An unexpected feasible route for the formation of organosulfates by the gas phase reaction of sulfuric acid with acetaldehyde catalyzed by dimethylamine in the atmosphere

Abstract

An understanding of the formation of organosulfates is required for elucidating the formation of secondary organic aerosols in atmosphere. Herein, we report a new feasible reaction pathway for the formation of organosulfates in the reaction of sulfuric acid (H₂SO₄) with acetaldehyde (CH₃CHO) catalyzed by dimethylamine ((CH₃)₂NH) using quantum chemical methods and reaction rate theory. We found that dimethylamine has a strong catalytic effect in the CH₃CHO + H₂SO₄ + (CH₃)₂NH reaction because the energy barriers of the CH₃CHO + H₂SO₄ + (CH₃)₂NH reaction are reduced by 18.28–23.08 kcal mol⁻¹ as compared to the CH₃CHO + H₂SO₄ reaction. The calculated results show that the CH₃CHO + H₂SO₄ + (CH₃)₂NH reaction can compete well with the traditional sink for CH₃CHO by hydroxyl radicals (OH), when the OH, H₂SO₄, and (CH₃)₂NH concentrations are 10⁴ molecules per cm³ during the night and 1.0 × 10⁶ and 3.2 × 10⁹ molecules per cm³ at below 240 K, respectively. The calculated results also show that the CH₃CHO + H₂SO₄ + (CH₃)₂NH reaction makes a limited contribution to the sink for sulfuric acid in the atmosphere. The present findings provide a new insight into the generation of organosulfates, which could be extended to other aldehydes with sulfuric acid catalyzed by amines in the atmosphere.

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Environmental significance

Organosulfates are key components in secondary organic aerosols. This study presents a new feasible route for the formation of organosulfates via the gas phase reactions of acetaldehyde with sulfuric acid catalyzed by dimethylamine. This mechanistic route could be extended to the reactions of other aldehydes with sulfuric acid catalyzed by amines in the atmosphere. However, organosulfates are often obtained by heterogeneous processes. Our findings also show that the CH₃CHO + H₂SO₄ + (CH₃)₂NH reaction can make an important contribution to the sink for acetaldehyde during the night at low temperatures. This study is of great significance for the accurate evaluation of the atmospheric environmental effects of CH₃CHO, particularly, air quality and atmospheric modeling and policies.

1. Introduction

Secondary organic aerosols (SOAs) are formed by the atmospheric oxidation of volatile organic compounds (VOCs),^1–8 which have important effects on the climate and environment, human health, and cloud condensation nuclei (CCN).^2,9–17 Although there are extensive studies on secondary organic aerosols, the formation process of secondary organic aerosols is still not completely clear because their formation is significantly influenced by many factors such as the complex atmospheric oxidation processes of VOCs and different sources of atmospheric particles.^2,9,18,19

The formation of secondary organic aerosols occurs by atmospheric nucleation,²⁰ which is determined by the formation and decomposition of molecular clusters of different sizes and chemical compositions.²¹ Previous studies have shown that sulfuric acid is the most common nucleating precursor and dimethylamine is an important component of atmospheric aerosol precursors in acid-base cluster reactions.^22–25 The strong interactions between dimethylamine and sulfuric acid can effectively form clusters,^26–29 which further contribute to the formation of secondary organic aerosols.^27,28,30

Acetaldehyde (CH₃CHO) is an important aldehyde with atmospheric concentrations of about 15.9 ppb and 45.60 ppb in major urban areas of China and Brazil, respectively.^31,32 CH₃CHO has serious impacts on the air environment,^33–36 and is emitted from anthropogenic and natural sources.^{32,35,37–41} Additionally, the photochemical degradation of VOCs has been considered to be the main source of acetaldehyde in the atmosphere.^31,37,42 Previous studies have shown that acetaldehyde makes an important contribution to the formation of secondary organic aerosols.^36,41 Organosulfates are formed via the heterogeneous reaction process of aldehydes as reported in the literature.^43,44 However, the formation of organosulfates by acetaldehyde has not been reported in the gas phase of the atmosphere.

