Introduction

Secondary organic aerosol (SOA) is a major contributor to global burden of fine particulate matter (more than 20% by mass)1,2,3, which have profound impacts on air quality, climate, and human health4,5,6,7,8. It is produced from photochemical oxidation of volatile organic compounds (VOCs), and this process yields oxygenated organic compounds (OOCs), some of which engage in aerosol growth, gas/particle partitioning, and aqueous-phase reactions9,10. On the other hand, OOCs emitted in quantities from biogenic and anthropogenic sources are also appreciable11,12,13,14,15. Some OOCs, such as aldehydes, ketones, and alcohols, have low volatility and high polarity and likely contribute to SOA formation by oligomerization in aqueous conditions16,17. Hence, the aqueous chemical behaviors of OOCs represent a dominant source of SOA in droplets, clouds, or aqueous aerosols18,19,20,21,22,23. High-molecular weight oligomer compounds, notably those proposed to contain alcohol linkages, have been proven as important components in the aqueous-phase reactions of OOCs and have been implicated as key players in aerosol formation and fine particle growth, cloud condensation nuclei, viscosity, and volatility in the atmosphere24,25,26. Owing to the incomplete knowledge of chemical composition and formation mechanisms of oligomers, however, the global SOA budget is consistently underpredicted in climate models, which is one of the largest uncertainties in the effects of SOA on climate and regional air quality27,28.

For typical OOCs, oligomer formation has been considered to involve addition, aldol condensation, and hemiacetal reactions, which are catalyzed under acidic conditions29,30,31,32. A cationic oligomerization mechanism was speculated for aqueous-phase reactions of dicarbonyls (i.e., glyoxal and methylglyoxal) by both experimental and theoretical studies, with carbenium ions as the key intermediates33,34. Poly-hydroxyl oligomers have been identified as the dominant particle-phase products, which provide reactive sites to form carbenium ions, leading to spontaneous oligomerization and rapid growth of aerosols35,36,37. Hence, this oligomerization presents a key mechanism for SOA formation of OOCs at urban, regional, and global scales. However, few works focus on oligomerization of dicarbonyl OOCs and neglect monocarbonyl OOCs (MOOCs) for SOA formation, which constitute a significant fraction of OOCs with wide variety and high abundance in urban areas38,39,40. Moreover, the oligomerization and polymerization reactions of MOOCs are of broad interest, including material science, biomedical, electronic, and biosynthesis fields as well as atmospheric chemistry in this work. For example, polymerization of aldehydes is an efficient method for producing sustainable and recyclable species, playing a key role in advancing green revolution in plastic engineering41,42.

Here, we elucidated the fundamental chemical mechanisms of octanal (OAL) and 2,4-hexadienal (HAL), as representative MOOCs, in sulfuric acid (H2SO4) aerosols, using theoretical calculations. First, we characterized the energetics of these newly discovered pathways using density functional theory (DFT) electronic structure calculations with dual-level direct dynamics. Second, a key intermediate was identified using reaction kinetics to unravel the nature of the aqueous-phase oligomerization mechanisms of MOOCs. Finally, we established a switchable mechanism of oligomerization, regulated by alcohols as initiators or terminators and discussed the implications of our results to explosive growth of particulate matter.

Results

Proton-mediated chain initiation reactions

In aerosol particle growth events, the hydration reactions of OOCs are believed as the initial steps contributing to SOA formation. Therefore, we first calculated two distinct hydration pathways in the H2SO4 aerosols, which proceed via (I) direct attack (RDHD) by water molecules and (II) indirect catalysis by H2O or H2SO4 (RIHD). In agreement with previous studies of OOCs33,37,43, the direct hydration of OAL (o-RDHD1) and HAL (h-RDHD1) possesses large energy barriers (ΔG‡, > 40 kcal mol−1) and small reaction energies (ΔGr), as shown in Supplementary Figs. 1 and 2. The potential energy surface (PES) along the reaction pathway illustrates that RIHD reactions of OAL and HAL to form diols (DLs) are also kinetically unfeasible, with ΔG‡ values of larger than 30 kcal mol−1 for o/h-RIHD1 catalyzed by H2O and of larger than 20 kcal mol−1 for o/h-RIHD2 catalyzed by HSO4−. Therefore, we explored the ionic hydration reactions of OAL and HAL (Fig. 1), which are found to be initiated by protonation (RH+) and hydroxide ion attack (ROH-). We did not identify any TS for the reaction pathways involved in ionic hydration reactions, and the optimized geometries of intermediates are depicted in Supplementary Fig. 3. As shown in Fig. 1, nucleophilic attack of OAL and HAL (o-ROH-1 and h-ROH-1) by OH− yields the anionic intermediates (AIs), corresponding to slightly exothermic and endothermic with the ΔGr values of −0.43 and 2.81 kcal mol−1, respectively. However, the initial protonation of OAL and HAL (o-RH+1 and h-RH+1) is strongly exothermic, leading to the formation of cationic intermediates (PCIs). The rate constants (k) are 1.62 × 109 and 1.72 × 109 M−1 s−1 for OH− attack on OAL and HAL, respectively, which are at least 2 times lower than those of H+ attack. It highlights that the attack of OAL and HAL by OH− are of minor importance compared with that by H+, specifically under the atmospheric acidic aerosol with the lower abundance of OH−.

