L.
Vereecken
*a,
G.
Vu
b,
A.
Wahner
a,
A.
Kiendler-Scharr
a and
H. M. T.
Nguyen
*b
aInstitute for Energy and Climate Research: IEK-8: Troposphere, Forschungszentrum Jülich GmbH, Jülich, Germany. E-mail: L.Vereecken@fz-juelich.de
bFaculty of Chemistry and Center for Computational Science, Hanoi National University of Education, Hanoi, Vietnam. E-mail: Hue.Nguyen@hnue.edu.vn
First published on 22nd July 2021
Terpenoids are an important class of multi-unsaturated volatile organic compounds emitted to the atmosphere. During their oxidation in the troposphere, unsaturated peroxy radicals are formed, which may undergo ring closure reactions by an addition of the radical oxygen atom on either of the carbons in the CC double bond. This study describes a quantum chemical and theoretical kinetic study of the rate of ring closure, finding that the reactions are comparatively fast with rates often exceeding 1 s−1 at room temperature, making these reactions competitive in low-NOx environments and allowing for continued autoxidation by ring closure. A structure–activity relationship (SAR) is presented for 5- to 8-membered ring closure in unsaturated RO2 radicals with aliphatic substituents, with some analysis of the impact of oxygenated substituents. H-migration in the cycloperoxide peroxy radicals formed after the ring closure was found to be comparatively slow for unsubstituted RO2 radicals. In the related cycloperoxide alkoxy radicals, migration of H-atoms implanted on the ring was similarly found to be slower than for non-cyclic alkoxy radicals and is typically not competitive against decomposition reactions that lead to cycloperoxide ring breaking. Ring closure reactions may constitute an important reaction channel in the atmospheric oxidation of terpenoids and could promote continued autoxidation, though the impact is likely to be strongly dependent on the specific molecular backbone.
![]() | (R1) |
Due to the much stronger C–H bond on carbons with a double bond, vinylic H-atoms do not migrate at a rate competitive to other atmospheric processes, and in autoxidation processes, the double-bonded carbons are thus more difficult to activate and oxidize, limiting the oxygen to carbon ratio O
:
C. In the atmosphere, however, the highest emissions of non-methane VOCs consist of isoprene (C5H8), monoterpenes (C10H16), and other terpenoids,15 most of which are (poly-)unsaturated compounds. Even for these compounds, highly oxidized compounds were measured with very high O
:
C ratios,7,9,16–19 indicating that all carbons can be oxidized without breaking the molecular backbone. One of the pathways that enables the oxidation of double-bonded carbons in a molecule is a ring closure reaction:
![]() | (R2) |
Ring closure reactions in RO2 and alkoxy radicals have been studied theoretically,20–27 and mechanisms incorporating these reactions for some compounds28 have been shown to provide a better agreement with experimental data. Still, these studies focused on a subset of molecules, and no structure–activity relationship (SAR) is available to enable systematic inclusion of such ring closure reactions in atmospheric chemical mechanisms.
In this work, we describe a theory-based SAR for ring closure in unsaturated RO2 radicals, examining 4- to 8-membered ring formation in linear and branched olefines. This SAR is directly applicable in mechanism development, can be readily implemented in software-assisted mechanism generation software such as GeckoA29,30 or SAPRC,31 and serves as a guide for further extensions examining a wider range of substituents. We also examine the ability of the product cycloperoxide radicals to undergo further autoxidation steps by H-migration, either at the peroxy radical or alkoxy radical stages of their subsequent chemistry.
The rovibrational data at the M06-2X or M06-2X-D3/aug-cc-pVTZ level combined with ZPE-corrected CCSD(T) barrier heights were then used to predict the thermal rate coefficient in a rigid rotor harmonic oscillator multi-conformer transition state theory (MC-TST) approximation,40 incorporating all conformers. Tunneling corrections are included based on an asymmetric Eckart barrier paradigm.41,42 As the reaction rates are low compared to the thermalization rate by collisions with the bath gas, no pressure dependence is expected under atmospheric conditions. As discussed below, the reverse reactions are expected to be too slow to compete, and no rate corrections were implemented for reverse reactions.
