Criegee + HONO reaction: a bimolecular sink of Criegee, and the missing non-photolytic source of OH^•

One of the most important puzzles in atmospheric chemistry is a mismatch between observed and modelled concentrations of OH^•/HO${}_{\mathrm{2}}^{•}$ in the presence of high concentration of volatile organic compounds. It is now well established that to fulfill this gap, one needs a reaction that is not only capable of producing OH^• but also able to act as a sink of HO${}_{\mathrm{2}}^{•}$. In the present work, we are proposing the Criegee + HONO reaction as a possible solution of this puzzle. Our quantum chemical and kinetic calculations clearly suggest that this reaction can not only be an important source of OH radical but can also act as a sink of HO₂ radical. Our study also suggests that HONO has the potential to act as a bimolecular sink of Criegee intermediates, and for some Criegee intermediates under certain atmospheric condition it can even surpass the traditionally known bimolecular sinks such as SO₂ and water dimer, even in high humid conditions.

1 Introduction

It is well-known that the atmospheric chemistry is mainly dominated by the radicals (Anderson, 1987; Monks, 2005). Particularly in the troposphere, these radicals are key in degrading various pollutants, a phenomenon as important as the ozone layer for the existence of life (Weinstock, 1969; Lelieveld et al., 2004). The primary radicals responsible for the oxidative power of troposphere come from the HO_X (OH^•, HO${}_{\mathrm{2}}^{•}$, RO^•, RO${}_{\mathrm{2}}^{•}$ etc.) family (Prinn, 2003; Ehhalt, 1987; Khan et al., 2018). Among them, OH^• is considered as the most important oxidant in the troposphere (Lelieveld et al., 2002, 2016). Although OH^• is the most studied radical in the atmosphere, there are still open questions regarding its sources in the atmosphere (Heald and Kroll, 2021; Yang et al., 2024). For a long time, it was believed that OH radicals are mainly formed in daytime via photolysis of tropospheric ozone (O₃), and nitrous acid (HONO) (Calvert et al., 1994; Alicke et al., 2003; Griffith et al., 2016; Aumont et al., 2003). But now, with various on-field measurements (Geyer et al., 2003; Ren et al., 2003; Emmerson and Carslaw, 2009), it is well established that OH radicals are also present at night in sufficient amounts. In fact, average nighttime concentration of OH^• (∼ 2.6 ×10⁵ molec. cm⁻³) is only one order of magnitude lower than its average daytime concentration (∼ 1.9 ×10⁶ molec. cm⁻³) (Emmerson and Carslaw, 2009). As the lifetime of OH^• is only ∼ 1 s, this much concentration of OH^• during night indicates its in situ generation via non-photolytic sources. The major non-photolytic source of OH^• is the recycling of HO${}_{\mathrm{2}}^{•}$ radicals (Whalley et al., 2011; Stone et al., 2012; Hofzumahaus et al., 2009; Smith et al., 2006; Hens et al., 2014). Specifically, during the daytime, the primary reaction contributing to this recycling process is NO${}^{•}+$ HO${}_{\mathrm{2}}^{•}$, whereas at night, the key reaction is NO${}_{\mathrm{3}}^{•}+$ HO${}_{\mathrm{2}}^{•}$ (Hall et al., 1988; Mellouki et al., 1988, 1993; Rai and Kumar, 2024). However, compared to photolytic sources, non-photolytic sources of OH^• remain less understood in atmospheric chemistry (Brown and Stutz, 2012; Emmerson and Carslaw, 2009). This is evidenced by the fact that, in the atmosphere with a high concentration of volatile organic compounds (VOCs), atmospheric models consistently under-predict the concentration of OH^• compared to the observed value (Emmerson and Carslaw, 2009; Stone et al., 2012). This discrepancy is especially pronounced in winter (Harrison et al., 2006; Heard et al., 2004; Slater et al., 2020) and indoor environments (Østerstrøm et al., 2025; Gomez Alvarez et al., 2013; Reidy et al., 2023), where light plays a minimal role. In addition, the discrepancy between measured and observed value of OH^• was also found to depend upon NO_X concentration. Both under low NO_X (Carslaw et al., 2001; Tan et al., 2001; Lelieveld et al., 2008; Tan et al., 2017) as well as high NO_X (above 6 ppbv) (Slater et al., 2020), the discrepancy was found to be quite significant. As the primary recycling of HO${}_{\mathrm{2}}^{•}$ to OH^• occurs via NO_X, the under-prediction of OH^• by models under low NO_X conditions suggests either the presence of another route for recycling or some new non-photolytic source of OH^•. This hypothesis is further strengthened by a few combined experimental and modelling studies. For example, Lu et al. (2012) have to introduce an artificial source of OH^• ↔ HO${}_{\mathrm{2}}^{•}$ inter-conversion (RO${}_{\mathrm{2}}^{•}+$ X ⟶ HO${}_{\mathrm{2}}^{•}$, HO${}_{\mathrm{2}}^{•}+$ X ⟶ OH^•) in their atmospheric model to match the experimental concentration profile. In an another study, to match the experimental OH concentration with models, Whalley et al. (2011) increased the concentration of VOCs in their model. Although their computed OH^• concentration becomes closer to experimental value, the mismatch between observed and measured concentration of HO${}_{\mathrm{2}}^{•}$ becomes worse.

