Bimolecular sinks of Criegee intermediates derived from hydrofluoroolefins – a computational analysis

Abstract

A novel range of stabilised Criegee intermediate (sCI) species with halogenated substituent groups have been identified as products to the reaction between with gaseous ozone and hydrofluoroolefins (HFOs), a series of recently-developed and increasingly prevalent haloalkene refrigerants. The bimolecular chemistry of this group of hydrofluoroolefin-derived sCIs (HFO-sCIs) has yet to be explored in any significant detail so this work evaluates the reaction chemistry of common tropospheric gaseous species with the following group of HFO-sCIs: syn- & anti-CF₃CHOO & syn- & anti-CF₃CFOO. Using high-level theoretical calculations (DF-HF/DF-LCCSD(T)-F12a//B3LYP/aug-cc-pVTZ), this study demonstrates that HFO-sCIs will deplete many pollutants (e.g. HCHO, SO₂ & H₂S) but also act as a source of other atmospheric contaminants (e.g. SO₃ & TFA). The bimolecular reactivity of the HFO-sCIs were compared against CH₂OO, the most frequently studied sCI, for which the general reactivity trend has been identified: k_THEO (syn-CF₃CHOO) < k_THEO (anti-CF₃CHOO) ≈ k_THEO (CH₂OO) ≪ k_THEO (anti-CF₃CFOO) < k_THEO (syn-CF₃CFOO). In general syn & anti-CF₃ substituents reduce overall sCI reactivity compared to similar non-halogenated sCI species, whereas both syn & anti-F substituents significantly increase HFO-sCI reactivity. While HFO-sCI reactivity is largely dictated by the identity and location of the sCI substituent groups, there are co-reactants that alter these observed trends in reactivity, for example HCl reacts more rapidly with CH₂OO than it does with syn- & anti-CF₃CFOO.

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Environmental significance

Emissions of new short-lived hydrofluoroolefin coolants have become increasingly widespread in the last decade and the breakdown of these hydrofluoroolefins will generate many secondary products, including a range of hydrofluoroolefin-derived stabilised Criegee intermediates (HFO-sCIs). Criegee intermediates are important OH radical sources and strong tropospheric sinks for many pollutants, but HFO-sCI reactivity has not yet been fully characterised. This computation chemistry study provides a greater understanding of the implications of the increased tropospheric HFO-sCI abundance. The enhanced bimolecular reactivity found for HFO-sCIs in this study indicates that several of the HFO-sCIs have heightened capacities to: react with toxins (e.g. methanol & trifluoroacetic acid); produce hydroperoxides implicated with forestry damage; and convert SO₂ to SO₃, a process implicated with generating H₂SO₄ and aerosols.

1 Introduction

The recent commercialisation of highly volatile hydrochlorofluoroolefins and hydrofluoroolefins (referred to collectively herein as HFOs) for use as coolants in refrigerator units have been developed to reduce greenhouse gas emissions and reduce stratospheric ozone loss.^1–6 Furthermore, as well as being used as blowing foam and as propellants, HFOs are very important working fluids for waste heat recovery applications in heat pumps, as they are stable, have favourable toxicity profiles and are compatible with many plastics and elastomers used in such set-ups.^7,8 When haloalkenes breakdown it is the Cl & Br radicals that are primarily implicated in ozone destruction in the upper atmosphere and therefore only HFOs containing Cl & Br atoms (e.g. HCFO-1233zd(E)) appear to marginally affect stratospheric ozone levels.^9–12 But their compact lifetime means HFOs are often depleted in the troposphere and contribute to only minimal ozone depletion.^9–12 Additionally, they are relatively non-toxic, have minimal impact on global warming due to their short lifespans, and have high ignition energies compared to the first generation of refrigerants used in the 19th century (e.g. NH₃, SO₂ & CH₃CHO).^{1–3,13–17} Moreover, whereas CO₂ dominates the lower IR wave numbers (600–750 cm⁻¹), HFCs/HCFCs are also strongly IR active in the higher wavenumbers (1000–1400 cm⁻¹), increasing their heat trapping ability.^9,18 In contrast, the longevity of the second-generation chlorofluorocarbon (CFC) refrigerants leads to depletion of stratospheric O₃, which results in more cases of skin cancer from the greater ground-level penetration of the carcinogenic high-frequency UV light.^19–21

The growing interest in alternative refrigerants stems from the fact that, while the hydrofluorocarbon (HFC) and hydrochlorofluorocarbon (HCFC) replacements that have been phased in since the 1970s do not replicate this ozone depletion, the lengthy lifetimes and high levels of IR activity of HFCs & HCFCs give them very high global warming potentials (GWP₁₀₀).^{2,9,19,22–26} In areas as widespread as China, the USA and the EU, the phasing in of HFOs has been increasingly integrated into regional regulations, to try and eliminate HCFC & HFC emissions, and this has led to HFOs seeing increasing use in refrigerators, insulation and vehicle cooling units.^1,27,28 For example, a UK government 2022 report on the “F gas regulation in Great Britain” documents that HFO-1234yf has dominated total refrigerant usage in new small vehicles since 2017 and HFO–HFC blends use could eliminate high GWP HFCs from transport refrigeration by 2050.²⁹ Modest concerns about both the tropospheric implications of HFO breakdown (e.g. TFA formation) and about the carbon-intensity of HFO production has meant that both the UK and the EU are currently assessing the role of HFOs in future climate regulations.³⁰ Many refrigerant experts and industrial leaders continue to strongly support HFO use and are consulting on such regulations with governments currently, especially as the alternatives to HFOs also have trade-offs in the areas of toxicity, flammability and/or high-pressure requirements.^31,32 Examples of CFCs, HCFCs, HFCs and HFOs with their GWP₁₀₀ and ODP values and lifespan are displayed in Table 1.

Table 1 A tabulation of important atmospheric attributes of examples from three different generations of refrigerants: chlorofluorocarbon (CFCs), hydrofluorocarbons (HFCs) and hydrofluoroolefins (HFOs). Attributes featured include: global warming potential over 100 years (GWP₁₀₀), ozone depletion potential (ODP), atmospheric lifetime, and any hydrofluoroolefin-derived stabilized Criegee intermediates (HFO-sCIs) produced from the ozonolysis of this species

Name	Structure	GWP100	ODP	Lifetime (year)	HFO-sCIs	Ref.
HFO-1234yf	CF3CF=CH2	4	0	10.5 days	CH2OO	2, 4 and 9
					Syn-/anti-CF3CFOO
HCFO-1233zd(E)	E-CF3CH=CHCl	14	0.0005	26 days	Syn-/anti-ClCHOO	2, 5 and 33
					Syn-/anti-CF3CHOO
HFO-1234ze(E)	E-CF3CH=CHF	<1	0	16.4 days	Syn-/anti-FCHOO	2, 9 and 34
					Syn-/anti-CF3CHOO
CFC-11	CFCl3	4660	1	45	—	2 and 9
CFC-12	CCl2F2	10 200	0.82	100	—	2
HFC-134a	CF3CH2F	3710	0.0013	13.4	—	2 and 26
HFC-245fa	CF3CH2CHF2	858	0	7.7	—	2 and 9

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One of the reasons for the short-lived nature of HFOs listed in Table 1, HFO-1234yf, HCFO-1233zd(E) and HFO-1234ze(E), all of which are now widely used as refrigerants or insulation foam, is that the unsaturated 〉C=C〈 bond makes HFOs more susceptible to these chemical loss mechanisms.^{1,3–5,27,35–39} The gas-phase reaction of HFOs with radicals, such as OH & Cl, and other reactive species, like O₃, are important atmospheric loss mechanisms for many such tropospheric alkenes, for example isoprene reaction with O₃ is responsible for ∼10% of the loss of this non-halogenated alkene globally.^{4–6,34,40–44} The importance of this HFO ‘ozonolysis’ loss process is increasing year-on-year because the rise of HFO emissions particularly in O₃-rich urban areas is likely to result in sizable increases tropospheric populations of the Criegee intermediate (CI) and aldehyde/ketone products of this process (see Fig. 1).^4,5,45–48 A recent rise in tropospheric trifluoracetic acid (TFA) abundance in Beijing has already been partially attributed to the reaction of OH radicals with HFOs and, as a similar increase in other HFO-derived products is likely in similar circumstances, determining the tropospheric impact these of new HFO-derived stabilised Criegee intermediates (HFO-sCIs) is very necessary.^{3,28,36,49–51}

Fig. 1 The general schematic for the ozonolysis of a standard alkene via a short-lived primary ozonide (POZ) intermediate products, which produces in a pair of final products: a Criegee intermediate (CI) and a carbonyl product (either aldehyde or ketone). A significant portion of the CI population is formed with a high degree of energy indicated by asterisk.

The efficiency of ozonolysis as a tropospheric depletion mechanism for HFOs is disputed because while the presence of halogenated groups in the HFO reduces the overall effectiveness of most major alkene depletion pathways, such as via reaction with OH or Cl, this varies considerably depending on the HFO.^{45–47,52,53} The maximum ozonolysis yield for most HFOs reviewed are around 1%, but a few studies indicate that up to 10% of the removal of some haloalkenes occur via reaction with O₃, a significant enough pathway that HFO ozonolysis is being investigated thoroughly at present.^47,52 Furthermore, while direct CI branching fraction measurements for HFO ozonolysis are not found in the literature, indirect measurements of their aldehyde/ketone co-products show strong yields for CF₃CHOO species and other similar CIs (>40%).^52,54 This indicates that ozonolysis of haloalkenes in general are a major pathway for producing HFO-sCIs, even if these halogenated sCIs are low in abundance and ozonolysis is not the dominant pathway for removal of HFOs. This is a highly important topic and of relevance to the study of Criegee intermediates. Relative HFO ozonolysis percentages have been avoided here due to this need for a much more thorough re-investigation.

CIs are produced from the ozonolysis of a large variety of both halo-alkenes and non-halogenated alkenes and the atmospheric role of these CIs have been the subject of increased scientific study in the literature in recent years.^5,6,34,48 This is due to the fact that a large portion of the CIs produced by alkene ozonolysis (35–50%) are formed with such excess of internal energy that they undergo a rapid unimolecular fragmentation process, which is an important non-photolytic source of the atmospheric ‘detergent’ HO˙ species. The remaining fraction are stabilised by collision, generating stabilised Criegee intermediates (sCIs), that can participate in bimolecular reactions with other atmospheric species. These sCIs deplete pollutants to such an extent that the simplest sCI, formaldehyde oxide (CH₂OO), can compete with the atmospheric “detergent” HO˙ species as a sink for polar pollutants, such as HNO₃ and SO₂, especially in CH₂OO-rich boreal forest environments ([CH₂OO] ∼ 1–5 × 10⁴ molec. per cm³).^42,55 To examine the capacity of sCIs to deplete pollutants is the purpose of this study, as well as much of the increased scientific examination of sCIs overall.

The theoretical literature (see Table 1) shows that the ozonolysis of prominent HFOs produces several particular HFO-derived stabilised Criegee intermediates (HFO-sCIs): CH₂OO, syn- & anti-FCHOO, syn- & anti-ClCHOO, syn- & anti-CF₃CHOO and syn- & anti-CF₃CFOO.^{4,5,45,46,53,56} Only the bimolecular chemistry of CH₂OO species has been explored in the experimental literature, although syn- & anti-CF₃CHOO and syn- & anti-ClCHOO have been experimentally identified.^57–66 In a small number of studies, the bimolecular chemistry of HFO-sCIs has been interrogated using computational chemistry techniques: CH₂OO somewhat exhaustively;^67–71syn- & anti-FCHOO and syn- & anti-ClCHOO in reactions with CO₂, H₂, MeOH and CH₄;^72–76 and syn- & anti-CF₃CHOO in reactions with CO₂, CF₃CH=CH₂ and H₂.^72,73,77 The literature has very little analysis of syn- or anti-CF₃CFOO. As much of the bimolecular chemistry of syn- & anti-FCHOO and syn- & anti-ClCHOO has already been previously studied in the computational literature, the HFO-sCIs explored herein are instead CH₂OO, syn-CF₃CHOO, anti-CF₃CHOO, syn-CF₃CFOO and anti-CF₃CFOO, which are labelled as sCIs 1–5 and are displayed in Fig. 2.^72–75

Fig. 2 Geometric structures of hydrofluoroolefin-derived stabilised Criegee intermediates, HFO-sCIs, labelled as sCIs 1–5, and co-reactants examined in this in this study. In each case, rate constants for each HFO-sCI + co-reactant reaction are evaluated.

