1
Degradation of three oxygenated alkoxy radicals of atmospheric interest: HOCH2O˙, CH3OCH2O˙, CH3OCH2OCH2O˙. RRKM theoretical study of the β-C–H bond scission and the 1,6-isomerisation kinetics

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj1

2
A detailed theoretical study on the pressure and temperature dependence of the rate constants k1, k2, k3 for the thermal β-C–H dissociation of the three radicals: HOCH2O˙, CH3OCH2O˙, CH3OCH2OCH2O˙ is presented.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj1

3
This investigation is extended to the rate constant k4 for the 1,6-H-shift isomerisation of CH3OCH2OCH2O˙.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj2

4
High-level ab initio computations (CCSD(T)//MP2) have been performed and combined with RRKM theory to obtain rate constants.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met1

5
The β-C–H scission pathway is predicted to occur with an activation energy of 10–13 kcal mol−1.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res1

6
Estimation of the competition between the β-C–H and β-C–O decompositions, the isomerisation process, and the reaction with oxygen has been done.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res2

7
At 760 Torr and 298 K, k1, k2, k3, k4 are 4.4 × 104 s−1, 5.2 × 104 s−1, 4.2 × 103 s−1 and 5.6 × 103 s−1 respectively.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res3

8
An interesting result is that the isomerisation through a seven-membered transition state may compete with the H-atom elimination from the CH3OCH2OCH2O˙ radical.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res4

Introduction

9
In this paper, we present a theoretical study of the three following β-C–H dissociations of oxygenated alkoxy radicals:HOCH2O˙ + M → HCOOH + H˙ + MCH3OCH2O˙ + M → CH3OCHO + H˙ + MCH3OCH2OCH2O˙ + M → CH3OCH2OCHO + H˙ + Mand of the isomerisation process:CH3OCH2OCH2O˙ + M → ˙CH2OCH2OCH2OH + Mfor which one pressure data were available at room temperature from experimental measurements.1–3

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj3

10
Actually, because of the increasing use as industrial solvents and fuel additives of oxygenated compounds such as ethers, their tropospheric oxidation has received significant attention.

Type: Motivation | Advantage: None | Novelty: None | ConceptID: Mot1

11
Dimethyl ether (DME) CH3OCH3, and dimethoxymethane (DMM) CH3OCH2OCH3, have been proposed as possible alternative diesel fuels.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac1

12
Atmospheric degradation of these compounds is initiated by ˙OH radical attack which abstracts an alkyl hydrogen, and the alkyl radical formed will rapidly add oxygen to give peroxy radicals RO2˙.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

13
In polluted atmosphere, peroxy radicals react with NO to give the corresponding alkoxy radicals RO˙.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

14
In the case of DME, these successive reactions CH3OCH3 + ˙OH → CH3OCH2˙ + H2OCH3OCH2˙ + O2 + M → CH3OCH2O2˙ + MCH3OCH2O2˙ + NO → CH3OCH2O˙ + NO2produce the simplest α-alkoxyalkoxy radical CH3OCH2O˙.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

15
By similar reactions, ˙OH oxidation of DMM gives two different alkoxy radicals, CH3OCH2OCH2O˙ and CH3OCH(O˙)OCH3 depending on the group (–CH3 or –CH2) from which there is H-abstraction.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac5

16
The most common reactions of alkoxy radicals are reaction with O2 (if an α-H is present), isomerisation via 1,5 H-shift through a 6-membered transition state and decomposition by β-C–C or β-C–O bond fission (if an ether oxygen atom is present).4

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac6

17
However, a kinetic study of the self-reaction of the peroxy radical CH3OCH2O2˙1 complemented by a detailed product analysis has provided evidence for a mechanism involving the rapid thermal decomposition of the alkoxy radical CH3OCH2O˙ by H-atom elimination occurring in competition with the reaction with O2.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac7