There have been various attempts to identify the missing source of OH^• in the atmosphere (Paulot et al., 2009; Peeters et al., 2014; Sander et al., 2019). For example, Peeters et al. (2009); Peeters and Müller (2010); Peeters et al. (2014) suggested that the oxidation of isoprene can regenerate HO_X radicals in the presence of light via isoprene-peroxy radical interconversion and isomerisation pathways (Leuven Isoprene Mechanism (LIM)). Although the introduction of LIM into chemical models were found to improve the value of modelled OH^• concentration, the modelled values still remain under-predicted (Crounse et al., 2011; Teng et al., 2017; Berndt et al., 2019; Novelli et al., 2020; Medeiros et al., 2022). Particularly, the LIM is more effective in regions where biogenic volatile organic compounds (BVOCs) dominate and NO_X concentration is ultra low, e.g. rain forest regions (Whalley et al., 2011; Feiner et al., 2016; Lew et al., 2020). In contrast, in regions where sufficient anthropogenic sources of VOCs are present, e.g. in polluted areas, LIM is not effective. In addition, LIM is not fundamentally a HO${}_{\mathrm{2}}^{•}$ to OH^• interconversion process, rather it is the recycling of VOCs to OH^•. In a recent study, Yang et al. (2024) suggested that aldehyde could be an additional source of OH^•. Authors proposed that the autoxidation of carbonyl organic peroxy radicals (R(CO)O₂) derived from higher aldehydes, can produce OH^• through photolysis (RAM mechanism). Though RAM mechanism efficiently predicts OH^• production at low NO_X concentrations, it still under-predicts the same at high NO_X concentrations. Interestingly, when both LIM and RAM are incorporated into a base model in the presence of moderate concentration of NO_X, OH^• concentration improves significantly, but the discrepancy in the modelled and observed HO${}_{\mathrm{2}}^{•}$ remains unresolved. It is also worth mentioning that photolysis is an important part of both, LIM and RAM, and hence, both of these mechanism do not offer any help in improving the model OH^• concentration in nocturnal environment. Furthermore, both LIM and RAM are also not directly involved in recycling of HO${}_{\mathrm{2}}^{•}$ to OH^•. The discrepancy in the model occurs during both day and night (Faloona et al., 2001; Hens et al., 2014; Geyer et al., 2003), and is associated with HO${}_{\mathrm{2}}^{•}$ to OH conversion (Whalley et al., 2011; Hofzumahaus et al., 2009). In light of these studies, we believe that the puzzle of missing OH^• source is very much alive and the key to this puzzle may be a non-photolytic source capable of HO${}_{\mathrm{2}}^{•}$ ↔ OH^• recycling.

In the present work, we are proposing reaction of Criegee intermediate with HONO as a source of OH^•. Criegee Intermediates (CIs) are formed during the ozonolysis of alkenes (Criegee, 1975; Johnson and Marston, 2008; Taatjes, 2017). In fact, alkene ozonolysis is a highly exothermic reaction produces energized CIs. Some of the energized CIs readily convert into OH^• via unimolecular decomposition, while the remaining CIs get collisionally stabilized (sCI) (Horie and Moortgat, 1991; Donahue et al., 2011; Novelli et al., 2014; Alam et al., 2011). sCIs can undergo either a thermal unimolecular dissociation or a bimolecular reaction. Depending upon concentration of the co-reactant and rate constant of such bimolecular reaction, the bimolecular reaction paths can be the main sink of sCI (Osborn and Taatjes, 2015; Lin et al., 2015; Sheps et al., 2014; Vereecken and Francisco, 2012). There are several studies in the literature that suggest CI reacts rapidly with the trace gases present in the atmosphere (Cox et al., 2020; Mallick and Kumar, 2020; Vereecken et al., 2015; Long et al., 2016, 2021). In this work, we are suggesting HONO as a new partner for the bimolecular reaction of Criegee intermediates that is capable of producing OH radicals. The concentration of CI (∼ 10⁴–10⁵ molec. cm⁻³) in the atmosphere is comparable with Cl^• (∼ 5.0 ×10⁴–3.0 ×10⁵ molec. cm⁻³) and OH^• (∼ 1.0 ×10⁵–4.0 ×10⁶ molec. cm⁻³) (Khan et al., 2018; Novelli et al., 2017). Similarly, nitrous acid (HONO) is also an important trace gas present in the nighttime atmosphere in a considerable amount (Li et al., 2021; Song et al., 2023). The average concentration of HONO is ∼ 8.9 ×10¹⁰ molec. cm⁻³, which can reach as high as ∼,6.9 ×10¹¹ molec. cm⁻³ during the fog event (Pawar et al., 2024). Although a general wisdom about HONO is, its concentration builds up in nighttime, and in daytime, it decomposes via photolysis to give OH^•, HONO itself is a highly reactive molecule and can participate in various bimolecular chemical reactions during night (Anglada and Sole, 2017; Lu et al., 2000; Wallington and Japar, 1989). Moreover, in indoor environments, high concentrations of OH^• have been found to strongly correlate with high concentrations of HONO (Gomez Alvarez et al., 2013). It is important to mention that, the reaction of HONO with the simple Criegee intermediate (CH₂OO) has already been investigated theoretically (Kumar et al., 2022). In that investigation, the major product was predicted to be hydroperoxymethyl nitrite (HPMN). We will show in the present work that the main product of this reaction is OH^• and this newly found path is the dominant path of the title reaction.

2 Methodology

2.1 Electronic structure theory

There are two parts of electronic structure theory; optimization and subsequent single-point energy calculations. The criteria behind choosing a method for optimization is; it should be computationally not very demanding and at the same time, it should accurately predict the geometries and frequencies of the species involved in the reaction. Based on these criteria, in the present work, the CCSD(T)/CBS//M062X/aug-cc-pVTZ level of theory was chosen, which is known to give reasonable results in various previous studies (Kumar et al., 2022; Vereecken et al., 2017, 2014; Vereecken, 2017) for reactions involving Criegee intermediates. Gaussian16 software package (Frisch et al., 2016) has been used to carry out all the optimization and single-point energy calculations. To estimate energies at CCSD(T)/CBS level of theory, first, we calculated the single point energies at CCSD(T)/aug-cc-pVDZ, and CCSD(T)/aug-cc-pVTZ level of theory, and then extrapolated these energies to corresponding CBS limit using the method of Varandas and Pansini (Varandas and Pansini, 2014; Pansini et al., 2016) (see Sect. S2 in the Supplement).

