Direct gas-phase formation of formic acid through reaction of Criegee intermediates with formaldehyde

Abstract

Ozonolysis of isoprene is considered to be an important source of formic acid (HCOOH), but its underlying reaction mechanisms related to HCOOH formation are poorly understood. Here, we report the kinetic and product studies of the reaction between the simplest Criegee intermediate (CH₂OO) and formaldehyde (HCHO), both of which are the primary products formed in ozonolysis of isoprene. By utilizing time-resolved infrared laser spectrometry with the multifunctional dual-comb spectrometers, the rate coefficient k_CH2OO+HCHO is determined to be (4.11 ± 0.25) × 10⁻¹² cm³ molecule⁻¹ s⁻¹ at 296 K and a negative temperature dependence of the rate coefficient is observed and described by an Arrhenius expression with an activation energy of (–1.81 ± 0.04) kcal mol⁻¹. Moreover, the branching ratios of the reaction products HCOOH + HCHO and CO + H₂O + HCHO are explored. The yield of HCOOH is obtained to be 37–54% over the pressure (15–60 Torr) and temperature (283–313 K) ranges. The atmospheric implications of the reaction CH₂OO + HCHO are also evaluated by incorporating these results into a global chemistry-transport model. In the upper troposphere, the percent loss of CH₂OO by HCHO is found by up to 6% which can subsequently increase HCOOH mixing ratios by up to 2% during December-January-February months.

Introduction

Being the simplest and most abundant organic acid in the atmosphere, formic acid (HCOOH) plays a crucial role in chemistry-climate interactions and to influence the atmospheric acidity. In the atmosphere, HCOOH can be produced from direct biogenic emissions, biomass burning as well as gas-phase and multi-phase chemical reactions; and it can be removed mainly through wet and dry deposition^1,2,3,4,5,6. The mixing ratio of atmospheric HCOOH is typically observed from sub-100 pptv to a few ppbv levels and the lifetimes of HCOOH are estimated to be 1–2 days and 1–2 weeks in the boundary layer and upper troposphere, respectively^3,5. Thanks to satellite observation techniques^1,5,6, the atmospheric abundance of HCOOH even in remote areas can be in-situ monitored. However, the current chemistry-climate models still cannot fully expound the unexpected high levels of observed HCOOH in the atmosphere. Typically, the HCOOH concentrations from modeling results are a factor of 2–5 times lower than that from observations^1,3,4,6. Recently, the oxidation of gas-phase methanediol (CH₂(OH)₂), formed by volatilization of the hydrated formaldehyde in cloud droplets, has been proposed to be an important source of the atmospheric HCOOH^7,8, but it might not explain the high concentration of HCOOH observed in the cloud-free regions such as upper troposphere and lower stratosphere (UT/LS). On the other hand, the oxidation of isoprene has been widely considered as a major source of atmospheric formic acid^9,10. According to the chamber experiments of isoprene oxidation⁹, nearly 30% and up to 40% of the global annual production of atmospheric HCOOH from gas-phase reactions can be contributed from the OH-initiated oxidation of isoprene and isoprene ozonolysis, respectively. Exploring the explicit chemical mechanisms of the HCOOH formation from the isoprene oxidation is hence of interest in atmospheric chemistry for solving the issue of the underestimated abundance of HCOOH by the chemistry-climate models. In recent studies, the four-carbon Criegee intermediates such as methyl vinyl ketone oxide (MVKO) and methacrolein oxide (MACRO) have been reported to be the main products from the ozonolysis of isoprene and they can further undergo unimolecular dissociation to form OH and hydrocarbon radicals^11,12,13. Besides the four-carbon Criegee intermediates, the simplest Criegee intermediate (CH₂OO) and formaldehyde (HCHO) are also the primary products generated, with yields of (61 ± 9) and (81 ± 16)%, respectively, in isoprene ozonolysis¹³. In the boundary layer and lower troposphere, the reaction of CH₂OO with water dimers¹⁴ has been recognized as the dominant sink for CH₂OO and its primary products were recently determined to be hydroxymethyl hydroperoxide (HMHP) and HCHO with the branching ratios of (55 ± 15) and (40 ± 10)%, respectively¹⁵. Although the reaction of HMHP with OH has been proposed to produce HCOOH with a yield of (45 ± 14)%¹⁶, it cannot explain the formation of HCOOH in the chamber experiments without OH scavengers⁹. Up to now, the reaction pathways related to the formation of HCOOH are barely understood, particularly for the environments with low concentrations of water and OH radicals.