CH₃CHO + H₂SO₄ + (CH₃)₂NH → CH₃CHO + H₂SO₄⋯(CH₃)₂NH → CH₃HC(OH)OSO₃H + (CH₃)₂NH (R1)

Herein, we have investigated the reaction of sulfuric acid with acetaldehyde catalyzed by dimethylamine in reaction (R1) using theoretical methods. We obtained the energy barriers and reaction rates of reaction (R1) to show the catalytic ability of dimethylamine. We propose a new mechanistic pathway for the formation of organosulfates via the homogeneous reaction process, whereas previous investigations considered the formation of organosulfates by heterogeneous reaction processes.⁴⁵ The present findings of this work not only provide a new source of organosulfates but are also likely to be applied in other aldehyde reactions with sulfuric acid catalyzed by dimethylamine.

2. Computational methods

In this article, all geometries and the corresponding frequencies of reactants, transition states, products, and complexes were optimized using the M06-2X⁴⁶ functional with the MG3S⁴⁷ basis set in the CH₃CHO + H₂SO₄ + (CH₃)₂NH reaction. The reliability of the M06-2X functional and its wide application have been demonstrated in previous studies on the atmospheric reactions of sulfuric acid and sulfuric acid molecular clusters.^48–53 The calculated results of the corresponding frequencies of reactants, complexes, transition states, and products using M06-2X/MG3S suggest that all stable structures have positive frequencies, while the transition state has only one imaginary frequency. The stability of the density functional theory method has been tested by using the keyword (stable = opt).^54,55 Intrinsic reaction coordinate (IRC)^56,57 calculations were utilized to determine whether the transition state corresponds to the reactants and products.

To obtain the relative energies more reliably, we did single-point energy calculations for these stationary points in the present investigation. Based on previous studies, the accuracy of CCSD(T)-F12a/jun-cc-pV(T+d)Z calculation results can be approximated to CCSD(T)/CBS.^58,59 Therefore, we have used the CCSD(T)-F12a^60,61 theoretical method and the jun-cc-pV(T+d)Z⁶² basis set to calculate the single-point energies to obtain reliable relative energies based on the optimization geometric structure of M06-2X/MG3S. The reliability of CCSD(T) has been confirmed by the T₁ diagnostic values of all species with the upper limit of 0.02 in the closed-shell systems.⁶³ The T₁ diagnostic values of all species in this article are below the upper limit of 0.02 (see Table S1†).

We calculated rate constants by using conventional transition state theory^64–66 with Eckart tunneling⁶⁷ for each reaction studied in this article. All electronic structure calculations were done using the Gaussian 16 (ref. 68) and Molpro 2019 (ref. 69) codes, while the rate constants were calculated using The Rate⁷⁰ code.

3. Results and discussion

The optimized geometries and calculated relative energies with zero-point vibrational correction for the reaction (R1) are shown in Fig. 1. Concerning the complexes and transition states reported here, we used the binding energies and energy barriers, which are equal to the relative energies obtained by CCSD(T)-F12a/jun-cc-pV(T+d)Z//M06-2X/MG3S, plus the relative zero-point vibrational correction by M06-2X/MG3S, respectively. The rate constants and equilibrium constants relative to the reaction (R1) are listed in Table 1. The relative Gibbs free energy for the reaction of acetaldehyde with sulfuric acid catalyzed by dimethylamine at 298 K is shown in Fig. S1.† We discuss the relative energies with zero-point vibrational correction based on CCSD(T)-F12a/jun-cc-pV(T+d)Z//M06-2X/MG3S calculated results unless otherwise stated.

Fig. 1 Calculated relative energies with zero-point vibrational correction for the reaction CH₃CHO + H₂SO₄ + (CH₃)₂NH → CH₃HC(OH)OSO₃H + (CH₃)₂NH at the CCSD(T)-F12a/jun-cc-pV(T+d)Z//M06-2X/MG3S level (in kcal mol⁻¹).

