Structure–Activity Relationships for 1,3-Dipolar Cycloaddition Reactions of Criegee Intermediates with Carbonyls

Abstract

Carbonyl oxides, or Criegee intermediates (CIs), are key species formed during the ozonolysis of alkenes and are an important atmospheric oxidant. However, direct measurements of CI gas-phase rate constants for many atmospherically relevant reactions are still unknown. Herein, we present various approaches for developing structure–activity relationships (SARs) to predict the reactivity of the simplest CI (formaldehyde oxide; CH₂OO) with a range of carbonyls that are significant primary emission components as well as secondary products of hydrocarbon oxidation in the atmosphere. Approaches include the application of Hammett analysis, frontier molecular orbital (FMO) theory, and global electrophilicity indices to develop SARs. By combining these parameters with available kinetic data, we establish substituent-based predictive models that extend to carbonyl species and CIs lacking measured rate constants that can enhance the predictive representation of CI chemistry in atmospheric models. Of the different approaches, Hammett constants yield the best correlations overall, however, low-cost quantum chemical calculations of orbital energies offer a practical alternative for systems lacking experimental substituent parameters. Finally, we extend this framework to explore the influence of substitution on the CI and the corresponding cycloaddition kinetics.

1. Introduction

Although the existence of Criegee intermediates (CIs, carbonyl oxides, R₁R₂COO) had been postulated since the 1930s, there were no means of directly measuring the gas-phase kinetics of these highly reactive intermediates until 2012, when it was discovered that photolysis of diiodomethane (CH₂I₂) in the presence of O₂ yields a significant amount of the simplest CI, formaldehyde oxide (CH₂OO), that can be used for direct kinetic studies. , This result was a major breakthrough, as accurate rate constants are required to characterize the impact of CIs on oxidation processes in the atmosphere and in combustion. These initial experimental measurements have been followed by an extensive body of work characterizing the spectroscopy and reactivity of CH₂OO and larger CIs (R₁R₂COO, where R₁ and R₂ are alkyl or vinyl groups), − providing an important means of benchmarking theoretical methods needed to model their reactions in the atmosphere.

Ozonolysis reactions are prominent low-temperature oxidation processes and are a major chemical sink of unsaturated hydrocarbons in the atmosphere. , Ozone (O₃) reacts with alkenes via a 1,3-dipolar cycloaddition across the double bond to form cyclic 1,2,3-trioxolanes, or primary ozonides (POZs), which decompose to form a carbonyl compound and a CI. As a coproduct of ozonolysis, carbonyls also act as important Criegee scavengers, reacting via an analogous 1,3-dipolar cycloaddition across the carbonyl double bond and leading to the formation of a cyclic 1,2,4-trioxolane species, or secondary ozonide (SOZ). , Reactions of CIs with carbonyls have been the focus of many recent direct experimental kinetics − and computational ,, studies.

1,3-dipolar cycloaddition reactions occur where an electron-rich 1,3-dipole (in this case, the CI) initiates bond formation via interaction with an electron-deficient dipolarophile (here, the carbonyl). The overall reactivity of this class of reaction has long been known to depend strongly on substituent effects, as argued by Sustmann in his discussion of Diels–Alder reactions. , The impact of different carbonyl substituents on reactivity toward CIs can be understood using concepts from frontier molecular orbital (FMO) theory. , Substituent electronic properties (electron-withdrawing vs electron-donating) inductively affect the electron density of the carbonyl, respectively lowering or raising the FMO energies. The result is stabilization or destabilization of the cycloaddition transition state, which consequently increases or decreases the corresponding rate constant. For instance, the room-temperature bimolecular rate constant for the reaction of CH₂OO with hexafluoroacetone ((CF₃)₂CO) is ∼100 times larger than that for the reaction with acetone ((CH₃)₂CO), , as the strongly electron-withdrawing trifluoromethyl (CF₃) groups significantly lower the energies of the FMOs, while the electron-donating methyl (CH₃) groups increase them. In lieu of orbital energies, which are typically obtained from ab initio calculations, the electron-withdrawing or donating character of substituents on the carbonyls can be quantified using Hammett substituent constants. , Hansch et al. organized the Hammett parameter coefficients for over 200 substituents that have several different electronic and steric properties.

Here, we provide an analysis of the kinetics of 1,3-dipolar cycloaddition reactions CIs with a range of carbonyl species. A sizable experimental data set now exists for reactions involving CH₂OO, although there are almost no equivalent measurements for other CIs, where substituent effects are expected to play a similar role. As an alternative, the reactions of larger (substituted) CIs with SO₂, which also proceed via a cycloaddition mechanism, will be used as a proxy. Following on from our previous work, ,,− , we propose various structure–activity relationships (SARs) based on Hammett substituent constants and applications of FMO theory to quantify the carbonyl substituent effect on reactivity with CH₂OO. The SARs provide a semiempirical means of estimating rate constants for CH₂OO + R₁R₂CO reactions without explicit applications of reaction rate theories that rely on accurate ab initio characterization of transition states geometries and properties. Precise quantification of thermochemical properties from ab initio calculations requires an accurate treatment of the electronic structure along with careful evaluation of the molecular partition functions that go beyond the rigid rotor harmonic oscillator (RRHO) model, by including hindered rotors or improved treatment of anharmonicity, as well as taking into account tunneling contributions. The convenient, low computational cost predictive SARs developed here can be used to estimate rate constants for reactions of CH₂OO with carbonyls, as well as the analogous reactions of larger CIs, which have received far less attention experimentally.

2. Methods

Electronic structure calculations of the unimolecular reaction intermediates and energies involved were performed with the Gaussian and GAMESS packages. , Initial geometry optimizations were carried out with the B3LYP/cc-pVDZ method and thermodynamic quantities were further refined with the CBS-QB3 compound method, which has been shown to provide reliable thermochemistry involving the main group elements at modest computational cost. Frequency analysis confirmed the transition states and minimum structures. In addition, the energies of the frontier molecular orbitals were obtained from the B3LYP/cc-pVDZ calculations. Previous work has shown the orbital energies calculated at a similar level of theory to provide linear correlation with molecular properties such as ionization potential, electron affinity, and excitation energy. This level of theory also can be reasonably scaled to larger systems.

3. Results

3.1. Overview of Reactions and Substituent Effects

Carbonyls are key oxidation products of hydrocarbons in the atmosphere and also contribute to primary emissions, making their atmospheric fate a subject of significant interest. The dominant removal pathways for most carbonyls are reaction with OH radicals and direct photolysis initiated by the presence of the n-π* transition in the carbonyl chromophore. − In addition, wet and dry deposition contribute for some water-soluble species. Aldehydes possess an abstractable hydrogen atom, making OH oxidation the primary atmospheric sink though photolysis is also significant. Aliphatic ketones such as acetone lack this abstractable hydrogen and are instead removed primarily by photolysis. α,β-Dicarbonyls such as biacetyl and pyruvic acid exhibit enhanced near-UV absorption and are dominated by photolysis. , Enals and enones react readily with OH radicals due to addition across the conjugated CC double bond, making this the dominant atmospheric sink for these species. ,

Reaction with CIs represents an additional potential sink for atmospheric carbonyls. Bimolecular rate constants have been measured for the reactions of the simplest CI (CH₂OO) with a range of organic carbonyl species (aldehydes, ,,,,− ,, ketones, ,,,,,, hydroxyketones, dicarbonyls, , enones and enals, , and keto acids , ), denoted in general as R₁R₂CO. The weighted average room-temperature (295–300 K) rate constants, listed in Table , span 2 orders of magnitude (from approximately 0.3 to 30 × 10^–12 cm³ s^–1) and clearly demonstrate that the identities of the carbonyl substituents affect the reactivity of R₁R₂CO toward CH₂OO. Taking formaldehyde (HCHO), acetaldehyde (MeCHO), and acetone (CH₃COCH₃, dMK) as examples, each successive replacement of H with CH₃ results in an approximately 3-fold decrease in the magnitude of the rate constant, such that k _HCHO > k _MeCHO > k _dMK.