According to the theoretical studies, HCOOH might be produced from the reaction of CH₂OO with HCHO. Supplementary Fig. 1 shows the integrated enthalpy profiles of the reaction CH₂OO + HCHO based on three theoretical investigations^17,18,19. The detailed descriptions of the enthalpy profiles are presented in Supplementary Note 1. Jalan et al. employed the RCCSD(T)-F12a/VTZ-F12//B3LYP/MG3S method and the Rice-Ramsperger-Kassel-Marcus (RRKM) theory to calculate the potential energy surface of the reaction CH₂OO + HCHO and to investigate its rate coefficients and reaction products¹⁷. In their work, the HCOOH was proposed to be the major product of the reaction CH₂OO + HCHO over a wide atmospheric conditions and the stable secondary ozonide (SOZ) can only be formed at high pressure (>2 atm). The predicted rate coefficient was reported to be 8.3 × 10⁻¹³ cm³ molecule⁻¹ s⁻¹ at 298 K and a small negative temperature dependence was obtained and described by k_CH2OO+HCHO (T) = 4.5 × 10⁻¹³ exp(0.36 kcal mol⁻¹/RT) cm³ molecule⁻¹ s⁻¹ in a temperature range of 260 − 350 K, where R is the molar gas constant and T is the temperature. In contrast to the predictions by Jalan et al.¹⁷, Elakiya et al.¹⁸ suggested that the formation of products HCOOH + HCHO is unfavorable and the dominant product channel is the formation of CO + H₂O + HCHO. In a more recent theoretical study¹⁹, Long et al. indicated that the rate coefficient of the reaction CH₂OO + HCHO has a strong negative temperature dependence and the rate coefficients k_CH2OO+HCHO (T) = 2.7 × 10⁻¹⁴ exp(4.58 kcal mol⁻¹/RT) cm³ molecule⁻¹ s⁻¹ were reported under high-pressure-limit and at 280 − 350 K. However, the theoretical results of the k_CH2OO+HCHO from Jalan et al.¹⁷ and Long et al.¹⁹ show a significant discrepancy. The 298 K rate coefficient reported by Long et al., 6.2 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹, was ∼75 times larger than the value predicted by Jalan et al., 8.3 × 10⁻¹³ cm³ molecule⁻¹ s⁻¹. Up to now, no experimental studies have been conducted to evaluate the kinetics and product yields of this potentially interesting reaction.

Herein, we report direct measurements of the rate coefficients and products of the reaction between CH₂OO and HCHO by employing mid-infrared laser systems coupled with a Herriott-type flash photolysis cell. The experimental approaches are described in Methods and illustrated in Supplementary Fig. 2. In addition to investigation of the temperature and pressure dependencies of the rate coefficients, we determine the branching ratios of primary product channels, HCOOH + HCHO and CO + H₂O + HCHO in the reaction CH₂OO + HCHO via simultaneous determination of HCOOH and CO using synchronized two-color time-resolved dual-comb spectroscopy at varied experimental conditions. The atmospheric implications of the reaction CH₂OO + HCHO are also evaluated by employing a global 3-D chemistry-transport model, STOCHEM-CRI. Our results may explain the observations of HCOOH in the simulation chamber and remote atmosphere at UT/LS height levels.

Results

Kinetic measurements of the reaction CH₂OO + HCHO

To determine the rate coefficients of the reaction between CH₂OO and HCHO and to evaluate their temperature and pressure dependencies, we first performed the kinetic measurements under different total pressures at 296 K. Over 63 measurements in seven sets were carried out at experimental conditions with [CH₂OO]₀ = (5.5–8.6) × 10¹² molecules cm⁻³, [HCHO]₀ = (1.8–34.5) × 10¹⁴ molecules cm⁻³, and total pressure P_T = 6.4–56.0 Torr at 296 K. For kinetic studies of the reaction CH₂OO + HCHO under pseudo-first-order conditions ([HCHO]»[CH₂OO]), the decay in the concentration of CH₂OO with time can be described using a single-exponential formula:

$${[{{{{{{\rm{CH}}}}}}}_{2}{{{{{\rm{OO}}}}}}]}_{{{{{{\rm{obs}}}}}}}({{{{{\rm{t}}}}}})={[{{{{{{\rm{CH}}}}}}}_{2}{{{{{\rm{OO}}}}}}]}_{0}\times \exp (-{k}_{{{{{{\rm{obs}}}}}}}\times {{{{{\rm{t}}}}}})$$

(1)

in which [CH₂OO]_obs (t) represents the observed CH₂OO concentration as a function of time, [CH₂OO]₀ represents the initial concentration of CH₂OO, and k_obs represents the overall decay rate coefficient for the observed CH₂OO:

$${k}_{{{{{{\rm{obs}}}}}}}={k}_{0}+{k}_{{{{{{\rm{CH}}}}}}2{{{{{\rm{OO}}}}}}+{{{{{\rm{HCHO}}}}}}}\times {[{{{{{\rm{HCHO}}}}}}]}_{0}$$

(2)

where k₀ is the decay rate coefficient contributed by the CH₂OO self-reaction and reactions of CH₂OO with other species generated in the reaction system, k_CH2OO+HCHO is the second-order rate coefficient of the reaction CH₂OO + HCHO, and [HCHO]₀ is the initial concentration of formaldehyde.

Figure 1 shows the representative temporal profiles of the CH₂OO measured at 1285.611 cm^‒1 under varied initial concentrations of HCHO, (1.8–20.4) × 10¹⁴ molecules cm⁻³, at a total pressure of 13.3 Torr and 296 K. Each observed profile (open symbol) was fitted with single-exponential curve (solid line) to derive the decay rate coefficient (k_obs). In addition, we also analyzed the time traces of CH₂OO with a kinetic model, as shown in Supplementary Fig. 3. The kinetic model, taking into account key reaction paths including the formation and self-reaction of CH₂OO as well as the CH₂OO + I reaction²⁰, have been used in other reaction kinetic studies such as CH₂OO + NO₂²¹ and CH₂OO + HCl²². The obtained first-order rate coefficients from the single-exponential and model fits as a function of [HCHO]₀ are displayed in Supplementary Fig. 4. The second-order rate coefficient k_CH2OO+HCHO, corresponding to the fitted slopes derived by using single-exponential and model fits, were consistent with each other, supporting the feasibility of kinetic analysis under pseudo-first-order conditions.