Also displayed in Fig. 2 is the targeted range of co-reactants selected for this computational study, including both H₂O & (H₂O)₂ because the global abundance of water vapour (∼0–40 000 ppm) means that these molecules are responsible for reacting with up to 95% of the total global flux of some atmospheric sCIs.^{67,68,78–83} As shown previously with the high abundance of TFA in Beijing, HFO breakdown produces a variety of secondary products, including HCHO, and so both TFA & HCHO are studied here as they like to have significant overlapping local concentrations with HFO-sCIs.^{3,4,28,36,49–51}

Some co-reactants (HNO₃, HCl & H₂S) are selected for study here because there are some environments in which CH₂OO competes with OH radicals to facilitate the depletion of these co-reactants, as noted by Khan et al.⁴² Furthermore, some co-reactants studied here, such as SO₂, are of interest because their reactions with sCIs are a competitive source for tropospherically relevant species such as SO₃, which is considered vital in aerosol nucleation pathways.^84,85 Another example is that sCI + MeOH & H₂O reactions produce a large proportion of the global flux of the α-alkoxyalkylhydroperoxides (AAAH) and α-hydroxy-hydroperoxides (HHP). These are oxidising species that cause both forest damage and SOA formation.^{67,68,72,78–80,83,86}

One last area of consideration in co-reactant targeting is that Kumar et al. propose that sCI reactivity with H₂X (X = O, S, Se, and Te) increases with the size of the X atom, referred to as heteroatom tuning of the co-reactants.⁸⁷ In this study, the co-reactants with low mass heteroatoms, H₂O & HF, are compared with species which have the same structures but larger heteroatoms of the same periodic group, H₂S & HCl, to see if all the HFO-sCIs in this chapter replicate the co-reactant heteroatom tuning patterns observed in the Kumar et al. study.⁸⁷ The last reactions featured are examined because the HCHO + sCIs 2 & 3 and sCI 1 + CF₃CHO reactions are part of the same multistep potential energy surface (PES) and so the theoretical rate constants (k_THEO) and product branching ratios (Γ_THEO) of sCI 1 + CF₃CHO can be determined with little additional computational cost. This is also the case for HCHO + sCIs 4 & 5 and sCI 1 + CF₃CFO reactions which are all part of the same multistep potential energy surface.

By using computational chemistry methods to review reactions with this variety of common tropospheric gas species, this study aims to evaluate to what degree the bimolecular chemistry of HFO-sCI (syn- & anti-CF₃CHOO and syn- & anti-CF₃CFOO) differs from that of CH₂OO, as well as the other non-halogenated sCIs.

2 Methodologies

This work employs a density functional theory (DFT) approach, using the hybrid B3LYP functional, and the Dunning correlation-consistent aug-cc-pVTZ basis set (B3LYP/aug-cc-pVTZ), is used to optimise the geometric structures of all minimum and transition state (TS) geometries, referred to collectively as stationary points.^88–99 Each minimum or TS structure is verified through evaluation of the number of imaginary frequencies from subsequent harmonic frequency calculations, performed at the same level of theory as the optimisation. TSs identified in this manner are mapped to the geometric minima that they bisect using intrinsic reaction coordinate (IRC) calculations. For very shallow TSs and barrierless reactions, IRC calculations become computationally challenging, therefore in these cases relaxed potential energy scans are performed using incremental separation of a molecular bond (which forms a key component of the reaction coordinate) until the local minima is reached. The relax surface scans for non-barrierless channels each have a local energy maximum, which denote the location of the TS structure on the potential energy surface, whereas the energy diagram for barrierless channels only display asymptotic Morse-like behaviour. Optimisations, harmonic frequencies, IRCs and potential energy scans are all performed using the Gaussian09 computational chemistry programme.¹⁰⁰ All optimisations in this study were performed on singlet surfaces.

Rate constants and PESs are constructed by using DFT optimised structures with energies refined using a higher level, ab initio approach. Single point molecular energy calculations, for all stationary points, are calculated using a localised, density fitted coupled cluster method with the same Dunning basis set (DF-HF/DF-LCCSD(T)-F12a/aug-cc-pVTZ).^{91,94–96,101–111} These molecular energies are calculated in the MOLPRO computational chemistry package.¹¹² All zero-point energies or Gibbs free energies in this study are calculated using the zero-point and free energy corrections acquired from the DFT harmonic frequency calculations. All relative energies (ΔE) referenced herein in the main body of this manuscript and in all PESs are zero-point corrected. This overall computational approach, when applied to the variety of sizes of sCIs and co-reactants in this study, provides both accurate energies and manageable computational cost. This computational approach is used in other studies in the literature too and it effectively describes the chemistry of sCI reactions with TFA & alcohols.^61,74 For further verification of the veracity of this computational approach, the theoretical rate constants (k_THEO) for the bimolecular sCI 1 reactions obtained in this study are benchmarked against experimental rate constants (k_EXP) from the literature.

The open source Master Equation Solver for Multi-Energy Well Reactions (MESMER) software is used to calculate the microcanonical kinetic reaction rates by deriving the individual energy-grained master equation (EGME) rate coefficients, which are then subsequently used to generate the overall master equation rate constant (k_THEO) and product branching ratios (Γ_THEO) of the system over a range of temperatures.¹¹³ Computational chemistry rate constants from other studies are also referred to as k_THEO constants, even if generated using differing methods. Master equation rate constants are referred to as k_ME values only in the ESI† to distinguish them from other theoretical rate constants. This software has been used extensively to solve analogous chemical problems, and has been utilised previously to evaluate Criegee intermediate reaction kinetics.^{76,84,114–119}

These MESMER calculations include a rigid rotor harmonic oscillator approximation, with structures and vibrational frequencies again taken from the DFT calculations, as shown by the example MESMER input in ESI Section S9.† ¹¹³ An inverse Laplace transform (ILT) capture rate coefficient of 1 × 10⁻¹⁰ cm³ s⁻¹ and an excess reactant concentration of 1 × 10¹⁶ molecule cm⁻³ are assumed.^76,113 The collisional energy transfer factor, 〈ΔE_down〉, was assigned as 300 cm⁻¹ for all minima. This has been shown to be a good approximation for systems involving nitrogen as a gas bath.^76,113,120 A 10 cm⁻¹ grain size was routinely used for the EGME calculations, however, for the larger systems, grain sizes are adjusted to reduce computational expense (ESI Sections 1.1–1.4†).

Low mass atom motion within the reaction mechanism is sometimes facilitated by quantum tunnelling, often accelerating the reaction. The effect of tunneling on the rate constant is determined herein using a non-ab initio tunneling correction called the asymmetrical Eckart constant (k_ECKART).¹²¹ This k_ECKART is calculated and then integrated directly into the k_THEO and Γ_THEO values through the MESMER software package, unless the reaction barriers are too low to support this methodology (these exceptions are stated in the ESI Section S1.1†).^76,113,121 In calculating the k_ECKART function, the probability of transmission through the one-dimensional energy barrier, p(E), needs to be calculated using eqn (1)–(7):

A = ΔH^‡,0K_f − ΔH^‡_r (5)

Calculating the probability of transmission involves estimating the barrier width between the reactants and products using: the forward and reverse zero-point corrected energy barriers, ΔH^‡,0K_f and ΔH^‡,0K_r, and the imaginary frequency of the associated TS describing the reaction coordinate, v^‡. The k_ECKART value is then determined using p(E) in eqn (8):

The irreversible final product formation processes are accommodated by the MESMER software by means of using an infinite “sink” approximation. In a system where a particular reaction channel that produces multiple products via a post-reaction complex (i.e. reactant → TS → post-reaction complex → product 1 + product 2) herein the formation of the post-reaction complex is treated as irreversible by MESMER when determining the k_ECKART & Γ_THEO values and it is assumed that ∼100% of this post-reaction complex separates into the final individual bimolecular products. This approximation reduces the computational intensity of MESMER calculations and introduces an error of less than 1%.^122,123 This use of the post-reaction complex can be seen in the MESMER example file in the ESI.†

In some multi-step reactions, a small number of the intermediate product → final products fragmentations involve progressing over an asymptotic Morse-like energy curve until the final separated products are formed, rather than fragmenting via a transition state. When Peltola et al. examined CH₂OO decomposing into HCO + OH and Blitz et al. studied CH₃NH breaking down into CH₃ + NH, both used a reverse inverse Laplace transformation (reverse ILT) method in MESMER to interpret these chemical pathways,^117,124 and both use the reverse ILT method with the experimental rate constant (k_EXP) of the equivalent forward reaction as the pre-exponential factor.^117,124 However, as the reaction channels in this study where the reverse ILT method is used have no literature k_EXP values instead the dipole–dipole capture limit rate constant, k_d–d, (discussed in the next paragraph) are used as the pre-exponential factors instead. Furthermore, this reverse ILT method requires using the term reverse = true in the activation energy component and assigning both final products as separate sink structures.

In a few previous studies, sCI reactions with other trace atmospheric species (e.g.sCI 1 + HCOOH, CH₃COOH or CF₃COOH) have produced such large k_THEO & k_EXP values that each sCI + co-reactant collision leads to a reaction.^{59–61,74,125} Under such conditions, it is proposed that k_THEO values can be more accurately modelled using a collision frequency model, such as the dipole–dipole capture limit, k_d–d. The k_d–d value is calculated using eqn (9) and (10):

C is a constant dependent on the anisotropy of the capture potential; μ_D1 and μ_D2 are the dipole moments of reactants 1 & 2; and μ is the total reduced mass of the system calculated using the mass of reactants 1 & 2 (m₁ & m₂).¹²⁶ The C value adopted can be either isotropic (4.08), adiabatic anisotropic (2.68) and non-adiabatic anisotropic (1.953).¹²⁶ The isotropic k_d–d constant is used in this study, as it is much used in the literature for bimolecular sCI reactions.^61,125

Frequently in this study, the rate determining step is barrierless or k_THEO > k_d–d (usually where k_THEO ≥ ∼10⁻¹⁰) and so the k_d–d is used as the overall rate constant, as it is a more true reflection of the tropospheric rate constant. As sCIs are polar in character, the isotropic k_d–d value is used over the more traditional collision limit (k_COLL) too, as k_d–d is better able to model the effect this polarity has on sCI — co-reactant collision frequency. However, the k_COLL values for each reaction, along with the adiabatic anisotropic and non-adiabatic anisotropic k_d–d values, are all listed in the ESI Section S3† for comparison. The rate constants generated in this work are analysed using the effective first-order rate constant, k_EFF, which accounts for the concentration of the co-reactant:³⁵

k_EFF = k_THEO[co-reactant] (11)

These k_EFF values in this work are calculated using previously reported co-reactant concentrations in example ‘important’ local environments. This data is displayed in Table 2 in the next section, alongside any known experimental rate constants for the same reactions. Further examples of other local co-reactant abundances in other environments and the effect they have on the k_EFF values are listed in ESI Section S4.†

3 Results & discussion

The bimolecular master equation rate constant (k_THEO), the dipole–dipole capture limit (k_d–d), and the effective rate constant (k_EFF), for the HFO-sCI reactions calculated in this study are found in Table 2. The co-reactant abundances featured in Table 2 are selected from locations where either the pollutant has a high enough concentration to be a potentially significant sCI sink and/or an area where humans may face a significant degree exposure of either the pollutant or the potential product of this reaction. These values are then used to generate the k_EFF values seen in Table 2 (to view the extended literature survey of the tropospheric abundances of the co-reactants, see ESI Section S4.2†). As most of these values are averages from single locations across a protracted period of time or a generalised upper-limit in certain urban environments from a variety of locations, most measurements occur over a range of temperatures that include 298 K. Either the k_THEO value or the k_d–d value are in bold to highlight which the rate constant is used to calculate each k_EFF value. Any Γ_THEO branching fractions of the two-step HFO-sCI reactions with aldehydes & SO₂ are not displayed in Table 2 and can be instead found in Sections 3.1 & 3.2.

