Volatile organic compounds (VOCs) from biogenic and anthropogenic sources are of particular importance due to their chemical reactivity and high abundance in the atmosphere (Piccot, 1992; Acosta Navarro et al., 2014). Gas-phase reactions of VOCs associated with photochemical oxidant cycles generally produce secondary organic aerosol (SOA) particle mass and increase tropospheric ozone concentration (Lim et al., 2005; Ziemann and Atkinson, 2012; S. Wang et al., 2020; Y. Wang et al., 2020; Ge et al., 2021; Ma et al., 2021). Hence, the emission of VOCs is a key process in controlling the formation and growth of new particles over continental regions. Oxidation of biogenic terpenes from terrestrial vegetation and aromatics from human activities generates a large number of organic carbonyls, which are major precursors of SOA (Altieri et al., 2006; Volkamer et al., 2001; Gomez Alvarez et al., 2007; Sareen et al., 2016; Yang et al., 2020). These organic carbonyls engage in a variety of reactions, including new particle formation, condensation / equilibrium partitioning, particle- and aqueous-phase reactions, leading to the formation of additional products in the particle phase (Loeffler et al., 2006; Kroll et al., 2005; Nozière et al., 2009; Marrero-Ortiz et al., 2019; Tuguldurova et al., 2019; Kua et al., 2011; Li et al., 2020; Shi et al., 2019; Xia et al., 2021).

Glyoxal (GL), an important and simple carbonyl compound, originates from the gas-phase oxidation of biogenic isoprene and anthropogenic aromatics (Volkamer et al., 2001; Gomez Alvarez et al., 2007; Lim et al., 2005). The global source of GL is estimated to be 45–56 Tg yr-1 (Fu et al., 2008; Myriokefalitakis et al., 2008), with a predicted contribution of 2.6 Tg C yr-1 to global SOA mass (Fu et al., 2008). GL and methylglyoxal contribute to 16 % of SOA mass during a severe haze episode in Hebei Province, China (J. Li et al., 2021). In Mexico City, GL contributes at least 15 % of SOA mass (Volkamer et al., 2007), and in the Pearl River Delta, China, 21 % of SOA formation originates from the heterogeneous reactions of GL and methylglyoxal (Ling et al., 2020). Hence, GL is a primary contributor to the rapid and efficient formation of SOA under urban environments. The aqueous-phase reaction of GL starts with hydration, subsequently forming several high-molecular-weight oligomers, such as dimers, trimers, tetramers, and pentamers (Hastings et al., 2005; Loeffler et al., 2006; Gomez et al., 2015; Kua et al., 2008; Avzianova and Brooks, 2013). Previous theoretical studies have suggested that the direct hydration of GL is thermodynamically and kinetically unfeasible (Shi et al., 2020; Ji et al., 2020). The rapid growth of SOA was observed in sulfuric acid nanoparticles (Jang et al., 2002; Huang et al., 2016; Surratt et al., 2007; Liggio et al., 2005b), while several other studies have revealed little effect of acids (such as sulfuric acid) on the formation of GL oligomers (Loeffler et al., 2006; Kroll et al., 2005). Hence, the aqueous-phase chemical reaction mechanism of GL and its role in SOA formation are still unclear.

On the other hand, brown carbon (BrC) is also generated by the aqueous-phase reaction of GL in the presence of amines or ammonium in the troposphere (Y. Li et al., 2021; Shapiro et al., 2009; Galloway et al., 2009; Lee et al., 2013; Maxut et al., 2015; Marrero-Ortiz et al., 2019; Tuguldurova et al., 2019; Kua et al., 2011). Zhang and co-workers have revealed a slight browning of glyoxal-amine mixtures (Marrero-Ortiz et al., 2019; Y. Li et al., 2021). They have also identified oligomers and N-heterocycles in NH4HSO4 and (NH4)2SO4, whereas only oligomers were detected in NaCl (Y. Li et al., 2021). Shapiro et al. have detected light-absorbing products, slowly formed from GL in a mildly acidic salt solution of (NH4)2SO4, using ultraviolet–visible (UV-vis) spectrophotometry, and matrix-assisted laser desorption ionization mass spectrometry (Shapiro et al., 2009). A chamber study of GL uptake to (NH4)2SO4 solution was performed using a high-resolution time-of-flight aerosol mass spectrometer and found that carbon–nitrogen (C-N) compounds are irreversibly produced in the solution (Galloway et al., 2009). However, De Haan et al. (2020) have described a rapid but reversible BrC formation in (NH4)2SO4 droplets in dry condition (RH <5 %) using cavity-attenuated phase shift single-scattering albedo spectrometry (De Haan et al., 2020). In addition, Powelson et al. (2014) found that the reaction of GL with methylamine is more effective than that with (NH4)2SO4 by using UV-vis and fluorescence spectroscopy (Powelson et al., 2014), while Lian et al. (2020) have proven that the synergistic effect of ammonium and amines contributes to the formation of imidazole in cloud processing (Lian et al., 2020). Most previous studies have shown that imidazole and high-molecular-weight light-absorbing C-N compounds are produced by different atmospheric chemical reactions of GL with amines / ammonium, but the reaction mechanism is yet to be clarified.