Fig. 1: Temporal profiles of the CH₂OO obtained under conditions with different [HCHO]₀.

The open symbols represent time-resolved signals of a CH₂OO absorption line at 1285.611 cm^‒1 recorded with a time resolution of 5 μs. The solid lines represent fitting curves. Each temporal profile was fitted with a single-exponential function to obtain the decay rate coefficient (k_obs). The data correspond to experiment 1–6 listed in Supplementary Table 1 with total pressure P_T = 13.3 Torr, temperature 296 K, and [CH₂OO]₀ ≈ 7.4 × 10¹² molecule cm⁻³. The derived k_obs as a function of [HCHO]₀ are shown in Supplementary Fig. 4.

Figure 2 depicts the obtained k_CH2OO+HCHO as a function of the total pressure at 296 K and the rate coefficients were observed to be pressure independent under the presented experimental conditions. A summary of experimental conditions and obtained k_obs rate coefficients of all kinetic measurements are listed in Supplementary Table 1. Considering one standard deviation of the k_CH2OO+HCHO obtained from 7 experimental sets (2%) and the errors in determination of [HCHO]₀ (4%), flow rates (3%), temperature (1%), and pressure (3%), the overall standard error was estimated to be ∼6% and the k_CH2OO+HCHO was hence obtained to be (4.11 ± 0.25) × 10⁻¹² cm³ molecule⁻¹ s⁻¹ at 296 K. Moreover, the temperature dependence of the rate coefficient was also investigated over the temperature range 268.6–336.5 K. Figure 3 shows the representative plots of k_obs vs. [HCHO]₀ at six different temperatures. The slopes of the plots of k_obs vs. [HCHO]₀ were found decreasing with temperature. The temperature dependence of the rate coefficients k_CH2OO+HCHO is shown in Fig. 4 and it was fitted with the Arrhenius expression:

$${k}_{{{{{{\rm{CH}}}}}}2{{{{{\rm{OO}}}}}}+{{{{{\rm{HCHO}}}}}}}({{{{{\rm{T}}}}}})={{{{{\rm{A}}}}}}\times \exp (-{{E}}_{{{{{{\rm{a}}}}}}}/{{{{{\rm{RT}}}}}})$$

(3)

where A is the pre-exponential constant, R is the molar gas constant, and E_a represents the activation energy for the reaction CH₂OO + HCHO. The A and E_a were, respectively, obtained to be (1.91 ± 0.15) × 10⁻¹³ cm³ molecule⁻¹ s⁻¹ and (–1.81 ± 0.04) kcal mol⁻¹, with an 1σ statistical error of fitting. A comparison of experimental and theoretical results of the rate coefficient for the reactions of CH₂OO with HCHO, CH₃CHO, and CH₃COCH₃ is shown in Supplementary Table 2. Both experimental and theoretical results indicate that rate coefficients decreases in the order k_CH2OO+HCHO > k_CH2OO+CH3CHO > k_{CH2OO+CH3COCH3}^17,23,24. The obtained k_CH2OO+HCHO in this work is 15 times smaller than the theoretical value reported by Long et al.¹⁹, but it is ~5 times larger than the predicted value from Jalan et al.¹⁷ Although this activation energy for CH₂OO + HCHO is not in agreement with the theoretical results, it is comparable with (–2.2 ± 0.7) kcal mol⁻¹ measured by Elsamra et al.²³ for reactions involving other ketones: CH₂OO + CH₃CHO and CH₂OO + CH₃COCH₃.

Fig. 2: Rate coefficients for the reaction CH₂OO + HCHO as a function of the total pressure.

Each rate coefficient is the fitted slope of the plot of k_obs against [HCHO]₀ of each experimental set at 296 K. The error bars include the errors of the fitted slope and determined [HCHO]₀.

Fig. 3: Plots of k_obs vs. [HCHO]₀ at six different temperatures.

The open symbols represent experimental data and the solid lines represent linear fitting curves. The data correspond to experiment sets 7, 8, 10, 12, 14, and 15 listed in Supplementary Table 1 with total pressure P_T = 21.3–21.4 Torr. The error bars represent the error of each k_obs obtained by fitting each CH₂OO temporal absorbance profile and the uncertainty of the determined [HCHO]₀.

Fig. 4: Arrhenius plot of the rate coefficients for the reaction CH₂OO + HCHO.

The blue circles represent experimental data and all of data are fitted (red solid line) with the Arrhenius expression, k_CH2OO+HCHO (T) = (1.91 ± 0.15) × 10⁻¹³ exp[(1.81 ± 0.04) kcal mol⁻¹/RT]. Here, each rate coefficient is the fitted slope of the plot of k_obs against [HCHO]₀ of each experimental set at different conditions. The error bars include the errors of the fitted slope and determined [HCHO]₀.

