Atmospheric oxidation mechanism of OH-initiated reactions of diethyl ether – the fate of the 1-ethoxy ethoxy radical

Abstract

The oxidation of diethyl ether (DEE) by hydroxyl radical is studied by means of density functional theory and coupled cluster methods. The OH-initiated reactions were found to proceed by H-atom abstraction from –CH₃ or –CH₂ groups of DEE, in which the latter reaction is found to be more favourable than the former. The secondary reactions associated with the peroxy radical and the following alkoxy radical chemistry of DEE is explored in detail. The 1-ethoxy ethoxy radical resulting from the peroxy radical chemistry of DEE undergoes –CH₃ as well as H-atom elimination reactions leading to the formation of ethyl formate and ethyl acetate in the respective reactions, where both reactions are kinetically competitive. The next significant reaction in the 1-ethoxy ethoxy radical decomposition is its reaction with O₂, where ethyl acetate and HO₂ are formed. The decomposition of the 1-ethoxy ethoxy radical via C–O bond cleavage is less feasible when compared to the above reactions. The reactions of 1-ethoxy ethoxy radicals with nitrates are largely thermodynamic driven, but poorly kinetic driven. The calculated results show that the major product from the oxidation chemistry of DEE is ethyl formate, followed by the formation of ethyl acetate in minor quantities. The results obtained from the current theoretical study are in excellent agreement with the available literature.

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Introduction

In recent years, oxygenated organic compounds have had profound applications as high-octane fuel additives, as an effort to reduce CO emissions. Among these compounds, diethyl ether (DEE) is omnipresent in the atmosphere due to its wide usage as a solvent and a substitute for engine fluid. The atmospheric degradation of diethyl ether is initiated by reaction with hydroxyl radicals. The diethyl ethers react with OH radical leading to the production of ozone in urban areas.¹ Also, the diethyl ether has been shown to be a free radical scavenger in secondary organic aerosol (SOA) formation in high yield.² Diethyl ether has a atmospheric reactivity factor of 1.9 to 7.1 which is higher than that of other oxygenates.³ The atmospheric oxidation of diethyl ether by OH radical was studied initially using irradiation experiments by Wallington et al.⁴ They elucidated the mechanism for the formation of formaldehyde, ethyl formate, tert-butyl formate, tert-butyl acetate and acetaldehyde from the OH initiated reaction and secondary reaction chemistry of DEE. Another study by Eberhard et al.³ reported the degradation pathways of DEE and concluded that the decomposition of 1-ethoxyethoxy radical yields an ethyl formate and a methyl radical as the major degradation products. The OH-initiated reaction of diethyl ether proceeds via the H-atom abstraction from the –CH₃ and –CH₂-groups of diethyl ether, as observed in OH-initiated reactions of 1,3-butadiene by OH radical⁵ and the secondary reaction chemistry from these reactions is shown below:

CH₃CH₂OCH₂CH₃ + ˙OH → CH₃CH₂OCH₂C˙H₂ + H₂O (1)

CH₃CH₂OCH₂CH₃ + ˙OH → CH₃CH₂OC˙HCH₃ + H₂O (2)

CH₃CH₂OCH₂C˙H₂ + ³O₂ → CH₃CH₂OCH₂CH₂OO˙ (3)

CH₃CH₂OC˙HCH₃ + ³O₂ → CH₃CH₂OCH(OO˙)CH₃ (4)

CH₃CH₂OCH₂CH₂OO˙ + NO → CH₃CH₂OCH₂CH₂O˙ + NO₂ (5)

CH₃CH₂OCH(OO˙)CH₃ + NO → CH₃CH₂OCH(O˙)CH₃ + NO₂ (6)

The alkoxy radicals formed in reactions (5) and (6) then undergo reactions with molecular oxygen yielding aldehydes and acetone along with the hydrogen peroxide:

CH₃CH₂OCH₂CH₂O˙ + ³O₂ → CH₃CH₂OCH₂CH(=O) + HO₂ (7)

CH₃CH₂OCH(O˙)CH₃ + ³O₂ → CH₃CH₂OC(=O)CH₃ + HO₂ (8)

The peroxy radical isomerization is the key reaction in the low temperature combustion of hydrocarbon fuels.⁶ Thus, the peroxy radicals formed from reaction (4) will undergo isomerisation at extremely low [NO] or [HOO], resulting in the experimentally observed products:

CH₃CH₂OCH(OO˙)CH₃ → CH₃C˙HOCH(OOH)CH₃ (9)

CH₃CH₂OCH(O˙)CH₃ → CH₃CH₂OCH(=O) + C˙H₃ (10)

CH₃CH₂OCH(O˙)CH₃ → CH₃CH₂OC(=O)CH₃ + H˙ (11)

CH₃CH₂OCH(O˙)CH₃ → CH₃CH₂O˙ + CH(=O)CH₃ (12)

J. J. Orlando studied the Cl-atom initiated reaction of diethyl ether using chamber experiments both in the presence and absence of NO.⁷ A laboratory experiment on the diethyl ether photoxidation examined the ratio of the different products formed from the oxidation reactions as a function of the pressure of oxygen and NO.⁸ This study emphasized that at relatively high pressures of NO, the following reaction pathways are dominant. Further, this study shows that the ratio between ethyl acetate and ethyl formate remains constant irrespective of the change in NO pressure.