18
CH3OCH2O˙ + M → CH3OCHO Methylformate (MF) + H˙ + MCH3OCH2O˙ + O2 → CH3OCHO Methylformate (MF) + HO2˙ The authors1 have obtained a value of the decomposition rate constant of about 3 × 103 s−1 (assuming kO2 ≈ 10−14 cm3 molecule−1 s−1) at 25 Torr total pressure.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac8

19
Moreover, it is shown in this work that the rate constant k2 for H-atom elimination exhibits a pressure dependence in the 25–800 Torr pressure range.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac9

20
In the same way, Wallington et al.,2 in a FTIR-smog chamber study of the atmospheric chemistry of DMM, analysed the fate of CH3OCH2OCH2O˙ by measuring the yield of methoxymethylformate (MMF) and suggested the occurence of the two pathways: CH3OCH2OCH2O˙ + M → CH3OCH2OCHO (MMF) + H˙ + MCH3OCH2OCH2O˙ + O2 → CH3OCH2OCHO (MMF) + HO2˙They observed that the yield of MMF, although sensitive to the O2 partial pressure, does not approach zero at the lowest O2 pressure.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac10

21
This gives evidence for the occurrence of reaction (3).

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac11

22
From a fit to their experimental data, they obtained the ratio k9/k3, and then k3 ≈ 4 × 103 s−1 at 296 K and 700 Torr total pressure.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac12

23
Moreover, their experimental results suggest that isomerisation (4) could be a competing atmospheric loss process.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac13

24
CH3OCH2OCH2O˙ + M → ˙CH2OCH2OCH2OH + MIn the same study, the authors analysed the fate of the other alkoxy radical, CH3OCH(O˙)OCH3 (produced by ˙OH attack to the –CH2 group of the DMM), by measuring the yield of dimethylcarbonate (DMC) and found it independent of the molecular oxygen partial pressure.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac14

25
They concluded that collision-induced H-atom elimination was the prime channel: CH3OCH(O˙)OCH3 + M → CH3OC(O)OCH3 (DMC) + H˙ + MThis conclusion has been successfully used in the computer simulation performed by Geiger and Becker.5

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac15

26
Veyret et al3. have provided the first evidence for H-atom elimination from HOCH2O˙ (reaction (1)) to explain a chain process in the photooxidation of formaldehyde.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac16

27
From their kinetic simulation at 298 K and 343 K, they proposed an order of magnitude of k1 ≈ 1200 s−1 at 298 K for 10–30 Torr total pressure of formaldehyde.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac17

28
Therefore, it appears that H-atom elimination may be a general decomposition mechanism for alkoxy bearing an oxygen functionality.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac17

29
Numerous theoretical studies have recently been devoted to the reactivity of alkoxy radicals.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac18

30
In particular, decomposition6,7 and isomerisation7,8 reactions have been investigated and structure-activity relationships (SAR) have been developed for the activation barrier or the rate constants.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac19

31
More recently, Rayez et al9. examined a novel rearrangement (α-ester rearrangement) of an oxygenated alkoxy radical and Ferenac et al10. studied the effect of oxygen-containing functional groups on the β-C–C and β-C–O decomposition and on the isomerisation of alkoxy radicals.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac20

32
Some theoretical results have also been presented about the β-C–H scission reactions of alkoxy7,11,12 (including oxygenated alkoxy12).

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac21

33
There is currently a considerable interest for the reactions of alkoxy radicals and especially for oxygenated alkoxy radicals, but only a few studies have concerned this particular reaction of H-atom elimination.

Type: Motivation | Advantage: None | Novelty: None | ConceptID: Mot2

34
In particular, no theoretical approaches have been used for providing general characteristics of this type of reactions and, at the end, to built SAR.

Type: Motivation | Advantage: None | Novelty: None | ConceptID: Mot3

35
Thus, it was interesting to study the thermal β-C–H scission of some oxygenated alkoxy radicals, namely HOCH2O˙, CH3OCH2O˙ and CH3OCH2OCH2O˙ (reactions (1)–(3)), as well as the isomerisation process (4) for CH3OCH2OCH2O˙.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj2

36
Our main objective in this study is to provide and compare the thermal unimolecular rate constants, k1, k2, k3, k4 obtained from RRKM calculations of the falloff curves.