Branching yields of HCOOH and CO

According to the theoretically computed enthalpy profiles, as shown in Supplementary Fig. 1, the reaction of CH₂OO with HCHO is expected to lead to the formation of HCOOH + HCHO or CO + H₂O + HCHO. To evaluate the branching yields of the two potential product channels, we empolyed two sets of dual-comb spectrometers to simultaneously measure the time-resolved absorption spectra of the HCOOH and CO near 8.9 and 4.5 μm, respectively. Figure 5 shows the representative time-resolved dual-comb spectra in the regions 1127.93−1128.54 and 2218.64−2219.09 cm⁻¹ with the spectral sampling spacing of 288 MHz (9.6 × 10⁻³ cm⁻¹) and the temporal resolution of 12 μs. With the addition of HCHO in the reaction system of CH₂I + O₂, a significant formation of HCOOH was observed, as shown in Fig. 5a. By contrast, no obvious absorption signal of HCOOH could be found for the experiment in the absence of HCHO, as shown in Fig. 5c. In addition, the strong absorption signals of a CO transition line at 2218.7455 cm⁻¹ were observed in both experiments with and without the addition of HCHO, as shown in Fig. 5b, d, respectively. Several weak absorption peaks were also found in Fig. 5b, d at very early reaction time and they could be tentatively assigned to the absorption of HCO radical. The HCO radical might be generated from the decomposition of the simplest Criegee intermediates and it could be further reacted away by excess O₂ to form HO₂ + CO^25,26.

Fig. 5: Time-resolved dual-comb spectra of HCOOH and CO.

The spectra were measured in the regions 1127.93−1128.54 cm⁻¹ (a) and (c) and 2218.64−2219.09 cm⁻¹ (b) and (d). The spectra a and b were recorded simultaneously after the 248-nm irradiation of a flowing mixture of CH₂I₂/HCHO/O₂/N₂ (0.016/0.123/14.9/0.04 Torr, P_T = 15.1 Torr, 296 K) over 5000 excimer laser shots. The spectra c and d were measured simultaneously after 248-nm laser photolysis of the flowing mixture of CH₂I₂/O₂/N₂ (0.016/14.9/0.04 Torr, P_T = 15.0 Torr, 296 K) over 5000 excimer laser shots. Here, the spectral sampling spacing is 288 MHz (9.6 × 10⁻³ cm⁻¹) and the temporal resolution is 12 μs.

By employing the high-resolution time-resolved dual-comb spectroscopy, the time-dependent concentrations of HCOOH and CO can be estimated by analyzing their rotationally resolved infrared absorption spectra. To estimate the concentration of the HCOOH in the reaction system, several transition lines of the ν₆ band of the trans-HCOOH near 1128 cm^–1 were measured with dual-comb spectroscopy and analyzed with well-characterized spectral parameters^27,28,29, as shown in Supplementary Fig. 5. Considering the uncertainty of line parameters of HCOOH (7%) and the standard deviation of residuals between observed and simulated spectra (7%), the uncertainty for each time-dependent concentration of HCOOH was estimated to be 10%. In each experiment, the CO was monitored using the high-resolution dual-comb spectra near 4.5 μm, as displayed in Supplementary Fig. 6. The concentration of CO was quantified by measuring a fundamental transition line, R(21) at 2218.7455 cm^–1, with the line strength of 2.855 × 10^–20 cm molecule^–1 29. By taking account into the uncertainty of the CO line strength (1%) and the analyzed error of the difference absorbance spectra (7%), the uncertainty of ~7% can be obtained for each time-dependent CO concentration.

To further determine the product yields of the reaction CH₂OO + HCHO, a simple kinetic model, as shown in Supplementary Table 3, was adopted to simulate the temporal concentration profiles of HCOOH and CO that formed from the reaction CH₂OO + HCHO. Based on our experiments and the theoretical predictions, three product channels were considered in the model:

$${{{{{{\rm{CH}}}}}}}_{2}{{{{{\rm{OO}}}}}}\, + \, {{{{{\rm{HCHO}}}}}}\to {{{{{\rm{HCOOH}}}}}}\,({{{{{\rm{cold}}}}}}\,{{{{{\rm{and}}}}}}\,{{{{{\rm{energized}}}}}})\\ \, +\, {{{{{\rm{HCHO}}}}}}\,({R}_{{{{{{\rm{1a}}}}}}}\,{{{{{\rm{and}}}}}}\,{R}_{1{{{{{\rm{a}}}}}}\hbox{'}})$$

$${{{{{{\rm{CH}}}}}}}_{2}{{{{{\rm{OO}}}}}}+{{{{{\rm{HCHO}}}}}}\to {{{{{\rm{CO}}}}}}({\nu}\ge 0)+{{{{{{\rm{H}}}}}}}_{2}{{{{{\rm{O}}}}}}+{{{{{\rm{HCHO}}}}}}\,({{R}}_{1{{{{{\rm{b}}}}}}}\,{{{{{\rm{and}}}}}}\,{R}_{1{{{{{\rm{b}}}}}}\hbox{'}})$$