Table 2 A tabulation of the reaction kinetics and the atmospheric impact of all HFO-sCI reactions studied here. Characteristics of each reaction listed in table includes co-reactant identity and atmospheric abundance ([co-reactant]); Criegee intermediate labelled by number (sCI); computational master equation rate constant (k_THEO);^a dipole–dipole capture limit (k_d–d); literature experimental rate constant (k_EXP); and effective rate constant (k_EFF = k_THEO or k_d–d × [co-reactant])^b

[Co-reactant] (molec. per cm^3)	sCI	k THEO (cm^3 s^−1)	k d–d (cm^3 s^−1)	k EXP (cm^3 s^−1)	k EFF (s^−1)
a “≫kd–d” refers to barrierless reactions that yield no kTHEO and that the kd–d value should be used instead. b In bold is the overall theoretical rate constant, which is the lowest between the kTHEO & kd–d values.
HCHO, 2.0 × 10^12 (Urban heavy traffic)^128	1	2.79 × 10^−12	1.06 × 10^−9	4.1 × 10^−12 (ref. 127)	5.60
	2	2.69 × 10^−13	8.04 × 10^−10	—	0.54
	3	2.49 × 10^−12	6.46 × 10^−10	—	5.0
	4	≫kd–d	7.20 × 10^−10	—	1447
	5	1.66 × 10^−11	7.07 × 10^−10	—	33.4
CF3CHO	1	≫kd–d	6.50 × 10^−10	—	—
CF3CFO	1	1.98 × 10^−12	3.34 × 10^−10	—	—
SO2, 4.1 × 10^11 (Beijing urban area)^129	1	≫kd–d	7.25 × 10^−10	3.9 × 10^−11 (ref. 63)	300
	2	1.90 × 10^−12	5.08 × 10^−10	—	0.79
	3	≫kd–d	4.08 × 10^−10	—	169
	4	≫kd–d	4.51 × 10^−10	—	186
	5	≫kd–d	4.42 × 10^−10	—	183
HNO3, 1.1 × 10^11 (Houston, Texas)^130	1	8.22 × 10^−9	8.45 × 10^−10	5.1 × 10^−10 (ref. 59)	94
	2	2.06 × 10^−11	5.93 × 10^−10	—	2.3
	3	8.87 × 10^−11	4.76 × 10^−10	—	9.8
	4	9.25 × 10^−8	5.26 × 10^−10	—	58
	5	7.53 × 10^−11	5.16 × 10^−10	—	8.4
TFA, 3.3 × 10^7 (Beijing higher emission areas)^28	1	≫kd–d	7.54 × 10^−10	3.5 × 10^−10 (ref. 61)	2.5 × 10^−2
	2	≫kd–d	4.96 × 10^−10	—	1.7 × 10^−2
	3	≫kd–d	3.98 × 10^−10	—	1.3 × 10^−2
	4	≫kd–d	4.35 × 10^−10	—	1.5 × 10^−2
	5	≫kd–d	4.27 × 10^−10	—	1.4 × 10^−2
H2O, 6.2 × 10^17 (∼80% humidity Sao Paulo)^132,133	1	1.18 × 10^−16	1.06 × 10^−9	2.4 × 10^−16 (ref. 131)	73
	2	1.35 × 10^−18	8.38 × 10^−10	—	0.83
	3	1.12 × 10^−16	6.73 × 10^−10	—	70
	4	5.13 × 10^−12	7.54 × 10^−10	—	3.2 × 10^6
	5	2.27 × 10^−13	7.40 × 10^−10	—	1.4 × 10^5
(H2O)2, 8.7 × 10^14 (∼80% humidity Sao Paulo)^132,133	1	3.28 × 10^−12	1.07 × 10^−9	7.5 × 10^−12 (ref. 131)	2.9 × 10^3
	2	2.71 × 10^−12	7.99 × 10^−10	—	2.4 × 10^3
	3	3.74 × 10^−12	6.42 × 10^−10	—	3.3 × 10^3
	4	1.14 × 10^−6	7.14 × 10^−10	—	6.2 × 10^5
	5	1.46 × 10^−9	7.01 × 10^−10	—	6.1 × 10^5
MeOH, 8.4 × 10^11 (Sao Paulo, Brazil)^135	1	1.20 × 10^−14	8.15 × 10^−10	1.1 × 10^−13 (ref. 134)	0.010
	2	9.43 × 10^−17	6.14 × 10^−10	—	7.9 × 10^−5
	3	3.30 × 10^−14	4.93 × 10^−10	—	0.028
	4	≫kd–d	5.50 × 10^−10	—	462
	5	3.31 × 10^−11	5.39 × 10^−10	—	28
H2S, 1.2 × 10^13 (industrial landfill)^137	1	7.06 × 10^−15	5.68 × 10^−10	1.7 × 10^−13 (ref. 136)	0.052
	2	1.96 × 10^−16	4.26 × 10^−10	—	1.4 × 10^−3
	3	5.72 × 10^−15	3.42 × 10^−10	—	0.042
	4	6.08 × 10^−13	3.81 × 10^−10	—	4.5
	5	1.23 × 10^−14	3.74 × 10^−10	—	0.091
HCl, 1.2 × 10^11 (daytime Los Angeles)^138	1	4.70 × 10^−10	6.06 × 10^−10	4.1 × 10^−11 (ref. 59)	58
	2	4.04 × 10^−15	4.51 × 10^−10	—	5.0 × 10^−3
	3	7.28 × 10^−11	3.62 × 10^−10	—	8.96
	4	1.64 × 10^−10	4.03 × 10^−10	—	20
	5	1.13 × 10^−10	3.96 × 10^−10	—	14
HF, 3.7 × 10^11 (near volcano vicinity ambient T)^139	1	3.32 × 10^−13	8.15 × 10^−10	—	0.12
	2	6.67 × 10^−18	6.14 × 10^−10	—	2.5 × 10^−6
	3	2.86 × 10^−15	4.93 × 10^−10	—	1.1 × 10^−3
	4	1.19 × 10^−11	5.50 × 10^−10	—	4.4
	5	3.66 × 10^−13	5.39 × 10^−10	—	0.14

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3.1 HFO-sCI reaction with formaldehyde (HCHO)

During an ozonolysis event that generates a Criegee intermediate, a carbonyl containing species (aldehydes and ketones) are very common co-products and as such these carbonyl moieties are co-located with sCIs during formation such that a further reaction between these two proximate species is probable. Formaldehyde (HCHO) is produced from the ozonolysis of a variety of alkenes, notably for this work that includes HFO-1234yf (see Fig. 3), and therefore examining any possible secondary reaction with HCHO is likely vital to understanding the overall tropospheric chemistry of these HFO-sCIs.^4,48,140

Fig. 3 The general schematic for the ozonolysis of HFO-1234yf producing a short-lived primary ozonide (POZ) followed by one of the pairs of final products, a Criegee intermediate (sCI 5 or anti-CF₃CFOO) and a carbonyl product (formaldehyde).

Also, as HCHO emissions are strong in areas of heavy urban traffic (up to 170 μg m⁻³) and HFOs are used in vehicle coolant units, there is a high probability of emissions overlap between HCHO and HFO-sCIs.^{36,128,141,142} Additionally as HCHO is carcinogenic and toxic if inhaled, sCIs depletion of tropospheric HCHO should be included in many atmospheric models.^143–145

3.1.1 The sCI 1 + HCHO reaction. All sCI + HCHO reactions in this study undergo an initial 1,3-cycloaddition (TS_C) step to a short-lived heteroozonide (HOZ) intermediate and the HOZ almost instantaneously fragments. The fragmentation is likely rapid because the HOZ is formed with significant excess energy and the HOZ structure has a high degree of tortional strain. When the HOZ fragments, it can form acid + aldehyde products via two different mechanistic processes: a high energy, 1-step channel or a lower energy, 2-step channel via a hydroxyalkyl formate (HAE) species. The schematics and barrier heights of the 1-step “TS_FAc” channel (in blue) and the 2-step “HAE channel” (in red) for sCI 1 + HCHO are seen in Fig. 4. The “TS_D” & “TS_HAE” labels are used to refer to the respective formation and breakup of the HAE species.

Fig. 4 The potential energy surface for the sCI 1 + HCHO reaction. The lowest energy transition state for each HOZ fragmentation pathway is displayed. The 1-step direct transfer channel via the TS_FAc barrier is in blue and a 2-step hydroxyalkyl ester (HAE) channel, via the TS_D & TS_HAE barriers, is red. Energies are relative to the raw reactants.

Computational assessments of the sCI 1 + HCHO reaction (Fig. 4) are characterised by a low energy TS_C barrier (∼−25 to −20 kJ mol⁻¹), which leads to high theoretical rate constants both here (k_THEO ∼ 2.79 × 10⁻¹¹ cm³ s⁻¹) and in the literature (k_THEO ∼ 4.03 × 10⁻¹⁰ cm³ s⁻¹).^71,146 The k_THEO value determined here is also similar to the k_EXP values measured for sCI 1 + HCHO by Luo et al., (4.11 ± 0.25) × 10⁻¹², as well as those determined for studies of the analogous sCI 1 + CH₃CHO reaction (3.0 × 10⁻¹³ to 1.7 × 10⁻¹² cm³ s⁻¹).^{64,65,127,147}

The sCI 1 + HCHO reaction produces only one final product set, HCOOH + HCHO, and of the two HOZ fragmentation mechanism, the TS_D barrier of the two-step HAE channel has a lower energy than the TS_FAc barrier to the one-step HOZ fragmentation channel (Fig. 4). Both findings are authenticated by similar results in prior studies.^71,146 Obtaining reliable TS_D & TS_FAc barriers is important because whereas the absolute height of the energy barrier(s) of the first reaction step dictates the k_THEO value, the crucial factor in determining the Γ_THEO branching fractions is the energy difference between the HOZ fragmentation barriers. This study also agrees with other computational studies in that that the second step of the two-step HOZ fragmentation, the breakdown of the HAE, involves a very low TS_HAE barrier (Fig. 4).^71,146

Given that the HAE is formed with considerably higher energy than the HAE → TS_HAE barrier height, the MESMER results discussed here are calculated on the assumption that formation of the HAE is the final step of that reaction channel and that all the HAE population reacts further to produce their acid + aldehyde products, with negligible populations of HAE remaining. These MESMER simulations yield a very similar result (Γ_THEO ∼ 0.973) to those in which the HCOOH + HCHO are set as the final products (Γ_THEO ∼ 0.978). As this methodology has been shown to have little effect on the accuracy, this ∼100% HAE → acid + aldehyde conversion principle is applied to the HCHO reactions with sCIs 2–5, for the purpose of reducing computational cost.