Table 1 The calculated equilibrium constants (K_eq1, molecules per cm³) and bimolecular rate constants (k_1, cm³ per molecules per s) for the H₂SO₄⋯(CH₃)₂NH + CH₃CHO over the temperature range of 200–298 K

	200 K	220 K	240 K	260 K	280 K	298 K
a The equilibrium constants of the H2SO4⋯(CH3)2NH complex with respect to H2SO4 and (CH3)2NH. b The bimolecular rate constants of the H2SO4⋯(CH3)2NH + CH3CHO reaction.
K eq1	2.33 × 10^−3	1.56 × 10^−5	2.43 × 10^−7	7.27 × 10^−9	3.63 × 10^−10	3.47 × 10^−11
k 1	1.55 × 10^−16	1.70 × 10^−16	1.90 × 10^−16	2.13 × 10^−16	2.40 × 10^−16	2.68 × 10^−16

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3.1. The CH₃CHO + H₂SO₄ reaction catalyzed by (CH₃)₂NH

The reaction of acetaldehyde with sulfuric acid catalyzed by dimethylamine is shown in Fig. 1, where there are three molecular reaction systems. In trimolecular reaction systems, there are three different entrance channels, and the probability of the three molecules colliding simultaneously in the gas phase of the atmosphere is very low, which has been reported in the literature.^36,71–75 Therefore, when the three molecules CH₃CHO, H₂SO₄, and (CH₃)₂NH first collide, two molecules of the three form a dimer, and then the dimer collides with the third molecule to form the ternary complex: H₂SO₄⋯(CH₃)₂NH + CH₃CHO, CH₃CHO⋯H₂SO₄ + (CH₃)₂NH, and CH₃CHO⋯(CH₃)₂NH + H₂SO₄.

We compared the calculated binding energies of the dimer complexes with the values from previous investigations in the literature. The computed binding energy of H₂SO₄⋯(CH₃)₂NH (M1A) is −22.18 kcal mol⁻¹ (see Table S2†), which is consistent with the value of −21.99 kcal mol⁻¹ at the CCSD(T)/aug-cc-pVTZ//ωB97XD/6-311++(2d,2p) level.⁷⁶ The binding energy of CH₃CHO⋯H₂SO₄ was computed to be −11.91 kcal mol⁻¹, which is slightly different from the value of CH₃CHO⋯H₂SO₄ (−12.59 kcal mol⁻¹) at the CCSD(T)-F12a/cc-pVTZ-F12//M06-2X/MG3S level (see Table S2 and Fig. S2†). The calculated binding energy of CH₃CHO⋯(CH₃)₂NH (−3.43 kcal mol⁻¹) is consistent with the value of −3.42 kcal mol⁻¹ calculated by the CCSD(T)-F12a/VTZ-F12//M06-2X/6-311++G(d,p).³⁶ Because the binding energies of the binary complexes in the entrance channel were obtained using different theoretical methods, they do not exactly match the values in the literature.⁷⁷ However, the differences are still small (around 0.5 kcal mol⁻¹).