In this work, the aqueous-phase chemistry of GL in the absence and presence of methylamine / ammonia (MA / AM) was systematically investigated using quantum chemical calculations. The fundamental chemical mechanisms of the formation of oligomers and N-heterocycles were investigated. The chemical composition and the product distribution were also estimated and characterized by conventional transition state theory considering solvent cage and diffusion-limited effects (Methods). The aerosol growth rate for the heterogeneous chemistry of GL was also evaluated under different atmospheric conditions. We paid special attention to the key factors in the formation of SOA and BrC from GL to provide insight into the important role of the aqueous-phase chemistry of GL.

All quantum chemical calculations were performed by means of the Gaussian 09 program (Frisch et al., 2009). The solvent effect of water in the aqueous phase was considered with a continuum solvation model (SMD) (Marenich et al., 2009). The solvation free energy includes two components: the bulk electrostatic contribution and the cavity-dispersion-solvent-structure contribution arising from short-range interactions between the solute and solvent molecules. Geometry optimization of all stationary points (SPs), such as reactants, transition states (TSs), intermediates, and products, was calculated using the M06-2X functional (Zhao and Truhlar, 2008) with the 6-311G(d,p) basis set (Ji et al., 2017, 2020), i.e., the M06-2X/6-311G(d,p) level, which has shown good performance in describing the geometrical optimization of the heterogeneous reactions of small α-dicarbonyls (Ji et al., 2020; Shi et al., 2020). Thermodynamic contributions and harmonic vibrational frequencies were calculated at the same level as that for geometry optimization to identify all SPs as either a TS (exactly with only one imaginary frequency) or the minima (zero imaginary frequency). Intrinsic reaction coordinate (IRC) calculations were implemented to construct the minimum energy pathway (MEP), verifying that each TS accurately connected the corresponding reactants and products. At the same level, TS was searched by examining the SP using the TS keyword in geometry optimization, while the absence of a TS was confirmed if no energy exceeded the bond dissociation energy along the reaction coordinate (Ji et al., 2020). The TSs for four deprotonation pathways in GL + MA / AM reaction systems were identified at the M06-2X/6-311G(d) level because none of them was searched at the M06-2X/6-311G(d,p) level (detailed discussion in the Supplement). Pointwise potential curve (PPC) scanning was performed to further confirm a barrierless process at the M06-2X/6-311G(d,p) level (Hazra and Sinha, 2011). For this method, all other geometric parameters were fully optimized, except for fixing the internal breaking or forming bond length (detailed in the Supplement).

Based on the aforementioned optimized structures, single-point energy (SPE) calculation was performed to refine potential energy surface (PES) with a more flexible basis set 6-311 + G(3df,3pd), i.e., at the M06-2X/6-311 + G(3df,3pd) level. For simplicity, hereinafter they are denoted as the X//Y, i.e., M06-2X//M06-2X level, where Y is an SPE calculation at the M06-2X/6-311 + G(3df,3pd) level and X is the geometry optimized at the M06-2X/6-311G(d,p) level. To further evaluate the results at the M06-2X//M06-2X level, a higher-level calculation using the CCSD(T) method with the flexible 6-311 + G(2df,2p) basis set was performed to refine the PESs. The CCSD(T) method (Lutnaes et al., 2009; Raghavachari and Trucks, 1989), i.e., coupled cluster approach with single and double substitutions including a perturbative estimation of connected triple substitutions, corresponds to a higher electronic correlation method. As discussed in the Supplement, the M06-2X//M06-2X level is suitable for predicting energies and kinetics, and also represents a compromise between computational efficiency and accuracy.

