The heterogeneous reaction mechanisms at the air–water interface were investigated using BOMD simulations, with enhanced sampling achieved via well-tempered metadynamics (MetaD). All simulations were performed using the CP2K 2023 software interfaced with the PLUMED 2.9.0 plugin (Bussi and Tribello, 2019; Kühne et al., 2020). The calculations of electronic structure were carried out by the QUICKSTEP module, with the Gaussian and plane wave (GPW) method and the Becke–Lee–Yang–Parr (BLYP) exchange-correlation functional (Perdew and Wang, 1992), which was supplemented with Grimme's D3 dispersion correction (Grimme et al., 2010). The DZVP-MOLOPT-SR-GTH Gaussian basis set and Goedecker–Teter–Hutter (GTH) pseudopotentials were employed to describe the valence and core electrons, respectively (Goedecker et al., 1996; Hartwigsen, 1998). The cutoff energy for the Gaussian basis set was set to 40 Ry, while that for the plane-wave basis set was 280 Ry. The NVT ensemble was employed, with a time step of 1.0 fs. The Nosé–Hoover thermostat (Evans and Holian, 1985) was adopted to control a constant temperature of 300 K. The simulated cell (15 Å × 15 Å × 45 Å) contained 128 water molecules, with the air–water interface defined by a vacuum region (∼ 30 Å) above the water slab (∼ 15 Å) along the z direction (Fig. S1 in the Supplement). The water slab was equilibrated for 10 ps using BOMD simulations, and the temperature and potential energy profiles confirmed the achievement of statistical equilibrium (Fig. S2). The details of the collective variable (CV) are provided in the Supplement.

To gain further insights into the interfacial reaction mechanisms, the wave function analysis of key structures was performed using the Multiwfn 3.8 program (Lu and Chen, 2012), while the results were visualized by VMD 1.9.3 (Humphrey et al., 1996). Specifically, the Mayer bond order (MBO) was calculated to quantify the strength of covalent bonds within the reactant molecules (Mayer, 1983). Interaction Region Indicator (IRI) analysis was carried out to examine the strength of localized interactions in prereactants and intermolecular noncovalent interactions within interfacial products, such as hydrogen bonds (HBs). The electron localization function (ELF) was applied to probe covalently bonded regions with high ELF values, indicative of strong electron localization.

To elucidate the heterogeneous formation pathways of nitrosamines, the reactions of MA and DMA with N₂O₄ were investigated at the air–water interface using BOMD simulations. Based on the previous studies of interfacial N₂O₄ chemistry, N₂O₄ exists as the symmetric dimer O₂N–NO₂, which can isomerize to the asymmetric form t-ONONO₂ (Finlayson-Pitts et al., 2003; Martins-Costa et al., 2019, 2020). Thus, t-ONONO₂ was used as the reactant to explore the heterogeneous N-nitrosation mechanisms of reactions between N₂O₄ and amines. In a three-component system consisting of t-ONONO₂, the amines (MA/DMA), and interfacial water, any two species can collide and react at the air–water interface. Three collision modes between MA/DMA and t-ONONO₂ on aqueous nanodroplet surfaces were examined (Scheme 1). Mode (i) corresponds to gaseous MA/DMA approaching t-ONONO₂ pre-adsorbed on the aqueous droplet surface. Mode (ii) describes a gaseous MA/DMA–t-ONONO₂ complex colliding with the aqueous interface. Mode (iii) involves gaseous t-ONONO₂ approaching MA/DMA pre-adsorbed on the aqueous surface.

Figure 1 corresponds to mode (i) in Scheme 1. Initially, t-ONONO₂ was placed at the air–water interface and equilibrated for 15 ps. Analyses of temperature and potential energy confirmed that statistical equilibrium was reached at 11.5 ps (Fig. S3). This equilibrated structure was used as the initial configuration. Notably, t-ONONO₂ underwent spontaneous heterolysis to form a stable (NO3-)(NO⁺) ion pair at the interface by 11.5 ps, which is consistent with previous interfacial simulations by Martins-Costa et al. (2020). For the MA-involved reaction (Fig. 1a), MA was initially in the gas phase at t = 0 ps with negligible interactions with the aqueous surface. It rapidly approached the interfacial NO⁺ ion, and by 0.99 ps, the N2 atom of MA and N1 atom of NO⁺ formed a N1–N2 bond, yielding the cationic nitrosamine c-CH₃NH₂NO⁺. To further understand the N-nitrosation of t-ONONO₂ with MA, electron localization function (ELF) analysis was performed for key structures. As shown in Fig. 1b, strong electron localization within the newly formed N1–N2 bond confirms the formation of the nitrosamine and nitrate ions. Extended BOMD simulations up to 21 ps verified that the products c-CH₃NH₂NO⁺ and NO3- remained stable at the air–water interface (Fig. 1c). Identical reactions from different initial conformations further support the robustness of this pathway (Fig. S4).