The binding energy of H₂SO₄⋯(CH₃)₂NH (−22.18 kcal mol⁻¹) is much lower than those of CH₃CHO⋯H₂SO₄ (−11.91 kcal mol⁻¹) and CH₃CHO⋯(CH₃)₂NH (−3.43 kcal mol⁻¹); this resulted in the equilibrium constant of H₂SO₄⋯(CH₃)₂NH being much larger than those of CH₃CHO⋯H₂SO₄ and CH₃CHO⋯(CH₃)₂NH in Table S3.† For example, the equilibrium constant of H₂SO₄⋯(CH₃)₂NH is at least 10⁶ and 10¹² larger than those of CH₃CHO⋯H₂SO₄ and CH₃CHO⋯(CH₃)₂NH at 298 K, respectively (see Table S3†). A larger equilibrium constant of the complex leads to a higher concentration in the atmosphere. For example, when the concentrations of CH₃CHO,^32,34 H₂SO₄,⁷⁸ and (CH₃)₂NH⁷⁹ are 1.12 × 10¹², 4.0 × 10⁸, and 3.2 × 10⁹ molecules per cm³, respectively, the calculated the concentrations of H₂SO₄⋯(CH₃)₂NH, CH₃CHO⋯H₂SO₄, and CH₃CHO⋯(CH₃)₂NH are 2.98 × 10¹⁵ to 4.97 × 10⁵, 7.34 × 10⁶ to 5.14 × 10¹ and 2.09 × 10⁻¹ to 1.47 × 10⁻² molecules per cm³, respectively at 200–340 K (see Table S3†). In particular, the concentrations of H₂SO₄ and (CH₃)₂NH were 4.0 × 10⁸ and 3.2 × 10⁹ molecules per cm³, respectively, while the corresponding concentration of the H₂SO₄⋯(CH₃)₂NH dimer was calculated to be 2.98 × 10¹⁵ to 4.64 × 10⁸ molecule per cm³ over the 200–280 K. The larger concentration of the H₂SO₄⋯(CH₃)₂NH dimer was caused by the larger equilibrium constant at low temperatures in Table S3.† Moreover, the concentration of the H₂SO₄⋯(CH₃)₂NH complex was much higher than those of CH₃CHO···H₂SO₄ and CH₃CHO⋯(CH₃)₂NH. In addition, the peak concentration of sulfuric acid in the atmospheric boundary layer during the daytime is about 10⁶–3 × 10⁷ molecules per cm³ and the addition of dimethylamine can stabilize clusters and reduce evaporation.^25,80 Therefore, we only considered the entrance channel CH₃CHO + H₂SO₄⋯(CH₃)₂NH in the present investigation.

The CH₃CHO + H₂SO₄⋯(CH₃)₂NH reaction occurs in one elementary step as depicted in Fig. 1, which is similar to the hydrolysis of acetaldehyde catalyzed by sulfuric acid, as well as the reaction of formaldehyde with sulfuric acid catalyzed by formic acid and other catalysts.^{34,36,50,51,53,81–83} It can be seen that when the H₂SO₄⋯(CH₃)₂NH complex and CH₃CHO act as reactants, the reaction occurs via the formation of pre-reaction complexes and then undergoes a unimolecular isomerization through these corresponding transition states responsible for the formation of the post-reaction complex. In the CH₃CHO + H₂SO₄⋯(CH₃)₂NH reaction, there is a concerted reaction mechanism where the hydrogen atom of the OH group in sulfuric acid is transferred to the oxygen atom of the carbonyl group in CH₃CHO by the amino group in dimethylamine, and the oxygen atom of the S=O group in sulfuric acid is simultaneously added to the carbon atom in CH₃CHO, where dimethylamine acts as a catalyst; this leads to the formation of the most stable post-reaction complex (CP1), which is a nucleation precursor of secondary organic aerosols.³¹ We also note that the formation of P1 is endothermic with respect to the H₂SO₄⋯(CH₃)₂NH and CH₃CHO reactants and, therefore, the reverse reaction is possible.

The pre-reaction complexes (CH₃CHO⋯H₂SO₄⋯(CH₃)₂NH) have an eight-membered ring structure with two hydrogen-bonded interactions and a van der Waals interactions. As can be seen from Fig. S4,† the bond lengths of the C1–O16 bond, the N5–H3 bond and the O15–H17 bond in C1A are the same as those in C1B. From C1A and C1B to TS1A and TS1B, the C1–O16 bond length decreased from 2.731 Å to 1.846 Å and 1.848 Å, the N5–H3 bond distance increased from 1.034 Å to 1.259 Å and 1.282 Å, and the O15–H17 bond was lengthened to 1.989 Å and 1.979 Å from 1.551 Å respectively. The O15–H18 bond in sulfuric acid was lengthened to 1.967 Å from 1.565 Å, and the N5–H3 bond increased to 1.283 Å from 1.033 Å and the bond distance between the C1 atom of the aldehyde group in CH₃CHO and the O17 atom of H₂SO₄ was shortened to 1.837 Å from 2.793 Å from C1C to TS1C. From a geometrical point of view, dimethylamine plays a crucial bridging role in the (CH₃)₂NH-catalyzed reaction of sulfuric acid with acetaldehyde.