3.1.2 The HCHO + sCIs 2 & 3 and CF₃CHO + sCI 1 reactions. The cycloaddition of sCI 2 + HCHO & sCI 3 + HCHO produce different HOZ conformers, HOZs 1 & 2 respectively, but these HOZ conformers can interconvert via an inversion TS_HOZ mechanism. This TS_HOZ barrier is much lower in energy than both the cycloreversion and HOZ fragmentation mechanisms (Fig. 5). Therefore, these HOZs generally interconvert freely and are treated as a single HOZ species when using MESMER to calculate the product branching fractions. Furthermore, during any of these reactions, (e.g.sCI 2 + HCHO), the HOZ species can fragment to produce any of the other reactant pairs (here sCI 3 + HCHO or sCI 1 + CF₃CHO), via cycloreversion pathways. The HOZ species produced by these reactions can also fragment (Fig. 5) to produce two different “acid + carbonyl” sets of products, TFA + HCHO or HCOOH + CF₃CHO, either through a one-step channel (via TS_TFA or TS_FAc2 respectively) or a two-step HAE channel (via TS_D1 & TS_HAE1 or TS_D2 & TS_HAE2 respectively). HOZ fragmentation can also proceed via “TS_ESTER” mechanisms to produce CF₃OCHO + HCHO.

Fig. 5 The collective potential energy surface for sCIs 2 & 3 + HCHO and sCI 1 + CF₃CHO reactions with minima energy structures of each HOZ fragmentation displayed. Energies are relative to the raw sCI 3 + HCHO reactants.

The relatively low TS_C barriers seen for the sCIs 2 & 3 reactions with HCHO in Fig. 5, lead to large k_THEO values (2.69 & 24.9 × 10⁻¹³ cm³ s⁻¹), although both reactions are less reactive than sCI 1 + HCHO (see Table 3). Studies of the bimolecular HFO-sCI chemistry are limited, but computational work on sCIs 1–3 reactions with H₂, CO₂ & CF₃CH=CH₂ are present in the literature and show similar trends to those identified here (Table 3).^72,73,77 For instance, the barriers to the HFO-sCIs + CO₂ reaction follow the same reactivity order (E_TS (sCI 2) > E_TS (sCI 1) > E_TS (sCI 3)) seen for these HCHO reactions.⁷² Furthermore, the anti-orientated sCI 3 is more reactive with CF₃CH=CH₂ than the syn-orientated sCI 2, the same result observed for sCIs 2 & 3 + HCHO.⁷⁷

Table 3 A tabulation of key kinetic information of HCHO reactions with the sCIs 1–3 reactions from this study contrasted with that other bimolecular sCIs 1–3 reactions from the literature featuring: the relative energy of the lowest transition state barrier [ΔE_TS] and theoretical rate constants [k_THEO]. Energies are relative to raw reactants

sCI	#sCI	ΔETS [kJ mol^−1]				k THEO [10^−13 cm^3 s^−1]
		H2	CO2	HCHO	CF3CH=CH2	k HCHO	k CF3CH=CH2
CH2OO	1	74.5	17.6	−20.8	−12.8	27.9	1.76
Syn-CF3CHOO	2	—	32.6	−11.6	−13.8	2.69	77.9
Anti-CF3CHOO	3	52.3	25.1	−19.0	−16.9	24.9	285
Reference		73	72	This study	77	This study	77

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While the inclusion of a single –CF₃ group does not significantly enhance the reactivity of sCIs 2 & 3, the presence of a single –CF₃ substituent in the aldehyde co-reactant increases its reactivity to such a degree that the cycloaddition of sCI 1 + CF₃CHO is barrierless and the k_d–d value (∼6.50 × 10⁻¹⁰ cm³ s⁻¹) is used as the rate constant. This could be due to a hypothetical inductive effect caused simply by adding any alkyl substituent to the aldehyde. But, despite the increased number of alkyl groups on CH₃CHO & (CH₃)₂CO the experimental literature suggests that their reactions with sCI 1 (k_EXP ∼ 10⁻¹–10⁻¹² cm³ s⁻¹) do not show the enhanced reactivity seen for the sCI 1 + CF₃CHO reaction.^65,71,147 However, the role of fluorine in –CF₃ substituents is explored in an experimental study by Taatjes and co-workers and they show that sCI 1 + (CF₃)₂COO has a larger k_EXP (∼3.0 ± 0.3 × 10⁻¹¹ cm³ s⁻¹) compared to the k_EXP of sCI 1 + (CH₃)₂COO (∼2.3 ± 0.3 × 10⁻¹³ cm³ s⁻¹).⁶⁵ This confirms the high reactivity seen for sCI 1 + CF₃CHO must emerge from the inductive impact that the fluorenes in the –CF₃ substituents have on the aldehyde reactivity.

Both HCHO + sCI 2 and HCHO + sCI 3 (Fig. 6) produce high yields of the sCI 1 + CF₃CHO (∼0.91–0.94), due to the barrierless nature of their cycloreversion mechanisms, with small contributions from Γ_TFA+HCHO (∼0.012–0.016) and Γ_HCOOH+CF3CHO (∼0.052–0.068). In contrast, during the sCI 1 + CF₃CHO reaction, the production of HCHO + sCIs 2 & 3 gives very low branching ratios (<0.001) because the energy barriers for producing HCHO + sCIs 2 & 3 are much larger than other HOZ fragmentation pathways. Consequently, the overall Γ_THEO of sCI 1 + CF₃CHO is dominated by Γ_HCOOH+CF3CHO ∼ 0.823 with most of this contribution coming from the two-step HAE pathways (Γ_TSD1 ∼ 0.746) with a smaller contribution from the one-step channel (Γ_TSFAc ∼ 0.077). The secondary product yield, Γ_TFA+HCHO ∼ 0.177, also has most of its contribution emerge from the two-step HAE pathways, Γ_TSD2&TSD3 ∼ 0.166. The TS_ESTER barrier is too high for the ester formation to have anything but a negligible yield for all three reactions.

Fig. 6 The fractional populations of reactants and products for the sCI 3 + HCHO reaction over time (the product branching fractions for the barrierless cycloreversion channels to sCI 1 + CF₃CHO are calculated using the same reverse ILT method described in the Methods section.^117,124 Excess HCHO reagent concentration is ∼1.0 × 10¹⁶ molec. per cm³. For other details on the conditions of the reaction see ESI Section S11†).

While no experimental or theoretical product ratios for sCI 1 + CF₃CHO are available in the literature, some of the analysis of the similar sCI 1 + CH₃CHO & PhCHO reactions does include computational calculations of HOZ fragmentation energy barriers. Examination of both the sCI 1 + CH₃CHO & PhCHO systems show patterns consistent with this work, including: that the formation of smaller acid final products was preferred over larger acid products, that the 2-step HAE channel was the favoured formation mechanism for these acids, and that ester formation was negligible.

3.1.3 The HCHO + sCIs 4 & 5 and CF₃CFO + sCI 1 reactions. sCI 5 + HCHO exhibits has a low energy TS_C barrier (∼−28.9 kJ mol⁻¹) whereas the cycloaddition of sCI 4 + HCHO is barrierless. This demonstrates that sCI 4 is more reactive than sCI 5 and that both these HFO-sCIs are significantly more reactive than sCIs 1–3. sCIs with larger substituents (e.g. –CH₃ or –CF₃) in the syn-position have been shown to decrease sCI reactivity, however here it is observed that sCI 4, which has a syn-orientated larger group, has greater reactivity than the anti-orientated sCI 5.^{60,79,148–151} Unlike the sCI 1 + CF₃CHO reaction, sCI 1 + CF₃CFO does not have barrierless cycloaddition (TS_C ∼−27 to −22 kJ mol⁻¹) and the k_THEO value of this reaction (∼2.0 × 10⁻¹² cm³ s⁻¹) is below the k_d–d capture limit. When compared to the k_THEO values of sCI 1 + HCHO & CF₃CHO (∼2.8 & 650 × 10⁻¹² cm³ s⁻¹), it is clear that the inductive effect of the –CF₃ substituent in the CF₃CFO is largely cancelled out by the larger deactivating effect of the –F substituent that is also present in CF₃CFO.

sCI 4 & sCI 5 reactions with HCHO are both integrated into the same reaction system as sCI 1 + CF₃CFO and therefore all sCI + aldehyde reactant pairs can also be produced during HOZ fragmentation in this overall reaction system. The Γ_THEO for both the sCIs 4 & 5 + HCHO reactions are dominated by yields of sCI 1 + CF₃CFO (∼0.84) with the remainder being the Γ_HCOOH+CF3CFO contribution (∼0.16). In contrast, the sCI 1 + CF₃CFO reaction has only negligible yields for sCIs 4 & 5 + HCHO (<0.0001) because their cycloreversion TS_C barriers are >100 kJ mol⁻¹ higher than the lower energy HOZ fragmentation barriers.

The primary product of the sCI 1 + CF₃CFO reaction is HCOOH + CF₃CFO (Γ_HCOOH+CF3CFO > 0.99), with the direct H-transfer TS_FAc channel producing almost all the formic acid yield. The higher barriers to the HAE pathway compared to the direct H-transfer channel seen here for the sCI 1 + CF₃CFO reaction system (see ESI Section S5†) is uncommon both in this study and in the literature.^71,146 However, in a literature analysis of anti-PhCHOO + PhCHO, the direct H-transfer mechanism also has a higher barrier (−19.2 kJ mol⁻¹) to phenylacetic acid formation than the two step HAE channel (−17.6 kJ mol⁻¹).¹⁴⁶ As noted in Table 4, ester formation continues to be negligible for all sCI + aldehyde reactions.

Table 4 A tabulated breakdown of the results from the HOZ fragmentation of all HFO-sCI + aldehyde & ketone studied here, giving the final product branching for each product set

Reaction sCI + HCHO	Final product branching ratio (ΓTHEO)
	Γ sCI1+R1CR2O	Γ HCHO+R1CR2OO	Γ HCOOH+R1CR2O	Γ TFA+HCHO	Γ ester+HCHO
a The product branching fractions of the barrierless cycloreversion channels that leads to either sCI 1 + CF3CHO or sCI 4 + HCHO are calculated using the same reverse ILT method described in Method section.^117,124
sCI 2 + HCHO	0.993^a	7.40 × 10^−5	0.006	0.001	1.78 × 10^−7
sCI 3 + HCHO	0.991^a	3.92 × 10^−6	0.007	0.002	1.02 × 10^−7
sCI 4 + HCHO	0.843	9.40 × 10^−9	0.156	—	3.06 × 10^−5
sCI 5 + HCHO	0.842	8.13 × 10^−9^a	0.158	—	4.98 × 10^−5
sCI 1 + R1CR2O	Γ HCHO+anti-R1CR2OO	Γ HCHO+syn-R1CR2OO	Γ HCOOH+R1CR2O	Γ TFA+HCHO	Γ ester+HCHO
sCI 1 + CF3CHO	1.47 × 10^−6	2.49 × 10^−5	0.823	0.177	2.14 × 10^−8
sCI 1 + CF3CFO	3.10 × 10^−14	3.51 × 10^−12^a	>0.999	—	1.74 × 10^−7

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3.1.4 Overview of sCI + aldehyde reactions. The key features of the sCI + aldehyde reactions are that the chemistry can be broadly divided into two steps: the cycloaddition into an HOZ intermediate, and the fragmentation of that intermediate into various products. The HFO-sCI + aldehyde reactions have large rate constants (k_THEO ∼ 10⁻¹³–10⁻¹⁰ cm³ s⁻¹) as the cycloaddition is either barrierless or proceeds via low energy TS_C barriers. The inclusion of –CF₃ substituents in the syn-position produces a reductive impact on the COO group of the sCI, as shown by the smaller rate constant of sCI 2 compared to the unsubstituted sCI 1 or the anti-substituted sCI 3. However, an –F substituent has an inductive effect on the sCI, particularly in the anti-position, as shown by the high reactivity of sCI 4. Considering the factors given above the reactivity of the HFO-sCIs studied here follows the following trend: k_THEO (sCI 2) < k_THEO (sCI 3) < k_THEO (sCI 1) < k_THEO (sCI 5) < k_d–d (sCI 4). The role these –H, –F or –CF₃ substituents have on the aldehyde reactivity trend, k_THEO (CF₃CFO) < k_THEO (HCHO) < k_THEO (CF₃CHO), is the opposite to that seen for the sCIs, k_THEO (CF₃CFOO) < k_THEO (CH₂OO) < k_THEO (CF₃CHOO). In the HOZ fragmentation stage of the sCI 1 + HCHO/CF₃CHO/CF₃CFO reactions, the yield is dominated by formation of formic acid + an aldehyde, with sCI 1 + CF₃CHO also producing sizable product branching fractions for HCHO + CF₃COOH (Γ_THEO ∼ 0.16). However, for sCIs 2–5 + HCHO reactions, the dominant product is sCI 1 + CF₃CHO/CF₃CFO (Γ_THEO ∼ 0.80–0.99), due to the low barrier to formation of this product pair.