2.2 Kinetics

Energetics calculations shed light only on enthalpic requirement of the reaction, for a barrierless process, entropy is an equally important factor. Therefore, to account for both, enthalpy and entropy, we have estimated the rate constant for CH₂OO + HONO reaction within a temperature range of 213–320 K. The mechanism of CH₂OO + HONO reaction can be represented by following reaction:

$$\begin{array}{}\text{(R1)}& {\mathrm{CH}}_{\mathrm{2}}\mathrm{OO}+\mathrm{HONO}\underset{k_r}{\stackrel{k_f}{\rightleftharpoons }}\mathrm{RC}\mathrm{1}\underset{\mathrm{TS}\mathrm{1}}{\stackrel{k_{\mathrm{uni}}}{\rightleftharpoons }}\mathrm{PC}\mathrm{1}\to {\mathrm{CH}}_{\mathrm{2}}\mathrm{O}+{\mathrm{OH}}^{•}+{\mathrm{NO}}_{\mathrm{2}}\end{array}$$

To calculate the overall rate constant of the title reaction, we have used the master equation approach as implemented in the MESMER software package. The Reaction (R1) proceeds in three steps. In the first step, the formation of RC occurs via a barrierless association of isolated reactants. MESMER uses the inverse-Laplace-transform (ILT) method to estimate the energy-dependent rate constant, k(E), for this step. This, in turn, requires fitted Arrhenius parameters as input to MESMER, which are obtained using KTOOLS code as implemented in the MultiWell suite of programs (Barker et al., 2021). KTOOLS uses variational transition state theory (VTST) for the barrierless reaction. The inputs for KTOOLS are energies and frequencies calculated on potential energy surface (PES) scans along the coordinate describing the dissociation of RC into isolated reactants. Each point on the PES serves as a trial transition state; KTOOLS searches for the transition state for which the reaction flux is minimized. In the present work, we have obtained this PES scan at CCSD(T)/CBS//M062X/aug-cc-pVTZ level of theory (Table S3 in Sect. S1 of the Supplement contains the energy as well as frequencies at each scan points).

In the next step, RC undergoes unimolecular dissociation to PC via a transition state. MESMER uses Rice-Ramsperger-Kassel-Marcus (RRKM) theory, including tunneling contributions via an unsymmetrical Eckart barrier to compute the unimolecular reaction rate. In the final step, PC spontaneously dissociates to form isolated products. It is important to mention that we do not find any tight transition state for product formation from PC; therefore, we have treated this step also using ILT assuming that rate constants are independent of temperature. The obtained rate constants within 213–320 K were then fitted with Arrhenius equation and supplied to the MESMER.

It is worth noting that the reactant complex (RC) and the transition state (TS) exhibit hindered rotational motions, and multiple conformations may exist due to different torsional angles. To account for this, we have used the HinderedRotorQM1D model in MESMER to compute rate constants. Specifically, we performed a one-dimensional potential energy scan of OH torsion along the N–O bond in both RC and TS at CCSD(T)/CBS//M062X/aug-cc-pVTZ level of theory, that covers the full 0 to 360° range. The resulting energy profiles are used to calculate the hindered rotor partition functions. During this scan, we found local minima in both RC and TS, suggesting that our originally optimized structures correspond to the global minimum conformers. To verify this, we also manually searched for other possible minimum conformers and again found that our original structures are global minimum conformers. The Lennard-Jones (L-J) model is used to calculate the collision frequency between reactants and the bath gas. To obtain the L-J parameters for RC, we performed a PES scan along the reaction coordinate separating bath gas from RC, and fitted the obtained PES with the 12-6 L-J potential expression. The fitted L-J parameters for RC turn out to be, σ=3.1 Å and ϵ=895.5 K. A single-exponential down model is used to describe the collisional energy transfer probability with a maximum energy grain size of 100 cm⁻¹ and ΔE_down=150 cm⁻¹.

Figure 1 The potential energy surface for CH₂OO + HONO reaction (in kcal mol⁻¹) obtained at CCSD(T)/CBS//M06-2X/aug-cc-pVTZ level of theory along with optimized geometries of species involved in the reaction.

3 Results and discussion

In the present work, we have investigated the reactions of Criegee intermediates (CIs) with nitrous acid (HONO). It is known that the reactivity of CI is greatly influenced by the substitution group present on carbon center of the CI. Therefore, to account for it, we have studied two types of CIs; the simplest Criegee intermediate (CH₂OO) and the dimethyl-substituted Criegee intermediate ((CH₃)₂COO). Another motivation for choosing (CH₃)₂COO comes from the fact that in contrast to simple Criegee which is formed only from the ozonolysis of ethene, the dimethyl-substituted Criegee intermediate can be generated from the ozonolysis of many highly abundant alkenes, such as terpenes and mycrene, and hence, the concentration of (CH₃)₂COO is significantly higher in the atmosphere. In this section, we will first discuss the energetics and kinetics of CH₂OO + HONO reaction, followed by (CH₃)₂COO + HONO reaction. The potential energy surface for CH₂OO + HONO reaction is depicted in Fig. 1. It is evident from Fig. 1 that reaction occurs in three steps; in the first step, CH₂OO interacts with H atom of HONO via hydrogen bonding and forms a stable reactant-complex (RC1), which is ∼ 10.1 kcal mol⁻¹ stable than isolated reactants. In the next step, RC1 undergoes a unimolecular transformation to form product-complex (PC1) which has stabilization energy of $\sim -\mathrm{44.7}$ kcal mol⁻¹ with respect to the isolated reactants. This happens via a transition-state (TS1) that is effectively ∼8.0 kcal mol⁻¹ below the isolated reactants. In the last step, PC1 undergoes unimolecular dissociation to form final products, i.e., CH₂O, OH^•, and NO₂. Gibbs free energy at 298 K associated with this conversion of PC1 to isolated products is $\sim -\mathrm{2.5}$ kcal mol⁻¹ (Sect. S4), which suggests that the formation of OH^• via CH₂OO + HONO reaction is a spontaneous process.

Figure 2 The potential energy surface for (CH₃)₂COO + HONO reaction (in kcal mol⁻¹) obtained at CCSD(T)/CBS//M06-2X/aug-cc-pVTZ level of theory along with optimized geometries of species involved in the reaction.

Table 1 Bimolecular rate constants (k_bi, in cm³ molec.⁻¹ s⁻¹) for CH₂OO/(CH₃)₂COO + HONO reaction within the temperature range of 213–320 K.