Type: Goal | Advantage: None | Novelty: None | ConceptID: Goa1

37
We evaluate also the magnitude of the H-atom elimination (and of the isomerisation) relatively to the β-C–O decomposition and to reaction with O2.

Type: Goal | Advantage: None | Novelty: None | ConceptID: Goa2

Computational details

38
The thermal rate constants of the unimolecular reactions (1) and (2) are obtained by applying the RRKM theory to predict the falloff behaviour using the KISTHEP package13 validated by comparison with the program FALLOFF.14

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met2

39
For the CH3OCH2OCH2O˙ radical, the two competitive reaction channels (β-C–H scission and isomerisation) are treated simultaneously with the program FALLOFF.14

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met3

40
Kinetics calculations were first performed with input data (structural and thermochemical parameters) obtained from CCSD(T)//MP2 ab initio calculations.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met4

41
A good agreement between the results of RRKM calculations and experimental data was obtained by slightly adjusting the value of the calculated threshold energy of the corresponding unimolecular reactions.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met5

Quantum chemistry calculations

42
Ab initio computations were carried out using the Gaussian98 software package.15

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met6

43
The HF-DFT (B3LYP)16/6-31G** theoretical level was used to yield an estimation of the enthalpy of (reactions (1)–(3)) and of the activation energy of the reactions that may compete with the β-C–H scission.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met7

44
In order to obtain reliable energetics, calculations were then performed at higher levels of theory: (i) G2-theory17 and (ii) CCSD(T)/cc-pVDZ//MP2(Frozen Core)/cc-pVDZ.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met8

45
In the last case, using cc-pVDZ basis set, all geometries were fully optimized at the unrestricted second-order Mőller-Plesset perturbation (UMP2) level of theory using the “frozen-core” approximation.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met9

46
It is to be noticed that UHF wave functions for the β-C–H transition states were contaminated by higher-lying spin states, with values of 〈S2〉 ∼ 0.85, while for the isomerisation one it was less contaminated (〈S2〉 ∼ 0.78).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res5

47
Harmonic vibrational frequencies and zero-point energies (ZPE) were also computed at the UMP2/cc-pVDZ level of theory and are not scaled.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met10

48
Single and double coupled-cluster theory with inclusion of a perturbative estimation for triple excitation18 was used to improve the accuracy on calculated energies.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met11

49
All transition states have been characterized by one imaginary frequency (first order saddle points) on the potential energy surface (PES).

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met12

50
Intrinsic reaction coordinate analyses (IRC) were performed at both HF-DFT(B3LYP) and UMP2 levels of theory in order to confirm that a specific transition state connects the designated local minima.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met13

Thermal unimolecular rate constants

51
The microcanonical rate constants are calculated by the standard RRKM expression: k(E) = αG(E)/hN(E) where α is the reaction path degeneracy, G(E) is the total number of states of the transition state with energy less than or equal to E, and N(E) is the density of states of the radical.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

52
To account for the two possible H-eliminations, the reaction path degeneracy α was set to two; more details are given in the next Section.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

53
For the possible 1,6-H-shift isomerisation of CH3OCH2OCH2O˙ radicals, reaction (4), α was set at 3.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod3

54
All species are treated as symmetric tops and the external K-rotor, associated with the smallest moment of inertia, is treated as an active degree of freedom completely coupled to the vibrations.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod4

55
Taking into account the possibility of several simultaneous unimolecular channels, the thermal rate constant for each channel is obtained by using the following expression:19 where Q is the partition function of the active degrees of freedom of the radical, Q‡i,rot and Qrot are the partition functions for adiabatic rotations of the transition state and of the radical, respectively, Ei,0 is the threshold energy, ω = βcZLJ[M] is the effective collision frequency where βc is the collisional efficiency, ZLJ is the Lennard-Jones collision frequency and [M] is the total gas concentration.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod5

56
ZLJ was calculated for the alkoxy radicals of interest using the parameters of selected nearest species (see details below).