$${{{{{{\rm{CH}}}}}}}_{2}{{{{{\rm{OO}}}}}}+{{{{{\rm{HCHO}}}}}}\to {{{{{\rm{other}}}}}}\,{{{{{\rm{products}}}}}}\,({R}_{1{{{{{\rm{c}}}}}}})$$

in which the branching ratios of the HCOOH (cold and energized) + HCHO and CO (v ≥ 0) + H₂O + HCHO product channels are y_HCOOH and y_CO, respectively, and the branching ratio of other products is 1− y_HCOOH – y_CO. In addition, the relative yields of the initially cold HCOOH and energized HCOOH^# were set to be α and 1− α, where the cold HCOOH corresponds the trans-HCOOH (v = 0) and HCOOH^# may include the trans-HCOOH (v > 0) and the higher-energy cis conformer of formic acid. The relaxations of the energized HCOOH^#, including trans-HCOOH (v > 0) to trans-HCOOH (v = 0) and the cis-HCOOH to trans-HCOOH conversions³⁰ were also taken into account in the model. Figure 6 shows the comparison of the measured and simulated temporal profiles of HCOOH. A fast formation rate of the initially cold HCOOH was  observed almost corresponding to the decay rate of CH₂OO and the slow formation of the part of HCOOH was observed with the rates of 100−200 s^–1. On the other hand, the reaction of CH₂OO with HCOOH was also considered in the model because of the fast rate coefficients of the reaction CH₂OO + HCOOH. The temperature-dependent rate coefficients of the reaction CH₂OO + HCOOH have been determined by Peltola et al.³¹ and the rate coefficient is (1.0 ± 0.03) × 10⁻¹⁰ cm³ molecule⁻¹ s⁻¹ at 296 K. We assumed that the rate coefficients of the reactions CH₂OO + HCOOH and CH₂OO + HCOOH^# are the same. By adding these reactions in the model, we observed that the y_HCOOH increased by ∼10% for experimental conditions with [CH₂OO]₀ = (3.2–3.8) × 10¹³ molecules cm⁻³, [HCHO]₀ = (2.2–4.0) × 10¹⁵ molecule cm⁻³, and T = 283−313 K. Figure 7 shows the comparison of the measured and simulated temporal profiles of CO. Because the CO can be formed from the direct decomposition of the CH₂OO and the reaction of HCO + O₂^25,26, we carried out the measurements by replacing HCHO to SO₂ to obtain the concentration profile of CO generated from instant decomposition of the energized CH₂OO^*. Additionally, the CO formed from the photodissociation of HCHO by 248-nm photolysis beam was also taken into account in each experiment set. The fractional yield of photodissociation of HCHO was obtained to be ~0.02% at 248 nm and approximately 8 × 10¹¹ molecule cm⁻³ of CO could be produced when the [HCHO]₀ of 4 × 10¹⁵ molecule cm⁻³ was used. Figure 7e indicates the corrected concentration profile of CO that represents the net production of CO by the reaction CH₂OO + HCHO. To analyze the concentration profile of CO with the kinetic model, the relative yields of the cold CO and the vibrationally excited CO^# (v > 0) were set to be β and 1− β. Furthermore, the relaxation of CO^# 32 were also taken into account in the mode. A summary of experimental conditions, fitting parameters, and the derived branching ratios (y_HCOOH and y_CO) is listed in Supplementary Table 4. Considering the uncertainty of [CH₂OO]₀ (10%), analyzed errors of the temporal concentration profiles (5%), and the uncertainties of each time-dependent concentration for HCOOH (10%) and CO (7%), we estimated the overall uncertainty of y_HCOOH and y_CO to be 15% and 13%, respectively. Figure 8 illustrates the pressure dependence of branching ratios for the primary product channels of the reaction CH₂OO + HCHO at 283 K, 296 K, and 313 K. The yields of HCOOH were found slightly increasing with pressure and decreasing with temperature. In comparison, the CO yields show a negative pressure dependence and the pressure-dependent variations become smaller at higher temperature. At the total pressure of 15.1 Torr at 296 K, the branching ratios for the formation of products HCOOH + HCHO (y_HCOOH) and CO + H₂O + HCHO (y_CO) were determined to be 0.43±0.06 and 0.57±0.07, respectively, indicating that all of CH₂OO were converted into HCOOH and CO + H₂O by HCHO. Most significantly, the HCOOH can be directly generated from the reaction CH₂OO + HCHO with the high yields of 37–54 % over the pressure range 15–60 Torr and temperature range 283–313 K. This work indicates that the reaction CH₂OO + HCHO might make a significant contribution to the HCOOH formation under wide atmospheric conditions.

Fig. 6: Temporal concentration profiles of HCOOH.

The black square represents measured temporal profile with a time resolution of 12 μs. The red solid line represents simulation profile using the kinetic model shown in Supplementary Table 3. Here, [CH₂OO]₀ = 3.71 × 10¹³ molecule cm⁻³, [HCHO]₀ = 4.0 × 10¹⁵ molecule cm⁻³, P_T = 15.1 Torr, and T = 296 K. Here, the data correspond to the experiment 1 listed in Supplementary Table 4.