CH₃CH₂OCH(O˙)CH₃ + NO → CH₃CH₂OCH(ONO)CH₃ → CH₃CH₂OC(=O)CH₃ + HNO (13)

CH₃CH₂OCH(O˙)CH₃ + NO₂ → CH₃CH₂OCH(ONO₂)CH₃ → CH₃CH₂OC(=O)CH₃ + HONO (14)

Reaction pathway (10) occurring via C–C bond cleavage of ethoxy radical was shown to be the major tropospheric fate for the ethoxy radical. The reaction enthalpy of the H-atom migration in alkoxy radicals is shown to be more exothermic than the C–C bond scission reactions in the unimolecular dissociation of alkoxy radicals.⁹ The estimated enthalpy change for the reaction (10) is −2.5 kJ mol⁻¹, whereas the H-atom elimination reaction (11) is thermoneutral.¹⁰ The results in an earlier study show that the H-atom abstraction from ethers occurs exclusively at the α-sites of C–H groups.¹¹ The branching ratio of the different product channels from the OH radical initiated reaction of aliphatic ethers was calculated using variational transition state theory and the calculated overall rate constant for diethyl ether reaction with OH radical is 1.4 × 10⁻¹¹ cm³ per molecule per s.¹² Ogura et al. derived the group rate expressions for H-atom abstraction reactions from ethers and intramolecular isomerization of their alkyl peroxy radicals by using quantum chemical methods and they made a comparison with experimental rate constants and also the corresponding reactions with alkanes.¹³ The isomerisation of ethoxy radicals has been studied extensively by ab initio methods and RRKM theory and was shown that the isomerisation reaction channels exhibit positive temperature dependence.¹⁴ A quantum chemical investigation on the isomerization and decomposition of oxygenated alkoxy radicals reported that the reaction of 1-ethoxy ethoxy radical with O₂ is its dominant atmospheric fate.¹⁵ The very earlier study reported the atmospheric life time of diethyl ether as 4.1 hours for OH-radical initiated reaction.¹⁶ The kinetics of the reaction of OH radical with ethers has been studied using pyrolysis experiments at 753 K by Tranter and Walker and their study concluded that the initial yield of C₂H₄ is 100% in the reaction between diethyl ether and OH radical.¹⁷ Another kinetic study by Porter et al. using laser photolysis resonance fluorescence (LPRF) technique along with a structure–activity relationship (SAR) study shows a significant deviation between the rate constants calculated from LPRF technique and from the SAR results which may be due to the stabilization of the corresponding transition states by hydrogen bonding.¹⁸

In most of the above mentioned studies, the formation of ethyl acetate and ethyl formate from the unimolecular dissociation of 1-ethoxy ethoxy radical was shown to be the dominant processes in the atmospheric oxidation of DEE. However, the thermochemistry of the reactions (1) through (14) is not well documented in the literature. There is scarce of data for the hydroxyl radical attack at the methyl group of diethyl ether and its subsequent reactions, which is also a plausible source for degradation of DEE in the atmosphere. Even though, a large number of literature exists for the kinetics of the OH-radical initiated reaction of diethyl ether, the kinetics of the alkoxy radical reaction pathways which are considered as the major pathways determining the atmospheric fate of diethyl ether is not reported in detail elsewhere. Hence, the aim of the present work is a quantum chemical investigation on the OH-radical initiated reactions of diethyl ethers and the subsequent peroxy and alkoxy radical chemistry described in reactions (1) to (14). The thermochemistry, reaction pathways and kinetics of these reactions will be explored in detail and compared with the available experimental results.

Computational details

The geometries of the stationary points involved in the oxidation of DEE by OH radical are optimized using M06-2X method¹⁹ with 6-311++G(d,p) basis set. The M06-2X method has been shown to give reliable results in determining the kinetics and mechanism of atmospheric reactions.^20–23 The nature of the stationary points has been verified by harmonic vibrational frequency analysis at the same level of theory. The connection of the calculated transition states with their respective minima was verified by intrinsic reaction coordinate (IRC) calculations. In a recent theoretical study by L. Vereecken et al.,²⁴ it was reported that the calculations using M06-2X/aug-cc-pVTZ and CCSD(T)/aug-cc-pVDZ provide the relative contribution of the reaction channels more accurately with average energy differences of only 2 kcal mol⁻¹. Hence, in the present study, single point energy calculations were performed using M06-2X/aug-cc-pVTZ, UCCSD(T)/6-311++G(d,p) and UCCSD(T)/aug-cc-pVDZ levels with the geometries optimized at M06-2X/6-311++G(d,p) level. The thermochemistry of the reactions are calculated using highly accurate CBS-QB3 method.²⁵ Further, the kinetics of the reactions are studied using canonical variational transition state (CVT) theory with small curvature tunnelling (SCT) corrections from the potential energy surface (PES) calculated at M06-2X/6-311++G(d,p) level of theory. All quantum chemical calculations were performed using Gaussian 09 program²⁶ and the kinetics calculations were performed using Gaussrate program,²⁷ which is an interface between Gaussian and Polyrate programs.²⁸