The binding energies of the pre-reaction complexes (C1A, C1B, and C1C) were computed to be −34.76, −34.76 and −35.10 kcal mol⁻¹ with respect to the separate reactants. Additionally, the binding energies of the CH₃CHO⋯H₂SO₄⋯(CH₃)₂NH complexes are also 11.60–13.76 kcal mol⁻¹ lower than those of the HCHO⋯H₂SO₄⋯NH₃ complexes at the M08-SO/maug-cc-pVTZ level.⁸¹ This shows that dimethylamine has a stronger ability to form molecular clusters, compared with ammonia.

In the CH₃CHO + H₂SO₄ + (CH₃)₂NH reaction, we found six different transition states (TS1A, TS1B, TS1C, TS1D, TS1E, and TS1F) as shown in Fig. S3.† The differences among them are produced by the relative orientation of the dangling OH group in sulfuric acid and the attack of CH₃CHO on the H₂SO₄⋯(CH₃)₂NH complex from different directions. The six transition states are three isomers, where each isomer has two conformations (TS1A and TS1D, TS1B and TS1E, TS1C and TS1F). Additionally, the energy barriers for TS1A, TS1B, TS1C, TS1D, TS1E and TS1F were computed to be −21.50, −21.14, −20.82, −18.78, −18.32 and −17.87 kcal mol⁻¹, respectively, shown in Fig. S3.† The energy barriers of TS1D, TS1E, and TS1F are higher than those of TS1A, TS1B, and TS1C by about 2.04–3.63 kcal mol⁻¹, therefore, we did not consider TS1D, TS1E, and TS1F for kinetics calculations.

From Fig. S2,† there are three different reaction pathways and the energy barriers of the CH₃CHO + H₂SO₄ reaction were computed to be 0.41, 0.43 and 1.58 kcal mol⁻¹ for TS2A, TS2B and TS2C in the CH₃CHO + H₂SO₄ reaction. Therefore, the energy barriers of the CH₃CHO + H₂SO₄ + (CH₃)₂NH reaction decreased by about 21.23–23.08 kcal mol⁻¹, as compared with the CH₃CHO + H₂SO₄ reaction. These results show that dimethylamine plays a remarkable catalytic role in the CH₃CHO + H₂SO₄ + (CH₃)₂NH reaction. Furthermore, some similar reactions have been studied previously. For example, the energy barrier of the HCHO + HNO₃ reaction was reduced by 21.97 kcal mol⁻¹ with the assistance of (CH₃)₂NH.⁸⁴ The energy barrier of the reaction between H₂SO₄ and HCHO decreased by 16–21 kcal mol⁻¹ when NH₃ was added to the catalyst.⁸¹ The energy barrier of the HCHO + H₂SO₄ reaction catalyzed by HCOOH is about 14.81 kcal mol⁻¹ lower than that of the HCHO + H₂SO₄ reaction.⁵³ Compared with these similar reactions, it can be seen that (CH₃)₂NH has an excellent catalytic effect. Thus, the above conclusions also suggest that dimethylamine plays a crucial catalytic role in the CH₃CHO + H₂SO₄ + (CH₃)₂NH reaction, and the reaction of acetaldehyde with sulfuric acid catalyzed by (CH₃)₂NH accelerates the formation of nucleation precursors in the atmosphere.

3.2. Kinetics

Because the temperature of the earth's atmosphere varies with the different regions, we considered the rate constants at different temperatures. Herein, we have calculated the rate constants for the three pathways of the trimolecular reaction using conventional transition state theory with Eckart tunneling in the temperature range between 200 and 298 K.