Fig. 7: Temporal concentration profiles of CO.

a The concentration profile of CO was measured after 248-nm laser photolysis of the flowing mixture of CH₂I₂/HCHO/O₂/N₂ (0.016/0.123/14.9/0.04 Torr, P_T = 15.1 Torr, 296 K). b The concentration profile of CO was measured after 248-nm laser photolysis of the flowing mixture of CH₂I₂/SO₂/O₂/N₂ (0.016/0.014/14.9/0.04 Torr, P_T = 15.0 Torr, 296 K). c The concentration profile of CO was measured after 248-nm laser photolysis of the flowing mixture of CH₂I₂/O₂/N₂ (0.016/14.9/0.04 Torr, P_T = 15.0 Torr, 296 K). d The concentration profile of CO was measured after 248-nm laser photolysis of the flowing mixture of HCHO/O₂/N₂ (0.123/14.9/0.04 Torr, P_T = 15.0 Torr, 296 K). e The corrected concentration profile of CO represents the net production of CO by the reaction CH₂OO + HCHO. f The concentration profile simulated using the kinetic model shown in Supplementary Table 3. Here, the data correspond to the experiment 1 listed in Supplementary Table 4.

Fig. 8: Product branching ratios at various pressures and temperatures.

The pressure dependences of branching ratios for products of the reaction CH₂OO + HCHO were obtained at a 283 K, b 296 K, and c 313 K. The error bars represent the overall uncertainties of y_HCOOH (black) and y_CO (red), that include the uncertainty of determined [CH₂OO]₀, analyzed errors of the temporal concentration profiles, and the uncertainties of each time-dependent concentration for HCOOH and CO, respectively.

Discussion

The atmospheric importance of the reaction of CH₂OO with HCHO depends upon its relatively scavenging ability to compete with the consumptions of CH₂OO by water vapor³³ as well as the HCHO by the OH radicals³⁴, affected by relative humidity (RH), temperature and photochemical conditions. Supplementary Fig. 7 shows the fractional contribution of the reactions, CH₂OO + HCHO, CH₂OO + H₂O, and CH₂OO + (H₂O)₂, to the total loss rate of CH₂OO over a relative humidity (RH) range of 1–50% at temperatures of 296, 273, and 250 K while the mixing ratios of HCHO are set to be 0.1 ppmv (Supplementary Fig. 7a) and 1 ppmv (Supplementary Fig. 7b) at 1 atm. In the ambient atmosphere, the mixing ratios of gaseous HCHO can be observed up to sub-ppmv and a few ppmv levels, respectively, in outdoor and indoor environments^35,36. With the reported mean concentration of HCHO in schools in Anhui (~1.4 ppm)³⁶ and rate coefficient of CH₂OO + HCHO at 296 K, the effective first-order rate coefficient is estimated to be ~143 s⁻¹ which is comparable to that (∼123 s⁻¹) of CH₂OO with water monomer at RH of 50% and 296 K, indicating the potential importance of the reaction CH₂OO + HCHO in indoor chemistry. At low temperature of 250 K (–23 °C), we found that the reaction CH₂OO + HCHO might compete well with the reaction CH₂OO + (H₂O)₂ for the removal of CH₂OO over the RH range below 25%, suggesting that the reaction CH₂OO + HCHO might also play a crucial role in the high-altitude atmosphere such as upper troposphere and lower stratosphere (UT/LS).

The model simulation results show that the reaction, HCHO + CH₂OO has little impact on modeled HCOOH surface level with increasing its level by up to 0.1% at the forested regions (Fig. 9). Compared with surface level, the concentration of CH₂OO was found to be higher (~400 molecules cm⁻³) at upper troposphere because of much lower water concentartions³⁷. Thus the CH₂OO + HCHO reaction can compete with the reaction CH₂OO + (H₂O)₂ at the upper troposphere. Figure 10 shows the annual zonal percentage loss of CH₂OO by HCHO and the annual zonal percentage changes in HCOOH mixing ratios. The model results show that the loss of CH₂OO by HCHO can contribute by up to 1% and 6% to the total loss of CH₂OO at the upper troposphere during June–July–August and December–January–February, respectively, as shown in Fig. 10a, b. The nonnegligible loss of CH₂OO by HCHO at the upper troposphere resulted in an increment of HCOOH mixing ratios by up to 2% during December–January–February months (Fig. 10d). The results can explain the high gas-phase mixing ratios of HCOOH observed in the high Arctic² and from the satellite observations at the altitude range of 10–16 km³⁸, as shown in Supplementary Fig. 8.

Fig. 9: Annual surface percentage changes in HCOOH mixing ratios.

a During June–July–August and b during December–January–February, on inclusion of the HCHO + CH₂OO reaction compared with the base case model.

Fig. 10: Annual zonal percentage loss of CH₂OO by HCHO and percentage changes in HCOOH mixing ratios.

The annual zonal percentage loss of CH₂OO by HCHO a during June–July–August and b during December–January–February; the annual zonal percentage changes in HCOOH mixing ratios c during June–July-August and d during December–January–February, on inclusion of the HCHO + CH₂OO reaction compared with the base case model.