The overall reaction was found to be exothermic by ∼ 17.3 kcal mol⁻¹ that lies close to the experimental value of ∼ 16.9 kcal mol⁻¹ (Ruscic and Bross, 2021), again confirming the adequacy of the methodology used. The computed bimolecular rate constant values ($k_{\mathrm{bi}}^{{\mathrm{CH}}_{\mathrm{2}}\mathrm{OO}}$) for CH₂OO + HONO reaction in the temperature range 213–320 K are given in Table 1. It is evident from Table 1 that the values of $k_{\mathrm{bi}}^{{\mathrm{CH}}_{\mathrm{2}}\mathrm{OO}}$ slightly decrease with increasing temperature, a typical character of a barrierless process. For example, at 213 K, values of $k_{\mathrm{bi}}^{{\mathrm{CH}}_{\mathrm{2}}\mathrm{OO}}$ is ∼ 1.17 $\times {\mathrm{10}}^{-\mathrm{11}}$ cm³ molec.⁻¹ s⁻¹ which becomes ∼ 6.3 $\times {\mathrm{10}}^{-\mathrm{12}}$ cm³ molec.⁻¹ s⁻¹ at 320 K. Figure 2 depicts the potential energy surface of (CH₃)₂COO + HONO reaction. It is evident from Fig. 2 that (CH₃)₂COO + HONO reaction also proceeds in three steps; in the first step, (CH₃)₂COO associates with HONO to form a stable reactant-complex (RC2) that is ∼ 14.2 kcal mol⁻¹ more stable than isolated reactants. Next, RC2 transforms into product-complex (PC2) having stabilization energy of $\sim -\mathrm{36.2}$ kcal mol⁻¹ with respect to isolated reactants. This transformation occurs through a transition state that lies ∼10.1 kcal mol⁻¹ below the isolated reactants. At last, PC2 undergoes unimolecular dissociation to form final products, i.e., (CH₃)₂CO, OH^•, and NO₂. Here also, the Gibbs free energy at 298 K associated with the conversion of PC2 to isolated products is $\sim -\mathrm{6.3}$ kcal mol⁻¹ (Sect. S4), making the overall product formation spontaneous. Using the energetics, we have also computed the rate constant for (CH₃)₂COO + HONO reaction employing master equation in the same 213–320 K temperature range. The calculated bimolecular rate constants ($k_{\mathrm{bi}}^{({\mathrm{CH}}_{\mathrm{3}}{)}_{\mathrm{2}}\mathrm{COO}}$) are listed in Table 1. It is evident from Table 1 that similar to CH₂OO + HONO reaction, here also the values of $k_{\mathrm{bi}}^{({\mathrm{CH}}_{\mathrm{3}}{)}_{\mathrm{2}}\mathrm{COO}}$ slightly decrease with increasing temperature across the whole range of temperature. But the bimolecular rate constant of (CH₃)₂COO + HONO reaction becomes ∼ 2.6 to 3.6 times higher compared to the same for CH₂COO + HONO reaction at all temperatures considered in the present work. For example, at 298 K, the value of $k_{\mathrm{bi}}^{({\mathrm{CH}}_{\mathrm{3}}{)}_{\mathrm{2}}\mathrm{COO}}$ is ∼ 2.03 $\times {\mathrm{10}}^{-\mathrm{11}}$ cm³ molec.⁻¹ s⁻¹, whereas the value of $k_{\mathrm{bi}}^{{\mathrm{CH}}_{\mathrm{2}}\mathrm{OO}}$ is only ∼ 7.2 $\times {\mathrm{10}}^{-\mathrm{12}}$,cm³ molec.⁻¹ s⁻¹.

It is worth noticing that, while computing the bimolecular rate constant, the capture rates of both the reactions are almost same (Table S6 in Sect. S5). The difference in the rate values of the two reactions depends on whether the reactant complex will proceed forward or backward, which further depends on the forward and backward Gibbs free energy barriers of the reactant complex. The Gibbs free energy profile at 298 K is shown in Fig. S2 of Sect. S4. It is evident from Fig. S2 that due to the higher stabilization of RC2 (corresponding to dimethyl-substituted CI), its reverse free energy barrier is high (∼ 2.9 kcal mol⁻¹), while the same is very low for RC1 (corresponding to simplest CI) ($\sim -\mathrm{1.3}$ kcal mol⁻¹). Consequently, the relative yields of product are higher for the (CH₃)₂COO + HONO reaction compared to CH₂COO + HONO reaction. Lastly, it is important to discuss the uncertainties associated with the computed rate constant due to limitations in the methodology (Fernández-Ramos et al., 2006). For example, a major source of uncertainty can originate from the fact that Criegee intermediates are known to possess moderate multireference character, and CCSD(T)/CBS sometimes fails in accurately predicting the energetics of such reactions (Rai and Kumar, 2022; Mallick et al., 2019; Mallick and Kumar, 2018). It is worth mentioning that for multireference systems, incorporating higher-level excitations at the coupled-cluster level yield energetics within chemical accuracy (Tajti et al., 2004; Misiewicz et al., 2018; Nguyen et al., 2013; Anand and Kumar, 2023; Rai and Kumar, 2023). To assess the uncertainty in the energetics arising from the multireference character, we have carried out CCSDT(Q)/CBS calculations for the smaller Criegee intermediate reaction, i.e., CH₂OO + HONO. We focused on key stationary points; the reactant complex (RC) and the transition state (TS). The various components of the post-CCSD(T) corrections (δ_T and δ_T(Q)) are provided in Table S4 of Sect. S2. It is evident from Table S4 that post-CCSD(T) corrections lead to only minor changes in the calculated energetics of CH₂OO + HONO reaction. Quantitatively, these corrections reduce the stabilization energy of RC by ∼ 0.54 kcal mol⁻¹, while increasing the barrier height by a similar ∼ 0.67 kcal mol⁻¹. Both variations fall well within the range of chemical accuracy. Furthermore, we have also estimated the capture and bimolecular rate constants using post-CCSD(T) energetics (see Table S9 in Sect. S5), which suggest that at 298 K, the bimolecular rate constants calculated at post-CCSD(T) and CCSD(T)/CBS levels are almost similar (5.53 × 10⁻¹² and 7.21 × 10⁻¹² cm³ molec.⁻¹ s⁻¹, respectively). This supports the reliability and computational efficiency of our chosen level of theory, CCSD(T)/CBS//M06-2X/aug-cc-pVTZ, for studying the title reaction.