As shown in Fig. 1d, the DMA-mediated formation of (CH₃)₂NHNO⁺ follows the same mechanism as that of MA. In both MA and DMA systems, nitrosamine cations form within ∼1 ps and remain stable at the interface throughout the simulations. Moreover, mode (ii) (Scheme 1) was also verified to be reactive. As shown in Fig. S5, the gaseous MA/DMA–t-ONONO₂ complex undergoes rapid N-nitrosation upon contacting the air–water interface, forming nitrosamine cations within 0.85 ps (MA) and 0.33 ps (DMA). These products also remain stable at the interface. Notably, mode (iii) did not yield direct N-nitrosation in any simulation. After equilibration, the N atom of MA/DMA formed hydrogen bonds with interfacial water, blocking the nucleophilic nitrogen site and inhibiting N-nitrosation. Interestingly, although mode (iii) does not produce nitrosamines directly, it efficiently promotes amine-mediated hydrolysis of t-ONONO₂ to generate HONO, protonated amine, and NO3-. Since HONO is also a key nitrosamine precursor, this pathway is explored in detail in a following section.

We further explored the role of amines in the heterogeneous hydrolysis of t-ONONO₂. Three collision modes at the air–water interface of aqueous aerosols were investigated (Scheme 2): (i) gaseous t-ONONO₂ colliding with pre-adsorbed MA/DMA; (ii) gaseous MA/DMA approaching pre-adsorbed t-ONONO₂; (iii) gaseous MA/DMA–t-ONONO₂ complex adsorbing onto the water surface.

Key structures and bond-length evolutions for MA- and DMA-mediated hydrolysis corresponding to mode (i) are presented in Fig. 2a–d. MA was initially positioned above the water slab and equilibrated for 10 ps. Temperature and potential energy profiles confirmed equilibrium within 10 ps (Fig. S6). At equilibrium, the N atom of MA formed a hydrogen bond (HB) with interfacial water. As shown in Fig. 2a, gaseous t-ONONO₂ does not interact with interfacial water (t = 0 ps). As the simulation proceeds, t-ONONO₂ approaches the interface and rapidly dissociates into an (NO3-)(NO⁺) ion pair, consistent with previous reports (Martins-Costa et al., 2020) showing that this ion pair forms on the femtosecond scale and remains stable for ∼ 100 ps at the air–water interface. Mayer bond order (MBO) and Interaction Region Indicator (IRI) analyses (Figs. S7, S8) revealed that the N2–O3 bond was the weakest, supporting this dissociation pathway. A pre-reactive complex formed at 7.54 ps, in which interfacial water bridged the (NO3-)(NO⁺) ion pair and MA via H1–O2⋅⋅⋅N1 and O2–H1⋅⋅⋅N2 hydrogen bonds (Fig. 2b). Subsequently, proton H1 transfers from H₂O to MA at 8.40 ps. The resulting OH⁻ then attacked the N1 atom of the NO⁺ ion, forming a new covalent N1–O2 bond and generating HONO by 8.48 ps. The final products are HONO, NO3-, and MAH⁺.

Similar to MA, DMA also initially formed a hydrogen bond with interfacial water (Fig. S9) and mediated t-ONONO₂ hydrolysis via an identical mechanism but on a shorter timescale (2.88 ps), ultimately yielding HONO, NO3-, and DMAH⁺ (Fig. 2c, d). The faster kinetics can be attributed to the stronger basicity of DMA relative to MA, which promotes more efficient proton transfer and accelerates bond cleavage in t-ONONO₂. Furthermore, ELF analysis of the final structures (Fig. 2e, f) confirms clear electron localization in the N1–O2 and N2–H1 covalent bonds, as well as fully separated HONO, MAH⁺, DMAH⁺, and NO3-. These results demonstrate that t-ONONO₂ undergoes “single-water” hydrolysis at the aqueous interface, with only one water molecule directly participating.