With regard to the CH₃CHO + H₂SO₄ + (CH₃)₂NH reaction, we only considered H₂SO₄^…(CH₃)₂NH and CH₃CHO as reactants, and the reaction mechanism is written as follows in (R2) and (R3):

(CH₃)₂NH + H₂SO₄ ↔ H₂SO₄⋯(CH₃)₂NH (R2)

H₂SO₄⋯(CH₃)₂NH + CH₃CHO → CH₃HC(OH)OSO₃H + (CH₃)₂NH (R3)

Thus, the total reaction rate of (R1) is computed as shown in the following eqn (1):

In the above equation, K_eq1 is the equilibrium constant of the complex H₂SO₄⋯(CH₃)₂NH relative to the reactants H₂SO₄ and (CH₃)₂NH, and k₁ represents the rate constant of reaction (R3). The calculated details are provided in the ESI.† The rate constant k₁ of the H₂SO₄⋯(CH₃)₂NH + CH₃CHO reaction was computed to be 1.55 × 10⁻¹⁶ to 2.69 × 10⁻¹⁶ cm³ per molecules per s at 200–298 K (see Table 1). The computed result shows that the bimolecular reaction of H₂SO₄⋯(CH₃)₂NH with CH₃CHO has a slightly positive temperature dependence. In addition, we also computed the bimolecular rate constant of the CH₃CHO + H₂SO₄ reaction.

CH₃CHO + H₂SO₄ → CH₃HC(OH)OSO₃H (R4)

The reaction rate of acetaldehyde with sulfuric acid is expressed as follows:

The rate constant k₂ of the reaction was computed to be 3.88 × 10⁻¹⁶ to 5.77 × 10⁻¹⁶ cm³ per molecule per s at 200–298 K, as shown in Table S4;† this is still a slightly positive temperature dependence.

3.3 Atmospheric implications

To estimate the catalytic ability of dimethylamine in the H₂SO₄ + (CH₃)₂NH + CH₃CHO reaction (R1), we considered the rate ratio of v₁/v₂, as written in eqn (3):

The rate ratio v₁/v₂ depends on both the concentration of dimethylamine and temperature. When the concentration of dimethylamine is 3.2 × 10⁹ molecules per cm³, measured in a contaminated environment,⁷⁹ the values of v₁/v₂ are in the range 2.98 × 10⁶ to 9.95 × 10⁰ at 200–260 K (see Table S5†). These results show that dimethylamine makes a significant contribution in the reaction of acetaldehyde with sulfuric acid at low temperatures. The results also indicate the strong catalytic ability of dimethylamine in the H₂SO₄ + (CH₃)₂NH + CH₃CHO reaction.

The main sink pathway of acetaldehyde is its reaction with OH with an atmospheric lifetime of about one day.^37,85 To further investigate the important atmospheric contribution of the H₂SO₄ + (CH₃)₂NH + CH₃CHO reaction, we compared the H₂SO₄ + (CH₃)₂NH + CH₃CHO reaction with CH₃CHO + OH. The rate ratio is expressed in eqn (4):

where k_CH3CHO+OH is the experimental rate constant of the CH₃CHO + OH reaction at different temperatures.⁸⁶