Another source of uncertainty in the computed rate constant may arise from the error in estimation of frequency. Such errors in frequency estimation may lead to 2σ (± 2 kcal mol⁻¹) uncertainties in the computed barrier heights. To account for this, we have assumed an uncertainty of ± 2 kcal mol⁻¹ in both well depths and reaction barriers. Using this assumption, we estimated the resulting uncertainty in the rate constants at 213 K and 298 K for the model reaction CH₂OO + HONO. Due to ± 2 kcal mol⁻¹ uncertainty in the reaction barriers and well depths, the deviation in the rate constant at 213 K is ∼ 1.17${}_{-\mathrm{0.84}}^{+\mathrm{1.8}}$ $\times {\mathrm{10}}^{-\mathrm{11}}$ cm³ molec.⁻¹ s⁻¹ (±2 kcal mol⁻¹ reaction barriers) and ∼ 1.17${}_{-\mathrm{0.08}}^{+\mathrm{0.08}}\times {\mathrm{10}}^{-\mathrm{11}}$ cm³ molec.⁻¹ s⁻¹ (±2 kcal mol⁻¹ well depths), respectively. At 298 K, the same becomes $\sim {\mathrm{7.21}}_{-\mathrm{5.12}}^{+\mathrm{11.04}}\times {\mathrm{10}}^{-\mathrm{12}}$ cm³ molec.⁻¹ s⁻¹ (±2 kcal mol⁻¹ reaction barriers) and $\sim {\mathrm{7.21}}_{-\mathrm{0.72}}^{+\mathrm{0.72}}\times {\mathrm{10}}^{-\mathrm{12}}$ cm³ molec.⁻¹ s⁻¹ (±2 kcal mol⁻¹ well depths), respectively. This study suggests due to 2σ error in the barrier height, there can be an error of a ∼ factor-of-two in the estimated rate constant values. Our analysis also suggests that the uncertainty in the rate constant estimation is much lower at low temperature region compare to high temperature regions. In addition, in the estimation of the partition function, the rigid rotor harmonic oscillator (RRHO) approximation is employed, which again can introduce some error in the final rate constant. For a typical 2σ error, the uncertainty arising from the RRHO approximation can also contribute approximately a factor-of-two uncertainty in the evaluated partition function ratios.

4 Atmospheric implications

After estimating the energetics and kinetics of title reaction, it is important to discuss the impact of title reaction in the atmospheric chemistry. The importance of title reaction in the atmosphere critically depends on how it competes with other known sinks of Criegee intermediate, i.e., H₂O, (H₂O)₂, NO₂, NO, CO, and SO₂. The efficiency of a chemical reaction in the atmosphere depends upon two factors; rate of reaction and concentration of co-reactants. The effective rate constant (k_eff) captures both of these factors as it is defined as the multiplication of bimolecular rate and concentration of co-reactants. Therefore, we have used k_eff to compare the effectiveness of title reaction compared to other sinks of Criegee intermediates. A list of effective rates for the reaction of CI with H₂O, (H₂O)₂, NO₂, NO, CO, and SO₂ at 298 K are provided in Table S7 of Sect. S5. To compute k_eff, the average concentrations of all the sinks have been taken from polluted urban environments. The corresponding rate coefficients of all the sinks are taken from experimental measurements. One can see from Table S7, the effective rate coefficients (k_eff) of CO, NO, and NO₂ are lower compared to those of SO₂, H₂O, and (H₂O)₂. For example, k_eff for the reaction of CI with SO₂ is 3.35 s⁻¹, while that for NO₂ is only 0.9 s⁻¹. Therefore, in the present work, we have focused our attention on a detailed comparison of the title reaction with SO₂, H₂O, and (H₂O)₂.

Figure 3 Effective rate constant comparison (k_eff, in s⁻¹) of CH₂OO + HONO with the k_eff of previously known sinks of CH₂OO. (a) Values are taken from reference (Lin et al., 2016). (b) Values are taken from reference (Onel et al., 2021).

As far as abundance of HONO is concerned, it is found in both regions; forested as well as polluted in significant amounts (Kim et al., 2015; Acker et al., 2006; Ren et al., 2010; Zhang et al., 2012; He et al., 2006; Su et al., 2008; Ren et al., 2006; Rondon and Sanhueza, 1989; Zhou et al., 2011; Pawar et al., 2024; Vereecken et al., 2012). Among the two, HONO concentrations are comparatively higher in polluted urban areas, such as megacities. Therefore, we expect HONO to play a more effective role as a sink for Criegee intermediates in such regions. Hence, we have used representative concentrations of HONO and SO₂ in urban areas for the primary comparison. The concentration of water varies greatly in the atmosphere depending upon saturation vapour pressure and relative humidity (RH) (Anglada et al., 2013; Rai and Kumar, 2025). Therefore, in the case of H₂O and (H₂O)₂, we have taken two concentrations; one calculated at 20 % RH, and the other calculated at 100 % RH. The former serves as lower limits of H₂O and (H₂O)₂ concentrations, whereas the latter serves as the upper limits of H₂O and (H₂O)₂ concentrations. For comparison, we have taken the rate constants reported by Lin et al. (2016) for H₂O and (H₂O)₂, and by Onel et al. (2021) for SO₂. In Fig. 3, we have compared the k_eff of CH₂OO + HONO with the k_eff of CH₂OO + H₂O/(H₂O)₂/SO₂ reactions.