1. Experimental Room-Temperature Rate Constants for Reactions of CH₂OO with Carbonyls (R₁R₂CO) .

class	species (abbreviation)	k exp/10–12 cm3 s–1	R1	R2
aldehydes	formaldehyde (HCHO) ,	3.90 ± 0.20	H	H
	acetaldehyde (MeCHO) ,,,,	1.24 ± 0.05	H	CH3
	propanal (EtCHO) ,	3.27 ± 0.25	H	CH2CH3
	n-butanal (nPrCHO) ,	2.65 ± 0.27	H	CH2CH2CH3
	isobutanal (iPrCHO) ,	2.33 ± 0.38	H	CH(CH3)2
ketones	acetone (dMK) ,,,,,	0.45 ± 0.01	CH3	CH3
	methyl ethyl ketone (MEK)	0.64 ± 0.02	CH3	CH2CH3
	hexafluoroacetone (HFA)	30.6 ± 2.7	CF3	CF3
hydroxyketones	hydroxyacetone (AcOH)	1.09 ± 0.15	CH3	CH2OH
	4-hydroxy-2-butanone (4H2B)	1.11 ± 0.26	CH3	CH2CH2OH
enals, enones	acrolein (ACR)	1.63 ± 0.19	H	CHCH2
	methacrolein (MACR)	0.44 ± 0.10	H	C(CH3)CH2
	methyl vinyl ketone (MVK)	0.50 ± 0.04	CH3	CHCH2
α -dicarbonyls	biacetyl (BiAc) ,	11.0 ± 0.9	CH3	CH3CO
	acetylpropionyl (AcPr)	10.9 ± 1.3	CH3	CH3CH2CO
			CH3CH2CO	CH3CO
keto-acid	pyruvic acid (PyrA) ,	19.6 ± 1.0	CH3	COOH
			OH	CH3CO
enolone	acetylacetone (AcAc)	0.80 ± 0.07	CH3	CHCH(OH)CH3

^aValues are weighted averages of reported measurements, with 1σ uncertainties.

In contrast to CH₂OO, rate constants for the analogous reactions of other CIs (R₁R₂COO, where R₁, R₂ are alkyl or vinyl groups) with organic carbonyls have not been reported. In lieu of those experimental measurements on substituted CIs with organic carbonyls, we will discuss instead the related reactions between CIs and sulfur dioxide (SO₂), which also proceed via a 1,3-dipolar cycloaddition mechanism and have been the subject of numerous kinetics studies. Experimental room-temperature rate constants for the R₁R₂COO + SO₂ reactions are compiled in Table and show that the reactivity is also affected by the identity of the CI substituents. ,,,− In going from CH₂OO to anti-CH₃CHOO to (CH₃)₂COO, successive replacement of each H with CH₃ results in a steady increase in the magnitude of the rate constant.

2. Experimental Room-Temperature Rate Constants for Reactions of Aliphatic Criegee Intermediates (R₁R₂COO) with SO₂ .

species	k exp/10–12 cm3 s–1	R1	R2
formaldehyde oxide (CH2OO) ,,,,− ,−	37.7 ± 0.3	H	H
acetaldehyde oxide (syn-CH3CHOO) ,,,,	25.0 ± 1.4	H	CH3
acetaldehyde oxide (anti-CH3CHOO) ,,	101 ± 8	H	CH3
acetone oxide ((CH3)2COO) ,	135 ± 4	CH3	CH3

^aValues are weighted averages of reported measurements, with 1σ uncertainties.

Criegee intermediates react with organic carbonyls via 1,3-dipolar cycloaddition reactions to form cyclic 1,2,4-trioxolanes, commonly referred to as secondary ozonides (SOZs). This pathway is illustrated schematically in Figure for reaction of CH₂OO with a representative asymmetric carbonyl, acetaldehyde (R₁ = H, R₂ = CH₃). The reactions proceed by formation of a near coplanar entrance-channel van der Waals complex (vdW) that then passes over the cycloaddition transition state (TS) resulting in SOZ formation. The relative energetics are shown in terms of the changes in the zero-point corrected electronic energies (ΔE) at 0 K and the free energies (ΔG) at 298 K. In terms of ΔE, the vdW complex and the TS are both lower in energy than the separated reactants. However, the entropic contribution to the free energy moves ΔG of both the entrance channel complex and the transition state structure above the reactants. In general, the cycloaddition TS is the highest point on the free energy surface and represents the rate determining step in the overall reaction mechanism. SOZ formation is exothermic by approximately 40–50 kcal mol^–1, and the energized product can undergo a range of further isomerization and decomposition reactions. It should be noted that for carbonyls with very low barriers to SOZ formation, the rate can be controlled by so-called “outer” complexes and transition states that occur at larger reactant separations. In the present work, our analysis focuses on the shorter range “inner” vdW complexes and TSs.

1.

CBS-QB3 zero-point corrected energy ΔE (blue, 0 K) and free energy ΔG (red, 298 K) profiles for reaction of CH₂OO with acetaldehyde to form a secondary ozonide (SOZ). Geometries of the entrance channel complexes (vdW), transition states (TSs), and SOZ products for the E and Z pathways described in the text are both shown, although energy differences are small.

Before proceeding, we briefly discuss some stereochemical aspects of the 1,3-dipolar cycloaddition mechanism. The CIs that will be discussed belong to the C_s point group and the carbonyl moiety of the coreactant is also planar. Ab initio calculations have shown that, in general, the reactions proceed via near coplanar entrance channel complexes (see Figure ), in which the CI and carbonyl species are separated by ∼2.5 Å. Closing the distance to ∼2.2 Å leads to a reactant-like early TS that is typically lower in energy than the reactants. Reaction can occur act at either face (obverse or reverse) of the CO group. For asymmetric carbonyl compounds (i.e., R₁ ≠ R₂), the CI can adopt two distinct orientations, which we classify as E and Z according to whether the central O atom of the CI is displaced toward the side of the lower or higher priority carbonyl substituent, respectively. These two conformers are shown in Figure . Substituent priority follows organic chemistry conventions (H < CH₃ < CH₂OH < CH₃O etc.). Reaction at either face of the carbonyl leads to stereoisomeric TSs and SOZs that have identical energies. The E and Z reaction pathways proceed via TSs with slightly different energies and lead to different ring puckering conformers of the SOZ products.

Qualitatively, the substituent effects can be understood from consideration of the frontier molecular orbitals, as originally proposed by Sustmann to describe the symmetry-allowed orbital interactions of Diels–Alder cycloaddition reactions. , The substituents are classified as electron-donating groups (EDGs) and electron-withdrawing groups (EWGs). A molecular orbital (MO) diagram for the reaction between CH₂OO and formaldehyde (R₁ = R₂ = H) is shown in Figure . The orbital interactions are labeled based on loose symmetry considerations. The occupied nonbonding (n _pC–pO ) orbital on CH₂OO and the unoccupied π* orbital of HCHO are loosely symmetric about a center of inversion, and they interact to form the molecular orbitals labeled S and S*. The antisymmetric orbitals are the occupied π orbital on HCHO and the unoccupied π* orbital of CH₂OO, which interact to form the molecular orbitals labeled A and A*. The nonbonding orbitals localized on heteroatoms are neglected. In general, the S-interaction involves a smaller orbital energy gap and is likely to be more significant in controlling reactivity (see Section below).

2.

Molecular orbital diagram for the 1,3-dipolar cycloaddition reaction between CH₂OO (left) and formaldehyde (right). The “symmetric” orbitals interact to form the molecular orbitals (S, S*) (connected by black solid lines), and the “antisymmetric” orbitals form the molecular orbitals (A, A*) (connected by gray dotted lines). The effects on the orbital energies of the CI or the carbonyl of replacing H atoms with electron-donating groups (EDGs) or electron-withdrawing groups (EWGs) are indicated with arrows.