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod6

57
In order to account for the centrifugal effect in the rate constant calculation, the factor Q‡i,rot/Qrot was included in the expression of ki(T) and ki(E) is evaluated at the energy E including 〈ΔEj〉 with 〈ΔEj〉 = (1 − I‡/I)kBT where I‡ and I are the average of the two largest moments of inertia.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod7

Results and discussion

Structural parameters

58
The geometries of the alkoxy radicals investigated are presented in Fig. 1, where the relevant geometrical parameters have been indicated.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs1

59
In the following, R1, R2, R3 refer to the three alkoxy radicals investigated and TS1, TS2, TS3 designate the corresponding transition states for β-C–H scissions.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res6

60
It can be pointed out that reactant R1 has C1 symmetry, that is, the hydroxyl H-atom is twisted out of the OCO plane (HOCO = 54.3° at the MP2 level of theory), thus leading to the existence of two optical isomers.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res7

61
This result is obtained whatever the level of theory used and can be explained by orbital analysis.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res7

62
Out of plane position of hydrogen atom allows for a largest delocalisation of the two electrons in molecular orbital depicted Fig. 2, and simultaneously accounts for the (i) minimization of interaction between the 2p lone pairs of each oxygen, (ii) optimisation of the intramolecular hydrogen bonding forces involving the in-plane 2p lone pair on the open-shell oxygen atom, (iii) maximisation of the π overlap, involving the hydroxyl oxygen 2p orbital (out of plane) and a CH2 fragment orbital, that describes the unpaired electron π delocalisation across the OCO skeleton atoms.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res8

63
The reactant R2 geometry is consistent with the one predicted by Francisco20 in his study of the CH3OCH2O˙ radical structure.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res9

64
As aforementioned, we have taken a reaction path degeneracy α of two in the following rate constant calculations for each alkoxy decomposition, reactions (1), (2) and (3).

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

65
Unlike the β-C–O decomposition (see Fig. 3), it is clear that H-elimination can occur by two distinct paths since two physically distinct β-C–H bonds can dissociate in each reactant (R1, R2, R3) to form a carbonyl group (see Fig. 1).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res10

66
Although these two H-atoms are differently situated and the two corresponding elimination paths are different, we have assumed, for computational purposes, that the loss of reactant proceeds with the same rate constant by each of the two pathways.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod8

67
This can be rationalized by examining the structure of each transition state (see TS1, TS2, TS3 in Fig. 1) and keeping in mind that the two pathways differ only by the position of the leaving H-atom: situated above or under the HCOO plane.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod8

68
For reaction (1), the two corresponding transition states have exactly the same properties, while some differences appear for reactions (2) and (3) due to asymmetrical environment around the leaving H-atom.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res11

69
For instance, our CCSD(T)//MP2 computations give a difference in potential energy of 0.3 kcal mol−1 between these two similar transition states for reaction (3).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res12

70
From an electronic structure point of view, the decomposition of the studied alkoxy radicals by β-C–H bond rupture involves transition state geometries (TS1, TS2, TS3) with more product-like character.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res13

71
For instance, in the transition state TS3 the C–O bond is shortened by about 0.13 Å (C–Oreactant = 1.36 Å, C–OTS3 = 1.23 Å) which corresponds to 90 percent of the final shortening (C–Oproducts = 1.21 Å).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res14

72
The breaking C–H bond in the transition state is significantly longer (by about 32 percent) than in the unperturbed radical.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res15

73
The structural parameters (vibrational frequencies and rotational constants) of reactants and transition states obtained at the MP2 level of theory for reactions (1)–(3) are presented in Table 1.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs2

74
It is worth noting that the transition state structures are well localized on the PES, with moments of inertia slightly lower than those of the corresponding radicals.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res16