From eqn (4), it can be seen that v₁/v_CH3CHO+OH is related to the concentrations of sulfuric acid, dimethylamine, and OH. Atmospheric sulfuric acid concentrations are in the range of 10⁴ to 4.0 × 10⁸ molecules per cm³ in different areas.^87–89 The concentration of (CH₃)₂NH is often 3.2 × 10⁹ molecules per cm³.⁷⁹ However, the concentration of OH is remarkably varied during the daytime and nighttime, with values in the range of 10⁴–10⁶ molecules per cm³.^90,91 When the concentration of (CH₃)₂NH is 3.2 × 10⁹ molecules per cm³ and the concentration of sulfuric acid is 10⁶, 10⁷, 4.0 × 10⁸ and 5.1 × 10⁹ molecules per cm³,⁹² the values of v₁/v_CH3CHO+OH at the different concentrations of OH are as listed in Tables S6–S9† at 200–298 K. When [(CH₃)₂NH] and [H₂SO₄] are 3.2 × 10⁹, and 1.0 × 10⁶ molecules per cm³, respectively, the rate ratio v₁/v_CH3CHO+OH as the function of OH concentration is shown in Fig. 2 at 200–298 K. When [OH], [CH₃CHO],^32,34 [H₂SO₄], and [(CH₃)₂NH] are 1.0 × 10⁶, 1.12 × 10¹², 1.0 × 10⁶, and 3.2 × 10⁹ molecules per cm³, respectively, the rate ratio of v₁/v_CH3CHO+OH is 3.67 at 220 K (listed in Table S6†); this shows that even if the OH concentration is very high during the daytime, the H₂SO₄ + (CH₃)₂NH + CH₃CHO reaction can make some contribution to the sink for CH₃CHO. Furthermore, when the OH concentration is further decreased to 1.0 × 10⁴ molecules per cm³ during the night, the three-molecule reaction of acetaldehyde with sulfuric acid catalyzed by dimethylamine can compete well with the CH₃CHO + OH reaction with the concentrations of H₂SO₄ (1.0 × 10⁶ molecules per cm³) and (CH₃)₂NH (3.2 × 10⁹ molecules per cm³) below 240 K in Table S6;† this shows that the H₂SO₄ + (CH₃)₂NH + CH₃CHO reaction contributes significantly to the formation of organosulfates and the sink for acetaldehyde. In particular, previous studies have shown that carbonyl compounds can promote the formation of secondary organic aerosols through oxidation, hydration, and other reactions.^39,93,94 Therefore, the H₂SO₄ + (CH₃)₂NH + CH₃CHO reaction may be expected to be like the other reactions of other aldehydes with sulfuric acid catalyzed by dimethylamine, responsible for the formation of organosulfates in the gas phase reaction of the atmosphere.

Fig. 2 Rate ratio v₁/v_CH3CHO+OH at [H₂SO₄] = 1.0 × 10⁶ molecules per cm³, and [(CH₃)₂NH] = 3.2 × 10⁹ molecules per cm³ at different temperatures and different OH concentrations.

We also compared the H₂SO₄ + (CH₃)₂NH + CH₃CHO reaction with the H₂SO₄ + OH reaction. The rate ratio is given in eqn (5):

where k_H2SO4+OH is the rate constant of the H₂SO₄ + OH reaction, which has been reported in the literature.⁹⁵ When [CH₃CHO] = 1.12 × 10¹² molecules per cm³, [(CH₃)₂NH] = 3.20 × 10⁹ molecules per cm³, [OH] = 10³, 10⁴, 10⁵, and 10⁶ molecules per cm³ respectively, the values of the rate ratio of v₁/v_H2SO4+OH are 1.10 × 10¹⁵ to 2.83 × 10⁴ at 200–298 K (see Table S10†). Therefore, the calculated results show that the H₂SO₄ + (CH₃)₂NH + CH₃CHO reaction can compete well with the H₂SO₄ + OH reaction.

The atmospheric lifetimes of sulfuric acid determined by heterogeneous processes are estimated to be approximately 10² s in polluted air and 10⁴ s in clean air.⁹⁶ In the H₂SO₄ + (CH₃)₂NH + CH₃CHO reaction, the corresponding atmospheric lifetime of sulfuric acid was estimated mainly based on the concentrations of acetaldehyde and dimethylamine and the corresponding reaction rates as listed in Table S11.† In previous studies, acetaldehyde concentrations of 0.10 ppb–45.60 ppb were measured in some rural areas and in ambient air.^97–99 With [(CH₃)₂NH] = 3.2 × 10⁹ molecules per cm³ and [CH₃CHO] = 2.46 × 10⁹ and 1.12 × 10¹² molecules per cm³, respectively, the atmospheric lifetimes of H₂SO₄ were calculated to be about 3.52 × 10⁻¹ to 1.37 × 10⁷ and 7.74 × 10⁻⁴ to 3.01 × 10⁴ s at 200–298 K (see Tables S11 and S12†). The atmospheric lifetime of sulfuric acid was 3.52 × 10⁻¹ and 7.74 × 10⁻⁴ s at 200 K, when the concentration of dimethylamine was 3.2 × 10⁹ molecules per cm³ and the concentration of acetaldehyde was 2.46 × 10⁹ and 1.12 × 10¹² molecules per cm³, respectively. Therefore, the H₂SO₄ + (CH₃)₂NH + CH₃CHO reaction only makes a limited contribution to the sulfuric acid sinks in the atmosphere.