Substituent groups raise or lower the FMO energies of the CI and the carbonyl relative to their values in CH₂OO and HCHO. The effect on reactivity can be understood qualitatively by considering the dominant (smaller orbital energy gap) S-interaction. Substituents that are more electron-withdrawing than H lower the frontier molecular orbital energies, while substituents that are more electron-donating raise them. As can be seen in Figure , electron-withdrawing substituents on the carbonyl decrease the S-interaction orbital energy gap, stabilizing the transition state, and increasing reactivity. Electron-withdrawing substituents on the CI serve to increase the S-interaction orbital energy gap, which leads to a decrease in reactivity. Electron-donating substituents have the opposite effects. On the CI they are activating, while on the carbonyl they are deactivating.

3.2. Thermodynamic Energy Relationships

The reactivity of 1,3-dipolar cycloaddition reactions can be characterized in terms of thermodynamic energy correlations as discussed by Ess and Houk, who explored the reactivity of a range of 1,3-dipoles including oxides, imines, and ylides. , In that work, it was shown that the Marcus-type relationship for electron transfer reactions holds for some 1,3-dipolar cycloaddition reactions but not others. However, in general, lower TS energies are associated with more exothermic reactions.

We have used the composite CBS-QB3 method to characterize the transition states and SOZ products for all but one of the CH₂OO + R₁R₂CO reactions listed in Table . The sole exception is the CH₂OO + HFA reaction, for which no TS could be located at the B3LYP/6–311G­(2d,d,p) level of theory used to optimize geometries within the CBS-QB3 method. Calculations were performed for both E and Z pathways for asymmetric carbonyls. Harmonic frequencies are used to estimate vibrational zero-point energies and evaluate thermal contributions to the enthalpy and free energy at 298 K using RRHO partition functions for all modes. The resulting zero-point corrected energies (ΔE _TS; ΔE _SOZ) at 0 K and free energies (ΔG _TS; ΔG _SOZ) at 298 K of the TSs and SOZs relative to the reactants are compiled in Table . For asymmetric carbonyls, the values reported in Table are the average of the E and Z conformer energies. The E pathway TSs are, on average, lower in energy for the unsaturated carbonyls by −0.4 kcal mol^–1, but are, on average, higher for the conjugated carbonyls by +0.8 kcal mol^–1. A full tabulation of the CBS-QB3 energies, enthalpies, and free energies, including the SOZ products, for each conformer can be found in the Supporting Information.

3. Zero-point Corrected Energies (ΔE at 0 K) and Free Energies (ΔG at 298 K) of the 1,3-Dipolar Cycloaddition Transition States and SOZ Products for CH₂OO + R₁R₂CO Reactions .

species	ΔE TS	ΔG TS	ΔE SOZ	ΔG SOZ
HCHO	–6.67	+3.64	–51.43	–40.20
MeCHO	–6.23	+5.24	–50.62	–38.12
EtCHO	–7.00	+4.74	–51.50	–38.64
nPrCHO	–7.23	+4.53	–51.27	–38.45
iPrCHO	–6.92	+5.02	–50.96	–38.02
dMK	–6.07	+5.51	–50.30	–37.55
MEK	–5.46	+5.88	–48.66	–35.74
HFA			–57.62	–44.29
AcOH	–5.92	+6.77	–48.22	–34.87
4H2B	–6.24	+5.99	–49.40	–36.00
ACR	–5.28	+6.17	–47.28	–34.99
MACR	–5.54	+6.12	–47.02	–34.48
MVK	–6.58	+5.54	–47.98	–34.99
BiAc	–8.79	+3.41	–49.94	–36.97
AcPr (ac)	–8.63	+4.35	–49.73	–36.02
AcPr (pr)	–8.86	+3.85	–50.03	–36.61
PyrA (keto)	–7.70	+4.71	–47.58	–34.39
PyrA (acid)	–7.55	+4.79	–41.44	–28.55
AcAc (enol)	–2.56	+9.97	–38.33	–24.88

^aAll values (kcal mol^–1) were calculated at the CBS-QB3 level. For asymmetric carbonyls, the values are averages over the E and Z pathways.

For all reactions, ΔE _TS < 0 and the cycloaddition transition states are submerged with respect to the reactants, as shown for CH₂OO + MeCHO in Figure . Values of ΔE _TS range from approximately −2 to −9 kcal mol^–1. The entropic contribution to the free energy at 298 K moves the ΔG _TS values above the separated reactants, leading to reaction barriers of +3 to +7 kcal mol^–1. The reaction of the dominant enolone tautomer of acetylacetone (AcAc) has an unusually high free energy barrier of approximately +10 kcal mol^–1. ΔG _TS is the maximum energy point on all free energy surfaces and therefore is rate limiting, according to the two-step model outlined in Reactions and below. Passage over the barrier results in SOZ formation, for which the overall free energy changes range from ΔG _SOZ ≈ −25 kcal mol^–1 (CH₂OO + AcAc) to −45 kcal mol^–1 (CH₂OO + HFA).

Figure shows the relationship between the free energies of the transition states ΔG _TS and the SOZ products ΔG _SOZ calculated at the CBS-QB3 level of theory for each reaction studied here. The values used are the average of those obtained for the E and Z pathways. The reactions fall into groups corresponding to (a) reactions involving saturated carbonyls (aliphatic aldehydes and ketones, hydroxyketones) and (b) reactions involving carbonyls with conjugated π systems (enones and enals, α-dicarbonyls, and the keto-acid PyrA). Both groups show a linear relationship between ΔG _TS and ΔG _SOZ, although there are two obvious outliers, highlighted in Figure . The first corresponds to reaction of PyrA at the acid CO and the second to reaction of AcAc, both of which were omitted from the linear fit. Cycloaddition at the carboxylic acid group of PyrA is unique among the carbonyl species studied, as it is the only case where the carbonyl is directly bonded to an electron-withdrawing oxygen heteroatom. This structural difference impacts both the thermochemistry and the SAR approach described in Section . As a result, we focus exclusively on the ketone carbonyl group of PyrA and reactions at the carboxylic acid group are not included in the SAR correlations discussed below. AcAc exists predominantly in its enol form, which introduces two additional reactive sites beyond the carbonyl: the CC double bond and the enolic −OH group. Reaction at the former site exhibits a comparable free energy barrier to carbonyl cycloaddition at the CBS-QB3 level and can contribute to the overall reactivity, as discussed further in Section below.

3.

Plot of CBS-QB3 transition state free energies at 298 K (ΔG _TS) vs overall free energies (ΔG _SOZ) for CH₂OO + R₁R₂CO reactions. Saturated carbonyls (aliphatic aldehydes, ketones, and hydroxyketones) are shown as circles and conjugated carbonyls (α-dicarbonyls, enals and enones, keto-acids, and enolones) are shown as triangles. The color scale is used to represent the experimental room-temperature rate constants. Linear fits to the saturated and conjugated data are shown as solid and dashed lines, respectively, with the shaded area representing 1σ confidence interval.

The linear fit for the saturated carbonyls gives a slope of 0.53 ± 0.05, near the value expected for a Marcus-type reaction $\mathrm{\Delta }\mathrm{\Delta }{E}^{*}\approx \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\mathrm{\Delta }\mathrm{\Delta }{E}_{\mathrm{r}}$ , while the slope for the conjugated species is steeper with a value of 0.88 ± 0.26. Using the former relationship, the free energy of the TS for the CH₂OO + HFA reaction, also highlighted in Figure , is estimated to be ΔG _TS = +1.6 kcal mol^–1. Though the correlations between the calculated ΔG _TS and ΔG _SOZ values hold, the relationship to bimolecular rate constant is more opaque. The color scale used for the data points in Figure represents the experimental values of log₁₀(k _exp), however no obvious trends are apparent in the data for reactions of either saturated or conjugated carbonyls that would allow rate constants to be estimated based on, for example, the reaction exothermicity.