75
This results in very small entropies of activation leading to low preexponential factors for these decomposition reactions (≈5 × 1012 s−1).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res17

76
It can be noticed that we have found, for reaction (2), another H-elimination channel involving at the beginning of this process a conformer of the reactant: R2′ (see Fig. 1).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res18

77
At the CCSD(T) level of theory, the calculated barrier is however about 2 kcal mol−1 larger, showing that this channel is not favoured.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res19

78
It is interesting to note that R3 conformer geometry reveals an intramolecular hydrogen bond.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs3

79
More explicitly, it forms a seven-membered ring structure making possible the isomerisation process (4).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res20

80
This possibility is examined below.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj3

81
The corresponding structure of the transition state (TS7) is given in Fig. 4 and structural parameters are reported in Table 1.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs4

Relative energies

82
As can be seen from Table 2, the enthalpies of β-C–H scission (1), (2) and (3) at 0 K (ΔrH°(0 K)) are of the same order of magnitude for each level of theory.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res21

83
For instance, the heat of reactions (1)–(3) derived from the G2 method are −1.0, −1.4 and −1.2 kcal mol−1, respectively.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs5

84
The estimated enthalpy of each reaction indicates it to be thermoneutral at the two levels of theory G2 (about −1 kcal mol−1) or CCSD(T)//MP2 (between −2 and −3 kcal mol−1).

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs6

85
Using isodesmic reactions for reaction (2), Good and Francisco12 have estimated a ΔH value of 3.0 kcal mol−1, consistent with our findings.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac22

86
It is not surprising that B3LYP gives values significantly different with respect to the other methods since a larger basis set would be necessary to better describe the large electronic changes occurring between reactant and products.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res22

87
Barrier heights (ΔH‡°(0 K)) for the β-C–H bond dissociations investigated in this work are summarized in Table 2.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs7

88
Comparison of these values to each other shows no significant difference at each level of theory for the three reactions.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res23

89
The studied β-C–H bond scissions involve a sizeable energy barrier (9–14 kcal mol−1).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res24

90
Hippler et al11. have computed activation barriers for such β-C–H bond dissociations for a set of twelve non-oxygenated alkoxy radicals and found values lying between 19 and 26 kcal mol−1.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac22

91
The fact that our computed barriers are about twice smaller than their values provides strong evidence for an effect of oxygen-substituents which increases the β-C–H dissociation rate.

Type: Hypothesis | Advantage: None | Novelty: None | ConceptID: Hyp1

92
Preceding the products, a shallow minimum has been spotted on the PES for each reaction corresponding to a weak-bound complex that is formed by just a few kcal mol−1 binding energy between H-atom and the corresponding co-product.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res25

93
In order to establish the relative importance of the H-atom elimination and of the β-C–O dissociation, an alternative reaction pathway, we also present an estimation of the energetic features for the latter channel for each alkoxy radical, at B3LYP theoretical level: HOCH2O˙ + M → HO˙ + H2CO + MCH3OCH2O˙ + M → CH3O˙ + H2CO + MCH3OCH2OCH2O˙ + M → CH3OCH2O˙ + H2CO + MThe values of calculated barriers (20–30 kcal mol−1, Table 2) agree favourably with those obtained by Ferenac et al10. at the same level of theory for other similar oxygenated alkoxy radicals (CH3CH2OCH2O˙: 20 kcal mol−1, CH3COOCH2O˙: 22 kcal mol−1).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res26

94
Good and Francisco12 have obtained an activation barrier of 23.1 kcal mol−1 at the G2 level of theory for reaction (12), which is in good agreement with our HF-DFT (B3LYP) value (21.4 kcal mol−1).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res27

95
The large activation energies obtained for the β-C–O bond scission (together with the Arrhenius factors found for this process at 298 K: A ≈ 1–2 × 1013 s−1) clearly show that this process is not favourable, as found by Good and Francisco12 for the CH3OCH2O˙ radical.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res28