Results and discussion

Thermochemistry

The thermochemistry, ΔH at 298.15 K of the studied oxidation reactions of diethyl ether calculated at CBS-QB3 method is illustrated in Fig. 1. The hydroxyl radical attack at –CH₂ group of diethyl ether is thermodynamically more favourable than the radical attack at –CH₃ group by ∼35 kJ mol⁻¹ in terms of enthalpy as well as free energy. The enthalpy of the reaction (2) with a value of −104.5 kJ mol⁻¹ is in reasonable agreement with the enthalpy of −107.6 ± 1.94 kJ mol⁻¹ calculated using available literature data.²⁹ The peroxy radical formation reactions (3) and (4) are highly exothermic and less exergonic as expected for the adduct formation reactions. The peroxy radical formed at –CH₂ radical position (reaction (3)) is comparatively more favourable than the addition of O₂ to methyl radical position. The oxidation of NO to NO₂ by peroxy radical leaving alkoxy radicals in reactions (5) and (6) are less exothermic and exergonic than the OH initiated reaction and O₂ addition reaction. The reactions of the so formed alkoxy radicals with O₂ molecule leading to the formation of aldehydes and acetone along with hydroperoxide are highly thermodynamically feasible, particularly the reaction (8) is highly exothermic and exergonic by −208.6 and −214.6 kJ mol⁻¹. This thermochemical value reflects the importance of 1-ethoxy ethoxy radical chemistry in the oxidation of diethyl ether. The isomerisation of the peroxy radical (reaction (9)) is not thermodynamically favourable with large positive enthalpy and free energy of +36.2 and +35.7 kJ mol⁻¹, respectively.

Fig. 1 The thermochemistry data for the reactions (1) to (14) calculated at CBS-QB3 method. The available literature data for ΔH₂₉₈ are given in blue colour in the left side.²⁹

Since, there is no literature value available for the heat of formation of 1-ethoxy ethoxy radical or the reaction enthalpies of reactions (8) to (14), we derived the heat of formation of 1-ethoxy ethoxy radical using atomization enthalpies [for details of this calculation, see ESI†]. The heat of formation of this radical is −28.4 kJ mol⁻¹.²⁹ By combining this value with the literature values of the heat of formation of other species involved in the reactions (8) to (14), the reaction enthalpies are calculated and compared with our CBS-QB3 results. The unimolecular dissociation of 1-ethoxy ethoxy radical into ethyl formate and methyl radical is exergonic and the calculated enthalpy of −21.3 kJ mol⁻¹ agrees quite well with the literature value of −18.5 ± 1 kJ mol⁻¹.²⁹ The reaction leading to the formation of ethyl acetate and H radical (reaction (11)) is less favourable than the reaction (10), showing that the C–C bond in 1-ethoxy ethoxy radical is weaker than the C–H bond. The unimolecular reaction resulting in the formation of ethoxy radical and acetaldehyde (reaction (12)) is highly endothermic with an endothermicity of +45.5 kJ mol⁻¹, which coincides well with the literature value of +48.2 ± 4 kJ mol⁻¹.²⁹ This reaction is mildly exergonic by −3.9 kJ mol⁻¹. The least favourability of this C–O bond cleavage reaction is in agreement with the experimental observation that the C–O bond cleavage in unimolecular reaction of 1-ethoxy ethoxy radical is negligible.³ As observed from Fig. 1, the most thermodynamically feasible reactions in the oxidation chemistry of diethyl ether are the reactions of 1-ethoxy ethoxy radical with NO and NO₂. The H-atom abstraction from the –CH group of 1-ethoxy ethoxy radical by NO is highly exothermic and exergonic by −204.2 and −207.7 kJ mol⁻¹, respectively. The exothermicity of this reaction calculated using atomization enthalpies and literature values is −191.6 ± 4.24 kJ mol⁻¹.²⁹ The large exothermicity and exergonicity of −329.8 and −329.5 kJ mol⁻¹ is calculated for H-atom abstraction from –CH group of 1-ethoxy ethoxy radical by NO₂ (reaction (14)). The enthalpy values calculated at CBS-QB3 method quite agrees with the literature value of −322.8 ± 0.84 kJ mol⁻¹.²⁹

Reaction mechanism and pathways

The reaction pathways for OH-initiated reactions of diethyl ether is calculated using geometry optimization at UM06-2X/6-311++G(d,p) level of theory and performing single point energy calculations on these optimized geometries at UM06-2X/aug-cc-pVTZ, UCCSD(T)/6-311++G(d,p) and UCCSD(T)/aug-cc-pVDZ levels. The OH radical attack at the –CH₃ and –CH₂ groups of diethyl ether proceeds via hydrogen bonded reactant and product complexes through the respective transition states. The reaction energy profile of the initial reaction (1) at various levels of theory is illustrated in Fig. 2. As it is observed from the figure, the energetics calculated at UM06-2X with 6-311++G(d,p) and aug-cc-pVTZ basis sets are in line with the energetics calculated at UCCSD(T)/aug-cc-pVDZ//UM06-2X/6-311++G(d,p) level of theory. The UCCSD(T)/6-311++G(d,p)//UM06-2X/6-311++G(d,p) level very slightly underestimates the energetics. But, in overall, it is observed that the deviation in energy between the DFT and coupled cluster methods is about 4 to 6 kJ mol⁻¹, which is accepted within the uncertainty of DFT limits. Also, the relative importance of the reaction channels does not change with respect to the choice of the method. In most of the reactions studied in the present work, the same trend is observed and hence the results obtained at UM06-2X/6-311++G(d,p) level of theory are discussed throughout the manuscript. The energetics obtained using other levels of theory are summed up in the ESI.†

Fig. 2 The energy profile of the reaction (1) calculated at different levels of theory.