Fig. 1: Chain initiation reactions leading to the formation of alcohol intermediates.
figure 1

a PESs of ODL and OML formation from OAL, along with the NPA charges of carbonyl C and O atoms in OAL. b PESs of HDL formation from HAL, along with NPA charges of carbonyl C and O atoms in HAL. The gray dashed lines suggest the nucleophilic attack of OH− to carbonyl C-atoms in OAL and HAL. Along the blue lines, DLs are formed from both OAL and HAL through protonation, hydration, and deprotonation. The gray lines represent the formation of OML from OAL with the participation of SO42− and HSO4− in deprotonation.

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As shown in Fig. 1, protonation occurs at carbonyl positions, which possess a prominent negative polarity to provide the characteristic site for protonation and to promote the electrostatic attraction to H+, since the electrostatic attraction between reactants plays a pivotal role in facilitating barrierless reactions within the realm of atmospheric aqueous chemistry33. Subsequently, the formation of DLs (ODL and HDL) from o- and h-PCI1 involves two hydration reactions and a loss of hydronium ion (H3O+) in two studied reaction systems, respectively, with the corresponding overall ΔGr values of −105.95 and −100.77 kcal mol−1 (Supplementary Tables 1 and 2). We found that for OAL reaction system, the alternative deprotonation of o-PCI1 (o-RH-abs1/2) occurs at α-position, which is initiated by HSO4− or SO42− (Supplementary Fig. 3), to yield a mono-hydroxyl alcohol (OML), with the ΔG‡ value of 16.70 or 9.41 kcal mol−1 (Fig. 1a). However, for HAL reaction system, deprotonation from h-PCI1 to form the mono-hydroxyl alcohol is hindered by steric hindrance in aerosol interior, attributable to the presence of C = C bond in α-position. Hence, the structural difference in OAL and HAL leads to the difference in main alcohol intermediates in H2SO4 aerosols.

To further elucidate the fate of OAL and HAL in chain initiation, the kinetic information involving k and branching ratio (Γ) is also evaluated (Fig. 2, Supplementary Tables 3 and 4). More than 70.0% of OAL or HAL undergo protonation to form CI, whose fate is governed by the competition between the subsequent deprotonation to form alcohol intermediates and the association with OH− back to OAL or HAL (Fig. 2). The k values were further estimated across the temperature range of 273–313 K (Supplementary Fig. 4), which show an increase in k values with rising temperature. For example, the k values of o-RH+1 and o-ROH-1 increase from 1.82 × 109 and 7.40 × 108 M−1 s−1 at 298 K to 5.73 × 109 and 2.33 × 109 M−1 s−1 at 313 K, respectively. Despite this, the Γ values of o/h-RH+1 remain above 70.0%, indicating that PCI formation is favorable across a wide range of atmospherically relevant conditions in the troposphere. The fate of PCIs is governed by the competition between the subsequent deprotonation to form alcohol intermediates and the association with OH− back to OAL or HAL (Fig. 2). Considering the branching ratios between reactions with H+ and with OH−, it is estimated that 49.0% of o-PCI1 undergoes deprotonation to yield alcohol intermediates (14.1% for OML and 34.9% for ODL), and 43.2% of h-PCI1 forms HDL to further propagate the chain growth. However, due to the low concentration of OH− in H2SO4 aerosols, we conclude that alcohol compounds represent the nearly exclusive intermediates in H2SO4 aerosols. Therefore, the following study focuses on the subsequent reactions of these alcohol compounds, i.e., DLs and MLs.

