$$\cdotmolecule^{-1}$$\cdot$s$^{-1}$ as for O$_2$ addition to CH$_2$C(O)CH$_3$ [46, 47], the back-decomposition of OOCH$_2$C(O)OOH radical could be estimated as $\sim$7.6$\times$10$^{-4}$ or $\sim$4.8$\times$10$^{-3}$ s$^{-1}$ at 298 K from the equilibrium constant. Further intramolecular H-migration in OOCH$_2$C(O)OOH, according to Knap and Jörgensen, is endothermic and highly reversible ($k_\rm{R}$$\approx5\times10^3 s^{-1}) and therefore negligibly slow [28]. Thus in the atmosphere, CH_2C(O)OOH would be transformed to OOCH_2C(O)OOH, which would react with NO/HO_2, forming OCH_2C(O)OOH, and then be converted to HC(O)C(O)OOH by reacting with O_2. Decomposition of OCH_2C(O)OOH to CH_2O+CO_2$$+$OH, with a barrier of ~65 kJ/mol (ROCBS-QB3) and a rate of $\sim$10$^2$ s$^{-1}$ at 298 K, is negligible compared to its reaction with O$_2$.

Ⅳ. CONCLUSION

Theoretical studies are carried out here to explore the role of the unimolecular H-migration in the carbonyl peroxy radicals by using quantum chemistry and RRKM-ME calculations. While prompt OH formation with high yields is found in the reactions of RCO radicals with O$_2$ under the conditions of reduced pressures ($<$0.5 bar), low O$_2$ concentrations, and elevated temperatures, it is negligible under atmospheric conditions. Reaction of RCO and O$_2$ would form RC(O)O$_2$ radical in the atmosphere. In the atmosphere, H-migration could be significant at least in CH$_3$CH$_2$CH$_2$C(O)O$_2$ and (CH$_3$)$_2$CHCH$_2$C(O)O$_2$, $e.g.$, with rates of $\sim$0.012 and $\sim$0.58 s$^{-1}$ at 298 K and atmospheric pressure. After the H-migration, subsequent reactions of Q6OOH-C4 would lead to the products with multi-functional groups, which might affect the aerosol formation process; while Q6OOH-C5 would transform to formaldehyde, acetone, and HO$_2$ radical in a few steps. Schemes 1 and 2 summarize the predicted new pathways of the two radicals after H-migration. This additional degradation pathway of RC(O)O$_2$ radicals would affect the formation of carbonyl peroxy nitrates (RC(O)OONO$_2$) and ozone. Adding such processes to the atmospheric oxidation mechanism of VOCs might be necessary for properly modeling the fate and effect of VOCs in the atmosphere.

Note that we have used the reaction energies and barrier heights at RHF-RCCSD(T)-F12a/cc-pVDZ-F12 (F12) level for the calculations of rates or rate coefficients for most cases. Comparing the three methods for electronic energies (Table S1 in supplementary materials), we can see that the F12 method usually predicts higher energy barriers than U/ROCBS-QB3. Therefore, the role of H-migration in RC(O)O$_2$ radicals would be more pronounced if using energies and barrier heights at U/ROCBS-QB3 levels. Nevertheless, our calculations here suggested the role of H-migrations in the atmospheric fate of long-chain and substituted carbonyl peroxy radicals.

Supplementary materials: Table containing relative energies in reactions of RCO and O$_2$ at various levels of theory (Table S1), and figures for fractional OH yields in reaction of CH$_3$CH$_2$CO and O$_2$ from RRKM-ME calculations (FIG. S1) and potential energy profiles for internal rotations in RC(O)O$_2$ radicals (FIG. S2) are given.

Ⅴ. ACKNOWLEDGMENTS

This work was supported by the National Key Research & Development Program (No.2017YFC0212800), the National Natural Science Foundation of China (No.21477038 and No.21677051), and the Natural Science Foundation of Guangdong Province (No.2016A030311005).

Reference