The reaction energy profile for the reactions (1) and (2) is shown in Fig. 3. The initial H-atom abstraction reactions (1) and (2) proceed through pre-reactant and product complexes as mentioned before and these are hydrogen bonded complexes which have been shown to be important in atmospheric chemistry.³⁰ The pre-reactant complexes show a hydrogen bonding interaction between the H-atom of OH group and the O-atom of DEE with O–H bond distance of 1.82 Å. This value is in agreement with an earlier study on H-atom abstraction from ethers by OH radical.¹² The stabilization energy for the pre-reactant complexes formed in reactions (1) and (2) are ∼32 kJ mol⁻¹ lower in enthalpy with respected to the isolated reactants. It is well noted from the Fig. 3, that the enthalpy barrier for H-atom abstraction from –CH₂ group of DEE is only 4.5 kJ mol⁻¹ less than the enthalpy barrier for H-atom abstraction from –CH₃ group of DEE. This shows that both the initial reactions (1) and (2) are equally favourable. The activation free energy barrier for reactions (1) and (2) is 33.4 and 25.4 kJ mol⁻¹, respectively. This free energy barrier shows that the O-atom in the neighbouring site of –CH₂ group stabilizes the radical. In the transition state (TS1) of reaction (1), the breaking C–H bond distance is 1.20 Å and the forming O–H bond distance is 1.33 Å, while in reaction (2), the corresponding TS2 has C–H and O–H distances of 1.15 and 1.53 Å, respectively. These transition states then proceed via product complexes (PC1 and PC2) in the exit reaction channel, which are also stabilized by hydrogen bonding. These complexes then lead to the isolated product channels of reactions (1) and (2) with the stabilization enthalpy of 21.2 and 20.5 kJ mol⁻¹, respectively. In the atmosphere, the radicals formed in reactions (1) and (2) are collisionally stabilized and react with O₂ to form their respective peroxy radicals (reactions (3) and (4)). The addition of O₂ to these radicals occur in a barrierless process as evident from the potential energy surface scan along the C–O coordinate as shown in ESI.† As observed experimentally,³ these peroxy radicals then react with NO, leading to the formation of ethoxy radicals, thereby oxidizing NO to NO₂ (reactions (5) and (6)). These reactions are also barrierless and their PESs are shown in ESI.†

Fig. 3 The energy profile of the OH-initiated reactions of DEE calculated at UM06-2X/6-311++G(d,p) level of theory.

The ethoxy radicals formed in reactions (5) and (6) may be decomposed through a H-atom elimination reaction, for instance, the reaction of ethoxy radical with O₂ (reactions (7) and (8)) eliminate a H-atom from the radical C position, thereby forming ethoxy acetaldehyde and ethyl acetate along with HO₂. The enthalpy energy profile of the reactions (7) and (8) is shown in Fig. 4. As reported in an earlier computational and kinetic study on the reaction of ethoxy radical with O₂,³¹ these reactions proceed via weakly bound pre-reactive complexes (RC3 and RC4), which are ∼7 kJ mol⁻¹ lower in enthalpy than the isolated reactants. These complexes then proceed via transition states (TS3 and TS4), which are H-bonded activated complexes showing H-bonding interaction between the eliminated H-atom from the radical site and the O-atom of O₂. The energy barrier associated with transition states, TS3 and TS4 are 39.7 and 27.8 kJ mol⁻¹, respectively. This shows that the formation of ethyl acetate and HO₂ in reaction (8) is kinetically plausible than the ethoxy acetaldehyde and HO₂ formation. The transition states then lead to the final isolated products through the product complexes (PC3 and PC4) which require stabilization enthalpies of 41.7 and 44.5 kJ mol⁻¹ to break into the respective isolated products.

Fig. 4 The energy profile for the decomposition of alkoxy radicals via reaction with O₂ calculated at UM06-2X/6-311++G(d,p) level of theory.