Fig. 2: Schematic representation of the competing pathways.
figure 2

a The preferred formation of ODL and OML via o-PCI1. The branching ratio of ODL formation is larger than that of OML. b The preferred formation of HDL via h-PCI1. Gray arrows represent reactions with OH−. The numbers denote the branching ratios of the essential pathways.

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Cation-mediated chain propagation of alcohol intermediates

The chain growth through direct reactions was firstly investigated and the constructed PESs are depicted in Supplementary Fig. 5. The addition and hemiacetal reactions of OAL and OML exhibit large energy barriers ( > 20.55 kcal mol−1) and small rate constants ( < 8.54 M−1 s−1), indicating their negligible contribution to chain growth (details in Supplementary Information). Natural population analysis (NPA) was performed to evaluate the characteristics of DLs and MLs (Supplementary Table 5), as is reflected by the negative polarity of hydroxyl groups, which represents a key character to combine with electrophilic reagents. Figure 3a presents the subsequent reactions of DLs and MLs, which are initiated by electrophilic species such as protons. Protonation of DLs and MLs is found to be barrierless and highly exothermic, leading to the formation of additional PCIs (o-PCI21, o-PCI22, and h-PCI21). Considering the large k values (~ 109 M−1 s−1) close to diffusion limitation, protonation processes of DLs exhibit the small half-lives ( < 10−3 s, Supplementary Fig. 6) across the typical tropospheric acidity range (details in Supplementary Information), which indicates efficient formation of PCIs to further oligomerization. These PCIs undergo a cationic rearrangement and subsequent dehydration, producing carbenium ions (CBs), which have been proven to be broadly produced from OOCs44,45. Subsequent dehydration to form Monomer-CBOML is inhibited due to a large ∆Gr value of 29.54 kcal mol−1 (Supplementary Table 6), suggesting that Monomer-CBOML is unstable and the majority of CBOML shifts reversibly to OML by equilibrium. Hence, Monomer-CBs are predominantly formed from diols (i.e., ODL and HDL) rather than mono-hydroxyl alcohol in OAL and HAL reaction systems.

Fig. 3: Dimerization and trimerization in OAL and HAL reaction systems.
figure 3

a PESs of dimer formation starting from ODL, OML and HDL (numbers marked with asterisk represent the energy barrier value). b PESs starting from dimers to CBs and subsequently to trimer formation in OAL and HAL reaction systems. Both dimerization and trimerization include two essential parts, i.e., CB formation and nucleophilic association of CBs with alcohol intermediates. The numbers above arrows denote the corresponding reaction energies (in kcal mol−1) for each reaction step. NPA charges of the carbenium site centers in CBs are also shown in the figure.

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Subsequently, formation of these three dimers is initiated by hydroxyl O-atoms via nucleophilic addition of Monomer-CBs by alcohol intermediates (such as ODL, HDL, and OML). Electrostatic attraction is more pronounced between Monomer-CBs and DLs (i.e., ODL and HDL) relative to Monomer-CBs and OML due to more negative charged hydroxyl O-atoms of ODL and HDL (Fig. 3a). For example, the reaction of Monomer-CBODL with ODL possesses a smaller ΔGr value of 7.17 kcal mol−1 relative to with OML (11.26 kcal mol−1), since more negative NPA charge on O-atom of ODL (−0.81 e) corresponds to a stronger polarity of ODL (Fig. 3a). In addition, carbon atom of C = C bond in OML also exhibits negative NPA charge of −0.31 e, indicating its attack to CB site of Monomer-CBODL. This acid-catalyzed aldol condensation exhibits an ΔG‡ of 10.18 kcal mol−1, with the k value of 6.37 × 108 M−1 s−1. A k value more than two times smaller than that of hydroxyl attack suggests the negligible contribution of acid-catalyzed aldol condensation to chain growth. In summary, dimerization of OAL and HAL includes nucleophilic addition, hydration, and deprotonation reactions, occur without energy barriers and are increased by ion-dipole interaction, to form two dimers in OAL reaction system and one dimer in HAL reaction system (Supplementary Tables 6 and 7). Geometrical structures listed in Fig. 3 reveal that there exist two hydroxyl groups in DimerDL (i.e., 2OH-DimerODL/HDL), originated from Monomer-CBDL (i.e., Monomer-CBODL/HDL), while one hydroxyl group is observed in 1OH-DimerOML, contributed from Monomer-CBODL. It indicates that the formation of di-hydroxyl dimers and mono-hydroxyl dimers are controlled by the number of hydroxyl groups in alcohol intermediates.