Reactant | Product ring + stereo | E b | E ring | k(298 K) | A | n | E a |
---|---|---|---|---|---|---|---|
CH2![]() |
4-Membered | 30.8 | 19.0 | 4.6 × 10−11 | 3.56 × 10−2 | 4.38 | 13![]() |
5-Membered | 29.0 | 2.6 | 2.3 × 10−10 | 5.15 × 101 | 3.08 | 13![]() |
|
CH2![]() |
5-Membered | 14.1 | 2.1 | 5.2 × 100 | 2.27 × 105 | 1.67 | 6019 |
6-Membered | 16.8 | 0.9 | 3.1 × 10−2 | 1.31 × 107 | 0.96 | 7547 | |
CH2![]() |
5-Membered (R*,S*) | 15.1 | 1.3 × 100 | 3.78 × 104 | 1.92 | 6328 | |
5-Membered (R*,R*) | 14.0 | 8.5 × 100 | 1.07 × 106 | 1.42 | 5919 | ||
5-Membered (total) | 14.0 | 2.0 | 9.7 × 100 | 7.71 × 104 | 1.87 | 5858 | |
6-Membered | 16.8 | 0.8 | 8.4 × 10−2 | 1.02 × 107 | 1.13 | 7462 | |
CH2![]() |
5-Membered | 14.4 | 2.0 | 8.7 × 100 | 8.73 × 105 | 1.59 | 6135 |
6-Membered | 17.5 | 1.6 | 2.2 × 10−2 | 1.48 × 108 | 0.71 | 7958 | |
CH2![]() |
5-Membered | 14.0 | 1.0 × 101 | 3.69 × 105 | 1.64 | 5908 | |
6-Membered | 16.4 | 9.4 × 10−2 | 6.43 × 106 | 1.10 | 7242 | ||
CH2![]() |
5-Membered | 14.0 | 1.1 | 1.0 × 101 | 1.19 × 105 | 1.83 | 5897 |
6-Membered | 16.1 | −0.2 | 1.9 × 10−1 | 8.61 × 106 | 1.15 | 7207 | |
E-CH(CH3)![]() |
5-Membered | 13.2 | 1.6 | 3.9 × 101 | 4.66 × 106 | 1.31 | 5713 |
6-Membered | 14.5 | −1.3 | 1.4 × 100 | 2.90 × 107 | 0.85 | 6452 | |
E-CH(CH3)![]() |
5-Membered (R*,S*) | 13.0 | 6.3 × 101 | 4.88 × 107 | 0.95 | 5656 | |
5-Membered (R*,R*) | 14.1 | 8.5 × 100 | 3.78 × 106 | 1.31 | 6109 | ||
5-Membered (total) | 13.0 | 1.5 | 7.2 × 101 | 4.42 × 106 | 1.36 | 5600 | |
6-Membered (R*,S*) | 15.8 | 1.7 × 10−1 | 2.83 × 107 | 0.82 | 7031 | ||
6-Membered (R*,R*) | 14.5 | 1.6 × 100 | 6.48 × 107 | 0.71 | 6436 | ||
6-Membered (total) | 14.5 | −1.2 | 1.7 × 100 | 5.90 × 106 | 1.12 | 6379 | |
Z-CH(CH3)![]() |
5-Membered | 13.2 | 0.6 | 3.7 × 101 | 1.81 × 107 | 1.06 | 5702 |
6-Membered | 16.0 | −2.3 | 1.3 × 10−1 | 5.48 × 107 | 0.66 | 7111 | |
Z-CH(CH3)![]() |
5-Membered (R*,S*) | 13.9 | 1.2 × 101 | 8.43 × 105 | 1.61 | 6042 | |
5-Membered (R*,R*) | 12.8 | 6.9 × 101 | 1.31 × 108 | 0.79 | 5653 | ||
5-Membered (total) | 12.8 | 0.5 | 8.1 × 101 | 1.96 × 106 | 1.49 | 5543 | |
6-Membered (R*,S*) | 15.8 | 1.5 × 10−1 | 5.57 × 107 | 0.69 | 7058 | ||
6-Membered (R*,R*) | 17.2 | 1.3 × 10−2 | 1.74 × 107 | 0.86 | 7709 | ||
6-Membered (total) | 15.8 | −2.2 | 1.6 × 10−1 | 4.53 × 106 | 1.11 | 6991 | |
CH2![]() |
5-Membered | 12.6 | 0.5 | 4.1 × 101 | 4.71 × 105 | 1.50 | 5335 |
6-Membered | 15.5 | −2.4 | 3.4 × 10−1 | 4.19 × 107 | 0.83 | 6953 | |
E-CH(CH3)![]() |
5-Membered | 11.0 | −1.5 | 7.9 × 102 | 1.26 × 107 | 1.04 | 4647 |
6-Membered | 12.6 | −2.8 | 7.0 × 101 | 2.60 × 108 | 0.64 | 5592 | |
E-CH(CH3)![]() |
5-Membered (R*,S*) | 13.2 | 3.4 × 101 | 9.00 × 106 | 1.21 | 5770 | |
5-Membered (R*,R*) | 11.0 | 1.3 × 103 | 2.22 × 108 | 0.69 | 4771 | ||
5-Membered (total) | 11.0 | −1.4 | 1.3 × 103 | 1.64 × 107 | 1.10 | 4684 | |
6-Membered (R*,S*) | 12.8 | 5.8 × 101 | 3.59 × 109 | 0.27 | 5811 | ||
6-Membered (R*,R*) | 14.6 | 2.1 × 100 | 3.23 × 109 | 0.22 | 6680 | ||
6-Membered (total) | 12.8 | −2.7 | 6.0 × 101 | 6.66 × 108 | 0.55 | 5761 | |
Z-CH(CH3)![]() |
5-Membered | 11.4 | −1.3 | 6.1 × 102 | 2.33 × 107 | 1.06 | 4947 |
6-Membered | 14.6 | −2.4 | 1.9 × 100 | 1.42 × 108 | 0.69 | 6572 | |
Z-CH(CH3)![]() |
5-Membered (R*,S*) | 12.7 | 6.9 × 101 | 4.60 × 105 | 1.69 | 5498 | |