As mentioned in the thermochemistry part, the unimolecular isomerisation of the peroxy radical (reaction (9)) formed in reaction (4) is not thermodynamically favourable. This reaction is also not kinetically favoured as reflected from the high energy barrier of 83.8 kJ mol⁻¹ [see Fig. 5]. The high lying transition state, TS5 involved in this isomerisation process is a six-membered cyclic transition state, where the migrating H-atom from –CH₂ group forms a H-bonding with the terminal O-atom of peroxy radical. The strain in this six-membered TS5 is the reason for the high lying energy barrier for this reaction, which is a common behaviour observed in 1,5-H shift reactions.^32,33 Further, a very earlier study by Atkinson et al. emphasized that the isomerisation of the alkoxy radical, which involves the H-atom abstraction from the –CH₂ group is analogous to the H-atom abstraction from the –CH₃ or –CH₂ groups by OH radical.³³ This is also true in the present study, where the reaction enthalpy barrier for reaction (1) involving H-atom abstraction from –CH₃ group of DEE is 33.3 kJ mol⁻¹, which is equal to the isomerisation energy barrier of 32.9 kJ mol⁻¹ in reaction (9). The unimolecular decomposition of the 1-ethoxy ethoxy radical through the cleavage of C–C bond leads to the formation of ethyl formate and methyl radical (reaction (10)). The activation enthalpy for this reaction is 32.9 kJ mol⁻¹. In the corresponding transition state, TS6, the C–C bond is already cleaved with a bond distance of 1.97 Å. This TS6 then proceeds through a product complex, PC5, which is ∼10 kJ mol⁻¹ lower in enthalpy than the isolated products. The other possible unimolecular reaction of 1-ethoxy ethoxy radical is the elimination of H-atom from the –CHO˙ site, resulting in ethyl acetate and H radical (reaction (11). The barrier for this reaction is about 15 kJ mol⁻¹ higher than the –CH₃ elimination reaction in (10). The breaking C–H bond distance in the associated transition state is 1.92 Å, showing a H-bonding interaction with the O-atom of –CHO group. The isolated products are then formed via a product complex, PC7 which is less stable than the isolated products by only 2.5 kJ mol⁻¹. On comparing the isomerisation reactions (10) and (11), it is well speculated that the –CH₃ group is a better leaving group than the H-atom. The difference in the energy barrier associated with the two processes can be linked to the lower yield of ethyl acetate than the ethyl formate in earlier experimental observations, which also claimed a rigorous limitation in the magnitude of the rate constant of reaction (11).^33,34 The calculated difference in energy barrier between the two reactions (15 kJ mol⁻¹) is quite comparable with the experimentally reported barrier difference of 2 to 3 kcal mol⁻¹ (∼12 kJ mol⁻¹).⁷ The cleavage of C–O bond in 1-ethoxy ethoxy radical forming ethoxy radical and acetaldehyde (reaction (12)) is a kinetically unfavourable process with a large enthalpy barrier of 60.5 kJ mol⁻¹. Also it is important to point out here that, the reaction was also not thermodynamically driven. In the transition state, TS8, the C–O bond is broken with a distance of 1.82 Å and a strong H-bond with a distance of 2.23 Å is noted between the O-atom of the radical and the H-atom of the closed-shell product. Even though, acetaldehyde formed in the reaction (12) is considered as a product of the oxidation of DEE, its contribution to the oxidation chemistry of DEE is less than 10% as reported in the study by J. J. Orlando,⁷ which is supported from our calculated energy barrier for this reaction. The TS8 then leads to a H-bonded product complex (PC9) which is stabilized than the isolated products by 12.2 kJ mol⁻¹ in terms of enthalpy. Concerning the most viable processes for unimolecular isomerisation of 1-ethoxy ethoxy radical, our computed results show that the elimination of –CH₃ group resulting in ethyl formate is rather more competitive than the H-atom elimination reaction. The C–O bond cleavage reaction resulting in acetaldehyde and ethoxy radical does not contribute significantly to the oxidation chemistry of ether, both kinetically as well as thermodynamically.

Fig. 5 The energy profile for unimolecular dissociation of the peroxy radical and 1-ethoxy ethoxy radical calculated at UM06-2X/6-311++G(d,p) level of theory.

Under tropospheric conditions, the decomposition of 1-ethoxy ethoxy radical can also proceed via reaction with nitrates. The potential energy profile for the reaction of 1-ethoxy ethoxy radical with NO and NO₂ is illustrated in Fig. 6. As observed from the Fig. 6, the reaction of the 1-ethoxy ethoxy radical with NO_x involve activated complexes, RONO and ROONO, which are more exothermic and impart internal energy to the nascent 1-ethoxy ethoxy radical. The activated complex RONO formed in reaction (13) then proceeds through a high lying transition state, TS9 with an activation enthalpy of 138.7 kJ mol⁻¹, showing the reaction to be least kinetically favourable. The TS9 then goes to the product complex, PC8 which requires 13.3 kJ mol⁻¹ energy to dissociate into the isolated products. Further, the dissociation of the ROONO complex into ethyl acetate and HONO in reaction (14) has a large activation barrier of 172 kJ mol⁻¹, through the transition state, TS10. The TS10 then proceeds via a product complex, PC9, which is highly exothermic and breaks into the isolated products with an enthalpy of 38.3 kJ mol⁻¹. Thus, the reactions of the 1-ethoxy ethoxy radical with nitrates are thermodynamically driven and not kinetically feasible.

Fig. 6 The energy profile for the dissociation of 1-ethoxy ethoxy radical on reaction with nitrates calculated at UM06-2X/6-311++G(d,p) level of theory.

The above results show that the initial H-atom abstraction from the –CH₂ group of DEE and its subsequent reactions are significantly contributing to the oxidation of DEE than that from the H-atom abstraction from –CH₃ and its secondary reactions. The ethyl formate and ethyl acetate are the major products formed from the oxidation of DEE. The unimolecular isomerisation of the peroxy radical (reaction (9)) is not competitive in the peroxy radical chemistry of the DEE, which is in contrary to the isomerisation of peroxy radical in the oxidation chemistry of DME.³⁵ For the alkoxy radical chemistry of DEE, the reaction of 1-ethoxy ethoxy radical with O₂ is as competitive as the unimolecular dissociation of 1-ethoxy ethoxy radical. This is in accordance with the earlier studies where the alkoxy radicals reaction with O₂ and unimolecular reactions are competitive.³⁶ Surprisingly, the reactions of 1-ethoxy ethoxy radical with nitrates are not competitive with its reactions with O₂ or unimolecular isomerisation reactions.

Kinetics

From the calculated energy barrier for the 1-ethoxy ethoxy radical decomposition and unimolecular reactions, it is well observed that the following reactions are significantly contributing to the alkoxy radical chemistry of DEE.