In the model, CH₂OO is produced only from ethene, propene, isoprene and β-pinene (assuming 33% of the total monoterpenes). But many of the monoterpenes and sesquiterpenes in the MEGAN model are CH₂OO precursors on ozonolysis³⁹. Including the unaccounted flux of reactive biogenic and anthropogenic terminal alkenes in STOCHEM-CRI model would result in significantly higher concentrations of CH₂OO than predicted by current model setting, and would increase the modeled impact of the loss of CH₂OO by HCHO herein.

Conclusion

In conclusion, we have performed kinetic and product determinations of the reaction of the simplest Criegee intermediate CH₂OO with HCHO by employing the highly flexible mid-infrared comb lasers and synchronized two-color time-resolved dual-comb spectroscopy. The bimolecular rate coefficients for the reaction CH₂OO + HCHO were evaluated over the temperature range 268.6–336.5 K at total pressure of 6.4–56.0 Torr.

The rate coefficient of (4.11 ± 0.25) × 10⁻¹² cm³ molecule⁻¹ s⁻¹ at 296 K was determined and the temperature-dependent rate coefficients were obtained and described using an Arrhenius expression with an activation energy of (–1.81±0.04) kcal mol⁻¹. Furthermore, the branching yields of the products HCOOH + HCHO and CO + H₂O + HCHO in the reaction CH₂OO + HCHO were evaluated by direct quantifications of HCOOH and CO with rotationally resolved infrared absorption spectroscopy. The branching ratios of the HCOOH and CO product channels were determined to be 37–54 % and 42–63 % under the experimental conditions with pressure of 15–60 Torr and temperature of 283–313 K, indicating that CH₂OO could be fully converted to HCOOH and CO + H₂O in the presence of excessive HCHO. These results could explain the high HCOOH levels observed in the chamber experiments of isoprene oxidation under low relative humidity (RH < 5%) and in the absence of the OH scavengers⁹. The 3-D global chemistry-transport modeling results show that the loss of CH₂OO by HCHO is nonnegligible which can increase HCOOH level by 2% in the upper troposphere during December–January–February months. Overall, the reaction CH₂OO + HCHO might have potential implications in the atmospheric chemistry of both outdoor and indoor environments and would make an important contribution to the HCOOH formation in atmosphere at the upper troposphere. Updating of model alkene inventory is anticipated to demonstrate that CH₂OO + HCHO reaction can have an even greater impact on HCOOH formation than our current suggested assessment.

Methods

Highly flexible mid-infrared comb lasers and synchronized two-color time-resolved dual-comb spectroscopy

Schematic of the experimental approaches for the kinetic and product studies of the reaction of the simplest Criegee intermediate (CH₂OO) with formaldehyde (HCHO) is illustrated in Supplementary Fig. 2. The mid-infrared comb lasers with switchable dual-comb and continuous-wave (cw) operation modes, as the probing beams were coupled into a Herriott reactor cell. The mid-infrared comb lasers were established based on difference frequency generation of the near infrared electro-optic comb lasers and the tunable cw lasers^40,41, thus the operating spectral region can be flexibly adjusted and expanded. In the kinetic measurements, we employed the mid-infrared laser with the cw operation mode at 7.8 μm to probe the CH₂OO sensitively. After passing through the Herriot cell, the mid-infrared laser was detected using a liquid-nitrogen-cooled HgCdTe detector (MCT) and the time-resolved signals were recorded by a data-acquisition board (DAQ). The minimal detectable concentration of CH₂OO, [CH₂OO] ≈ 8 × 10¹⁰ molecule cm⁻³, was estimated by recording the temporal profiles of the CH₂OO absorption line at 1285.611 cm^‒1 with a time resolution of 5 μs and 200 averages. This level of sensitivity can allow us to perform the kinetic measurements using low concentration of CH₂OO and to implement kinetic studies of the reaction CH₂OO + HCHO under pseudo-first-order conditions ([HCHO]»[CH₂OO]). Furthermore, another two sets of dual-comb lasers with central wavelengths, respectively, near 8.9 and 4.5 μm were used to determine the formic acid (HCOOH) and carbon monoxide (CO), both of which are theoretically predicted products of the reaction between CH₂OO and HCHO. To record time-resolved dual-comb spectroscopy before and after laser photolysis of precursor mixtures, both the excimer laser and DAQ were synchronized with the multi-heterodyne signals of the dual-comb laser. With high-resolution time-resolved dual-comb spectroscopy, the spectral sampling spacing is corresponding to the repetition frequency of the employed comb laser and the spectral sampling points can be increased by interleaving dual-comb spectra measured with different spectral sampling spacings^26,42. In addition, the concentration of each probed species can be estimated by the obtained absorbance spectra and the line strengths of the molecular transitions taken from the database²⁹. Moreover, the temporal resolution in the time-resolved measurements can be simply adjusted from μs to ms level by setting the length of dual-comb interferogram used for generation of each time-dependent Fourier transform (FT) spectrum. Therefore, we can analyze the same experimental raw data with different time-resolution to obtain the best quality of the time-resolved spectra.