3.3. Transition State Theory

A canonical transition state theory (CTST) treatment can be applied to the reaction scheme shown in Figure , involving a two-step model for the overall reaction rate which is written in general as

$$\mathrm{CI}+{\mathrm{R}}_1{\mathrm{R}}_2\mathrm{CO}\stackrel{K_{\mathrm{eq}}}{\leftrightarrow }\mathrm{vdW}$$ R1

$$\mathrm{vdW}\stackrel{k_{\mathrm{SOZ}}}{\to }\mathrm{SOZ}$$ R2

If it is assumed that equilibrium is established for vdW complex formation (i.e., vdW complex decomposition is faster than conversion to the SOZ), then the overall rate constant for the reaction can be expressed as

$$k=K_{\mathrm{eq}}{k}_{\mathrm{SOZ}}$$ 1

where K _eq is the equilibrium constant for vdW complex formation and k _SOZ is the rate of passage over the cycloaddition TS. Combining the statistical mechanical expressions for K _eq and the TST expression for k _SOZ leads to the Eyring equation for the overall temperature-dependent rate constant:

$$k=\kappa \frac{k_{\mathrm{B}}^2}{h{p}^{°}}{T}^2\exp \left(-\frac{\mathrm{\Delta }{G}_{\mathrm{TS}}}{RT}\right)$$ 2

where κ is the tunneling coefficient (assumed here to be unity); k _B is the Boltzmann constant; T is temperature; h is the Planck constant; R is the gas constant; p° is standard pressure (1 bar); and ΔG _TS is the standard free energy of the TS relative to the reactants. The factor k _B /hp° evaluates to 2.88 × 10^–12 cm³ s^–1 K^–2. Application of CTST to calculate thermal rate constants requires only ΔG _TS which is available from the ab initio calculations, or from the relationships shown in Figure , if only ΔG _SOZ is available.

Figure shows how the CTST thermal rate constant at 298 K varies as a function of ΔG _TS, calculated using eq . The experimentally measured rate constants are also plotted against the CBS-QB3 ΔG _TS values, which are averaged over the E and Z addition pathways for clarity. All the experimental data, except for the AcAc reaction, lie below the CTST line. However, as noted above, AcAc reacts faster than expected due to an additional competitive pathway involving analogous 1,3-dipolar cycloaddition at the CC bond, which is calculated to have a similar barrier height at the CBS-QB3 level.

4.

Plot of experimental room-temperature rate constants vs calculated transition state free energies (ΔG _TS) calculated at the CBS-QB3 level. Saturated carbonyls (aliphatic aldehydes, ketones, and hydroxyketones) are shown as circles and conjugated carbonyls (α-dicarbonyls, enals and enones, keto-acids, and enolones) are shown as triangles. The variation in the TST rate constant with ΔG _TS, calculated at 298 K, is shown in red.

Most experimental rate constants are at least an order of magnitude smaller than the CTST prediction. The largest discrepancy is found for the HCHO reaction, arguably the simplest to treat computationally, for which the observed rate constant is 140 times smaller than the CTST prediction. The systematic overprediction of rate constants suggests a systematic underestimation of the CBS-QB3 free energies of activation, ΔG _TS. Comparison of CBS-QB3 calculated activation free energies (ΔG _TS) with those derived from experimental rate constants gives a consistent average offset of +1.75 kcal mol^–1. Application of this uniform correction brings the CTST predictions into good agreement with experimental values, as shown in Figure S1 of the Supporting Information.

With the exponential sensitivity of rate constants to the transition state barrier height, even minor errors in the computed transition state free energy can result in substantial discrepancies in predicted kinetics. To enhance the accuracy of theoretical rate constants, refinement of transition state energies is needed. High-level correlation methods such as CCSD­(T)/CBS and CCSDT­(Q)/CBS offer improved electronic structure accuracy, but are very computationally expensive for larger systems and can still introduce errors of approximately 0.4–1.0 kcal mol^–1 in 0 K heats of formation. This degree of accuracy in ΔG _TS values produces rate constants that vary by factors of 2–6. Furthermore, a more rigorous (and laborious) treatment of the rotational and vibrational partition functions beyond the conventional rigid rotor-harmonic oscillator (RRHO) approximation such as hindered rotor models may be necessary to improve the reliability of room-temperature rate constant calculations. It is, however, not obvious when such effort is required if computation is to be used to predict a rate constant. As noted above, the largest discrepancy between the TST rate constant calculated using CBS-QB3 free energies is for the comparatively simple and computationally most tractable CH₂OO + HCHO reaction. Experimental rate constants for reactions involving larger carbonyl species with methyl or larger alkyl substituents, reactions for which hindered rotor treatments may have been anticipated, are much better reproduced by TST using simple RRHO partition functions, likely due to cancellation of errors.

3.4. SARs for CH₂OO + R₁R₂CO Reactions

Obtaining accurate TST rate constants is challenging, particularly as molecular size increases, and high-level ab initio calculations of electronic energies and sophisticated treatments to determine molecular partition functions are required. Here, we describe alternative strategies to estimate CI + R₁R₂CO reactivity through structure–activity relationships (SARs) that are capable of reliably predicting rate constants without requiring high-level ab initio calculations. The SARs presented in this work are based on empirical correlations with experimental rate constants and do not rely on TST predictions for parametrization. The SARs are based on the model for 1,3-dipolar cycloaddition reactions described by Sustmann, , in which the electron-donating or electron-withdrawing characters of the substituents determine reactivity through their influence on the energies of the frontier molecular orbitals, as illustrated in Figure .

The general form of the SARs is presented in eq :

$${\log }_{10}{k}_{\mathrm{SAR}}=a+b\lambda$$ 3

where λ is a quantifiable property that characterizes the electron-donating or withdrawing character of the substituents or their effect on the substituted carbonyl. We focus on two alternative approaches: Hammett constants, which have been tabulated for a broad range of substituents, and the frontier molecular orbital energies, which are readily obtained from low-cost DFT calculations.

The SARs presented here focus on room-temperature rate constants which are further assumed to represent high-pressure limit values. Previous experimental studies have demonstrated that the high-pressure limit for 1,3-dipolar cycloaddition reactions of carbonyls with Criegee intermediates is reached at relatively low pressures (∼20–30 Torr of air) indicating negligible pressure dependence under tropospheric conditions. ,, Temperature-dependent measurements for CH₂OO reactions with carbonyls have generally shown weak negative temperature dependences with comparable activation energies (−E _a/R ≈ 1000 K). ,, Therefore, the room-temperature SARs described below could be extended to other atmospherically relevant temperatures, although with increased uncertainty.

3.4.1. Hammett Substituent Constants

Hammett constants were originally developed to quantify the impact of meta and para substituents on the pK _a of meta and para substituted benzoic acids, although they have found applicability in the study of a broad range of organic reactions. The Hammett relationship is defined in eq :

$${\log }_{10}\left(\frac{K_{\mathrm{X}}}{K_{\mathrm{H}}}\right)=\rho {\sigma }_{\mathrm{X}}$$ 4

where K _X and K _H are acid dissociation constants for the substituted and the unsubstituted species (X = H), respectively. , For aromatic systems, the substituent constants depend on the location of substitution, and are identified as σ_m and σ_p. The sensitivity of a particular reaction to the substituent effect is captured by the factor ρ in eq , where ρ = 1 for the benzoic acid dissociation equilibrium. Following the discussion in Hansch et al., the substituent electronic effects can be split into a field/inductive component characterized with the σ_I constant, and a resonance component, characterized with the σ_R constant.

While the standard meta and para position Hammett constants (σ_m and σ_p) work well in many cases, there are known situations in which further parametrization is required. To a first approximation, negative values indicate an EDG (σ < 0; deactivating on the carbonyl) and positive values indicate an EWG (σ > 0; activating on the carbonyl). However, other substituent effects can also influence reactivity. For instance, steric effects can play a large role, as is the case for ortho substituents in the benzoic acid reaction series and Taft parameters have been developed to describe the steric influence of a given substituent.

In comparing gas- and aqueous-phase acidities of benzoic acid, the ΔΔG(gas) is approximately an order of magnitude larger than the corresponding ΔΔG(aq). However, Hammett substituent constants still perform reasonably well even in describing gas-phase reactions, , and the use of tabulated Hammett constants could provide a method to predict rate constants for CH₂OO + R₁R₂CO reactions and insight into the expected reactivity of a given carbonyl. Equation can be modified by replacing the acid dissociation equilibrium constants with the bimolecular reaction rate constants and rearranged to yield eq

$${\log }_{10}(k_{\mathrm{X}})={\log }_{10}(k_{\mathrm{H}})+\rho {\sigma }_{\mathrm{X}}$$ 5

which has the same form as the general linear SAR eq .