CH₃CH₂OCH(O˙)CH₃ + ³O₂ → CH₃CH₂OC(=O)CH₃ + HO₂ (8)

CH₃CH₂OCH(O˙)CH₃ → CH₃CH₂OCH(=O) + C˙H₃ (10)

CH₃CH₂OCH(O˙)CH₃ → CH₃CH₂OC(=O)CH₃ + H˙ (11)

The rate constants for these reactions are calculated using CVT/SCT method from the PES calculated at UM06-2X/6-311++G(d,p) level of theory over the temperature range of 218–348 K and is shown graphically in Fig. 7. The interplay between the three reactions is well understood from the rate constants. The rate constant remains almost constant till 298 K and after the room temperature, for the reactions (8) and (10) the rate constant show a rapid increase with increase in temperature. In the case of unimolecular dissociation process (10), the rate constant increases with increase in temperature, following the fact that the alkoxy radical will quickly undergo C–C bond scission into carbonyl and alkyl radicals at high temperature.⁹ This result agrees well with the earlier theoretical study which showed that the isomerization/decomposition of alkoxy radicals exhibit positive temperature dependence.¹⁴ The rate constant for H-atom elimination from 1-ethoxy ethoxy radical remains constant over the whole temperature range studied. From Fig. 7, it is well noted that the unimolecular dissociation reactions are kinetically more competitive than the reaction of 1-ethoxy ethoxy radical with O₂. The calculated rate constant for the reaction of 1-ethoxy ethoxy radical with O₂ at 298 K is 11.6 × 10⁻¹⁴ cm³ per molecule per s, which is in good agreement with the previously reported rate constant of ∼10⁻¹⁴ cm³ per molecule per s for the reactions of alkoxy radicals with O₂.⁹ Further, the rate constant for unimolecular dissociation of 1-ethoxy ethoxy radical (reaction (10)) by experimental studies is 2 × 10⁶ s⁻¹ at 298 K and 2 × 10⁴ s⁻¹ at 220 K,⁷ whereas our calculated rate constants are 1 × 10⁸ s⁻¹ and 2 × 10⁶ s⁻¹, at the respective temperatures. It is important to point out here that the experimental rate constants for reaction (10) represent lower limits to the rate constants. The rate constant calculated for reaction (11) at 298 K is 3.9 × 10⁴ s⁻¹. This rate constant is quite in comparison with the observed rate constant of 1 × 10⁵ s⁻¹ for the dissociation of alkoxy radical by H-atom elimination from –CH group.³⁷

Fig. 7 The calculated rate constant for the reactions (8), (10) and (11) over the temperature range of 218–348 K.

The rate constant ratio between the reactions (10) and (8) was obtained by fitting the rate constant derived from all rate constants in the temperature range 218–298 K by J. J. Orlando.⁷ The Table 1 summarizes the rate constant ratio between reactions (10) and (11) and (10) and (8) along with the results of J. J. Orlando. The observed discrepancy between our calculated results and the experimental results is well attributed to the statement that the even a difference of 2 kcal mol⁻¹ difference in energy barrier leads to a change in rate constant of 30–100 times along the studied temperature range.³⁴ On comparing the rate constant ratio calculated for the reactions between (10) and (11) and that between (10) and (8), two important conclusions can be drawn. The reaction (8) resulting in ethyl formate is the major oxidation product of the alkoxy radical chemistry of DEE over the tropospheric temperature range and ethyl acetate is also formed in minor quantities mainly from H-atom elimination from 1-ethoxy ethoxy radical, and the reaction (8) representing the source of ethyl acetate is relatively less contributing. However, the calculated rate constant for reaction (11) suggest that the H-atom elimination reaction is relatively rapid than the –CH₃ elimination reaction by a factor of 10⁴. To address this issue further experimental investigation on the H-atom elimination from 1-ethoxy ethoxy radical is needed.

Table 1 Rate constant ratio between the reactions ((10) and (11), k₁₀/k₁₁) and reactions ((10) and (8), k₁₀/k₈) compared with the ratio obtained from data fits

Temperature/K	k10/k11 × 10^3	k10/k8 (molecule cm^−3)	Exp. (k10/k8)^7 (molecule cm^−3)
218	2.44	2.02 × 10^24	4.0 × 10^18
228	2.78	6.30 × 10^22	9.5 × 10^18
238	3.05	2.97 × 10^22
248	3.23	1.45 × 10^22	2.6 × 10^19
258	3.33	7.70 × 10^21
268	3.36	4.43 × 10^21	6.0 × 10^19
278	3.31	2.63 × 10^21
288	3.22	1.64 × 10^21
298	3.09	1.06 × 10^21	1.89 × 10^20
308	2.93	7.09 × 10^20
318	2.77	4.90 × 10^20
328	2.60	3.47 × 10^20
338	2.43	2.52 × 10^20
348	2.27	1.87 × 10^20

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In the troposphere, the ethyl formate is the dominant oxidation product from the decomposition of 1-ethoxy ethoxy radical. The atmospheric lifetime of ethyl formate with respect to OH radical is 58 days³ and that of ethyl acetate is 8 days. This clearly suggests that the ethyl acetate has less probability in impacting the air quality. Our calculated thermochemistry of the H-atom elimination reaction, energy barrier and the rate constant ratio between reactions (10) and (11) are also in favour of this statement.³⁸ The long life time of ethyl formate suggests that ethyl formate will further undergo photooxidation by other atmospheric species leading to products impacting the atmosphere further.