5-Membered (R*,R*) | 11.0 | 1.2 × 103 | 3.48 × 107 | 1.01 | 4773 | ||
5-Membered (total) | 11.0 | −1.4 | 1.3 × 103 | 1.25 × 106 | 1.54 | 4668 | |
6-Membered (R*,S*) | 16.7 | 5.1 × 10−2 | 1.03 × 108 | 0.71 | 7594 | ||
6-Membered (R*,R*) | 14.3 | 3.3 × 100 | 7.67 × 107 | 0.80 | 6411 | ||
6-Membered (total) | 14.3 | −2.7 | 3.4 × 100 | 1.90 × 107 | 1.02 | 6365 | |
C(CH3)2![]() |
5-Membered | 12.2 | 0.5 | 2.6 × 102 | 1.17 × 108 | 0.91 | 5414 |
6-Membered | 13.8 | −2.4 | 3.8 × 100 | 1.75 × 108 | 0.50 | 6100 | |
C(CH3)2![]() |
5-Membered (R*,S*) | 13.0 | 6.0 × 101 | 1.37 × 107 | 1.25 | 5801 | |
5-Membered (R*,R*) | 11.9 | 3.8 × 102 | 1.17 × 109 | 0.52 | 5340 | ||
5-Membered (total) | 11.9 | 0.4 | 4.4 × 102 | 1.77 × 107 | 1.22 | 5227 | |
6-Membered | 13.5 | −2.8 | 5.4 × 100 | 2.91 × 106 | 1.16 | 5897 | |
C(CH3)2![]() |
5-Membered | 9.7 | −2.7 | 7.5 × 103 | 2.85 × 108 | 0.64 | 4230 |
6-Membered | 11.0 | −5.2 | 2.6 × 102 | 1.40 × 107 | 0.83 | 4657 | |
CH2![]() |
6-Membered | 16.2 | −0.7 | 1.6 × 10−1 | 2.20 × 103 | 2.19 | 6559 |
7-Membered | 18.4 | 0.5 | 4.5 × 10−3 | 2.35 × 106 | 1.23 | 8071 | |
CH2![]() |
6-Membered | 14.5 | −1.4 | 7.0 × 10−1 | 7.64 × 102 | 2.27 | 5935 |
7-Membered | 16.6 | 0.2 | 6.0 × 10−2 | 5.50 × 106 | 1.17 | 7448 | |
E-CH(CH3)![]() |
6-Membered | 15.4 | 4.3 × 10−1 | 4.04 × 106 | 1.15 | 6736 | |
7-Membered | 16.4 | 8.6 × 10−2 | 1.01 × 108 | 0.69 | 7393 | ||
Z-CH(CH3)![]() |
6-Membered | 15.0 | 1.9 × 100 | 3.93 × 108 | 0.46 | 6493 | |
7-Membered | 17.3 | 1.8 × 10−2 | 1.65 × 108 | 0.49 | 7669 | ||
C(CH3)2![]() |
6-Membered | 13.7 | 1.8 × 101 | 4.88 × 109 | 0.14 | 6027 | |
7-Membered | 15.7 | 2.0 × 10−1 | 3.78 × 108 | 0.34 | 6955 | ||
E-CH(CH3)![]() |
6-Membered | 13.4 | 8.0 × 100 | 3.12 × 106 | 1.13 | 5757 | |
7-Membered | 14.1 | 2.2 × 100 | 6.66 × 106 | 1.08 | 6284 | ||
Z-CH(CH3)![]() |
6-Membered | 13.8 | 7.9 × 100 | 5.74 × 108 | 0.40 | 6071 | |
7-Membered | 15.3 | 4.4 × 10−1 | 9.96 × 106 | 0.96 | 6677 | ||
C(CH3)2![]() |
6-Membered | 12.2 | 8.6 × 101 | 6.52 × 108 | 0.43 | 5455 | |
7-Membered | 12.8 | 1.2 × 101 | 2.08 × 105 | 1.54 | 5518 | ||
CH2![]() |
7-Membered | 17.7 | 3.4 × 10−3 | 4.78 × 104 | 1.65 | 771 | |
8-Membered | 16.4 | 9.9 × 10−3 | 1.22 × 102 | 2.37 | 6825 | ||
E-CH(CH3)![]() |
7-Membered (R*,S*) | 16.7 | 2.0 × 10−2 | 7.02 × 106 | 0.95 | 7479 | |
7-Membered (R*,R*) | 16.7 | 1.2 × 10−2 | 1.22 × 104 | 1.88 | 7316 | ||
7-Membered (total) | 16.7 | 0.1 | 3.2 × 10−2 | 5.57 × 105 | 1.41 | 7370 | |
8-Membered (R*,S*) | 14.7 | 6.8 × 10−2 | 1.58 × 103 | 1.80 | 6053 | ||
8-Membered (R*,R*) | 14.7 | 7.2 × 10−2 | 2.31 × 102 | 2.14 | 6038 | ||
8-Membered (total) | 14.7 | 1.0 | 1.4 × 10−1 | 1.03 × 103 | 1.99 | 6040 | |
Z-CH(CH3)![]() |
7-Membered (R*,S*) | 16.3 | 2.9 × 10−2 | 4.29 × 105 | 1.26 | 7061 | |
7-Membered (R*,R*) | 16.1 | 2.1 × 10−2 | 5.51 × 102 | 2.14 | 6664 | ||
7-Membered (total) | 16.1 | −0.8 | 4.9 × 10−2 | 3.38 × 104 | 1.69 | 6871 | |
8-Membered (R*,S*) | 15.9 | 1.5 × 10−2 | 1.78 × 104 | 1.47 | 6677 | ||
8-Membered (R*,R*) | 16.0 | 1.0 × 10−2 | 7.07 × 102 | 1.91 | 6563 | ||
8-Membered (total) | 15.9 | 0.1 | 2.5 × 10−2 | 9.45 × 103 | 1.65 | 6631 |
Reactant | Product ring | E b | k(298 K) | A | n | E a | Ref. |
---|---|---|---|---|---|---|---|