Previously, for more limited data sets, we have shown that the rate constants for CH₂OO + R₁R₂CO reactions correlate with the sum of the para position Hammett constants (∑σ_p) for the carbonyl substituents. Here we extend the analysis to include the relationship between the experimental rate constants and the meta, para, field/inductive, and resonance substituent constants. Although, the meta and para designations used in traditional Hammett analysis are specific to aromatic systems and do not apply here, as all substituents are bonded directly to the carbonyl. Furthermore, the field/inductive and resonance substituent constants are employed here as descriptors of the electron-donating or electron-withdrawing character of each substituent, without implying a direct physical interpretation specific to aromatic systems for which they were originally developed.

In the analysis, we continue to assume that the electronic effects of the substituent constants are additive, i.e., the variables in eq are λ = ∑ σ _i = σ _i,R1 + σ _i,R2 where i indicates the meta, para, field/inductive, or resonance constants. Table compiles the ∑σ _i values for each carbonyl species, using data from Hansch et al. Figure shows semilog plots of k _exp against ∑σ_m, ∑σ_p, ∑σ_I, and ∑σ_R. The values of a and b obtained from unweighted linear fits of the data to eq , along with the associated statistical parameters, are shown in Table . The fit parameter a corresponds to log₁₀ k _HCHO while b represents the reaction sensitivity (ρ). The quality of the linear correlation as measured by Pearson’s r and R ² values follows the order: ∑σ_I < ∑σ_m < ∑σ_p < ∑σ_R.

4. Empirical Total Hammett Substituent Constant ρσ_total for a Given Carbonyl along with the Corresponding Sums of σ_m, σ_p, σ_I, and σ_R (meta, para, Field/Inductive, and Resonance, Respectively) Hammett Substituent Constants .

species	ρσtotal	∑σm	∑σp	∑σI	∑σR
HCHO	0	0	0	+0.07	–0.07
MeCHO	–0.50	–0.07	–0.17	+0.04	–0.21
EtCHO	–0.08	–0.07	–0.15	+0.03	–0.18
nPrCHO	–0.17	–0.06	–0.13	+0.04	–0.17
iPrCHO	–0.22	–0.04	–0.15	+0.07	–0.22
dMK	–1.01	–0.14	–0.34	+0.02	–0.36
MEK	–0.79	–0.14	–0.32	+0.01	–0.33
HFA	+0.89	+0.86	+1.08	+0.77	+0.31
AcOH	–0.55	–0.07	–0.17	+0.04	–0.21
4H2B	–0.55	–0.19	–0.34	–0.05	–0.29
ACR	–0.38	+0.06	–0.04	+0.16	–0.20
MACR	–0.95	+0.09	+0.05	+0.16	–0.11
MVK	–0.89	–0.01	–0.21	+0.13	–0.34
BiAc	+0.45	+0.31	+0.33	+0.34	–0.01
AcPr (ac)	+0.52	+0.31	+0.35	+0.35	–0.04
AcPr (pr)		+0.31	+0.31	+0.33	+0.02
PyrA (keto)	+0.70	+0.30	+0.28	+0.35	–0.07
PyrA (acid)		+0.50	+0.18	+0.66	–0.53
AcAc	–0.69

^aSee Table for substituents.

5.

Semilog plots of k _exp for CH₂OO + R₁R₂CO reactions vs the sum of the (a) meta, (b) para, (c) field/inductive, and (d) resonance Hammett constants for substituents R₁ and R₂. Unweighted linear fits to the data are also shown with shaded areas representing 1σ confidence intervals.

5. Parameters Obtained from Unweighted Linear Fits of log₁₀(k _exp/10^–12 cm³ s^–1) vs Hammett Substituent Constant Sums (∑σ_m, ∑σ_p, ∑σ_I, and ∑σ_R), Frontier Molecular Orbital Energy Gaps (ΔE _A, ΔE _S), and Global Electrophilicity Index (GEI) Calculated at The B3LYP/cc-pVDZ Level for CH₂OO + R₁R₂CO Reactions .

variable	intercept, a	gradient, b	Pearson’s r	R 2
∑σm	0.24 ± 0.10	1.80 ± 0.37	0.79	0.63
∑σp	0.37 ± 0.09	1.36 ± 0.25	0.82	0.64
∑σI	–0.02 ± 0.13	2.24 ± 0.50	0.77	0.59
∑σR	0.84 ± 0.12	3.02 ± 0.52	0.84	0.71
ΔE A	–4.36 ± 1.42	0.61 ± 0.18	0.65	0.42
ΔE S	3.01 ± 0.75	–0.49 ± 0.14	–0.68	0.46
GEI	–0.81 ± 0.29	0.37 ± 0.09	0.73	0.54

^aValues are shown with 1σ statistical uncertainties.

As can be seen in Figure , the presence of electron-withdrawing substituents (σ > 0) on the carbonyl is associated with larger rate constants, while the presence of electron-donating substituents (σ < 0) is associated with smaller rate constants. The observed slopes (b = ρ > 1) indicate a greater sensitivity to substituent effects in these gas-phase reactions compared to that observed in the aqueous benzoic acid ionization equilibrium.

Alternatively, it is possible to develop a specific ρσ scale for the CH₂OO + R₁R₂CO 1,3-dipolar cycloaddition reactions, where the unsubstituted carbonyl is represented by formaldehyde (R₁ = R₂ = H). The Hammett relationship can be written as eq :

$${\log }_{10}\left(\frac{k_{{\mathrm{R}}_1{\mathrm{R}}_2\mathrm{CO}}}{k_{\mathrm{HCHO}}}\right)=\rho {\sigma }_{\mathrm{total}}=\rho ({\sigma }_{\mathrm{X},{\mathrm{R}}_1}+{\sigma }_{\mathrm{X},{\mathrm{R}}_2})$$ 6

Using the experimental rate constant for the reaction of CH₂OO with formaldehyde (k _HCHO = 3.9 × 10^–12 cm³ s^–1) the values of ρσ_total can be calculated using eq for each the reactions listed in Table . The resulting values of ρσ_total values are compiled in Table .

This scheme allows the calculation of σ_X for specific substituents with σ_X,H defined as zero and with the reaction sensitivity (ρ) set to 1. For instance, the rate constant for an aldehyde will directly give the σ_X for the non-hydrogen substituent. For symmetric carbonyls such as HFA, the substituent constant for CF₃ is simply σ_X,CF3 = σ_total,HFA/2. For methyl, we have used the average values of σ_X,CH3 = −0.50 from σ_total,MeCHO and σ_total,dMK/2. However, both approaches give a nearly identical value for σ_X,CH3 . We use this value for subsequent calculations of σ_X in Table . For instance, σ_X,CH2OH is calculated from σ_total,AcOH – σ_X,CH3 . We employ average values for ethyl (derived from EtCHO and MEK) and vinyl (derived from ACR and MVK) using this methodology. A plot showing the application of the empirical substituent constants back to the known carbonyls is included as Figure S1 in the Supporting Information.

6. Empirical Hammett Substituent Constants σ_X for Various Substituents Based on Measured Rate Constants (ρσ_total) Assuming ρ = 1 .

substituent	σX
C(CH3)CH2	–0.95
CH3	–0.50
CHCH2	–0.38
CH(CH3)2	–0.22
CH2CH3	–0.18
CH2CH2CH3	–0.17
CH2OH	–0.06
CH2CH2OH	–0.05
H	0
CF3	0.45
C(O)CH3	0.95,

^aThe substituents are ordered from most electron donating to most electron withdrawing.

^bAverage from MeCHO and dMK.

^cACR and MVK.

^dPrH and MEK.

^eBiAc.