Three dimers then repeat protonation reactions at hydroxyl groups and dehydration to form Dimer-CBs, which subsequently engage in associated reactions with alcohol intermediates (DLs or MLs) to yield three trimers in OAL reaction system and one trimer in HAL reaction system (Fig. 3b). Notably, there is a zero-hydroxyl trimer (i.e., 0OH-TrimerOML2) among these trimers, which does not proceed further tetramerization due to the lack of reactive sites of protonation, exhibiting the dead characteristics to oligomerization. Similarly, a dead tetramer (0OH-TetramerODL+OML2) is also formed, attributable to the successive engagement of ML in oligomerization (Fig. 4 and Supplementary Table 8). However, for living trimers and tetramers with mono- or di-hydroxyl groups, the subsequent oligomerization is not governed by ML, but the sites for protonation are provided by their hydroxyl groups. As summaries in Figs. 3 and 4, dimerization, trimerization, and tetramerization involve two essential steps, (i) protonation and dehydration to CBs and (ii) formation of oligomers by the reactions of CBs with alcohol intermediates. However, a major distinction between OAL and HAL reaction systems lies in the tetramerization, which is blocked by dead 0OH-TrimerOML2 in OAL reaction system but efficiently proceeded by living 2OH-TrimerHDL2 in HAL reaction system. This disparity is mainly attributed to the structural difference in alcohol intermediates between OAL and HAL reaction systems, leading to the formation of dead trimers that cannot further engage in tetramerization in OAL reaction system but all living trimers successively yielded in HAL reaction system. That is, mono-hydroxyl alcohol plays a predominant role in driving the formation of dead oligomers, but di-hydroxyl alcohol regulates the formation of living oligomers, implying that MOOCs leading to SOA formation is likely governed by mono- or di-hydroxyl alcohol intermediates.

Fig. 4: Formation and propagation of oligomers.
figure 4

a The OAL oligomerization mechanism to tetramers and pentamers includes CB formation and nucleophilic association, with both dead and living oligomers formed. b The tetramerization and pentamerization of HAL include CB formation and nucleophilic association, with all resulting oligomers exhibiting living characters. Dead and living oligomers are marked in pinkish-red and light blue regions, respectively. The numbers above arrows denote the corresponding reaction energies (in unit of kcal mol−1) for each reaction step.

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Oligomerization mechanisms

To further evaluate the generality of the mechanism of MOOC oligomerization to polymerization, pentamer formation was also investigated in OAL and HAL reaction systems as provided in Supplementary Information. Combing the results of oligomerization, a major distinction is found between dimerization and trimerization/tetramerization, which lies in whether dead oligomers are produced to block oligomerization. Therefore, pentamers are yielded via protonation, hydration, and deprotonation reactions of living tetramers but are prevented by dead tetramers. In H2SO4 aerosol, dead oligomers are continuously formed and accumulated in OAL reaction system, but if terminating the exposure to H2SO4, they undergo hydrolysis, dehydration, and deprotonation reactions back to OAL, thereby leading to a reversible uptake of OAL. However, an irreversible uptake of HAL imputes to two aspects: one is that the enhanced basicity of HAL by the conjugated structure facilitates the subsequent proton-mediated chain initiation reactions46,47, and another is that living oligomers (such as dimers, trimers, and tetramers) provide the abundant precursors for subsequent chain propagation.