3.2 HFO-sCIs reactions with sulphur dioxide (SO₂)

Toxic sulphur dioxide (SO₂) emitted from various sources, including the burning of fossil fuels and volcanic eruptions, has a major role as an effective gaseous sCI sink and the sCI + SO₂ reaction is therefore of significant prominence in the literature.^{63,78,81,82,84,85,131,149,152–158} This reaction is considered responsible for between ∼1% of the loss of syn-CH₃CHOO in rural environments to ∼22% of the loss of “syn-CH₃-anti-(trans-CH₂=CH)–COO” in boreal forests.¹⁵⁹ Furthermore, the importance of this reaction is increased because the dominant final product of this reaction is SO₃, which is a source of organosulphates and is involved in the formation and growth of secondary organic aerosol (SOA) nuclei.^84,85,160 The promotion of SOA nucleation, caused by increased SO₃ yields, is vital to understand because the prevalence of aerosols in urban environments can cause serious respiratory problems and premature death.^161–165 Also, depending on the aerosol type, they can absorb and scatter solar radiation and therefore influence climate temperatures.^161,164,165

3.2.1 The sCI 1 + SO₂ reaction. All HFO-sCIs in this study, as well as many sCIs studied in the literature, react with SO₂ through a general two-step reaction scheme, via a short-lived 5-member ozonide ring.^84,159 These pathways produce cyclic intermediates, which are often called heteroozonides too, but it can also be referred to as a secondary ozonide (SOZ) and to prevent confusion with the HCHO reaction, that SOZ label is used in these SO₂ reactions.⁸⁴ The SOZs produced from sCI 1 + SO₂ are generated in either an exo- (SOZ 1) or an endo- orientation (SOZ 2), depending on the orientation of the SO₂ (Fig. 7) in the cycloaddition transition state, TS_EXO and TS_ENDO respectively. As also observed in the experimental and theoretical literature, the sCI 1 + SO₂ reaction is highly reactive and so when both TS_ENDO and TS_EXO pathways were evaluated it was found that both reactions were barrierless.^{63,64,84,85,153,154,166} This meant that therefore means that the k_d–d limit (7.25 × 10⁻¹⁰ cm³ s⁻¹) is adopted as the rate constant for the sCI 1 + SO₂ reaction.

Fig. 7 A Schematic of the cycloaddition process for sCI 1 + SO₂: featuring the endo- & exo-cycloaddition transition states (TS_EXO & TS_ENDO) and the endo- & exo-SOZ intermediate products (SOZs 1 & 2).

The SOZ interconversion via the inversion of the S atom is known to require >180 kJ mol⁻¹ excess energy, which exceeds barriers to both cycloreversion (via TS_EXO & TS_ENDO) and SOZ fragmentation (Fig. 8).⁸⁴ This would impede SOZ interconversion but, as the R₁ and R₂ substituents in sCI 1 are identical, SOZs 1 & 2 can freely interconvert over low energy pseudorotation TS_SOZ barriers (see Fig. 8), which this means that SOZs 1 & 2 behaves as a single SOZ species.

Fig. 8 The potential energy surface of sCI 1 + SO₂ with minima energy structures of each SOZ fragmentation displayed. Energies are relative to the raw reactants.

The next stage of the sCI 1 + SO₂ reaction is the fragmentation of the SOZ to produce either SO₃ + HCHO via the TSSO₃ channel or SO₂ + HCOOH via the TS_acid channel. All SOZ fragmentation channels studied here are single-step mechanisms and the acid-producing mechanisms from each HFO-sCI + SO₂ reaction system exclusively produces a single acid species. Kuwett et al. have performed a comprehensive analysis of both SO₂ reactions with sCIs 1 & (CH₃)₂COO comprising a numerous range of major and minor SOZ fragmentation pathways, including a homolytic O–O bond fission to produce a 1,5-(bis)oxy diradical intermediate product.⁸⁴ While the self-reaction of this diradical intermediate produces important products, such as SOCO rings, sulphurous anhydrides or 1,3-(bis)oxy diradicals, its yield is so minor that 1,5-(bis)oxy diradical pathways are not explored for sCIs 1–5 + SO₂ here.⁸⁴

The final product branching fraction for sCI 1 + SO₂ is dominated by SO₃ + HCHO (Γ_SO3 ∼ 0.966) with a subordinate yield HCOOH + SO₂ (Γ_acid ∼ 0.034) because the TSSO₃ 1 & 2 barriers (Fig. 8) are significantly lower in energy than the TS_acid 1 & 2 structures. This dominance of SO₃ + CF₃CHO in the Γ_THEO value is in agreement with that calculated in the literature (Γ_SO3 ∼ 0.973–0.984).⁸⁴

3.2.2 The sCIs 2 & 3 + SO₂ reactions. The sCI 2 + SO₂ reaction is unique amongst the HFO-sCI + SO₂ reactions studied here in that the cycloaddition process is not barrierless and structures for the TS_ENDO & TS_EXO barriers can be readily computationally determined. The TS_ENDO barrier (−18.3 kJ mol⁻¹) is lower in energy than TS_EXO (−17.6 kJ mol⁻¹) and so the endo-orientated SOZ 2 yield is greater than exo-orientated SOZ 1 at a ratio of 0.69 : 0.31. Even though all other SO₂ reactions with sCIs 1–5 are barrierless, sCI 2 + SO₂ still has a substantially large theoretical rate constant (k_THEO = 1.90 × 10⁻¹² cm³ s⁻¹). As both the TS_EXO & TS_ENDO channels of sCI 3 + SO₂ are barrierless, the k_d–d value (4.08 × 10⁻¹⁰ cm³ s⁻¹) is assigned as the rate constant and SOZs 3 & 4 are produced in equal fractions.

Due to the high energy barrier for interconversion via inversion of the S atom (>180 kJ mol⁻¹), the SOZ 1 & 2 conformers, produced from the SO₂ reaction with the monosubstituted sCI 2, cannot interconvert with each other without reverting to the initial reactants. This likewise applies to the mono-substituted sCI 3 + SO₂, which also produces endo and exo conformers SOZs 3 & 4. During some sCI + SO₂ reactions, the SOZs produced can interconvert via a pseudorotation TS_SOZ mechanism and circumvent the higher barrier via S atom inversion, but this can only transpire during reactions with sCIs with the same R₁ & R₂ substituents (e.g.sCI 1 or (CH₃)₂COO). Instead, when SOZ 1 surmounts the pseudorotation TS_SOZ 1 barrier it isomerises into the SOZ 3 conformer and the TS_SOZ 2 pseudorotation makes possible the SOZ 2 ↔ SOZ 4 interconversion (Fig. 9). This also means that SO₂ reactions with sCIs 2 & 3 are part of the same integrated PES, through the TS_SOZ 1 & 2 isomerisation channels (Fig. 9 and 10). This phenomena of 2 × non-interchangeable sets of SOZs also applies to SO₂ reactions with sCIs 4 & 5 and, according to the literature, SO₂ reactions with syn- & anti-CH₃CHOO.⁸⁴

Fig. 9 Collective diagram of all SOZs produced by sCIs 2 & 3 + SO₂ reactions and the pseudorotation TS_SOZ barriers that facilitate SOZ 1 ↔ SOZ 3 and SOZ 2 ↔ SOZ 4 interconversions. Structures included and energies relative to sCI 3 + SO₂.

Fig. 10 The collective potential energy surface for sCIs 2 & 3 + SO₂ reactions with minima energy structures of each SOZ fragmentation displayed. Energies are relative to the raw sCI 2 + SO₂ reactants.

During the SOZ fragmentation of either sCI 2 + SO₂ & sCI 3 + SO₂ reactions, the reverse sCI + SO₂ reactant pairs can be produced through cycloreversion, as both reactions are part of the same potential energy surface. The SOZ fragmentation can also proceed through: TSSO₃ into SO₃ + CF₃CHO, TS_acid into SO₂ + TFA, or TS_Ester into SO₂ + CF₃OCHO. It was noted above that the cycloaddition step of the SO₂ + sCI 2 reaction produced a large yield of the SOZ 2 & 4 conformer set and a small yield of the SOZ 1 & 3 conformer set, whereas the SO₂ + sCI 3 produced fairly even yields of each SOZ set. Furthermore, these stereochemically distinct SOZ sets each have their own fragmentation pathways, as SOZ 1 & 3 breakdown via TSSO₃ 2, TS_acid 1 & TS_Ester 1 and SOZ 2 & 4 fragments via TSSO₃ 1, TS_acid 2 & TS_Ester 2. The overall product branching ratio for sCI 2 + SO₂ is very similar to that of sCI 3 + SO₂, so it appears that the differing SOZ yields seen in these two reactions has little overall effect on the product branching fraction.

sCI 2 + SO₂ does produce a small yield of sCI 3 + SO₂ from the cycloreversion channel, whereas the sCI 2 + SO₂ yield from sCI 3 + SO₂ reaction is negligible. This is because cycloreversion to sCI 2 + SO₂ has to overcome TS barriers, whereas cycloreversion to sCI 3 + SO₂ only has to overcome the energy of required to reform the raw reactants. The product branching fraction for ester formation is slight. The dominant final products for both the sCIs 2 & 3 + SO₂ reactions are CF₃CHO + SO₃ (Γ_THEO ∼ 0.995) with only a very minor yield of TFA + SO₂ (Γ_THEO ∼ 0.003).

3.2.3 sCIs 4 & 5 + SO₂ reactions. Both SO₂ reactions with sCIs 4 & 5 are barrierless, so their k_d–d values (4.51 & 4.42 × 10⁻¹⁰ cm³ s⁻¹) are used for the rate constants for these reactions and their exo- & endo-SOZ conformers are produced in almost equal yields. The sCIs 4 & 5 + SO₂ reactions are part of the same integrated reaction system and the phenomenon of 2 sets of non-interchangeable SOZs also applies to this system (Fig. 11) but this has little impact on SOZ fragmentation yields (Table 5).

Fig. 11 The collective potential energy surface for sCIs 4 & 5 + SO₂ reactions with minima energy structures of each SOZ fragmentation displayed. Energies are relative to the raw sCI 4 + SO₂ reactants.