Conclusions

The atmospheric oxidation of diethyl ether (DEE) by OH radical is studied using the state-of-art quantum chemical methods. The calculated DFT results were found to be in good agreement with the coupled cluster results. The initial H-atom abstraction from –CH₃ and –CH₂ groups of DEE and their subsequent reactions with other atmospheric species is studied in detail. The initial H-atom abstraction and secondary propagation with O₂ resulting from the –CH₂ H-atom abstraction reactions are energetically more favourable than the corresponding –CH₃ H-atom abstraction reactions. The isomerisation of the peroxy radical is thermodynamically as well as kinetically not favourable. The 1-ethoxy ethoxy radical formed in the peroxy radical oxidation and subsequent reaction with NO reacts with O₂ resulting in ethyl formate and this reaction is competitive with the unimolecular dissociation of 1-ethoxy ethoxy radical by –CH₃ group and H-atom elimination, resulting in ethyl formate and ethyl acetate as products, respectively. The dissociation of 1-ethoxy ethoxy radical via C–O bond cleavage is not as competitive as the above reactions. The reactions of 1-ethoxy ethoxy radical with nitrates resulting in ethyl acetate along with HNO and HONO products are the thermodynamically driven reactions with a larger exothermicity, but these reactions are not kinetically favourable. The calculated reaction rate constants for the plausible alkoxy radical chemistry of DEE show that the unimolecular dissociation of 1-ethoxy ethoxy radicals (reactions (10) and (11)) are kinetically more favourable than the reaction of 1-ethoxy ethoxy radical with O₂. Further, both the –CH₃ and H-atom elimination reactions are equally competitive, where the latter is about 10⁴ times more rapid than the former. The plausibility of the alkoxy radical chemistry of DEE arranged in terms of kinetic favourability is as shown below:

CH₃CH₂OCH(O˙)CH₃ → CH₃CH₂OCH(=O) + C˙H₃ (10)

CH₃CH₂OCH(O˙)CH₃ → CH₃CH₂OC(=O)CH₃ + H˙ (11)

CH₃CH₂OCH(O˙)CH₃ + ³O₂ → CH₃CH₂OC(=O)CH₃ + HO₂ (8)

CH₃CH₂OCH(O˙)CH₃ → CH₃CH₂O˙ + CH(=O)CH₃ (12)

The results show that the ethyl formate is the major oxidation product in the oxidation chemistry of DEE, followed by ethyl acetate formation in comparably less quantities to ethyl formate, but its contribution is significant as reflected from the rate constants. Our computed results are in excellent agreement with the experimental study on oxidation of DEE by Cl by J. J. Orlando.⁷ From the present theoretical analysis, we conclude that the major oxidation products resulting from the DEE oxidation by OH radicals are ethyl formate and ethyl acetate, which have more possibility to involve in photooxidation in the troposophere further, whereas the co-products such as methyl radical and H radical have the greater chance to further initiate photooxidation process.

Acknowledgements

The authors thank the University Grants Commission (UGC), Govt. of India, for granting the research project under Major Research Project.