96
This is in line with experimental findings of Wallington et al2. and Geiger and Becker5 who suggest that decomposition of CH3OCH2OCH2O˙ via reaction (13) is of minor importance.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac23

97
There are no possible isomerisation reaction by 1,5 H-shift through a six-membered transition state for these three alkoxy radicals.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res29

98
However, Wallington et al2. suggest that an unknown reaction, accounting for about 9% of the fate of CH3OCH2OCH2O˙, should be an isomerisation reaction.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac24

99
Our CCSD(T)//MP2 calculations show that the 1,6-H-shift (reaction (4)) (ΔH‡°(0 K) = 10.7 kcal mol−1) is more favoured than the 1,4 H-shift (ΔH‡°(0 K) = 20.6 kcal mol−1).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res30

100
In view of our results (G2 and CCSD(T)//MP2 in Table 2), this 1,6-isomerisation channel through a 7-membered transition state may be energetically competitive with the β-C–H scission.

Type: Hypothesis | Advantage: None | Novelty: None | ConceptID: Hyp2

101
Concerning the CH3OCH2O˙ radical, the 1,2 and 1,4 H-shifts have not been taken into account in our kinetic treatment.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod9

102
Indeed, the corresponding B3LYP activation energies (ΔH‡°(0 K) = 27.6 and 24.4 kcal mol−1 respectively) are very large compared to the β-C–H one (ΔH‡°(0 K) = 13.3 kcal mol−1) (the B3LYP predicted Arrhenius A factors being similar at 298 K: Aβ-C–H = 6 × 1012 s−1, Aisom = 2–4 × 1012 s−1).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res31

Rate constants

103
Structural parameters (vibrational frequencies and rotational constants) listed in Table 1 are employed in the RRKM calculations for H-elimination reactions (1), (2) and (3) and isomerisation reaction (4).

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs8

104
There are no data available for the Lennard-Jones parameters, σ and ε/k, of the three studied alkoxy radicals.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac25

105
Values were evaluated from tabulated values of nearest species or were based on the recommendation of Gilbert and Smith21 using the boiling point of similar species.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met14

106
These estimated values are also reported in Table 1.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs9

107
For the HOCH2O˙ radical, experiments3 were performed in formaldehyde as buffer gas.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac26

108
Therefore the evaluated Lennard-Jones parameters of this species are reported in Table 1 along with those of N2 used as buffer gas for the two other alkoxy radicals.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs10

109
When N2 is the buffer gas, the collisional efficiency βc is taken equal to 0.2 which is a reasonable value at 298 K. For reaction (1), the collisional efficiency of formaldehyde is unknown.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod10

110
Here, we have choosen to use βc = 0.2 as for N2.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod10

111
As discussed below, doubling this value has no significant effect on the k1 pressure dependence under atmospheric conditions.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res32

112
As proposed by Troe,22 a temperature dependence for βc ∝ T−1 was used in calculations.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod11

113
As above-mentioned, in first step of the calculation, all the energetic input data used in the statistical RRKM calculations were taken from the CCSD(T)//MP2 results.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met15

114
Then, taking into account that the ab initio values of the barrier height E0 are calculated with uncertainties of about 1–2 kcal mol−1, E0 was adjusted in order to fit at best the available kinetic experimental data.

Type: Method | Advantage: None | Novelty: None | ConceptID: Met15

115
The best fit was obtained with E0 = 9.6, 10.7, 12.6 and 11.5 kcal mol−1 for reactions (1), (2), (3) and (4), respectively.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs11

116
These values are reported in Table 3, along with the values obtained from CCSD(T)//MP2 calculations.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs12

117
It can be seen that the adjustments (0.8–2.5 kcal mol−1) are within the margin of errors (both experimental and theoretical).