Figure 3 shows that HONO is a minor sink of simplest Criegee intermediate (CH₂OO) compare to SO₂, H₂O and (H₂O)₂. In fact, at 100 % RH, k_eff of CH₂OO + (H₂O)₂ is the dominant reaction across the entire temperature range (213–320 K). At 20 % RH, k_eff for CH₂OO + (H₂O)₂ and CH₂OO + H₂O remain dominant at higher temperatures, specifically within 235–320 and 260–320 K, respectively. However, at lower temperatures, k_eff of CH₂OO + HONO becomes dominant, surpassing both, CH₂OO + (H₂O)₂ and CH₂OO + H₂O in the range of 213–235 and 213–260 K, respectively. Although CH₂OO + HONO reaction dominates over CH₂OO + (H₂O)₂ and CH₂OO + H₂O at low temperature and low humidity, it remains only a minor contributor compared to CH₂OO + SO₂ reaction at the same conditions. For example, k_eff values of CH₂OO + SO₂ reaction are ∼ 5 times higher than that of CH₂OO + HONO reaction within the whole temperature range, indicating that CH₂OO + HONO reaction is never a dominant sink of CH₂OO intermediate.

Figure 4 Effective rate constant comparison (k_eff, in s⁻¹) of (CH₃)₂COO + HONO with the k_eff of previously known sinks of (CH₃)₂COO. (a) Values are taken from reference (Vereecken et al., 2017). (b) Values are taken from reference (Smith et al., 2016).

Similarly, we have compared our dimethyl substituted Criegee reaction ((CH₃)₂COO + HONO) with other known bimolecular reactions of (CH₃)₂COO. Here also, we have computed k_eff for the comparison (see Fig. 4). The rate constants of (CH₃)₂COO + SO₂ reaction (Smith et al., 2016) is known in the range of 283–303 K, and hence, we have compared its k_eff in this temperature range with (CH₃)₂COO + HONO reaction. Figure 4 shows that unlike CH₂OO + HONO reaction, here k_eff of (CH₃)₂COO +HONO is ∼ 2 times higher than the same for (CH₃)₂COO + SO₂ reaction within 283–303 K. In addition, it is worth mentioning that under certain atmospheric conditions, concentration of HONO can be quite high compared to SO₂. For example, during fog events, it is well known that concentration of SO₂ drops significantly (Zhang et al., 2013) while concentration of HONO increases (Pawar et al., 2024), making HONO a potentially major bimolecular sink of Criegee intermediates in fog-like environments. In addition, as SO₂ mainly comes from human activities, its concentrations are high in polluted areas and become quite very low in tropical forests and rural areas. In fact, its concentrations fall below detection limits in tropical forest regions (Vereecken et al., 2012). In contrast, although HONO concentration is high in polluted regions compared to a clean environment, due to the various in situ sources, HONO is present in reasonable amounts even in tropical forest areas (Zhang et al., 2012). Therefore, in this region also, HONO is a more effective sink of CI compared to SO₂. Moreover, CI + HONO reaction is a hydrogen atom transfer (HAT) process, and hence, the presence of water can effectively catalyze this reaction (Buszek et al., 2012; Viegas and Varandas, 2012; Rai and Kumar, 2025). In contrast, the presence of water, particularly droplets and aerosols, can act as a sink for SO₂ (Zhang et al., 2013), and hence, in the presence of water, Criegee + SO₂ reaction should be less important compared to CI + HONO reaction. After establishing that compared to SO₂, HONO is a more effective sink for (CH₃)₂COO under most of the conditions, at last, it is important to compare it with (CH₃)₂COO + H₂O/(H₂O)₂ reactions (Vereecken et al., 2017).

It can be seen from Fig. 4 that even at 100 % RH, k_eff of (CH₃)₂COO + HONO can dominate over k_eff of (CH₃)₂COO + H₂O and (CH₃)₂COO + (H₂O)₂ for a relatively wider range of temperatures. For example, the dominant temperature range of (CH₃)₂COO + HONO is, 213–275 K for (CH₃)₂COO + (H₂O)₂ and 213–290 K for (CH₃)₂COO + H₂O. At 20 % RH, k_eff of (CH₃)₂COO + HONO becomes dominant over k_eff of both, (CH₃)₂COO + H₂O and (CH₃)₂COO + (H₂O)₂ in almost whole temperature range (213–310 K). For example, at 298 K, k_eff of (CH₃)₂COO + HONO is ∼ 1.8 s⁻¹, which is 1.6 times and 2.2 times higher than the same for (CH₃)₂COO + H₂O and (CH₃)₂COO + (H₂O)₂, respectively. This suggests that the major bimolecular sink of substituted CI can be its reaction with HONO in the atmosphere even in the presence of high humidity and SO₂. At last, it is important to compare the k_eff of (CH₃)₂COO + HONO reaction with the unimolecular dissociation rate of (CH₃)₂COO. Figure 4 also contains the unimolecular dissociation rate of (CH₃)₂COO. It is evident from Fig. 4 that unimolecular dissociation remains the dominant removal path of (CH₃)₂COO above 225 K temperature. Only below 225 K temperature, the bimolecular reaction of (CH₃)₂COO + HONO becomes dominant. To conclude, although HONO is a dominant bimolecular sink for (CH₃)₂COO, it is still primarily removed by its unimolecular dissociation, particularly at room temperature. For example, the unimolecular dissociation rate of (CH₃)₂COO is ∼ 276 s⁻¹ at room temperature (Fang et al., 2017) whereas the k_eff of (CH₃)₂COO + HONO is only ∼ 1.8 s⁻¹. Interestingly, the unimolecular rate increases rapidly with temperature, while for the bimolecular reaction (CH₃)₂COO + HONO, k_eff decreases only slightly. As a result, at lower temperatures, k_eff may become comparable to the unimolecular dissociation rate of (CH₃)₂COO. For example, at 213 K, k_eff and the unimolecular rate constants are 3.80 and 1.82 s⁻¹, respectively. A comparison between k_eff and the unimolecular dissociation rate constant of (CH₃)₂COO within 213–320 K is provided in Table S8 of Sect. S5. It is evident from Table S8 that under conditions of high HONO concentration and low temperature, the bimolecular reaction of (CH₃)₂COO with HONO can compete with its unimolecular dissociation.