3.4.2. Taft Analysis

We employed Taft analysis to investigate substituent effects on the measured rate constants for the cycloaddition of CH₂OO to carbonyl compounds. Unlike the Hammett approach, Taft analysis explicitly accounts for the influence of steric effects in addition to polar (electron-donating or -withdrawing) contributions. It should be noted that Taft substituent constants are derived from a different reference reaction system (acid- or base-catalyzed ester hydrolysis) than the conventional Hammett parameters. In general, Taft relationships are expressed by eq :

$${\log }_{10}(\raisebox{1ex}{$k$}\!\left/ \!\raisebox{-1ex}{$k_0$}\right.)={\rho }^{*}{\sigma }^{*}+\delta E_{\mathrm{S}}$$ 7

where σ* and E _S represent the polar and steric substituent constants, respectively, and the coefficients ρ* and δ quantify the relative sensitivities of the reaction series to these electronic and steric contributions. In contrast to traditional Hammett parameters, Taft constants are referenced (k ₀) to the methyl group, for which both σ* and E _S are defined as zero. In this work, available σ* and E _S values were compiled from two sources, , however, Taft parameters were not available for all the carbonyls presented in Table . The specific values adopted here are included in the Supporting Information in Table S2.

Using these substituent constants, we performed a two-parameter least-squares fit and obtained values of ρ* = 0.36 and δ = 0.17. These results indicate that the cycloaddition is more sensitive to polar effects than to steric influences. Using these fitted parameters, we constructed a correlation of log₁₀(k _exp) versus ρ*σ* + δE _S, as shown in Figure . Overall, a good correlation is obtained for the subset of carbonyl species evaluated here, with an R ² value of 0.85. Therefore, the SAR derived from the Taft analysis above can be used to predict CH₂OO + carbonyl rate constants and provides a better R ² value than the Hammett approaches described above. However, the applicability of this approach is more limited by availability of σ* and E _S values and it lacks some of the generality offered by the other SAR approaches presented.

6.

Taft analysis for CH₂OO + R₁R₂CO reactions with available σ* and E _S parameters. Two-parameter least-squares fit are shown with 1σ confidence intervals (red) and obtained values of ρ* = 0.36 and δ = 0.17 (R ² = 0.85).

3.4.3. Frontier Molecular Orbital Theory

Figure illustrates the frontier molecular orbitals (FMOs) that govern the reactivity of CIs with carbonyls. The FMO energies were computed using routine B3LYP/cc-pVDZ calculations, a method that is both reliable and readily scalable to larger molecular systems. The interaction can be defined in terms of the magnitudes of the energy gaps ΔE _A and ΔE _S, defined as in eqs and :

$$\mathrm{\Delta }{E}_{\mathrm{A}}=|E(\mathrm{CI},{\pi }^{*})-E({\mathrm{R}}_1{\mathrm{R}}_2\mathrm{CO},\pi )|$$ 8

$$\mathrm{\Delta }{E}_{\mathrm{S}}=|E(\mathrm{CI},n_{{\mathrm{p}}_{\mathrm{C}}}-n_{{\mathrm{p}}_{\mathrm{O}}})-E({\mathrm{R}}_1{\mathrm{R}}_2\mathrm{CO},{\pi }^{*})|$$ 9

For a given CI, the FMO energies are unchanged and the energy gaps are determined by the identity of the R₁ and R₂ substituents on the carbonyl. Although both A and S orbital interactions contribute to the energy of the cycloaddition transition state, ΔE _S < ΔE _A for all of the CH₂OO + R₁R₂CO reactions listed in Table , so reactivity is primarily controlled by ΔE _S. Semilog plots of k _exp versus ΔE _A and ΔE _S, evaluated at the B3LYP/cc-pVDZ level, are shown in Figure a,b, respectively, along with unweighted linear fits to the general SAR eq . The values of a and b, along with the associated statistical parameters, are collected in Table .

7.

Semilog plots of k _exp for CH₂OO + R₁R₂CO reactions vs frontier molecular orbital energy gaps (a) ΔE _A and (b) ΔE _S, and (c) the global electrophilicity index, GEI. Unweighted linear fits to the data are also shown with shaded areas representing 1σ confidence intervals.

As expected, log₁₀(k _exp) correlates positively with ΔE _A and negatively with ΔE _S, consistent with the stabilizing effect of smaller ΔE _S gaps on the transition-state energy. Larger experimental rate constants are observed for carbonyls bearing electron-withdrawing substituents, which lower the LUMO energy of R₁R₂CO, thereby decreasing ΔE _S and increasing ΔE _A (see Figure ). The fits to ΔE _S display slightly higher correlation coefficients than those for ΔE _A, indicating the symmetric interaction exerts the greater control over the observed reactivity.

A similar approach to quantify the electrophilic character of the carbonyls is the global electrophilicity index (GEI). GEI is particularly useful for comparing the reactivity of electrophiles across a series of molecules in reactions where electron transfer is important, such as cycloaddition reactions. , The GEI is related to the chemical potential (μ) and hardness (η) as defined in eq :

$$\mathrm{GEI}=\frac{{\mu }^2}{2\eta }$$ 10

The chemical potential and hardness of a given R₁R₂CO molecule can be calculated from the energies of the HOMO (the nonbonding n _O orbital) and LUMO (the π* antibonding orbital) molecule using eqs and :

$$\mu =\frac{(E_{\mathrm{HOMO}}+E_{\mathrm{LUMO}})}{2}$$ 11

$$\eta =\frac{(E_{\mathrm{LUMO}}-E_{\mathrm{HOMO}})}{2}$$ 12

Figure c shows a semilog plot of k _exp versus GEI, evaluated using B3LYP/cc-pVDZ calculations.

The correlation is again linear, indicating that the GEI provides a useful single-parameter descriptor of reactivity for the CH₂OO + R₁R₂CO reactions. The GEI-based SAR performs slightly better than those based on ΔE _A or ΔE _S, with larger absolute values of Pearson’s r and higher R ² coefficients. Overall, correlations using Hammett substituent constants still yield somewhat stronger agreement with experimental rate constants. However, SARs constructed from low-cost DFT calculations such as GEI offer advantages in generality as this approach does not depend on tabulated substituent parameters and can be readily extended to a broader range of molecular structures, as will be discussed in more detail below.

3.4.4. Extension to CI + SO₂ Reactions

The Sustmann model for 1,3-dipolar cycloaddition reactions implies that electron-donating and electron-withdrawing substituents on the CI (R₁R₂COO) will also influence reactivity toward carbonyls. As noted earlier and shown in Figure , the effects are reversed: electron-donating substituents on the CI are now activating, while electron-withdrawing substituents are deactivating, In the absence of experimental rate constants for reactions of Cn CIs (n = 1–3 i.e., R₁, R₂ = H or CH₃, giving the CIs CH₂OO, anti-CH₃CHOO, syn-CH₃CHOO, and (CH₃)₂COO) with a common organic carbonyl, we use the Cn + SO₂ reactions, which also proceed via a 1,3-dipolar cycloaddition mechanism, as proxies. The experimental rate constants are summarized in Table . Plots of log₁₀(k _exp) against the various Hammett substituent constant sums, the orbital energy gaps, and GEI are shown in Figures S2 and S3 in Supporting Information, while linear fit parameters are compiled in Table S4. The syn and anti conformers of CH₃CHOO show marked isomer-specific reactivity toward SO₂. ,, The use of Hammett substituent constant sums explicitly does not distinguish between syn-CH₃CHOO and anti-CH₃CHOO and the energies of the frontier molecular orbitals are almost identical. Consequently, for all variables used, the rate constant for the syn-CH₃CHOO + SO₂ reaction deviates significantly from the trend and it was omitted from the linear fits to eq . However, fits including syn-CH₃CHOO can be found in the Supporting Information (Figure S5). The practical significance of this deviation from the SAR models is limited as unimolecular decomposition is likely a far more significant process than reaction for syn-CH₃CHOO. Further experimental results could provide more insight. Overall, the ΔE _S relationship provides the strongest (negative) correlation as quantified by the Pearson’s r and R ² values.