To quantify the impact of hydroxyl group numbers on the oligomerization of MOOCs, we defined a term of n(-OH) in living oligomers, which refers to the number of hydroxyl groups in oligomers. A following regular pattern is deduced (Fig. 5): if the n(-OH) equals 1, oligomerization of MOOCs occurs with di-hydroxyl alcohol as initiator and terminates with mono-hydroxyl alcohol as terminator; but if the n(-OH) is more than 1, the propagation of next generation-oligomers is not governed by alcohol intermediates until the mono-hydroxyl oligomers [n(-OH)= 1] are yielded. That is, alcohols with one hydroxyl group act as terminators since no additional hydroxyl groups engage in the further oligomerization, while alcohols with multiple hydroxyl groups serve as initiators because they provide the additional hydroxyl groups as active sites to attack CBs. This switchable mechanism is also suitable to explain the oligomerization of other OOCs. For example, rapid oligomerization of dicarbonyl compounds, such as glyoxal and methylglyoxal, which are ubiquitous in the atmosphere48 and are significant precursors for SOA formation49,50. Satisfying the characteristics of n(-OH) > 1, dicarbonyl oligomerization proceeds efficiently and rapidly to propagate oligomers, and abundant di- and poly-hydroxyl alcohols are formed as initiators. Then the regular pattern also provides an insight that dicarbonyl oligomerization will be inhibited by ubiquitous mono-hydroxyl alcohols as terminators, leading to the formation of dead oligomers with the characteristics of n(-OH) < 1. Further studies are needed to determine whether the proposed mechanisms are applicable to a broader range of VOCs beyond carbonyl compounds and influence aging processes. Hence, switchable oligomerization mechanism of MOOCs involving di- and poly-hydroxyl alcohols represents a key pathway for SOA formation. To illustrate the key factor of alcohol in oligomerization in realistic atmosphere, a reaction rate [r(Alcohol)] function is established to estimate the influence of H2SO4 concentration ([H2SO4]) on the formation of alcohol intermediates (i.e., DLs and MLs). And the reaction rate [r(Alcohol)] function is defined to describe how the speeds of DL and ML formation vary as a function of the H2SO4 concentration from 5 × 10−8 to 5 × 10−3 M, corresponding to the available aerosol pH values in the atmosphere, and an ideal H2SO4 aerosol environment is assumed where acidity is solely supported by full dissociation of sulfate acid and the concentration of OAL/HAL is constant (Supplementary Fig. 7). As discussed in Supplementary Information, the speeds of DL and ML formation in OAL reaction system are equal when [H2SO4] is 137 M, which represents an unrealistic pH in H2SO4 aerosol. Hence, in the atmosphere, oligomerization of OAL cannot be terminated by MLs produced through its own reaction system. However, considering highly abundant mono-hydroxyl compounds in urban atmospheric environment, oligomerization of MOOCs can be terminated by other mono-hydroxyl alcohols but be initiated by other poly-hydroxyl alcohols. Considering that massive alcohols are originated from primary and secondary emissions51, switchable oligomerization governed by alcohols may be more applicable to explain whether explosive growth of PM2.5 is occurred in urban atmospheric environment.

Fig. 5: Alcohol-governed oligomerization of MOOCs.
figure 5

If the number of hydroxyl groups [n(-OH)] in oligomers is ≤ 1, dead oligomers are yielded, or oligomerization is terminated by mono-hydroxyl alcohols (pinkish-red regions); but if the n(-OH) > 1, oligomers propagate, and the processes are not governed by alcohols (light blue regions).

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Discussion

In this work, we explored and established a switchable oligomerization mechanism of typical atmospheric MOOC, which is governed by a key species of alcohols. This mechanism involves three essential reaction steps, (i) protonation, hydration, and deprotonation to yield the major alcohol intermediates, i.e., mono- and di-hydroxyl alcohols, (ii) protonation and dehydration of these alcohol intermediates to form CBs, and (iii) formation and propagation of oligomers by association reactions of CBs with alcohol intermediates. Using the calculated rate constants, the aerosol growth rates (AGR) by OAL and HAL oligomerization were estimated, and the AGR calculation in detail is listed in Supplementary Information. Assuming 0.1 ppb concentrations of OAL/HAL, and particle concentration, particle density, and hygroscopic growth factor are assumed as 100 μg m−3, 1.6 g cm−3 and 1.4, respectively. The AGR value of HAL in the weakly acidic aerosol (pH = 6) is estimated to be 1.55 μg m−3 h−1, which is larger than that of OAL. It is explained by the unlimited chain growth of HAL due to the living characteristics of the formed oligomers, in line with the experimentally observed irreversible uptake46,47.