a Temperature-dependent rate coefficients re-evaluated from original B3LYP/6-31G(d,p) quantum chemical data and reported barrier heights. | |||||||
CH2![]() ![]() |
5-Membered | 13.1 | 1.3 × 102 | 8.05 × 108 | 0.65 | 5757 | This work |
6-Membered | 17.4 | 1.1 × 10−1 | 3.05 × 1011 | −0.16 | 8271 | This work | |
E-CH(OH)![]() |
6-Membered | 12.9 | 2.8 × 101 | 7.15 × 109 | 0.06 | 5879 | Novelli et al.24 |
Z-CH(OH)![]() |
6-Membered | 15.1 | 2.1 × 100 | 3.48 × 1016 | −2.28 | 7260 | Novelli et al.24 |
E-CH(OH)![]() |
6-Membered | 10.6 | 9.2 × 102 | 6.24 × 108 | 0.40 | 4689 | Novelli et al.24 |
Z-CH(OH)![]() |
6-Membered | 13.0 | 7.5 × 101 | 2.08 × 1014 | −1.42 | 6124 | Novelli et al.24 |
CH2![]() |
6-Membered | 16.2 | 9 × 10−1 | 1.52 × 1016 | −1.71 | 8235a | Vereecken and Peeters20 |
CH2![]() |
6-Membered | 17.0 | 1 × 10−1 | 1.29 × 1016 | −1.75 | 8710a | Vereecken and Peeters20 |
Z-C(CH3)(CH2ONO2)![]() |
5-Membered | 27.5 | 2.1 × 10−9 | 2.07 × 109 | 0.42 | 13062 | Vereecken et al.25 |
E-C(CH3)(CH2ONO2)![]() |
5-Membered | 28.6 | 7.2 × 10−11 | 3.43 × 104 | 1.90 | 13292 | Vereecken et al.25 |
CH2![]() |
5-Membered | 26.6 | 2.2 × 10−8 | 3.87 × 104 | 2.13 | 12028 | Vereecken et al.25 |
Z-CH(CH2ONO2)![]() |
5-Membered | 27.4 | 3.1 × 10−9 | 9.51 × 108 | 0.50 | 12845 | Vereecken et al.25 |
E-CH(CH2ONO2)![]() |
5-Membered | 26.7 | 2.0 × 10−9 | 5.01 × 107 | 0.74 | 12514 | Vereecken et al.25 |
CH2![]() |
5-Membered | 27.7 | 5.1 × 10−9 | 1.03 × 107 | 1.31 | 12722 | Vereecken et al.25 |
CH2![]() |
5-Membered | 14.4 | 7.7 × 100 | 1.04 × 107 | 1.19 | 6218 | Vereecken et al.25 |
6-Membered | 14.7 | 2.1 × 100 | 2.69 × 107 | 0.91 | 6420 | Vereecken et al.25 | |
CH2![]() |
5-Membered | 13.4 | 4.1 × 101 | 9.60 × 109 | 0.12 | 5951 | Vereecken et al.25 |
6-Membered | 15.7 | 1.5 × 100 | 2.47 × 1013 | −1.00 | 7384 | Vereecken et al.25 | |
(R,R)-CH2![]() |
6-Membered | 14.1 | 3.9 × 100 | 2.73 × 10−5 | 4087 | Chen et al.27 | |
7-Membered | 16.4 | 6.6 × 10−1 | 3.62 × 10−4 | 5384 | Chen et al.27 | ||
(R,S)-CH2![]() |
6-Membered | 15.1 | 3.0 × 100 | 1.75 × 1010 | 6568 | Chen et al.27 | |
7-Membered | 16.5 | 3.2 × 10−1 | 6.22 × 1010 | 7609 | Chen et al.27 | ||
CH2![]() ![]() |
9-Membered | 16.2 | 3.5 × 10−2 | 1.98 × 109 | 7297 | Chen et al.27 | |
(S,S)-CH2![]() |
5-Membered | 12.8 | 2.3 × 102 | 1.04 × 1011 | 5640 | Chen et al.27 | |
6-Membered | 14.1 | 2.0 × 101 | 5.50 × 1010 | 6178 | Chen et al.27 | ||
(S,R)-CH2![]() |
5-Membered | 13.3 | 4.5 × 101 | 4.14 × 1010 | 5943 | Chen et al.27 | |
6-Membered | 16.0 | 1.4 × 100 | 1.88 × 1011 | 7440 | Chen et al.27 | ||
(S,S)-CH2![]() |
5-Membered | 11.7 | 3.3 × 102 | 3.03 × 106 | 1.29 | 4906 | This work |
6-Membered | 14.4 | 1.2 × 101 | 1.25 × 1011 | −0.11 | 6692 | This work | |
(S,R)-CH2![]() |
5-Membered | 10.5 | 1.7 × 103 | 7.73 × 106 | 1.16 | 4482 | This work |
6-Membered | 12.8 | 4.9 × 101 | 2.68 × 108 | 0.69 | 5793 | This work |
The small impact of alkyl substitution around the radical moiety allows for a significant reduction of the complexity of the SAR, and concomitantly the needed number of calculations to derive the SAR. For larger molecules, we have thus only explicitly characterized the –CH2OO˙ moieties, and derive the SAR to predict the expected average across primary, secondary, and tertiary peroxy radicals.