4. Discussion

4.1. CH₂OO + Aldehydes, Ketones, and Hydroxyketones

The aldehydes (HCHO, MeCHO, EtCHO, nPrCHO, and iPrCHO) deviate from the SAR predictions, generally reacting faster than predicted from all substituent Hammett substituent constant sums, FMO, and GEI. One possible explanation is steric accessibility: the CO in these aldehydes is more easily approached by CH₂OO than in ketones bearing two non-hydrogen substituents. However, even within this aldehyde subset, steric effects do not follow the expected trend. For example, iPrCHO reacts faster than MeCHO despite its bulkier isopropyl group. This is likely due to the reactive geometry involving CH₂OO approaching in a planar orientation above or below the carbonyl which minimizes steric hindrance. As a result, the steric effects are less important than the electron-withdrawing or donating effect.

For aliphatic ketones (dMK and MEK), the presence of two electron-donating substituents results in smaller rate constants, consistent with Hammett substituent constant SAR predictions. The ethyl group has a slightly less negative σ_p than methyl, in agreement with experimental measurements showing MEK reacting faster than dMK. However, the experimental rate constants are slightly lower than the Hammett SAR predictions. The carbonyl π* orbital energies for the two ketones are nearly identical, and orbital energy gaps and GEI SARs predict near equivalent rates.

The introduction of a hydroxyl group in the hydroxyketones (AcOH and 4H2B) makes the substituent moderately more electron withdrawing, leading to an increased rate constant. Both compounds are well described by the SAR approaches. Finally, HFA exhibits the largest measured rate constant of any carbonyl studied, consistent with the presence of two strongly electron-withdrawing −CF₃ substituents that substantially lower the LUMO energy and enhance the electrophilic character of the carbonyl center. The experimental rate constant is also in good agreement with both Hammett- and FMO-based predictions.

From an atmospheric perspective, aliphatic aldehydes generally react more rapidly with OH radicals through hydrogen abstraction at the aldehydic position. However, trifluoroacetaldehyde (TFA), as discussed further below, exhibits a slower reaction with OH, but has a comparatively large rate constant for reaction with CH₂OO. Consequently, reaction with stabilized CIs may constitute a significant atmospheric removal pathway for TFA, although its presence in the atmosphere has not been established. TFA could possibly be produced from the atmospheric oxidation of fluoroolefins or degradation of per- and polyfluoroalkyl substances (PFAS), but its abundance and role in atmospheric chemistry is not well documented. Finally, the aliphatic ketones and hydroxyketones generally exhibit smaller rate constants for reaction with CH₂OO, and their atmospheric removal is expected to be dominated by reactions with OH radicals and by direct photolysis as detailed below.

4.2. CH₂OO + α, β-Unsaturated Carbonyls

Conjugation of the carbonyl leads to pronounced substituent effects that deviate more strongly from the SAR predictions. For MACR and MVK, conjugation with the π-electron-donating vinylic group results in a slower reaction than expected, whereas for BiAc, AcPr, and PyrA, conjugation with π-electron-withdrawing groups accelerates the reaction. In particular, the rates for MACR and MVK are substantially slower than predicted by Hammett correlations or FMO theory and fall below the linear fits. It should be noted, however, that these measurements were conducted at relatively low pressure (∼4 Torr, He) and may not represent the high-pressure limit. , Further experiments to characterize the pressure dependence of these reactions would provide insight into the reactivity of MACR and MVK. The α-dicarbonyl compounds exhibit comparatively large rate constants for reaction with CH₂OO, with k > 10^–11 cm³ s^–1. The atmospheric reactions of CH₂OO with α-dicarbonyls are discussed further below with a focus on glyoxal and methylglyoxal.

4.3. Application of SARs to CI Reactions with Atmospherically Relevant Carbonyls

4.3.1. Reactions of CH₂OO

Estimates of room-temperature rate constants based on the Hammett resonance constants and GEI SARs for reactions of CH₂OO with a selection of unstudied atmospherically relevant carbonyls are presented in Table along with the corresponding error estimate for each model. The Hammett resonance constants and GEI provided the best statistical fit to the experimental data (highest R ² values) and were therefore used for rate constant estimations. Other SAR predictions for these carbonyls are included in the Supporting Information (Table S3). Where possible, the rate constants based on the empirical Hammett constants compiled in Table are also included.

7. Predicted Room-Temperature Bimolecular Rate Constants (k/10^–12 cm³ s^–1) for CH₂OO Reactions with Selected Carbonyls Based on Various SARs .

species (abbreviation)	∑σR	GEI	∑σX
trifluoroacetaldehyde (TFA)	16.3 ± 2.2	5.9 ± 2.8	10.9 ± 0.2
diethyl ketone (dEK)	0.9 ± 0.2	0.8 ± 0.3	1.69 ± 0.05
methyl isopropyl ketone (MiPrK)	0.5 ± 0.1	0.8 ± 0.3	0.74 ± 0.04
glycolaldehyde (Glyc)	4.3 ± 0.5	1.8 ± 0.7	3.44 ± 0.07
glyoxal (Gly)	10.6 ± 1.3	34.2 ± 21.7
methylglyoxal (MGly; ald)	17.4 ± 2.4	15.2 ± 8.6	34.7 ± 0.7
MGly (keto)	3.9 ± 0.5
crotonaldehyde (Cro)	1.5 ± 0.3	3.0 ± 1.3

^aUncertainties are 1σ based on the statistical uncertainties in the linear SAR fits. The GEI method does not distinguish between the aldehyde and ketone carbonyl groups for MGly and yields a single predicted rate constant.

The test set covers aldehydes, ketones, hydroxycarbonyls, α-dicarbonyls, and enals: Specifically: trifluoroacetaldehyde (CF₃CHO, TFA), methyl isopropyl ketone (CH₃COCH­(CH₃)₂, MiPrK), diethylketone ((C₂H₅)₂CO, dEK), glyoxal (CHOCHO, Gly) and methylglyoxal (CH₃COCHO, MGly), glycolaldehyde (HOCH₂CHO, Glyc), and crotonaldehyde (CH₃CHCHCHO, Cro). Collectively, these compounds represent important classes of carbonyls found in the atmosphere that span a wide range of electronic environments and substituent effects.

Trifluoroacetaldehyde (or fluoral, CF₃CHO, TFA) is an oxidation product of hydrofluoroolefin refrigerants. TFA reacts with OH with a reported rate constant of ∼6 × 10^–13 cm³ s^–1. Using the empirical Hammett constants (σ_X), the OH radical rate constant is more than an order of magnitude smaller than the SAR-predicted rate constant for the corresponding CI reaction (Table ), suggesting that CIs may serve as an important atmospheric sink for TFA. Based on estimated ambient concentrations where [OH] exceeds [CH₂OO] by approximately 2 orders of magnitude, the ratio k _CI[CH₂OO]/k _OH[OH] ≈ 0.2 indicates that the reaction with CIs can represent a competitive loss pathway. However, due to the slow reaction with OH, direct photolysis and reaction with HO₂ have been estimated to be major loss channels of TFA, as well as wet and dry deposition.

We have also provided estimates for the rate constants for the aliphatic ketones MiPrK and dEK. As expected, these compounds are predicted to exhibit relatively small rate constants on the order of ∼10^–13 cm³ s^–1. Their low reactivity toward CH₂OO suggests that reactions with OH radicals and direct photolysis , will dominate their removal under typical atmospheric conditions.