References

1. R. G. Derwent, M. E. Jenkin, S. M. Saunders and M. J. Pilling, Atmos. Environ., 1998, 32, 2429–2441.
2. K. Sato, S. Inomata, J.-H. Xing, T. Imamura, R. Uchida, S. Fukuda, K. Nakagawa, J. Hirokawa, M. Okumura and S. Tohno, Atmos. Environ., 2013, 79, 147–154.
3. J. Eberhard, C. MüLler, D. W. Stocker and J. A. Kerr, Int. J. Chem. Kinet., 1993, 25, 639–649.
4. T. J. Wallington and S. M. Japar, Environ. Sci. Technol., 1991, 25, 410–415.
5. Z. Li, P. Nguyen, M. F. de Leon, J. H. Wang, K. Han and G. Z. He, J. Phys. Chem. A, 2006, 110, 2698–2708.
6. D. R. Glowacki and M. J. Pilling, ChemPhysChem, 2010, 11, 3836–3843.
7. J. J. Orlando, Phys. Chem. Chem. Phys., 2007, 9, 4189–4199.
8. S. A. Cheema, K. A. Holbrook, G. A. Oldershaw, D. P. Starkey and R. W. Walker, Phys. Chem. Chem. Phys., 1999, 1, 3243–3245.
9. A. C. Davis and J. S. Francisco, J. Am. Chem. Soc., 2011, 133, 18208–18219.
10. L. Batt, Int. J. Chem. Kinet., 1979, 11, 977–993.
11. L. Chen, T. Uchimaru, S. Kutsuna, K. Tokuhashi, A. Sekiya and H. Okamoto, Int. J. Chem. Kinet., 2009, 41, 490–497.
12. C. Zavala-Oseguera, J. R. Alvarez-Idaboy, G. Merino and A. Galano, J. Phys. Chem. A, 2009, 113, 13913–13920.
13. T. Ogura, A. Miyoshi and M. Koshi, Phys. Chem. Chem. Phys., 2007, 9, 5133–5142.
14. Z. F. Xu, K. Xu and M. C. Lin, ChemPhysChem, 2009, 10, 972–982.
15. M. A. Ferenac, A. J. Davis, A. S. Holloway and T. S. Dibble, J. Phys. Chem. A, 2003, 107, 63–72.
16. A. C. Lloyd, K. R. Darnall, A. M. Winer and J. N. Pitts Jr, Chem. Phys. Lett., 1976, 42, 205–209.
17. R. S. Tranter and R. W. Walker, Phys. Chem. Chem. Phys., 2001, 3, 4722–4732.
18. E. Porter, J. Wenger, J. Treacy, H. Sidebottom, A. Mellouki, S. Téton and G. LeBras, J. Phys. Chem. A, 1997, 101, 5770–5775.
19. Y. Zhao and D. Truhlar, Theor. Chem. Acc., 2008, 120, 215–241.
20. A. Karton, A. Tarnopolsky, J. F. Lamere, G. C. Schatz and J. M. L. Martin, J. Phys. Chem. A, 2008, 112, 12868–12886.
21. G. Zheng, Y. Zhao and D. G. Truhlar, J. Phys. Chem. A, 2007, 111, 4632–4642.
22. L. Sandhiya, P. Kolandaivel and K. Senthilkumar, J. Phys. Chem. B, 2014, 118, 3479–3490.
23. L. Sandhiya and K. Senthilkumar, RSC Adv., 2014, 4, 7749–7759.
24. L. Vereecken, J. N. Crowley and D. Amedro, Phys. Chem. Chem. Phys., 2015, 17, 28697–28704.
25. J. A. Montgomery, M. J. Frisch, J. W. Ochterski and G. A. Petersson, J. Phys. Chem., 1999, 110, 2822–2827.
26. M. J. E. A. Frisch, Gaussian 09, Revision B.01, Gaussian, Inc., Wallingford CT, 2009.
27. J. Zheng, S. Zhang, J. C. Corchado, Y.-Y. Chuang, E. L. Coitiño, B. A. Ellingson and D. G. Truhlar, Gaussrate Version, 2015.
28. J. Zheng, S. Zhang, B. J. Lynch, J. C. Corchado, Y.-Y. Chaung, P. L. Fast, W. P. Hu, Y. P. Liu, G. C. Lynch, K. A. Nguyen, C. F. Jackels, A. F. Ramos, B. A. Ellingson, V. S. Melissas, J. Villa, I. Rossi, E. L. Coitino, J. Pu and T. V. Albu, POLYRATE version, 2015.
29. Obtained using a combination of values from Tables S1.1–S1.3† and also the heat of formation of 1-ethoxy ethoxy radical calculated using atomization enthalpies in the present study – see ESI† for details.
30. M. T. Sucarrat and J. M. Anglada, ChemPhysChem, 2004, 5, 183–191.
31. O. Setokuchi and M. Sato, J. Phys. Chem. A, 2002, 106, 8124–8132.
32. R. Atkinson, J. Phys. Chem. Ref. Data, Monogr., 1994, 2, 1.
33. R. Atkinson, Int. J. Chem. Kinet., 1997, 29, 99–111.
34. J. J. Orlando, G. S. Tyndall and T. J. Wallington, Chem. Rev., 2003, 103, 4657–4690.
35. C. M. Rosado-Reyes, J. S. Francisco, J. J. Szente, M. M. Maricq and L. Frøsig Østergaard, J. Phys. Chem. A, 2005, 109, 10940–10953.
36. F. Caralp and W. Forst, Phys. Chem. Chem. Phys., 2003, 5, 4653–4655.
37. A. C. Baldwin, J. R. Barker, D. M. Golden and D. G. Hendry, J. Phys. Chem., 1977, 81, 2483–2492.
38. V. F. Andersen, T. A. Berhanu, E. J. K. Nilsson, S. Jørgensen, O. J. Nielsen, T. J. Wallington and M. S. Johnson, J. Phys. Chem. A, 2011, 115, 8906–8919.

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Footnote

† Electronic supplementary information (ESI) available: Reaction enthalpies (ΔH₂₉₈, kJ mol⁻¹) and free energies (ΔG₂₉₈, kJ mol⁻¹) of the reactions involved in the oxidation of diethyl ether by OH radical using CBS-QB3 method is shown in Table S1. Available literature data for the heat of formation [kJ mol⁻¹] for some of the reactive species involved in the oxidation of diethyl ether by OH radical is shown in Table S1.1. Enthalpies of formation, ΔH⁰_f [kJ mol⁻¹] of the atoms is shown in Table S1.2. CBS-QB3 total energies of the atoms [in Hartrees] Table S1.3. Reaction enthalpies (ΔH₂₉₈, kJ mol⁻¹) and free energies (ΔG₂₉₈, kJ mol⁻¹) of the reactions involved in the oxidation of diethyl ether by OH radical using CBS-QB3 method is shown in Table S1.4. Reaction scheme for the OH initiated oxidation reactions of diethyl ether is shown in scheme S1. Energetics of the stationary points, relative energy [kJ mol⁻¹] of the reactive species involved in Scheme S1 are summarized in Tables S2 to S2.2. PES scan of the reactions (3)–(6) performed at UM06-2X/6-311++G(d,p) level of theory is shown in Fig. S1. Reaction scheme for the reactions of alkoxy radical with molecular oxygen is shown in Scheme S2. Energetics of the stationary points, relative energy [kJ mol⁻¹] of the reactive species involved in Scheme S2 are summarized in Tables S3–S3.2. Reaction scheme for the Isomerization reactions of peroxy radical and unimolecular dissociation of 1-ethoxy ethoxy radical is shown in Scheme S3. Energetics of the stationary points, relative energy [kJ mol⁻¹] of the reactive species involved in Scheme S3 are summarized in Tables S4–S4.2. Reaction scheme for the reactions of alkoxy radical with NO and NO₂ is shown in Scheme S4. Energetics of the stationary points, relative energy [kJ mol⁻¹] of the reactive species in the PES of reactions in Scheme S4 are summarized in Tables S5–S5.2. Calculated rateconstants (cm³ per molecule per s) of reaction (8, 10 and 11) is shown in Tables S6–S6.2. Optimized structure of the stationary points involved in the oxidation of diethyl ether by OH radical. See DOI: 10.1039/c6ra14801h

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