The oxo group in acylperoxy radicals, –C(O)OO˙, was reported to accelerate RO2 radical H-migration reactions by an order of magnitude.11,43,44 Exploratory calculations on acylperoxy radicals (Table 2) indicate that the acyl group also accelerates ring closure by up to a factor 25.
For ring closure on the inner carbon of the double bond, the stereo-specificity on the outer double bonded carbon has little influence and is not considered explicitly in the SAR. For these reactions, the reactivity trend prediction could potentially be even further simplified by considering only 4 template categories, i.e. a double bond with 0, 1, 2 or 3 additional alkyl substituents. However, this reduction does not work well for ring closure on the outer carbon, where the stereo-substitution and positioning of the substituents have a larger impact. To keep the SAR setup similar for both types of ring closure, we choose at this time to use categories with site-specific substitution on the double bond for both closures. This will also aid in future extensions to oxygenated compounds, where the impact of site-specificity is likely to be more pronounced.
Table 3 summarizes the SAR as a lookup table, listing room temperature k(298 K) and rate coefficients k(T) for T = 200–450 K. Fig. 1 compares the explicit rate predictions in Table 1 against the SAR predictions; to our knowledge there are no direct experimental data available against which we can validate the SAR. The SAR captures the reactivity trends in the source data well (goodness of fit). Considering the uncertainty on the theoretical source data (of the order of a factor 3 to 5), and the uncertainty caused by omitting some of the minor influences on the rate coefficient, we estimate an overall uncertainty on the SAR predictions of a factor of 10 for aliphatic unsaturated RO2. For oxygenated RO2, Table 2 suggests that the deviation can be significantly larger, and care should be taken when trying to apply the SAR outside its field of applicability.
Olefinic substituents | k(298 K) | A | n | E a | Olefinic substituents | k(298 K) | A | n | E a |
---|---|---|---|---|---|---|---|---|---|
γ-Unsaturated RO2 radicals (CH2![]() |
|||||||||
5-Membered ring closure | 6-Membered ring closure | ||||||||
CH2![]() |
6.6 × 100 | 2.84 × 105 | 1.67 | 6019 | CH2![]() |
3.9 × 10−2 | 1.64 × 107 | 0.96 | 7547 |
CH(CH3)![]() |
4.8 × 101 | 1.15 × 107 | 1.19 | 5708 |
E-CH(CH3)![]() |
1.8 × 100 | 3.64 × 107 | 0.85 | 6452 |
Z-CH(CH3)![]() |
1.3 × 10−1 | 6.88 × 107 | 0.66 | 7111 | |||||
C(CH3)2![]() |
3.3 × 102 | 1.47 × 108 | 0.91 | 5414 | C(CH3)2![]() |
4.8 × 100 | 2.19 × 108 | 0.50 | 6100 |
CH2![]() |
5.2 × 101 | 5.91 × 105 | 2.27 | 5935 | CH2![]() |
4.3 × 10−1 | 5.26 × 107 | 1.17 | 7448 |
CH(CH3)![]() |
8.7 × 102 | 2.15 × 107 | 1.05 | 4797 |
E-CH(CH3)![]() |
8.8 × 101 | 3.26 × 108 | 0.64 | 5592 |
Z-CH(CH3)![]() |
2.4 × 100 | 1.78 × 108 | 0.69 | 6572 | |||||
C(CH3)2![]() |
9.4 × 103 | 3.57 × 108 | 0.64 | 4230 | C(CH3)2![]() |
3.2 × 102 | 1.76 × 107 | 0.83 | 4657 |
δ-Unsaturated RO2 radicals (CH2![]() |
|||||||||
6-Membered ring closure | 7-Membered ring closure | ||||||||
CH2![]() |