The rate constants (k) of the pathways with TSs were calculated using the conventional transition state theory (TST) (Gao et al., 2014; Galano and Alvarez-Idaboy, 2009) based on the above PES information: 1k=σkBThexp-ΔG‡RT, where h and kB are the Planck and Boltzmann constants, respectively, ΔG‡ represents the activation barrier energy with the thermodynamic contribution corrections and solvent cage effects, and σ is the reaction path degeneracy. To simulate realistic conditions in the solution, the rate constants are refined by using solvent cage effects (Okuno, 1997) and diffusion-limited effects (Collins and Kimball, 1949). For some of the reactions with low free-energy barriers, the rate constants are found to be close to the diffusion limit, which is calculated using the Collins–Kimball theory (Gao et al., 2014). The k values of the pathways without TSs are controlled by the diffusion-limit effect and thereby are equal to the diffusion-limited rate constants: 2kD=4πRDABNA, where R is the reaction distance, NA denotes the Avogadro number, and DAB represents the mutual diffusion coefficient of reactants. The branching ratio (Γ) was determined by the following equation: 3Γ=kktotal, where the k corresponds to the rate constant of each pathway, and the ktotal is the sum of the k value for each parallel pathway. A detailed description of the kinetics is provided in the Supplement.

This study provides valuable insight into the aqueous chemistry of GL and also reveals the rate-limiting steps in the absence and presence of MA / AM. In the absence of MA / AM (Fig. 5), the cation-mediated oligomerization is characterized by barrierless pathways and strong electrostatic attraction as follows: (I) protonation, hydration, and deprotonation of GL to yield DL and TL, (II) protonation and dehydration to yield CBs, and (III) the formation of dimers from the association reactions of CBs with DL and TL. Each dimer repeats steps (II) and (III) to propagate the oligomerization. In the presence of MA / AM, step (III) starts from nucleophilic addition of CBs with MA / AM rather than with DL / TL due to the stronger electrostatic attraction between CBs and MA / AM (Fig. 2). However, the key mechanistic step in the propagation of N-heterocycles is deprotonation of N-containing cationic intermediates. Our results of two distinct mechanisms indicate that BrC formation is more dependent on the aerosol content of inorganic compounds or inorganic salts rather than particle acidity, compared with the formation of SOA.

On the other hand, there exist the competing pathways with the initial protonation pathway for the cationic oligomerization of GL without and with MA / AM, (i.e., the association reactions of CIs with OH-). These competing pathways lead to CIs returning the corresponding reactants and affect the fate of GL. Figure S20 and Table S1 present the ΔGr and k values of the association reactions for some key CIs with OH-. Generally, the fate of CIs at each step is dominantly determined by the initial protonation rather than the reaction with OH-. For example, the ΔGr value of the association pathway of CI11 with OH- is -66.8 kcal mol-1, and its k value is 1.47 × 109 M-1 s-1. Compared with the protonation of GL to CI11, this reaction is thermodynamically and kinetically unfavorable. The branching ratios show that 70 % of GL proceeds via the protonation pathway to finally form DL. Because protonation is favorable in the acidic aerosol, the cation-mediated oligomerization of GL without and with MA / AM can efficiently proceed to contribute to SOA and BrC under the atmospheric conditions.

Using our predicted heterogeneous GL reaction rates, the aqueous heterogeneous lifetime (τ) of GL is estimated to be 3.60 min under the urban conditions, somewhat shorter than that of experimental data (5.0 min) (Liggio et al., 2005a). However, the τ values are 89 and 61 min under rural and remote conditions due to low GL levels, respectively (Liggio et al., 2005a). It indicates a more important role of the aqueous heterogeneous reaction of GL in urban air quality relative to other conditions. On the other hand, the τ values determined here for rural, remote, and urban conditions are all lower than those of the photolysis (211 min) and photooxidation of GL (Liggio et al., 2005a). Especially, the τ value under the urban condition is significantly shorter than the total gas-phase loss (125 min) (Liggio et al., 2005a). The results indicate that even under relatively clean conditions, the heterogeneous GL loss rates are faster than the loss rates due to other gas-phase processes and are significantly rapid in polluted regions. Given that GL contributes to 6.9 % of the total radical production at midday (Aiello, 2003), the heterogeneous GL loss to particles implies the reduction of HOx and demands further study. Our work reveals the fundamental chemical mechanism of SOA and BrC formation from small α-dicarbonyls and also provides the kinetic and mechanistic data for atmospheric modeling to assess the budget of SOA and BrC formation on urban, regional, and global scales.