Finally, it is important to assess the extent to which the title reaction can contribute in resolving the puzzle of mismatch between measured and modelled OH^•/HO${}_{\mathrm{2}}^{•}$ concentrations. It is important to mention that during daytime, HONO undergoes rapid photolysis; therefore, its concentration is higher in the absence of light, e.g. at night, indoors, in winter, etc. For example, the photolysis rate of HONO is known to be ∼ 10⁻³ s⁻¹, which is several orders of magnitude higher than the effective rate constant of its reaction with Criegee intermediates (∼ 10⁻⁷–10⁻⁶ s⁻¹, computed using maximum Criegee concentration of ∼10⁵ molec. cm⁻³) (Shabin et al., 2023). Therefore, during the peak of daytime, title reaction does not contribute much to OH^• production; rather, it can play a key role in nocturnal atmospheric chemistry, specifically at times when both, concentrations of HONO and CI are high, and, at the same time, the presence of light is minimal.

To understand the efficiency of the title reaction in affecting OH^• concentration in a nocturnal environment, we can compare it with NO${}_{\mathrm{3}}^{•}+$ HO${}_{\mathrm{2}}^{•}$ reaction, which is a well-known source of OH^• at nighttime. The rate constants for CH₂OO + HONO reaction are ∼ 2 times higher compared to NO${}_{\mathrm{3}}^{•}$ + HO${}_{\mathrm{2}}^{•}$. For example, at 298 K, the rate value for CH₂OO + HONO is $\sim \mathrm{7.21}\times {\mathrm{10}}^{-\mathrm{12}}$ cm³ molec.⁻¹ s⁻¹, which is almost double compared to the rate value (Rai and Kumar, 2024) for NO${}_{\mathrm{3}}^{•}$ + HO${}_{\mathrm{2}}^{•}$, i.e., $\sim \mathrm{3.36}\times {\mathrm{10}}^{-\mathrm{12}}$ cm³ molec.⁻¹ s⁻¹. In the atmosphere, average concentration of both NO${}_{\mathrm{3}}^{•}$ and HO${}_{\mathrm{2}}^{•}$ are ∼10⁸ molec. cm⁻³(Bottorff et al., 2023; Brown and Stutz, 2012), thus combined concentration turns out to be ∼10¹⁶ molec.² cm⁻⁶. Similarly, the combined concentration will be ∼10¹⁵ molec.² cm⁻⁶ for CH₂OO + HONO under high concentrations of CI (∼10⁵ molec. cm⁻³)(Khan et al., 2018) and HONO (∼ 10¹⁰ molec. cm⁻³) (Pawar et al., 2024). It suggests that CH₂OO + HONO reaction may be somewhat slower in producing OH^•. However, since the rate of (CH₃)₂COO + HONO reaction is one order of magnitude higher compared to NO${}_{\mathrm{3}}^{•}+$ HO${}_{\mathrm{2}}^{•}$, we believe both NO${}_{\mathrm{3}}^{•}+$ HO${}_{\mathrm{2}}^{•}$ and title reactions should be of similar importance as far as the production of nighttime OH^• is concerned. In other words, title reaction has the potential to serve as a significant contributor to OH^• production in nighttime atmospheric chemistry.

Figure 5 Top panel: Concentration profiles of HO${}_{\mathrm{2}}^{•}$ and OH^• using CH₂OO + HONO reaction into the model. Bottom panel: Concentration profiles of HO${}_{\mathrm{2}}^{•}$ and OH^• using (CH₃)₂COO + HONO reaction into the model.

Another factor worth noting is, besides OH^•, the title reaction produces HCHO/(CH₃)₂CO, and NO${}_{\mathrm{2}}^{•}$ as products. It is well known that both HCHO/(CH₃)₂CO (Gao et al., 2024; Long et al., 2022; Hermans et al., 2004) and NO${}_{\mathrm{2}}^{•}$ (Christensen et al., 2004) can act as sinks for HO₂ radicals (corresponding reactions are listed in the box below).

It suggests that title reaction has the potential for recycling of HO${}_{\mathrm{2}}^{•}$ ↔ OH^• process. To illustrate the ability of title reaction in recycling HO${}_{\mathrm{2}}^{•}$ ↔ OH^• process, we have developed a kinetic model consisting of the following reactions (see Sect. S3):

$$\begin{array}{}\text{(R2)}& {\displaystyle }\begin{array}{rl}{\mathrm{CH}}_{\mathrm{2}}\mathrm{OO}/({\mathrm{CH}}_{\mathrm{3}}{)}_{\mathrm{2}}\mathrm{COO}& +\mathrm{HONO}\underset{{\mathrm{k}}_{({\mathrm{CH}}_{\mathrm{3}}{)}_{\mathrm{2}}\mathrm{COO}}}{\overset{{\mathrm{k}}_{{\mathrm{CH}}_{\mathrm{2}}\mathrm{OO}}}{⟶}}{\mathrm{OH}}^{•}\\ & +\mathrm{HCHO}/({\mathrm{CH}}_{\mathrm{3}}{)}_{\mathrm{2}}\mathrm{CO}+{\mathrm{NO}}_{\mathrm{2}}^{•}\end{array}\text{(R3)}& {\displaystyle }\mathrm{HCHO}/({\mathrm{CH}}_{\mathrm{3}}{)}_{\mathrm{2}}\mathrm{CO}+{\mathrm{HO}}_{\mathrm{2}}^{•}\underset{{\mathrm{k}}_{({\mathrm{CH}}_{\mathrm{3}}{)}_{\mathrm{2}}\mathrm{CO}}}{\overset{{\mathrm{k}}_{\mathrm{HCHO}}}{⟶}}{\mathrm{HOCH}}_{\mathrm{2}}\mathrm{OO}/({\mathrm{CH}}_{\mathrm{3}}{)}_{\mathrm{2}}\mathrm{C}\left(\mathrm{OH}\right)\mathrm{OO}\text{(R4)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{2}}^{•}+{\mathrm{HO}}_{\mathrm{2}}^{•}\stackrel{{\mathrm{k}}_{{\mathrm{NO}}_{\mathrm{2}}^{•}}}{⟶}{\mathrm{HO}}_{\mathrm{2}}{\mathrm{NO}}_{\mathrm{2}}\end{array}$$

This model requires two key components: first, the rate coefficients of the relevant reactions, which have been taken from the recommended literature values (Gao et al., 2024; Hermans et al., 2004; Long et al., 2022; Christensen et al., 2004), and second, a list of realistic initial concentrations of the reactive species involved in HO${}_{\mathrm{2}}^{•}$ ↔ OH^• recycling process (Table S5 in Sect. S3). We first tracked the change in concentration of OH^• and HO${}_{\mathrm{2}}^{•}$ using the first kinetic model consisting of CH₂OO + HONO reaction, followed by second model consisting of (CH₃)₂COO + HONO reaction.