2.0 × 10−1 | 2.76 × 103 | 2.19 | 6559 | CH2![]() |
5.6 × 10−3 | 2.95 × 106 | 1.23 | 8071 |
CH(CH3)![]() |
1.1 × 100 | 5.00 × 107 | 0.81 | 6614 |
E-CH(CH3)![]() |
1.1 × 10−1 | 1.27 × 108 | 0.69 | 7393 |
Z-CH(CH3)![]() |
2.2 × 10−2 | 2.07 × 108 | 0.49 | 7669 | |||||
C(CH3)2![]() |
2.3 × 101 | 6.12 × 109 | 0.14 | 6027 | C(CH3)2![]() |
2.4 × 10−1 | 4.74 × 108 | 0.34 | 6955 |
CH2![]() |
8.7 × 10−1 | 9.59 × 102 | 2.27 | 5935 | CH2![]() |
7.6 × 10−2 | 6.90 × 106 | 1.17 | 7448 |
CH(CH3)![]() |
1.0 × 101 | 5.30 × 107 | 0.77 | 5914 |
E-CH(CH3)![]() |
2.8 × 100 | 8.35 × 106 | 1.08 | 6284 |
Z-CH(CH3)![]() |
5.6 × 10−1 | 1.25 × 107 | 0.96 | 6677 | |||||
C(CH3)2![]() |
1.1 × 102 | 8.18 × 108 | 0.43 | 5455 | C(CH3)2![]() |
1.5 × 101 | 2.61 × 105 | 1.54 | 5518 |
ε-Unsaturated RO2 radicals (CH2![]() |
|||||||||
7-Membered ring closure | 8-Membered ring closure | ||||||||
CH2![]() |
4.2 × 10−3 | 6.00 × 104 | 1.65 | 7714 | CH2![]() |
1.2 × 10−2 | 1.53 × 102 | 2.37 | 6825 |
CH(CH3)![]() |
2.7 × 10−2 | 2.64 × 107 | 0.82 | 7550 |
E-CH(CH3)![]() |
4.1 × 10−1 | 1.86 × 102 | 2.33 | 5788 |
Z-CH(CH3)![]() |
4.5 × 10−2 | 2.53 × 103 | 1.85 | 6400 | |||||
C(CH3)2![]() |
3.5 × 10−1 | 2.30 × 109 | 0.21 | 7098 | C(CH3)2![]() |
1.0 × 100 | 1.73 × 103 | 1.90 | 5432 |
CH2![]() |
2.6 × 10−2 | 4.42 × 104 | 1.63 | 7036 | CH2![]() |
1.5 × 10−1 | 4.09 × 102 | 2.27 | 6215 |
CH(CH3)![]() |
3.7 × 10−1 | 1.21 × 107 | 0.89 | 6663 |
E-CH(CH3)![]() |
1.8 × 101 | 9.19 × 102 | 2.18 | 4861 |
Z-CH(CH3)![]() |
9.8 × 10−1 | 4.40 × 101 | 2.55 | 5471 | |||||
C(CH3)2![]() |
4.0 × 100 | 5.19 × 107 | 0.70 | 6078 | C(CH3)2![]() |
7.2 × 101 | 4.23 × 100 | 2.78 | 3870 |
![]() | ||
Fig. 1 Goodness of fit for the structure–activity relationship relative to the calculated (total) rate coefficients in Table 1. The solid line depicts 1![]() ![]() |
![]() | (R3) |
These rearrangements have been theoretically characterized by Møller et al.48 to have high reaction barriers of 13 to 17 kcal mol−1 for the substitution patterns in this work, and Vereecken and Peeters20 argue that the geometric constraints caused by the ring structure will further hamper this reaction, with a calculated energy barrier exceeding 25 kcal mol−1 for a 6-membered ring. The theoretical work by Møller et al.48 predicts rate coefficients <102 s−1 for non-cyclic non-oxygenated β-hydroperoxy alkyl radicals, making epoxide-alkoxy radical formation negligible compared to O2 addition under atmospheric conditions. For multi-substituted β-hydroperoxy alkyl radicals, however, rates as high as 107 to 1010 s−1 are predicted, which would dominate recombination with O2. Møller et al. summarize the structural requirements for fast epoxidation reactions, concluding that an OH group is needed on the alkyl radical site, and another oxygenated group. For ring closure reactions, this implies that epoxidation would only be important for RO2 with a double bond carrying an OH substituent (i.e. an enol) and simultaneously another oxygenated group on the other carbon of the double bond. Such substitution patterns make up only a very small fraction of the atmospherically relevant unsaturated RO2 radicals, and are not considered further at this time.