The main atmospheric implication of the oligomerization is that in step (iii), the dead oligomers will be produced if mono-hydroxyl alcohols engage in association reactions, terminating SOA formation, while if di-hydroxyl alcohols are involved in, association reactions form living oligomers, which subsequently repeat the steps of (ii) and (iii) to propagate the oligomers. Therefore, infinite formation of SOA from aqueous-phase reactions of MOOCs is determined by alcohols with the characteristic of the number of hydroxyl groups more than 1. This newly discovered switchable oligomerization mechanism revealed by our results helps explain particulate matter explosive growth in China, where alcohols are abundant and ubiquitous in urban atmospheric environment. Moreover, the aging processes of VOCs involve oxidation, multiphase, and aqueous reactions; therefore, the proposed alcohol-governed oligomerization could influence these processes. Further studies are needed to determine the extent of the proposed mechanism’s impact on VOC aging.

Methods

Electronic structure optimization

All the geometrical optimization and energy calculations were carried out with Gaussian 09 package suite52. The solvent effect was simulated by the solvation model based on density (SMD)53, which has been widely adopted in numerous studies for its good performance in simulating the solvent effects54,55,56,57, particularly its ability to accurately describe both charged and uncharged species involved in this study. Geometrical structures of stationary points, including reactants, complexes, products and transition states (TSs), were optimized using the hybrid density functional M06-2X method58,59 with the 6-311 G(d,p) basis set60, i.e., the M06-2X/6-311 G(d,p) level. Frequencies and thermodynamic contribution were calculated at the same level as that for geometry optimization to check all stationary points either a TS (with only one imaginary frequency) or the minima (without any imaginary frequencies). For comparison, some structural parameters were verified by experimental results and other methods. The calculated infrared spectra agree well with experimental results (Supplementary Fig. 8). Furthermore, the geometric parameters were also optimized by using other density functional methods (B3LYP and MPWB1K) and the classic ab initio MP2 method (Supplementary Fig. 9) show that the data obtained by four levels, including bond length and bond angles, are consistent with each other, with the maximum errors less than 1.50% (Supplementary Table 9). These comparison results indicate that the M06-2X method accurately describes the low-level parameters such as geometries and frequencies in the reaction systems. The structural parameters of all possible reaction pathways are summarized in Supplementary Data S1 and S2. For the barrier process, the minimum energy pathway was constructed by using intrinsic reaction coordinate, to confirm the reliable connection between TS and the corresponding reactants and products; the barrierless process was confirmed by scanning the pointwise potential curve61, in which all geometric parameters were fully optimized except for fixing the internal breaking or forming bond length (Supplementary Fig. 10).

Computation of energies and rate constants

Energetic calculation was performed at the M06-2X/6-311++G(3df,3pd) level62 to yield more accurate potential energy surfaces (PESs) based on the above geometrical optimization. To justify the performance of M06-2X method for describing PESs, the single point energies (SPEs) were evaluated by higher level and more expensive calculations, ab initio CCSD(T) method. As discussed in Supplementary Information, the mean absolute error in energy between the M06-2X and CCSD(T) methods is 1.68 kcal mol−1 for the evaluated pathways, indicating that the M06-2X method offers reliable energy descriptions and more importantly, represents a compromise between the computational efficiency and accuracy. To justify the performance of M06-2X method and the adopted basis sets for describing PESs, the single point energies (SPEs) were evaluated by higher level and more expensive calculations, ab initio CCSD(T) method, and the other basis sets including def2-TZVP, def2-TZVPP, pcSseg-2 were explored (Supplementary Figure 11). As discussed in Supplementary Information, the mean absolute error in energy between the M06-2X and CCSD(T) methods is 1.68 kcal mol−1 for the evaluated pathways, and the uncertainties of these basis sets in describing SPEs are small and the same mechanistic conclusions can be obtained. It indicates that the M06-2X method with the 6-311++G(3df,3pd) basis set offers a reliable energy description and more importantly, represents a compromise between the computational efficiency and accuracy. In PES construction, the energy barrier (ΔG‡) and reaction energy (ΔGr) are defined as ΔG‡ = GTS − GR, and ΔGr = GP − GR, respectively, where GR, GTS, and GP represent the free energies of reactants, TSs, and products.

For the reaction pathways with well-defined TSs, the rate constants were calculated by using conventional transition-state theory63 based on the above PES information. The solvent cage effect and free volume theory were considered to simulate the real aqueous environment. For barrierless reaction pathways, the rate constants are estimated using the diffusion-limited rates. Electrostatic potential (ESP) and natural bond orbital (NBO) methods were applied for characteristic analysis and of reactive site prediction of main species. More detailed calculation for kinetics, ESP and NBO analysis is shown in Supplementary Information.