Initial concentrations of relevant species (HCHO, HONO, (CH₃)₂CO, and HO${}_{\mathrm{2}}^{•}$) are chosen based on literature values representing polluted urban conditions (Vereecken et al., 2012; Pawar et al., 2024). Although the average concentration of OH^• can vary within ∼10⁴–10⁶ molec. cm⁻³ in the atmosphere, we have used a modelled value of it in the present work. In CH₂OO + HONO reaction model, the initial OH^• concentration was set to ∼10⁴ molec. cm⁻³, while in (CH₃)₂COO + HONO model, it was set to ∼10⁵ molec. cm⁻³. This difference was chosen based on how much OH each reaction is expected to produce when no in situ reactions are taking place from the byproducts of the title reaction. Since (CH₃)₂COO + HONO reaction can generate more OH, starting with a higher initial concentration helps one observe a noticeable change in OH^• levels during the simulation. This makes it easier to observe and compare the effect of OH^• production between the two reactions. It is important to mention that the maximum concentration of OH^• can be taken as ∼10⁵ molec. cm⁻³ in the kinetic model. This is because the production of OH^• is limited by the available concentration of CI which can be as high as ∼ 10⁵ molec. cm⁻³. Therefore, taking OH^• concentration more than ∼ 10⁵ molec. cm⁻³ would produce no effect on the concentration of OH^•. This also reveals the fact that the title reaction is capable of producing OH^• in regions where the concentration of OH^• is already low. Similarly, the concentration of NO₂ can vary within ∼10¹⁰–10¹² molec. cm⁻³ in polluted urban regions. However, in the present model, we have kept it at ∼10¹⁰ molec. cm⁻³ in order to observe a clear numerical change in the values of HO${}_{\mathrm{2}}^{•}$. Taking a high concentration of NO₂ (∼10¹² molec. cm⁻³) would drastically consume HO${}_{\mathrm{2}}^{•}$, and a gradual change would not be observed.

We have divided the simulation results into two parts; first we will discuss CH₂OO + HONO reaction followed by (CH₃)₂COO + HONO. The model results have been shown in Fig. 5.

It is evident from Fig. 5 that CH₂OO + HONO reaction increases OH^• concentration while simultaneously reducing HO${}_{\mathrm{2}}^{•}$ concentration. Quantitatively, this reaction increases OH^• production by five times its initial value while decreasing HO${}_{\mathrm{2}}^{•}$ production by more than one order of magnitude. Furthermore, when we consider dimethyl-substituted Criegee intermediate reaction ((CH₃)₂COO + HONO), OH^• production has been found to increase by only a factor of two compared to its initial concentration, while HO${}_{\mathrm{2}}^{•}$ production again decreases by the same one order of magnitude (Fig. 5). The difference in OH^• production can be attributed to the fact that, in case of (CH₃)₂COO + HONO, the initial OH^• concentration was taken to be ∼10⁵ molec. cm⁻³ compared to ∼10⁴ molec. cm⁻³ in case of CH₂OO + HONO. This further strengthens the fact that the effect of title reaction on OH^• production will be more pronounced in the conditions where OH^• concentration is lower in the atmosphere, e.g., at night. The overall simulation results suggest that incorporating title reaction into atmospheric models can improve their accuracy in predicting OH^• and HO${}_{\mathrm{2}}^{•}$ concentrations. It is important to note that the kinetics model used in the present work is priliminary. However, a more realistic impact of the title reaction on the budget of both OH^• and HO${}_{\mathrm{2}}^{•}$, requires a more complete modeling. In order to do so, one needs accurate estimation of the rate constants for the reaction of HONO with various important Criegee intermediates. For bigger Criegee intermediates, computation will be more costly and require a separate study. In addition, being a HAT reaction, the effect of humidity on the title reaction is also important to build a complete model.

5 Conclusions

In this work, we have studied the energetics and kinetics of bimolecular reaction of simple and dimethyl-substituted Criegee with HONO using high-level electronic structure theory and chemical kinetics. Our quantum chemical calculations suggest that both of the reactions are barrierless and kinetic calculations reveal that reaction of substituted Criegee with HONO is ∼ 2.6–3.6 times faster than simple Criegee + HONO reaction. By comparing it with other known sinks of CI, we have shown that HONO can serve as a major bimolecular sink for bigger Criegee intermediate ((CH₃)₂COO) and minor contributor at low humidity and low temperature for simple CH₂OO. In addition, we have also shown that title reaction can be an important source of OH^• in nocturnal atmosphere. In addition, the products of CI + HONO reaction can be a sink for HO₂ radicals, and hence this reaction is capable of HO${}_{\mathrm{2}}^{•}$ ↔ OH^• recycling. Consequently, this reaction can be key in fulfilling the gap between the observed OH radicals and modelled values. Although in urban areas, HONO can be the dominant sink of certain CIs, it is important to notice that larger Criegee intermediates predominantly originate from biogenic volatile organic compounds (BVOCs). On the other hand, HONO concentrations in forested regions are also found to be moderate (∼10⁸ to 10¹⁰ molec. cm⁻³). Therefore, we believe a separate study is required to understand the fate of larger Criegee intermediates in the presence of HONO. At last, we look forward to the experimental verification of our results.