Reactant | H-migration span | E b | E product | k(298 K) | A | n | E a |
---|---|---|---|---|---|---|---|
a The α-OOR alkyl radical has a very small barrier to decomposition at the current level of theory. | |||||||
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1,5-Ha (syn-side) | 23.8 | 15.4 | 4.3 × 10−5 | 5.48 × 10−16 | 8.39 | 6771 |
1,6-Hb (α-peroxide) | 21.2 | 8.4 | 1.2 × 10−2 | 1.17 × 10−36 | 14.93 | 1998 | |
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1,5-Ha (syn-side) | 24.5 | 14.1 | 2.5 × 10−5 | 2.92 × 10−29 | 12.84 | 5370 |
1,6-Hb | 25.0 | 13.6 | 5.0 × 10−6 | 1.55 × 10−33 | 13.91 | 4735 | |
1,7-Hc (α-peroxide) | 26.2 | −34.6 | 1.9 × 10−5 | 1.73 × 10−113 | 39.78 | −6613 | |
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1,5-Ha (syn-side) | 22.5 | 14.4 | 1.3 × 10−3 | 1.15 × 10−23 | 10.97 | 4864 |
1,5-Ha (anti-side) | 28.9 | 3.4 × 10−7 | 3.07 × 10−55 | 21.18 | 2988 | ||
1,6-Hb | 23.7 | 11.9 | 9.9 × 10−5 | 4.45 × 10−36 | 14.83 | 3670 | |
1,7-Hc | 25.3 | 13.7 | 4.1 × 10−6 | 1.42 × 10−30 | 12.79 | 4924 | |
1,7-Hd (α-peroxide) | 26.4 | −37.0 | 1.7 × 10−5 | 1.17 × 10−112 | 39.42 | −6621 | |
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1,5-Ha (syn-side) | 23.8 | 12.8 | 1.4 × 10−4 | 2.20 × 10−35 | 14.83 | 4041 |
1,5-Ha (anti-side) | 26.0 | 7.2 × 10−6 | 1.00 × 10−44 | 17.86 | 3650 | ||
1,6-Hb | 21.2 | 12.3 | 1.9 × 10−3 | 5.31 × 10−19 | 9.19 | 4923 | |
1,7-Hc | 24.7 | 10.1 | 1.9 × 10−5 | 5.15 × 10−45 | 17.31 | 2242 | |
1,8-Hd | 27.1 | 11.8 | 5.3 × 10−7 | 2.04 × 10−47 | 18.05 | 2910 | |
1,7-He (α-peroxide) | 28.1 | −37.4 | 1.2 × 10−6 | 6.70 × 10−121 | 41.96 | −7163 | |
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1,5-Ha (α-peroxide) | 28.1 | 14.6 | 1.6 × 10−7 | 1.02 × 10−45 | 18.19 | 4670 |
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1,5-Ha | 24.2 | 13.8 | 4.5 × 10−5 | 1.54 × 10−27 | 12.23 | 5340 |
1,6-Hb (α-peroxide) | 28.3 | 15.2a | 2.0 × 10−7 | 1.03 × 10−39 | 16.12 | 5219 | |
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1,5-Ha | 25.1 | 13.9 | 2.1 × 10−5 | 1.65 × 10−31 | 13.64 | 5241 |
1,6-Hb | 26.2 | 15.6 | 4.3 × 10−6 | 5.50 × 10−23 | 10.54 | 6308 | |
1,7-Hc (α-peroxide) | 26.3 | 11.2a | 3.1 × 10−6 | 1.17 × 10−48 | 18.73 | 2688 |
The rate of reaction can be seen to be strongly dependent on the size of the ring, the position of abstraction in that ring, and the span of the H-migration. Compared to similar H-migrations in non-cyclic hydrocarbons,10,11 the predicted rate varies by as much as 2 orders of magnitude due to the differences in ring strain, barrier height and tunneling. Fig. 2 shows the ratio kcyclic(T)/knoncyclic(T) of the predicted rates for the cycOO-RO2 (Table 4) over the predictions by the SAR by Vereecken and Nozière,11 where we used the SAR-predicted rate of α-OOH-substituted H-atoms as a proxy for the α-OOR H-atoms in the cycOO-RO2, and where the SAR predictions were corrected by a factor of 2 to account for the inaccessible anti-H-atoms. As can be seen, the cycOO-RO2 have significantly different rate coefficients than non-cyclic RO2, where especially below 350 K the rate coefficient ratio is strongly temperature dependent due to the differences in energy, entropy, and tunneling between cyclic and non-cyclic RO2. Even within a specific reaction class, the ratio kcyclic(T)/knoncyclic(T) varies significantly, with e.g. 1,5- or 1,6-H-migration rates in cycloperoxide-CH2OO˙ radicals being significantly faster, about similar, or significantly slower than their non-cyclic counterpart (Fig. 2). Likewise, the temperature-dependence of the ratio is very different between α-OOR-1,6-H-migrations compared to α-OOR-1,7-H-migrations. For cycloperoxide-OO˙ radicals, there can be many orders of magnitude difference between the rates at the lower temperatures, even within a given reaction class. Hence, while on average the rate coefficients for cycOO-RO2 are only a factor ∼4 below those of non-cyclic RO2, the large scatter of a factor 25 indicates that reactivity trends are not transferable between cyclic and non-cyclic RO2.
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Fig. 2 Ratio of the rate coefficient for H-migration in cycloperoxide-RO2 radicals against SAR-predictions11 for analogous H-migrations in oxygenated non-cyclic RO2. Dashed line: 1![]() ![]() |
To investigate the impact of the peroxide group in the ring, we examined some molecular isomers of the cycOO-RO2 radicals, shown in Table 5; note that these compounds can not be formed by the mechanism of RO2 ring closure described above, and these structures may not even have atmospheric formation channels. The position of the peroxide group in the ring changes which H-migration spans lead to an α-OOR radical product, which directly affects the rate of reaction. Comparing the data from Table 4 against Table 5, we also find an order of magnitude difference in rate for the 1,5-alkyl-H-migration out of a seven-membered ring that differs only in the position of the (remote) peroxide group, indicating that the position of the peroxide group affects the barrier height even if not directly involved in the reaction. Comparing against a cyclohexyl-peroxy radical, we find that the corresponding 6-membered cycloperoxide-peroxy radical isomers both have higher barrier heights, likely caused by the increased ring strain induces by the different bond lengths and bond angles around the endo-cyclic oxygen atoms. We conclude that the presence of a peroxide functionality, and its precise position in the ring, can have a large impact on the reaction rate; at the present time we do not have sufficient data to systematically characterize such influence.