Table 5 A tabulated breakdown of the outcomes from SOZ fragmentation of the sCIs 1–5 + SO₂ reactions studied here, giving the final product branching for each product set

Reaction	sCI#	Product branching ratio (ΓTHEO)
		Γ SO3+aldehyde	Γ SO2+acid	Γ SO2+ester	Γ SO2+other CI
a The product branching fractions of the barrierless cycloreversion channels that lead to SO2 + sCIs 3, 4 or 5 are calculated using the same reverse ILT method described in Method section.^117,124
CH2OO + SO2	1	0.968	0.032	N/A	N/A
Syn-CF3CHOO + SO2	2	0.9922	0.0019	<0.0001	SO2 + sCI3: 0.0059^a
Anti-CF3CHOO + SO2	3	0.9973	0.0027	<0.0001	SO2 + sCI2: <0.0001
Syn-CF3CFOO + SO2	4	0.9860	N/A	0.0090	SO2 + sCI5: 0.0050^a
Anti-CF3CFOO + SO2	5	0.9955	N/A	0.0045	SO2 + sCI4: <0.0001^a

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The only other SOZ fragmentation calculated here are TSSO₃ & TS_ESTER channels, as an SOZ → acid channel cannot transpire from SO₂ reactions with sCIs 4 & 5 (Fig. 11). The cycloreversion channel has a negligible yield in the sCI 5 + SO₂ reaction and a minor role in sCI 4 + SO₂ reaction (Table 5). While TS_ESTER 1 & 2 are not extremely high in energy, the ester yield is still small (Γ_{SO2+ CF3OCHO} ∼ 0.01). The low TSSO₃ barriers and the minor yields of other products means that the predominant products from SOZ fragmentation are SO₃ + CF₃CHO (∼0.986 & 0.996).

3.2.4 Overview of sCI + SO₂ reactions. There are several key results from this analysis of the HFO-sCI + SO₂ reactions, including that all these reactions are initiated via a cycloaddition generating a short-lived SOZ ring, that then fragmented. sCI 2 + SO₂ was the only reaction without a barrierless cycloaddition step, which confirms that the syn-orientated sCI 2 is less reactive than the anti-orientated sCI 3. This contributes to producing an HFO-sCI + SO₂ general reactivity trend of: k_THEO (sCI 2) < k_d–d (sCI 3) < k_d–d (sCI 5) < k_d–d (sCI 4) < k_d–d (sCI 1). Lastly, the most dominant products of these reactions were SO₃ + aldehydes (Γ_SO3+aldehyde ∼ 0.96–0.99) with only small yields of either acids, esters or other sCIs. This implies that emissions of the HFO-sCIs will lead to consequentially higher local concentrations of SO₃ and subsequently higher concentrations of atmospheric aerosols.

3.3 HFO-sCIs reactions with organic and inorganic acids

Both organic acids such as TFA & carboxylic acids, and inorganic acids including HNO₃ & HCl, are prevalent in various tropospheric environments (see ESI Section S4.2† for more details) and sCIs is their capacity to deplete these acids.^{49,59,77,130,138,139,167}

3.3.1 HFO-sCI reactions with HNO₃. The sCI + HNO₃ reaction almost exclusively forms a nitrooxyalkyl hydroperoxide (NAHP) species by reacting via a 1,4-insertion mechanism, such as that seen in Fig. 12. In previous studies of sCI 1 + HNO₃ the chemistry of NAHP fragmentation was also calculated, but as this process occurs over a long timescale, NAHP breakdown is beyond the scope of this study. In contrast, the HOZ/SOZ fragmentation in the sCI + HCHO or SO₂ reactions occurs almost instantaneously.^168,169 NAHP can also be produced via a 1,2-insertion mechanism, but it has been excluded from this study as this barrier is ∼30 kJ mol⁻¹ greater in energy than the 1,4-insertion barrier.¹⁶⁹

Fig. 12 The potential energy surfaces for the sCI 1 + HNO₃ (black) and sCI 4 + HNO₃ (red) reactions. Energies are relative to raw reactants.

None of the 1,4-insertion processes for HFO-sCI + HNO₃ reactions studied here are barrierless, but the high reactivity of sCI 1 + HNO₃ means that the k_THEO value (8.21 × 10⁻⁹ cm³ s⁻¹) is so great that the k_d–d limit (8.45 × 10⁻¹⁰ cm³ s⁻¹) is used as the rate constant instead. This k_d–d limit is also similar to the k_EXP [295 K] value (5.4 × 10⁻¹⁰ cm³ s⁻¹) from the experimental Foreman et al. study.⁵⁹

The trend in reactivity indicated by these HFO-sCI + HNO₃ relative barrier heights, ΔE_TS (sCI 2) > ΔE_TS (sCI 3) > ΔE_TS (sCI 1) > ΔE_TS (sCI 5) > ΔE_TS (sCI 4), further verifies the HFO-sCI reactivity series seen in previous sections. However, the overall reactivity trend, k_THEO (sCI 2) < k_THEO (sCI 3) < k_THEO (sCI 5) < k_d–d (sCI 4) < k_d–d (sCI 1), is altered by the rate constants of HNO₃ reactions with sCIs 1 & 4, which reaching the k_d–d limit, and an surprisingly low k_THEO value for sCI 5 + HNO₃ (7.57 × 10⁻¹¹ cm³ s⁻¹).

3.3.2 HFO-sCI reactions with TFA. In general, sCIs 1–5 react with TFA to produce a hydroperoxy ester (HPE) species through a barrierless minimum energy pathway (e.g.Fig. 13). The barrierless minimum energy pathway calculated here for sCI 1 + TFA is similar to literature schemes and its k_d–d capture limit (7.54 × 10⁻¹⁰ cm³ s⁻¹) is found to be in close proximity to the k_EXP rate constant (3.4 × 10⁻¹⁰ cm³ s⁻¹).⁶¹

Fig. 13 The barrierless minimum energy pathway for the sCI 4 + TFA reaction. Energies displayed here are derived from using the B3LYP/aug-cc-pVTZ approach. Energies displayed here are relative to raw reactants.

Altering the sCI substituents does not alter the barrierless nature of the HFO-sCI + TFA reaction profiles studied here (see ESI Section S8.5†). For this reason, all the sCIs 1–5 + TFA reactions use the k_d–d values as rate constants (3.98–7.54 × 10⁻¹⁰ cm³ s⁻¹).

3.4 HFO-sCI reactions with water monomer and dimer

Due to the high tropospheric concentration of water vapour, water acts as the most prevalent bimolecular sink for sCIs, and therefore examining the chemistry of sCIs 1–5 reactions with H₂O & (H₂O)₂ is essential. sCIs 1–5 reactions with H₂O proceed through only two reaction channels (TSH₂O 1 and TSH₂O 2), whereas sCIs 1–5 reactions with (H₂O)₂ proceed via four pathways: TS(H₂O)₂ 1, TS(H₂O)₂ 2, TS(H₂O)₂ 3 and TS(H₂O)₂ 4 (see ESI Section S8.9†). One commonality between these reactions is that the primary product is an α-hydroxy-hydroperoxide (HHP), which is implicated in both forest damage and generating crucial secondary products (inc. H₂O₂, organic acids & aldehydes).^86,170–176

As the yields of the HHP products are sizable, the atmospheric fate of these HHPs is the subject of many scientific studies.^{67,68,131,150,157,177–179} Under standard conditions, photolysis, deposition, and reaction with hydroxyl radicals are usually the main sinks for HHPs, but the excess internal energy within the HHP at the point of formation increases the significance of thermal unimolecular HHP decay.^131,177 The primary unimolecular decay mechanism for hydroxymethyl hydroperoxide (HMHP), the product of CH₂OO + H₂O, is the elimination of H₂O₂ to produce formaldehyde, with some yields from minor channels that produce either H₂O + HCOOH or OH + OCH₂OH.^180,181 Sheps et al. showed in a study of CH₂OO + (H₂O)₂ that while ∼55% of the HMHP remained stable, this excess energy led to ∼40% of the HMHP fragmenting to produce H₂O₂ and formaldehyde, both of which are implicated in biogenic degradation.¹³¹ Halogenated HHPs produced from sCIs 2–5 are also likely to be produced with excess energy, and therefore exploring the breakdown of these products may be useful in the future.

The k_THEO value produced for sCI 1 + H₂O (1.18 × 10⁻¹⁶ cm³ s⁻¹) is within the range of literature k_EXP values (0.25–13 × 10⁻¹⁶ cm³ s⁻¹), and is particularly close to the rate constant found by Sheps et al. (k_EXP [293 K, 50 Torr] ∼ 2.4 × 10⁻¹⁶ cm³ s⁻¹).^{64,78,131,182,183} Furthermore, both the k_THEO value in this study and the k_EXP value found in the literature agree that sCI 1 + H₂O reactions slower than sCI 1 reactions with HNO₃, SO₂ or TFA.^{59,61,63,64,85,153,154,166}

The computational rate constants of the sCIs 4 & 5 + H₂O reactions were found to have a negative temperature dependence, where 200 K < T < 400 K, whereas sCIs 1, 2 & 3 + H₂O all have a positive temperature dependence within the same range (see ESI Section 1.2†). The general reactivity trend for these sCI + H₂O reactions continues the trend observed throughout most of this study k_THEO (sCI 2) < k_THEO (sCI 3) ≤ k_THEO (sCI 1) < k_THEO (sCI 5) < k_THEO (sCI 4). The theoretical trend of sCI 4 being more reactive than sCI 5 is partially obscured by rate constants being near to or exceeding the k_d–d limit, however as neither the k_THEO values for sCI 4 + H₂O (5.13 × 10⁻¹² cm³ s⁻¹) or sCI 5 + H₂O (2.27 × 10⁻¹³ cm³ s⁻¹) reach the k_d–d limit, sCI + H₂O would provide an experimental case study to verify if k_THEO (sCI 4) does exceed k_THEO (sCI 5) in bimolecular reactions.

In contrast, HFO-sCI + (H₂O)₂ reactions are faster as a result of sCI 5 + (H₂O)₂ having a lower reaction barrier than sCI 5 + H₂O (Fig. 14). The greater reactivity of sCI + (H₂O)₂ reactions is evidenced by k_EXP values found for sCI 1 + (H₂O)₂ (4.0–8.2 × 10⁻¹² cm³ s⁻¹), which are in close proximity to the large k_THEO value calculated here (3.28 × 10⁻¹² cm³ s⁻¹).^{78,131,156–158,184} In line with previous HFO-sCI reactions, sCI 2 + (H₂O)₂ has the lowest k_THEO value (2.71 × 10⁻¹² cm³ s⁻¹) but unusually the sCI 3 reaction with (H₂O)₂ has a greater k_THEO value (3.74 × 10⁻¹² cm³ s⁻¹) than sCI 1. None of the 4 × TS(H₂O)₂ channels for H₂O reactions with either sCI 4 or sCI 5 are barrierless, but the very high reactivity of these reactions leads to very large k_THEO values (1.14 × 10⁻⁶ & 1.46 × 10⁻⁹ cm³ s⁻¹). This means that the k_d–d constants of sCIs 4 & 5 + H₂O (∼7 × 10⁻¹⁰ cm³ s⁻¹) are used as the rate constants instead. Overall the reactivity trend for HFO-sCI + (H₂O)₂ reactions: k_THEO (sCI 2) < k_THEO (sCI 1) ≈ k_THEO (sCI 3) < k_d–d (sCI 5) ≈ k_d–d (sCI 4).

Fig. 14 The potential energy surfaces for the sCI 5 + H₂O (in black) and sCI 5 + (H₂O)₂ (in red) reactions. Energies are relative to raw reactants.