Herriott reactor cell and precursor preparation

To monitor the transient molecules generated upon laser photolysis of precursor mixtures, the Herriott-type reactor cell was constructed based on a pair of 2-inch concave gold mirrors and a double-layer glass tube. The mirrors were designed with a radius of curvature of 400 mm, a 25-mm-diameter center hole allowed passage of the excimer laser as the photolysis beam, and a 4-mm-diameter off-axis hole served as the entrance and exit of the mid-infrared probe beams. With the Herriott multipass cell, an optical path length of the probe beam was determined to be 41.8 m and the overlapped path between the photolysis and probe beams was estimated to be 13.4 m. The double-layer glass tube as the main body of the reactor can be temperature controlled from 268 to 338 K by a liquid circulator. The main stream of the flowing mixtures was also pre-cooled or pre-heated, before being introduced to the Herriott cell. To study the reaction between CH₂OO and HCHO, we performed flash photolysis of flowing mixtures of CH₂I₂/HCHO/O₂/N₂. A small stream of O₂ was bubbled through the liquid CH₂I₂ (Sigma-Aldrich, 99% purity) before entering the reactor and the mixing ratio of CH₂I₂ in O₂ can be measured by UV absorption in a 55-cm quartz cell at 285 nm. The formaldehyde (HCHO) was prepared by heating paraformaldehyde (Sigma-Aldrich, 95% purity) to 100–130 °C and then passed through a cold trap at −40 °C to remove coproducts such as water and other impurities, before being controlled by a mass flow controller and introduced to a 40-cm absorption cell. The mixing ratio of the gaseous HCHO in the bath gas O₂/N₂ before injection into the main reactor was determined by employing UV absorption spectra and the absorption cross section of HCHO in region 350−358 nm⁴³. The Herriott mirrors and cell windows were also purged by a small stream of N₂. The total flow rate of over a few thousands standard cm³ min⁻¹ was typically used at our experimental conditions. The partial pressure of each precursor in the Herriott reactor cell can be calculated according to the flow rate of each stream, mixing ratios of the pre-mixtures, and the total pressure.

Global chemistry-transport model

Model simulations were conducted by a 3-D global chemistry and transport model, STOCHEM-CRI^44,45 to assess the loss of HCHO by CH₂OO and the subsequent formation of HCOOH throughout the troposphere. STOCHEM-CRI is a Lagrangrian model where the tropospheric layer of the atmosphere is divided into 50,000 air parcels of constant mass. The model allows chemical processes within the air parcel, alongside the emission and removal processes, to be uncoupled from the transportation of the parcel. Within the model, both transport and chemical processes are driven by meteorological archived data from the U.K. Meteorological Office (UKMO) Unified Model. The UKMO model operates across a grid resolution of 1.25^o longitudes by 0.83^o latitude and 12 unevenly spaced vertical levels, with the upper boundary up to 100 hPa⁴⁶. The output data from the model run has a resolution of 5° longitude by 5° latitude and has 9 vertical levels, which span from the surface up to an altitude of 16 km. The chemical mechanism used in STOCHEM is the common representative intermediate mechanism version 2 and reduction 5 (CRI v2-R5). The details of the CRI v2-R5 mechanism can be found in Jenkin et al.⁴⁷, Watson et al.⁴⁸, Utembe et al.⁴⁹ and Jenkin et al.⁵⁰. Further amendments to the chemical mechanism with the addition of Criegee field are reported by Chhantyal-Pun et al.³⁷ Emissions of the species within STOCHEM are categorized into surface emissions, stratospheric sources, and the three-dimensional emissions. Surface emissions from ocean, soil, vegetation, and biomass burning are distributed using monthly two-dimensional source maps with a resolution of 5° longitude by 5° latitude⁵¹. The total emissions for nitrogen oxides, carbon monoxide, and nonmethane volatile organic compounds (NMVOCs) included in the model were adapted from the Precursors of Ozone and their Effects in the Troposphere (POET) inventory⁵². Further details of the STOCHEM emissions inventory for all species can be found in Khan et al.⁵³ Wet deposition and dry deposition are the two main techniques used in STOCHEM to remove chemical species from air parcels at the boundary layer. Dry deposition is accounted for using a resistance approach in STOCHEM and the rate at which it occurs depends on whether a Lagrangian air parcel is treated as being above land or the ocean. The dry deposition velocities used in STOCHEM were adapted from the annual mean values calculated from the MATCH global model⁵⁴. Wet deposition is the elimination of soluble species through dissolution in precipitation. These dissolved substances may have environmental origins or may mix with precipitation as it falls. To determine wet deposition loss rates, wet deposition equations in STOCHEM combine species-dependent scavenging coefficients taken from Penner et al.⁵⁵ with scavenging profiles and precipitation rates.

The base case simulation conducted was based on the reference condition described in Chaantyal-Pun et al.³⁷ with additional amendment of the CRI mechanism by adding HCOOH + CH₂OO reaction (k = 0.7 × 10⁻¹⁰ cm³ molecule⁻¹ s⁻¹)⁵⁶. Another simulation was conducted with inclusion of HCHO + CH₂OO reaction yielding of HCOOH + HCHO (43%) and CO + H₂O + HCHO (57%) in STOCHEM-CRI. Both simulations were conducted with 1998 meteorology data for a period of 24 months with the first 12 allowing the model to spin up. Analysis were performed on the subsequent 12 months of data.