4. Conclusions

In this article, the reaction mechanisms and kinetics of the trimolecular reaction of sulfuric acid with acetaldehyde catalyzed by dimethylamine have been investigated using high-level quantum chemical methods and conventional transition state theory with Eckart tunneling. The calculated results show that dimethylamine has a strong catalytic effect in the H₂SO₄ + (CH₃)₂NH + CH₃CHO reaction responsible for the formation of organosulfates in the gas phase of the atmosphere, which was previously considered via heterogeneous processes. The calculated kinetic results reveal that the H₂SO₄ + (CH₃)₂NH + CH₃CHO reaction can be an important sink for acetaldehyde in the atmospheric gas-phase reactions below 240 K when the OH concentration is about 10⁴ molecules cm⁻³ and the H₂SO₄ concentration is about 1.0 × 10⁶ molecules per cm³. Moreover, the H₂SO₄ + (CH₃)₂NH + CH₃CHO reaction makes only a limited contribution to the sink for sulfuric acid. The present findings show that organosulfates can be formed via the reaction of CH₃CHO with sulfuric acid catalyzed by dimethylamine, which provides a new insight into the initial nucleation process for sulfuric acid, amines, and aldehydes.

Conflicts of interest

The authors declare no competing financial interests.

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China and (4211001056, 41775125 and 91961123), by Guizhou Provincial Science and Technology Projects, China (CXTD [2022]001), and by the Science and Technology Foundation of Guizhou Provincial Department of Education, China (No. KY [2021]014 and KY[2021]107).

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Footnote

† Electronic supplementary information (ESI) available: The T₁ diagnostic values for all the species as listed in Table S1; the calculated relative energies with zero-point vibrational correction of the dimer complexes as listed in Table S2; the calculated equilibrium constants and the concentration of the dimer complexes when the [(CH₃)₂NH] = 3.2 × 10⁹, [H₂SO₄] = 4 × 10⁸, [CH₃CHO] = 1.12 × 10¹² molecule per cm³ for the H₂SO₄ + (CH₃)₂NH + CH₃CHO in the temperature range of 200–298 K as listed in Table S3; the rate constants of the CH₃CHO + H₂SO₄ reaction as listed in Table S4; the rate ratio of each reaction as listed in Table S5; the rate ratio of the v₁/v_CH3CHO+OH at different OH concentrations in the temperature range of 200–298 K ([(CH₃)₂NH] = 3.2 × 10⁹, [H₂SO₄] = 10⁶, 10⁷, 4.0 × 10⁸ and 5.1 × 10⁹ molecule per cm³ respectively) as listed in Tables S6–S9; the rate ratio of the v₁/v_H2SO4+OH at different OH concentrations in the temperature range of 200–298 K([(CH₃)₂NH] = 3.2 × 10⁹, [CH₃CHO] = 1.12 × 10¹² molecule per cm³ respectively) as listed in Table S10; calculated atmospheric lifetime of H₂SO₄ ([(CH₃)₂NH] = 3.2 × 10⁹, [CH₃CHO] = 2.46 × 10⁹ and 1.12 × 10¹² molecule per cm³ respectively) as listed in Tables S11 and S12; molecular coordinates and molecular frequencies as listed in Table S13; Gibbs free energy reaction profile of CH₃CHO + H₂SO₄ + (CH₃)₂NH reaction at 298 K as listed in Fig. S1; relative energies with zero point correction for the CH₃CHO + H₂SO₄ reaction at 0 K as listed in Fig. S2; relative energies with zero point correction for CH₃CHO + H₂SO₄ + (CH₃)₂NH reaction as listed in Fig. S3; selected geometrical parameters as shown in Fig. S4; intrinsic reaction coordinate results of TS1A, TS1B, TS1C, TS1D, TS1E and TS1F as listed in Fig. S5–S10. See DOI: https://doi.org/10.1039/d2ea00159d

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