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs13

118
Those values show that the β-C–H scission pathway can be predicted to occur with an activation energy of 10–13 kcal mol−1.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs14

119
It should be noted that in the particular case of the CH3OCH2OCH2O˙ radical, the 1,6-H-shift isomerisation reaction (4) was taken into account, using the data reported by Wallington et al.2

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod12

120
In air conditions, they report that the β-C–H scission accounts for 7% of the total reaction, the 1,6-H-shift isomerisation for 9% and the reaction with oxygen for 84%.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac27

121
Consequently, at 296 K and 760 Torr, the experimental values are k3 ≈ 4 × 103 s−1 and k4 ≈ 5 × 103 s−1.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac28

122
The falloff curves are shown in Fig. 5 for reactions (1)–(4).

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs15

123
As can be anticipated for reactions having similar threshold energies, the increasing complexity of the radical from HOCH2O˙ to CH3OCH2OCH2O˙ results in a decrease of the broadening of the falloff.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res33

124
In order to compare, the predicted pressure dependence of the β-C–H dissociation rate constants k1, k2 and k3, the values of the high-pressure limiting rate constant k∞ and the ratio Γ = k760/k∞ (k∞ ≡ kTST obtained using adjusted E0) are listed in Table 3.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs16

125
The same calculation was performed for upper tropospheric conditions (220 K and 150 Torr).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res34

126
It is interesting to point out that, for reactions (1) and (2) at 298 K and 760 Torr total pressure, the rate constant is still strongly pressure dependent (Γ = 0.05 and 0.35, respectively).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res35

127
This is in good agreement with measurements of Jenkin et al1. for reaction (2).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res36

128
The same situation is observed at 150 Torr and 220 K (upper tropospheric conditions).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res37

129
In contrast, reactions (3) and (4) are near the high pressure limit (Γ = 0.85 and 0.90, respectively).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res38

130
It appears from falloff curves (Fig. 5) that the extrapolated values at 760 Torr of the rate constants of reactions (1) and (2) are about one order of magnitude higher than that of reactions (3) and (4).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res39

Uncertainties on E0 values

131
From the calculated falloff of the rate constant k1 (HOCH2O˙), it is deduced that the experimental value3 of the rate constant, obtained at 25 Torr, is in the low-pressure part of the falloff with k25/k∞ ≈ 10−3.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res40

132
Therefore errors on βc and ZLJ are directly propagated on the calculated value of the rate constant and thus, on the deduced value of E0.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res41

133
For example, doubling the formaldehyde collisional efficiency (βc = 0.4 rather than 0.2) leads to a new fitted E0 value of 10.1 kcal mol−1 (instead of 9.6 kcal mol−1).

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs17

134
Similarly, by inspection of Fig. 5, it is clear that the k2 experimental value of Jenkin et al1. for CH3OCH2O˙ radical, obtained at 25 Torr, is in the low-pressure part of the falloff.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res42

135
This experimental value is obtained relatively to the rate constant of the reaction with O2, with [O2] in the range (1–6) × 1017 molecule cm−3.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met16

136
This results in large uncertainty on the experimental value of the dissociation rate constant of (1–6) × 103 s−1.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res43

137
Therefore, we consider that the calculated values of E0, obtained by fitting of our statistical calculations to experimental results, have an uncertainty of ±1 kcal mol−1.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res44

138
It is worth noting that, for reaction (2), our RRKM calculated falloff fitted to the experimental value of rate constant at 25 Torr, has predicted the kinetic behaviour which is experimentally observed at 760 Torr1 for this reaction.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res45

139
In fact, it is indicated in ref. 1 that the rate constant is pressure dependent and that competition with the O2 reaction exists at 760 Torr, [O2] > 1018 molecule cm−3, which corresponds to rate constants >1 × 104 s−1.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac29

140
This is in good agreement with our calculated value of 5.2 × 104 s−1 at 760 Torr.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res46

141
In addition to β-C–H bond scission (3) our calculations show that the 1,6-isomerisation (4) through a seven-membered transition state is a possible competing loss process for the CH3OCH2OCH2O˙ radical.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res47

142
For these two competitive unimolecular (reactions (3) and (4)), ab initio calculations predict dissociation barrier heights of the same order of magnitude (at the G2 and CCSD(T) levels of theory, Table 2).