For the alternative fate by decomposition, rates for cycOO-RO are expected to be well predicted by the SAR by Vereecken and Peeters,58 and its recent update in Novelli et al.;59 this SAR includes the impact of the ring. For the cycOO-RO in Table 6 that decompose by CH2O elimination, barrier heights ≤7.5 kcal mol−1 and rates k(298 K) ≥ 8 × 107 s−1 are predicted, while cycOO-RO with the radical O-atom implanted on the ring preferentially break the ˙OC–COO bond, with SAR-predicted barriers of ≤8.5 kcal mol−1 and k(298 K) ≥ 1 × 107 s−1. In both cases, an α-OOR alkyl radical is formed, which are known to decompose without (significant) barrier to a carbonyl and an alkoxy radical;49,50 both classes of cycOO-RO in Table 6 will thus lead to two fragments: HCHO and a non-cyclic carbonyl-alkoxy radical, as shown below.
Given the high rate of decomposition compared to H-migration in cycOO-RO, the main fate of most cycOO-RO in Table 6 is fragmentation and decyclization of the ring originally formed in the unsaturated RO2 ring closure. Only for the largest rings studied, where ring strain in the H-migration TS is lowest, H-migration may contribute for a non-negligible fraction.
Comparing the data for cycOO-RO radical isomers different only by the position of the peroxide group in the ring (Tables 5 and 6), we find that the site-specificity of the peroxide group can affect the rate coefficient by over an order of magnitude, with sometimes large differences in barrier height for otherwise comparable processes. As for the H-migration in cycOO-RO2 radicals, we thus conclude that the rate coefficients are isomer-specific and do not readily generalize to generic cycloperoxides.
The fastest reactions are found for formation of 5 and 6-membered rings. For addition on the inner carbon, larger rings have an entropic disadvantage and the rate coefficient gradually decreases as the cyclic chain becomes longer. For addition on the outer carbon, which is more affected by the geometric impact of the double bond in the TS ring structure, this reduction of the rate for longer chains is not as pronounced, and for rings up to 8 atoms the energetic advantage of the longer chain compensates for the increasing entropic disadvantage. The rate coefficient is most affected by substitution on the double bond, with higher substitution leading to faster ring closure reactions. The stereo-specificity of the substitution on the double bond is most important for ring closure on the outer carbon, where it affects the rate coefficients at 298 K by an order of magnitude. Preliminary calculations and literature data on oxygenated substituents suggest that the latter can greatly enhance the rate of ring closure.
H-Migration in the product cycloperoxide RO2 radicals was examined for H-atoms implanted directly on the ring structure, including migration of α-OOR H-atoms which leads to ring decomposition. The reaction rates were found to be highly dependent on the ring size and migration span, and are poorly correlated to the H-migration rate in non-cyclic RO2 especially below 350 K. On average, the rate of migration is slower than the equivalent migration in non-cyclic RO2. It is proposed that H-migration in substituted cyclic RO2 could be driven mainly by migration of substituent H-atoms.
H-Migration in the cycloperoxide alkoxy radicals formed from the product cycloperoxide RO2 was also examined, and compared to SAR-predictions for decomposition reactions. The migration of H-atoms on the ring is typically slower than for non-cyclic alkoxy radicals, owing to the ring strain in the H-migration TS. For the specific molecular skeleton resulting from the ring closure in the parent unsaturated RO2 radical, we find that the dominant fate of the cycloperoxide alkoxy radicals is formation of a carbonyl fragment and a non-cyclic carbonyl-alkoxy radical. It is proposed that H-migration in cyclic RO could become important when migrating substituent H-atoms instead of ring H-atoms.
As multi-unsaturated compounds such as isoprene and the monoterpenes make up the bulk of the non-methane organic matter emitted to the atmosphere, unsaturated RO2 radicals are common in the atmosphere, and ring closure reactions could have a significant impact on the oxidation of some volatile organic compounds. For some compounds it was already shown that RO2 ring closure reactions have a large impact on the product distribution.20–23,28 However, the overall impact of these reactions on the atmospheric oxidation of such compounds can not be quantified in this work, as it is likely to differ greatly between the individual compounds and thus requires detailed analysis of each specific oxidation mechanism. Specifically, the impact of substituents is not covered in the current work, and could have profound impact on the chemical mechanisms of the individual compounds.
Footnote |
† Electronic supplementary information (ESI) available: Details on the algorithm for the conformer search; the geometries, rovibrational characteristics and energies of all reactants, TS and products characterized in this study are available at the M06-2X level of theory. Where available, CCSD(T) energies and T1 diagnostics are also provided. See DOI: 10.1039/d1cp02758a |
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