The α-dicarbonyls are particularly significant because of their abundance as secondary oxidation products of isoprene and aromatic hydrocarbons, as well as their central role in aqueous-phase chemistry and secondary organic aerosol formation. Accurate estimation of their gas-phase reactivity is therefore critical for understanding their atmospheric lifetime and partitioning. , In addition, measurements on BiAc, AcPr, and PyrA demonstrate that α,β-dicarbonyls react rapidly with CH₂OO. For Gly, the two carbonyls are equivalent and the rate constant for reaction with CH₂OO is estimated to range from ∼13–44 × 10^–12 cm³ s^–1. In comparison, the measured rate constant for reaction of glyoxal with OH radical is ∼9 × 10^–12 cm³ s^–1. Given that the tropospheric OH radical concentration is estimated to be approximately 2 orders of magnitude larger than that of CIs, reaction with OH is expected to represent the dominant atmospheric sink. However, reaction with CI could make some contribution to glyoxal loss rates especially under conditions of elevated CI concentrations. The reactivity of MGly is expected to be dominated by attack at the aldehyde carbonyl, which is predicted to be faster than reaction at the ketone carbonyl. Based on the SAR approaches, the rate constant for CI addition at the aldehyde site is estimated to fall in the range of 17–35 × 10^–12 cm³ s^–1 For comparison, the measured rate constant for OH radical reaction with MGly is ∼13 × 10^–12 cm³ s^–1. These similar magnitudes suggest that, under conditions of elevated CI concentrations such as regions with high biogenic alkene emissions or during nighttime periods when OH concentrations are lower, reaction with stabilized CIs could represent a non-negligible atmospheric sink for methylglyoxal.

Finally, Table also includes estimates for two additional aldehydes, Glyc and Cro. These aldehydes are predicted to have similar rate constants with values of ∼10^–12 cm³ s^–1. For comparison, atmospheric glycolaldehyde is primarily removed through OH radical reaction and wet deposition due to its high water solubility. In the gas phase, Glyc reacts with OH radical with an estimated rate constant of ∼1 × 10^–11 cm³ s^–1 which is approximately an order of magnitude larger than its estimated rate constant for reaction with CH₂OO. The major atmospheric sink for crotonaldehyde is reaction with OH radical (k ∼ 2 × 10^–11 cm³ s^–1) with a minor contribution from direct photolysis. Given these relative rate constants, the reaction of CH₂OO with either glycolaldehyde or crotonaldehyde is expected to represent only a minor atmospheric loss process.

4.3.2. Reactions of Substituted CIs

While this work focuses primarily on reactions of formaldehyde oxide (CH₂OO) with carbonyls, for which the most extensive kinetic data are available, many other important stabilized Criegee intermediates exist in the atmosphere. However, we can provide valuable perspective in the application of these SAR approaches to the available kinetic data for other SCIs. The major atmospheric source of CIs is ozonolysis of isoprene (CH₂C­(CH₃)­CHCH₂), , which is outlined in Scheme . Ozone addition at either of the two CC bonds in isoprene produces formaldehyde oxide (CH₂OO) along with two unsaturated CIs: methylvinylketone oxide (MVKO) and methacrolein oxide (MACRO). − Due to the presence of syn and anti conformers for the asymmetric intermediates, isoprene ozonolysis yields five distinct stabilized Criegee intermediates (SCIs): CH₂OO, syn-MVKO, anti-MVKO, syn-MACRO, and anti-MACRO. ,, In addition to these conjugated CIs produced from isoprene, we will discuss the aliphatic CIs acetaldehyde oxide (CH₃CHOO) and acetone oxide ((CH₃)₂COO). For asymmetric CIs where R₁ ≠ R₂, the syn and anti isomers exhibit different reactivity and unimolecular decomposition kinetics. There has been previous work on substituent effects in the unimolecular pathways and for the reaction with H₂O and (H₂O)₂ with substituted CIs. In contrast, the CI + H₂O reaction involves nucleophilic addition of water to the carbonyl oxide. Because of these mechanistic differences, the substituent effects that govern reactivity are expected to differ between the two reaction types.

1. Reactions and Products for Ozonolysis of Isoprene Yielding Three Different Stabilized Criegee Intermediates: Formaldehyde Oxide (CH₂OO), Methylvinylketone Oxide (MVKO), and Methacrolein Oxide (MACRO).

While likely less accurate than the Hammett-based approaches, the FMO energy gap SARs are most generally applicable as they rely on readily calculable properties of both the CI and the carbonyl. Using B3LYP/cc-pVDZ orbital energies and the ΔE _S SAR, we have estimated the room-temperature rate constants for the reactions of the CIs anti-CH₃CHO, (CH₃)₂COO, MACRO, and MVKO with a subset of the organic carbonyls. For the conjugated CIs MVKO and MACRO, four distinct isomers/conformers (the conjugated π system may be cis or trans about the α C–C bond and the orientation of the terminal O atom is syn or anti as in CH₃CHOO). The relative stabilities of the conformers vary by a few kcal mol^–1, but the frontier molecular orbital energies are very similar- average ΔE _S values are used in the SAR calculation.

The estimated room-temperature rate constants for reactions of the four CIs with HCHO, dMK, HFA, and BiAc are compiled in Table , where propagation of the statistical uncertainties in the SAR fits suggest overall uncertainties of around a factor of 2. As has been observed for the Cn + SO₂ reactions, sequential substitution of H by CH₃ increases the predicted rate constant for a given carbonyl. Conjugation in the α,β-unsaturated CIs lowers their reactivity slightly relative to their aliphatic analogs. Predicted MACRO rate constants are around 10% smaller than those for anti-CH₃CHOO, and MVKO rate constants are similarly smaller than those for (CH₃)₂COO. However, based on the predicted rate constants, reactions with carbonyls are less likely to compete significantly with alternative pathways such as unimolecular decomposition as an atmospheric sink for these larger CIs.

8. Predicted Room-Temperature Bimolecular Rate Constants (k/10^–12 cm³ s^–1) for a Selection of CI + R₁R₂CO Reactions Using the ΔE _S SAR .

R1R2CO	anti-CH3CHOO	(CH3)2COO	MVKO	MACRO
HCHO	3.7	4.9	4.4	3.3
dMK	1.5	1.9	1.7	1.3
HFA	25.5	33.2	29.8	22.4
BiAc	14.2	18.4	16.5	12.4

^a1σ accuracy estimated within factor of two.

4.3.3. Expected Accuracy of SARs

The uncertainties reported in Table reflect statistical fitting uncertainties and do not account for potential systematic errors in the underlying computational methods or experimental rate constant measurements. As discussed in Section of the Results, CBS-QB3 systematically underestimates activation free energies by approximately 1.75 kcal mol^–1. However, this offset is consistent across the data set, and the SARs are based on relative trends rather than absolute barrier heights. Overall, we estimate the SARs for CH₂OO predict rate constants to within a factor of 2–3 for saturated aldehydes and ketones. Larger uncertainties should be expected for carbonyls with competitive reaction pathways, such as α,β-unsaturated carbonyls or carboxylic acids. For substituted CIs, there is limited data available to limited experimental data are available for validation. Propagation of statistical uncertainties indicate accuracy on the order of a factor of 2 (Table ), but these predictions should be considered more tentative pending further experimental validation.

5. Conclusions

Hammett analysis and FMO theory have been used to construct SARs that are based on correlations with experimental rate constants. The reaction between CH₂OO and HCHO was used as a baseline case to explain how substituent effects of EWGs and EDGs on the carbonyl can influence the rate of the reaction. An inverse correlation was found between the π* orbital energy of the carbonyls and the bimolecular rate constants for the reaction with CH₂OO. The strong linear correlation provides a SAR to predict rate constants for the reactions of CH₂OO with carbonyls. While Hammett constants provide the best correlation, low-cost quantum chemical calculations of orbital energies offer a practical alternative for predicting rate constants, especially for molecules lacking experimental or tabulated substituent parameters. Further exploration of steric effects beyond the Taft analysis presented here could enhance the SARs for carbonyls with bulkier substituents.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsearthspacechem.5c00398.

• CBS-QB3 zero-point corrected energies (ΔE at 0 K) and free energies (ΔG at 298 K) of the transition states for 1,3-dipolar cycloaddition reactions of CH₂OO with various carbonyls; Taft substituent constants; predicted room-temperature bimolecular rate constants (k/10^–12 cm³ s^–1) for CH₂OO reactions with selected carbonyls based on various SARs; analysis of a uniform +1.75 kcal/mol correction to ΔG _TS of CBS-QB3 TST results; empirical Hammett constants applied back to model set; Cn + SO₂ Hammett substituent constants and FMO energy gaps, GEI; and additional fits including syn-CH₃CHOO (PDF)

The authors declare no competing financial interest.