Criegee intermediates exhibit a mixed biradical and zwitterionic character and it has been shown that the more reactive zwitterionic dominated COO moieties have the larger ratio of OO and CO bond lengths, R_OO/R_CO or q.^68,74 Given these observations, sCIs 2 & 3 (q = 1.064 & 1.071) appear to have a more biradical COO moiety than sCI 1 (q = 1.078), whereas sCIs 5 & 4 (q = 1.101 & 1.114) are more zwitterionic. Anglada et al. noted in a computational study of sCI + H₂O reactions that the degree of this zwitterionic nature of the carbonyl oxide moiety, and consequentially it's reactivity, can be tuned by modification of the substituents.⁶⁸ Furthermore, in a computational study of sCI + alcohol reactions it is noted that the electron-withdrawing nature of F substituents in syn- & anti-FCHOO is likely to increase the unsaturated nature of the zwitterionic carbonyl oxide. This then generates a more electropositive central C atom, which is more vulnerable to nucleophilic attack by the alcohol's electronegative O atom. This study shows the same positive relationship between electron-withdrawing groups, zwitterionic COO moiety and high reactivity seen in the literature, as shown by the fact that increases in q values in the HFO-sCI series mostly correlates with the growth in rate constant: k_THEO (sCI 2) < k_THEO (sCI 3) ≈ k_THEO (sCI 1) < k_THEO (sCI 5) < k_THEO (sCI 4).

3.5 Impact of heteroatom tuning on HFO-sCI reactions

It has been suggested that for sCI + H₂X (X = O, Si, Se & Te) reactions, as the central X atom in the H₂X co-reactant is substituted with larger group XVI elements, the rate constant increases.⁸⁷ In this section, the computational analysis of the sCIs 1–5 + H₂S reactions is compared with sCIs 1–5 reactions with H₂O (& MeOH) to determine if these heteroatom tuning trends apply to HFO-sCIs too. To see if the effects observed from heteroatom tuning group XVI-centred co-reactants also apply to group XVII-centred co-reactants, analysis of HFO-sCI + HF & HCl reactions is also included in this section.

3.5.1 HFO-sCI reactions with hydrogen sulphide (H₂S). The HFO-sCI + H₂S reactions proceed through two hydrogen abstraction transition states to produce hydrosulphide alkyl hydroperoxide, following a reaction process similar to that observed for most sCI + H₂S reactions studied in the computational and experimental literature.^87,136,185 The rate constant for sCI 1 + H₂S determined here (k_THEO ∼ 7.06 × 10⁻¹⁵ cm³ s⁻¹) is larger than that for sCI 1 + H₂O in this study (k_THEO ∼ 1.18 × 10⁻¹⁶ cm³ s⁻¹). This difference in reactivity is substantiated by the fact that a literature k_EXP value for sCI 1 + H₂S observed by Smith et al. (1.7 × 10⁻¹³ cm³ s⁻¹) is much larger than the k_EXP range observed in the literature for sCI 1 + H₂O (0.25–13 × 10⁻¹⁶ cm³ s⁻¹).^{64,78,131,136,182,183} When analysing sCIs 2 & 3 reactions with H₂S each also show much larger k_THEO values than their reactions with H₂O, as observed in Fig. 15. Therefore, the theoretical results of H₂S reactions with sCIs 1–3 help to substantiate the general trend observed by Kumar et al. and the experimental literature that, if the central X atomic element of H₂X is substituted with an element further down group XVI on the periodic table, then the k_THEO value for the sCI + H₂X reaction increases.⁸⁷

Fig. 15 A comparison of the impact that heteroatom tuning of the group XVI-centred co-reactant (identity in the legend) has on the bimolecular rate constant (k_THEO) of different HFO-sCI reaction. Of note in this figure is the large increase in reactivity for sCIs 4 & 5 + H₂O and MeOH that is not observed for H₂S reactions.

One other point that may be noteworthy is that sCI 3 & sCI 1 exhibit similar rate constants throughout all three reactions featured in Fig. 15, as well as throughout much of this study. In much of the literature the non-fluorinated equivalent to sCI 3, anti-CH₃CHOO, exhibits a higher bimolecular rate constant to sCI 1 in reactions with H₂O, MeOH & SO₂.^{61,74,79,148,151} This may well be due to the presence of hyperconjugative α-H atoms in the anti-CH₃ substituent and that α-F atoms on the anti-CF₃ group rather than hyperconjugative α-H atoms reduces the inductive impact the substituent has on sCI 3 reactivity.⁵⁶

In contrast to the patterns seen for the sCIs 1–3 + H₂S reactions, the rate constants observed for the H₂S reactions with sCIs 4 & 5 are both smaller than those of the equivalent H₂O reactions (Fig. 15). To determine whether this stagnation of the sCI + H₂S rate constant was due to increased overall steric bulk, the k_THEO values were for the HFO-sCI reactions with the bulkier MeOH (which also proceeds via a hydrogen abstraction mechanism) were determined. However, no such stagnation in the rate constants of sCI 4 & 5 + MeOH reactions emerges (Fig. 15).

3.5.2 HFO-sCIs reactions with HF & HCl. The Gr17-centred HX compounds, HF & HCl, react with sCIs via similar hydrogen abstraction mechanisms as the sCI + H₂X reactions, which means the heteroatom tuning trends seen for the HFO-sCI + H₂X reactions may be replicated.^59,186 For instance, sCI 1 + HCl has a considerably lower barrier (Fig. 16) to reaction than sCI 1 + HF, following the trend that the co-reactant with larger heteroatoms (HCl) will have greater reactivity in reactions with sCIs 1–3. The resulting k_THEO value for sCI 1 + HF (3.32 × 10⁻¹³ cm³ s⁻¹) is smaller than both the k_THEO value (4.70 × 10⁻¹⁰ cm³ s⁻¹) and its literature k_EXP rate constant (1.7 × 10⁻¹³ cm³ s⁻¹) for sCI 1 + HCl.⁵⁹ All sCIs 1–3 reactions with HCl yield a rate constant that is ∼10³–10⁴ cm³ s⁻¹ larger than the equivalent HFO-sCI + HF reaction, much larger than the equivalent reactivity difference of sCIs 1–3 + H₂S over that of H₂O (∼10¹–10² cm³ s⁻¹).

Fig. 16 The potential energy surfaces for selected sCI reactions with HF and HCl. On the potential energy surfaces on the left, feature sCI 1 + HF, in black, and sCI 4 + HF, in red. On the potential energy surfaces on the right, feature sCI 1 + HCl, in black, and sCI 4 + HCl, in red. Energies are relative to raw reactants.

Fig. 16 displays that the fluorinated sCI 4 has much lower reaction barrier with HF than the unsubstituted sCI 1 has, demonstrating the continued activating effect that the –F substituent has on the sCI reactivity. The inductive impact of the –F substituent results in sCI 4 and sCI 5 having substantially larger rate constants (1.19 × 10⁻¹¹ & 3.66 × 10⁻¹³ cm³ s⁻¹) compared to the sCI 1 + HF reaction. In contrast, the energy barrier of the sCI 4 + HCl reaction does not decrease compared to that of sCI 1 + HCl (Fig. 16), replicating the observation that heteroatom tuning does not have an inductive effect on reactions involving sCIs 4 & 5. In fact, –F substituents in sCIs 4 & 5 in combination with the heteroatom tuning of the co-reactant leads not just to the same stagnation effect seen for sCIs 4 & 5 + H₂S reactions, but instead to a reductive effect on reactivity for the sCIs 4 & 5 + HCl reactions, compared to sCIs 4 & 5 + HF. This reductive effect is so clear that the rate constants for HCl reactions with sCI 4 (1.64 × 10⁻¹⁰ cm³ s⁻¹) and sCI 5 (1.13 × 10⁻¹⁰ cm³ s⁻¹) are both smaller than that of the equivalent sCI 1 reaction for the only time in this study. The cause of these stagnation/reductive effects can potentially be explained in terms of the repulsion between the sCI substituent groups and increased steric interactions, although a deeper exploration into such factors would probably require experimental analysis and verification.⁵⁶

4. Atmospheric implications of HFO-sCIs bimolecular sinks

HFO emissions, and subsequently HFO-sCIs, are projected to become much more abundant as the use of HFO become increasingly widespread in refrigerators, insulation and vehicle cooling units, as is being seen in China, the USA and the EU.^1,27,28 The chemistry of sCIs and other atmospheric species are typically included in atmospheric models in sets of like chemistries or taxonomic groups, where their reactivity can be estimated on the basis of their structure, and this work suggest sCIs 2–5 can be grouped into any such wider sCI classification system.^{40,70,187,188} Similar taxonomic groupings are already used in atmospheric models to estimate the chemistry of large groups of molecules and therefore reduce the computational processing power required to run simulations.¹⁸⁹ However, integrating HFO-sCIs into a wider taxonomic sCI framework faces particular difficulties, principally because of the differing effects non-halogenated groups (–CH₃ and –H) and halogenated groups (–CF₃ and –F) have on the conjugation, hyperconjugation and steric interactions the sCI.^56,72–75 One example of this is the difficulty of including the stagnation/reduction in reactivity of sCIs 4 & 5 seen during reactions with H₂S & HCl, a phenomenon not exhibited by other sCIs studied here or in the prior literature.^{59,64,78,87,131,136,182,183} This shows that system-by-system computational analysis, or indeed ultimately experimental analysis is still vital for understanding the chemistry of many bimolecular sCI reactions.

The effective rate constants, k_EFF, a product of the rate constant and the atmospheric abundance of the co-reactant, is used here as a primitive system of measuring the potential tropospheric impact of each bimolecular HFO-sCI reaction studied (Table 1).

The sCI reactions with water are the dominant bimolecular sink for the HFO-sCIs due to the abundance water vapour.^{42,67,68,70,150,179} However, whether the sCI reaction with H₂O or (H₂O)₂ is more prevalent depends not only on the relative abundance of the H₂O or (H₂O)₂, but also on the identity of the sCI. For instance, the k_EFF ((H₂O)₂) for sCI 2 is around 10³ s⁻¹ larger than the equivalent k_EFF (H₂O), because the natural abundance of H₂O (6.2 × 10¹⁷ molec. per cm³) over that of (H₂O)₂ (8.7 × 10¹⁴ molec. per cm³) is overcome by the fact that the sCI 2 has a 10⁶ cm³ s⁻¹ larger k_THEO ((H₂O)₂) than k_THEO (H₂O). sCIs 1 & 3 also exhibit larger k_EFF ((H₂O)₂) than k_EFF (H₂O) by between 10¹–10³ s⁻¹, meaning that tropospheric removal of the sCI occurs more readily via reaction with the water dimer than the monomer. But, whereas the rate constants for sCIs 4 & 5 + H₂O reactions are much enhanced, the sCIs 4 & 5 + (H₂O)₂ systems are so reactive that the k_d–d capture limits are used as the rate constants, and the gap between these k_d–d ((H₂O)₂) and k_THEO (H₂O) values is much reduced. Consequently, the k_EFF (H₂O) for sCI 5 is similar to the equivalent k_EFF ((H₂O)₂) value and the k_EFF (H₂O) for sCI 4 is larger than k_EFF ((H₂O)₂), as seen in Table 6.