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs18

143
Similar values are returned by RRKM kinetic analysis of experimental results (in Table 3).

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs19

144
Therefore, our ab initio calculations give theoretical support to the Wallington et al2. assumption suggesting that a competing isomerisation is likely to occur.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con1

145
However, further calculations are needed (for example CASPT2 computations) to confirm this.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con2

146
Actually, due to the existence of spin contamination (see computational details), the computed β-C–H activation energy for reaction (3) is less reliable than the isomerisation one.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res48

147
The predicted relatively low barrier height ≈11 kcal mol−1 for this isomerisation seems to arise from the presence of an oxygen atom next to the CH3 group.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res49

148
This is to link to the observation of Dibble et al10. who studied the 1,5 H-shift isomerisation reactions of CH3OCH2CH2O˙ and CH3CH2OCH2O˙ radicals.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac30

149
They observed that the activation barrier for isomerisation is lower by about 10 kcal mol−1 when the oxygen is adjacent to the methyl group from which abstraction occurs than when it is closer to the alkoxy radical center.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac31

150
Estimation can be made of the competition between the β-C–H scission and the reaction with oxygen (the isomerisation process (4) has also been considered for CH3OCH2OCH2O˙ radical).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res50

151
Assuming kO2 ≈ 10−14 cm3 molecule−1 s−1 (see ref. 4), about 45% of HOCH2O˙, 50% of CH3OCH2O˙ and 7% of CH3OCH2OCH2O˙ dissociate, and 9% of CH3OCH2OCH2O˙ undergo isomerisation under conditions of the lower troposphere (760 Torr, 298 K and 20% O2).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res50

152
In the upper troposphere (150 Torr, 220 K and 20% O2), due to the barrier heights and the falloff effect of the unimolecular reactions, dissociations and isomerisation are negligible compared to reaction with oxygen.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res51

153
Pressure and temperature dependencies of the β-C–H scission rate constant can be presented using the conventional Troe's equation:23 in order to provide a quick and convenient way of calculating the pressure dependence of the rate constant values in the range (220 K–300 K).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res52

154
The three parameters k0, k∞ and Fc have been derived from the non-linear fitting of the above equation to the presented RRKM results at two temperatures.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res53

155
The resulting expressions of k0(T), k∞(T) and Fc(T) are given in Table 4, along with those corresponding to Fc = 0.6.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res54

Conclusion

156
In the last few decades, there have been indications from experimental studies that rapid H-atom elimination might be a general decomposition mechanism for alkoxy radicals bearing an oxygen functionality.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac32

157
A theoretical study on the fate of the three following alkoxy radicals: HOCH2O˙, CH3OCH2O˙ and CH3OCH2OCH2O˙ is presented.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj1

158
The presence of an ether functional group in alkoxy radicals appears to lower the β-C–H bond scission activation energy (by about 10 kcal mol−1).

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con3

159
From our RRKM analysis based on ab initio data, under tropospheric conditions, the rate constants k1 and k2 for the two first radicals are about one order of magnitude higher than for the largest radical.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con4

160
Furthermore, it turns out that in the tropospheric pressure range, k1 and k2 are strongly pressure dependent while k3 is near the high-pressure limit.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con5

161
The results of the present investigation show that the competition between the β-C–H bond scission and reaction with O2, can only be significant under conditions of the lower troposphere.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con6

162
In addition to β-C–H bond scission and reaction with O2, our calculations show that possible competing loss process for CH3OCH2OCH2O˙ radical is the 1,6-isomerisation, through a seven-membered transition state.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res55

163
This is a very unusual case, since typically only the 1,5 isomerisation is considered.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res56

164
Such a behaviour may be expected for larger oxygenated alkoxy radicals.

Type: Hypothesis | Advantage: None | Novelty: None | ConceptID: Hyp3

165
This may be interesting for atmospheric modelling since isomerisation leads to products different from those generated by the β-C–H bond scission and reaction with O2.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con7