Table 6 A tabulation of the effective rate constants (k_EFF) for the HFO-sCI + co-reactant reactions, determined in this study using the product of the theoretical rate constant and the co-reactant abundance. This table shows a primitive calculation of the atmospheric impact of each reaction. If the k_EFF value is written in italics, the dipole–dipole capture limit (k_d–d) was used to calculate the k_EFF value because the master equation rate constant (k_THEO) exceeded the k_d–d limit or because the reaction was barrierless

Co-reactant	k EFF (s^−1)
	CH2OO	Syn-CF3CHOO	Anti-CF3CHOO	Syn-CF3CFOO	Anti-CF3CFOO
	sCI 1	sCI 2	sCI 3	sCI 4	sCI 5
HCHO	5.6	0.54	5.0	1447	33.4
SO2	300	0.79	169	186	183
HNO3	94	2.3	9.8	58	8.4
TFA	2.5 × 10^−2	1.7 × 10^−2	1.3 × 10^−2	1.2 × 10^−2	1.2 × 10^−2
H2O	73	0.83	70	3.2 × 10^6	1.4 × 10^5
(H2O)2	2.9 × 10^3	2.4 × 10^3	3.3 × 10^3	6.2 × 10^5	6.1 × 10^5
MeOH	0.010	7.9 × 10^−5	0.028	462	28
H2S	0.085	1.4 × 10^−3	0.042	4.5	0.091
HCl	58	5.0 × 10^−3	8.96	20	14
HF	0.12	2.5 × 10^−6	1.1 × 10^−3	4.4	0.14

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This great preference for HFO-sCI + H₂O & (H₂O)₂ reactions leads to the significant production of fluorinated α-hydroxy-hydroperoxides, which have been implicated in forest damage and associated with generating important secondary products like H₂O₂, organic acids and aldehydes, albeit that the primary emission locations for HFO are likely to be in urban environments.^86,170–176 HFO-sCI + MeOH reactions are not as competitive as the equivalent H₂O & (H₂O)₂ reactions, but because, MeOH is emitted from vehicles that run off biofuel and HFOs are used in vehicle coolant units, the HFO-sCI & MeOH species have greater concentration overlap in many urban environments.^135,190,191 Under such circumstances, emissions of α-alkyoxyalkyl hydroperoxides (AAAHs), a significant functionalised peroxide, are increased and these AAAHs have also been implicated in forest damage and SOA formation.^{67,68,78–80,83,86,170}

HFO-sCI reactions with aldehydes are quite uncompetitive compared to the reactions with H₂O & (H₂O)₂ but the products of their reactions include organofluoride aldehydes and TFA, both known to contribute to respiratory problems.¹⁹² Furthermore the sCIs 2–5 reactions with HCHO lead to high yields of sCI 1 sometimes with a large excess of energy, that easily leads to CI fragmentation and therefore contributes to the tropospheric population of the ‘atmospheric detergent’ OH radical.^70,82

The sCI + SO₂ reaction is known to act as a sink for ∼20% of some sCIs in boreal forest, however the high uptake of the reactions with H₂O & (H₂O)₂ means that they do not contribute hugely to the overall depletion of sCIs 2–5.¹⁵⁹ However the SO₂ reactions with sCIs 2–5 also seem to produce SO₃ at a higher efficiency than reactions with sCI 1 and (CH₃)₂COO, and this tropospheric SO₃ will then contribute to atmospheric H₂SO₄ and aerosol formation.^84,193–196

TFA may have a disproportionate impact on HFO-sCI bimolecular chemistry because both HFO-sCIs and TFA emerge from the breakdown of HFOs and so they may see a large population overlap with HFO-sCIs. The large rate constants from sCI reactions with TFA, HNO₃ and HCl found here indicate a high reactivity between sCIs and other organic and inorganic acids. However, even in seaside areas, where HCl concentrations are elevated, the contribution that sCI 1 could make the minor and the role of sCIs 4 & 5 would be even more reduced, due to the high k_EFF values of the sCI + H₂O & (H₂O)₂ reactions. The non-water reactions (e.g. sCI reactions with HF, SO₂ & H₂S) would contribute more to the depletion of HFO-sCI population in dry environments, such as near active volcanoes.^{82,139,197–199}

After collisional stabilisation, sCIs are less energetic so fewer unimolecular fragmentation mechanisms have energy barriers low enough to compete with bimolecular reactions as sinks for sCIs under tropospheric temperature and pressure conditions.⁴² According to Guidry et al., the central mechanism for the fragmentation of both syn- & anti-CF₃CHOO is via a 1,3-ring closure to produce a dioxirane ring, both of which produce energy barriers (∼80 kJ mol⁻¹) higher than anti-CH₃CHOO (∼70 kJ mol⁻¹) and more similar to those of CH₂OO (70–100 kJ mol⁻¹).²⁰⁰ The unimolecular rate constant (k_UNI) of a reaction path and k_EFF are both equivalent and effective tools to show the efficiency of the respective reaction path as an sCI sink but, while Wang et al. have identified syn- & anti-CF₃CHOO experimentally, no k_UNI values were identified in either the Wang et al. or Guidry et al. studies.^66,200 Therefore, the k_UNI for CH₂OO (∼0.3 s⁻¹) is used here instead as it may be the closest analogue to that of syn- & anti-CF₃CHOO.^42,70 On the basis of these premises, while the k_UNI value used here is greater than many of the k_EFF value for syn- & anti-CF₃CHOO found in Table 6, the k_EFF value for other reactions, particularly syn- & anti-CF₃CHOO + (H₂O)₂, are greater still. This indicates that bimolecular reactions can compete with unimolecular decomposition.

No equivalent k_UNI analogue could be found for syn- & anti-CF₃CFOO especially considering the role of the –F substituent in CI fragmentation in isolation is also challenging. One study by Ljubić and Sabljić calculated that the anti-F substituent induced a lower anti-FCHOO fragmentation barrier (TS_UNI ∼ 47.3 kJ mol⁻¹), whereas syn-FCHOO saw no such effect (TS_UNI ∼ 83.5 kJ mol⁻¹).²⁰¹ It is quite possible that the anti-F substituent could therefore theoretically induce a higher k_UNI for syn-CF₃CFOO, but this might be offset by the lack of any tunnelling effect and the steric hinderance of the syn-CF₃ substituent. Nevertheless, no computational or experimental literature exists of the syn- & anti-CF₃CFOO unimolecular fragmentation reactions, and an assessment of these reactions has been not been deliberated here, due to the need for a more in-depth analysis of these reactions than the kind of provisional evaluation that would be covered in this study.

5. Conclusion

It has been shown that the individual steric and electronic features of HFO-sCIs impact upon their bimolecular chemistry in a way that transcends the choice of tropospheric co-reactant species. The chemistry of sCI 2 (syn-CF₃CHOO) & sCI 3 (anti-CF₃CHOO) have consistency with existing reactivity trends in the literature, particularly that sCIs with a syn-orientated sterically bulky group are significantly less reactive than anti-orientated sCIs. However, sCI 3 is distinctive because it exhibits similar rate constants to the unsubstituted sCI 1 (CH₂OO), whereas sCIs with similar orientations like anti-CH₃CHOO yields larger rate constants. The literature indicates that the presence of hyperconjugative α-H atoms in the anti-CH₃ group has an inductive impact on the sCI, but here the presence of α-F atoms in the anti-CF₃ group appears to reverse this activating effect.

The especially large bimolecular rate constants for sCI 4 (syn-CF₃CFOO) & sCI 5 (anti-CF₃CFOO) emerge from the inductive –F substituents they possess. Moreover, the inductive impact of the –F substituent is greater in the case of sCI 4 because of the anti-position of the –F substituent, and so the k_THEO (sCI 4) exceeds the k_THEO (sCI 5). However, with some notable exceptions, the HFO-sCIs studied here follow the reactivity series: k_THEO (sCI 2) < k_THEO (sCI 3) ∼ k_THEO (sCI 1) < k_THEO (sCI 5) < k_THEO (sCI 4).

One exceptionally distinct observation in this study is that the overall sCI reactivity series is influenced by the choice of co-reactant, as shown when contrasting the reactivity of sCIs 1–5 reactions with different group-XVI and group-XVII centred co-reactants. When sCI + H₂O & HF are compared with sCI + H₂S & HCl respectively, sCIs 1–3 reactions with H₂S & HCl produced comparatively larger rate constants, in line with previous literature observations.⁸⁷ However, this does not always apply as the –F substituent appear to obstruct the large S and Cl atoms from reaching the reaction site during sCIs 4 & 5 reactions with H₂S and HCl and this leads to a smaller rate constant.

This work demonstrates that for all sCIs considered, reaction with H₂O or (H₂O)₂ is the biggest tropospheric sink of HFO-sCIs, due primarily to the natural abundance of water vapour. Furthermore, these sCI reactions with water produced functionalised hydroxide products called α-hydroxy-hydroperoxide (HHP) that have been implicated with biogenic damage.^{42,67,68,78–80,83,86,134,170} While bimolecular reaction with other trace pollutants are less likely to be sinks for HFO-sCIs, sCIs 2–5 all have a significant capacity to react with tropospheric species such as MeOH, TFA & HNO₃ and yield other functionalised hydroperoxides.

The uncommon nature of these HFO-sCIs is also demonstrated in the multi-step reactions with HCHO, where sCIs 2–5 react (via a short-lived HOZ) to produce another sCI, a highly energised sCI 1, a product not commonly found in other studies of sCI + aldehyde reactions.^65,71,147 A similar full mechanistic analysis of the reactions using a two-step HFO-sCI + SO₂ systems show that these reactions have very high rate constants and all produce high yields of SO₃ + R₁R₂CO (0.90–0.99). This production of SO₃ would also lead to H₂SO₄ formation and aerosol nucleation. Furthermore, HFO-sCI reactions with both HCHO & SO₂ systems are found to produce CF₃CHO or CF₃CFO, which are known to contribute to respiratory problems.

In summary, HFO-sCIs are shown to have very unique chemistry, because the –F substituent has a large activation affect on the COO group, whereas the α-F atoms in the CF₃ group are mildly deactivating. If any sCI taxonomic classification is established, sCIs 2 & 3 could be categorised as part of syn-sCI and anti-sCI groups respectively, whereas sCIs 4 & 5 could be categorised in a separate “electronegative substituent” taxonomic group.

Author contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Conflicts of interest

The authors declare no competing financial interest.

Abbreviations

sCI	Stabilized Criegee intermediate
AAAHs	Alkoxyalkyl hydroperoxides
HHP	Hydroxy-hydroperoxides
HFO-sCIs	Hydrofluoroolefin-derived stabilized Criegee intermediate
TFA	Trifluoracetic acid
HOZ	Heteroozonide
SOZ	Secondary ozonide
NAHP	Nitrooxyalkyl hydroperoxide
HAE	Hydroxyalkyl formate
CH2OO	sCI 1
syn-CF3CHOO	sCI 2
anti-CF3CHOO	sCI 3
syn-CF3CFOO	sCI 4
anti-CF3CFOO	sCI 5

Acknowledgements

This work was partially supported by Advanced Research Computing at Cardiff and High Performance Computing (HPC) Wales, a company formed between the Universities and the private sector in Wales which provides the UK's largest distributed supercomputing network. Dr J. M. Beames was supported in initiating this research through Marie Skłodowska Curie Individual Fellowship NPTC (701593). This work was partially supported by the Natural Environment Research Council (NERC) through the Integrated Research Observation System for Clean Air (OSCA) grant (NE/T001984/1). Information on the data underpinning the results presented here is shown in the ESI.†

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Footnote

† Electronic supplementary information (ESI) available: A full breakdown of the master equation rate constants (k_ME) and canonical rate constants (k_CAN) through temperature range of 200 K < T < 500 K at p = 760 Torr for sCIs 1–5 reactions with the following co-reactants: HCHO, SO₂, HNO₃, TFA, HF, HCl, H₂S, H₂O, (H₂O)₂, MeOH; calculated product yields for sCIs 1–5 reactions with HCHO, SO₂; calculated values for sCI 1 + co-reactant rate constants at selected temperatures and pressures for direct comparison with experiment; calculated values for the effective rate constants for sCI + co-reactant reactions under various conditions; relative energies [kJ mol⁻¹] of stationary point for sCI + co-reactant reactions; computed dipole–dipole and gas collision limits; discussion on the partially barrierless sCI 4 + MeOH reaction; Cartesian coordinates and vibrational frequencies of all stationary points, and IRCs of all transition states in this study; an example MEMSER input file for the sCI 1 + HNO₃ (PDF). See DOI: https://doi.org/10.1039/d3ea00102d

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