For mode (ii) (Scheme 2), gaseous MA/DMA approaches pre-adsorbed t-ONONO₂. Key structures and bond-length evolutions are shown in Figs. 3 and S10. For the MA-involved reactions (Figs. 3a and S10a), MA initially resides in the gas phase without notable interactions with the interfacial water. By 16.27 ps, MA forms an O4–H2⋅⋅⋅N2 HB with H₂O. Concurrently, interfacial water connects NO⁺ ion and MA via a two-water bridge (O3–H1⋅⋅⋅O4–H2), forming a pre-reactive complex. At 16.69 ps, the H2 proton transfer from H₂O to MA generates MAH⁺ and OH⁻, which rapidly moves toward H1 of the proximate water molecule to form another OH⁻. At 16.74 ps, O3–N1 bond formation between NO⁺ and second OH⁻ concludes the reaction, producing HONO, NO3-, and MAH⁺ as the final products. Notably, the catalytic hydrolysis mechanism depends on the contact configuration between gaseous MA and the interface. As shown in Figs. 3b and S10b, the gaseous MA approaches interfacial water, forming the O5–H3⋅⋅⋅N2 HB at 2.57 ps. Meanwhile, interfacial water connects the NO⁺ ion to MA via a three-water bridge (O3–H1⋅⋅⋅O4–H2⋅⋅⋅O5–H3), forming a pre-reactive complex. Proton transfer from water to MA occurs at 4.14 ps, followed by proton relay along the water bridge that produces OH⁻. By 4.35 ps, NO⁺ reacts with OH⁻ via O3–N1 bond formation to produce fully separated HONO, NO3-, and MAH⁺. For MA, a pre-reactive complex forms via two-water or three-water bridges between NO⁺ and MA. Proton transfer occurs along the water bridge, followed by OH⁻ attack on NO⁺ to form HONO. Remarkably, the three-water-bridge pathway proceeds approximately four times faster than the two-water-bridge pathway. This kinetic enhancement may stem from the greater stability of the “three-water bridge” structure, whose larger spatial configuration hinders rotation at the water interface, thereby stabilizing its connections with NO⁺ and MA at both ends and facilitating proton transfer.

For the DMA-involved reactions (Figs. 3c, d and S10c, d), the interfacial hydrolysis of t-ONONO₂ follows the same mechanism but proceeds even more rapidly (∼ 1–2 ps). This acceleration is again attributed to the stronger basicity of DMA, a result consistent with collision mode (i). Notably, in MA-mediated hydrolysis, proton transfer through a three-water bridge occurs faster than through a two-water bridge, highlighting the catalytic advantage of increasing the length of interfacial water bridge. In contrast, DMA-mediated hydrolysis exhibits nearly identical reaction times for single-water and two-water bridges (∼ 1–2 ps), indicating that additional water molecules provide little further kinetic enhancement. This can be attributed to the stronger basicity of DMA than MA, which enables rapid proton abstraction from interfacial water and facilitates proton transfer, thereby promoting hydrolysis.

It is worth noting that the gas-phase pre-reactive complex t-ONONO₂–MA/DMA shown in Scheme 2 (iii) is structurally identical to that presented in Scheme 1 (ii). However, when this complex collides with the air–water interface, it preferentially undergoes N-nitrosation rather than hydrolysis. This difference can be understood from the distinct elementary steps involved in the two pathways. In the N-nitrosation pathway (Scheme 1 (ii)), the preformed t-ONONO₂–MA/DMA complex already possesses an N⋅⋅⋅N interaction between the amine and the NO moiety of t-ONONO₂. Upon adsorption at the air–water interface, the interfacial environment facilitates the transfer of the NO group to the amine, leading to the formation of the nitrosamine cation. In contrast, the hydrolysis pathway requires nucleophilic attack by interfacial water molecules on the t-ONONO₂ moiety, accompanied by concerted solvent-assisted proton transfer. The BOMD trajectories suggest that the pre-existing N⋅⋅⋅N interaction between the amine and the NO moiety may reduce the accessibility of interfacial water molecules to the reactive site and hinder their adoption of a favorable orientation for nucleophilic attack. Consequently, the preformed gas-phase complex preferentially undergoes N-nitrosation upon collision with the air–water interface, whereas the competing hydrolysis pathway is kinetically disfavored.

Overall, MA- and DMA-catalyzed interfacial hydrolysis of t-ONONO₂ can promote aerosol growth through enhancement of hygroscopicity, owing to the formation of (i) nitrate (NO3-) and (ii) protonated amines (MAH⁺ and DMAH⁺), which substantially increase aerosol water uptake (Deng et al., 2026; Ning et al., 2023, 2024). The MA- and DMA-mediated hydrolysis of t-ONONO₂ proceeds on the picosecond timescale and efficiently produces HONO. This high HONO yield is governed by the synergistic coupling between interfacial water bridges and amine basicity, which facilitate proton transfer.

Given the high reactivity of HONO, its kinetic behavior warrants investigation at the air–water interface. As shown in Fig. S11, IRI analysis reveals weak noncovalent interactions between HONO and interfacial water, supporting the finding by Chen et al. (2025a) that HONO predominantly exists in its neutral form at the interface of aqueous microdroplets. More importantly, HONO is recognized as a key precursor to N-nitrosodimethylamine (NDMA) (Ge et al., 2011; Karl et al., 2012), despite its relatively slow bimolecular reaction rate with DMA in the aqueous phase (∼ 0.1 M⁻¹ s⁻¹) (Karl et al., 2012). However, the heterogeneous reaction mechanism of HONO with DMA at the air–water interface remains poorly understood, yet its elucidation is essential to assess their contribution to particulate nitrosamine formation.

To evaluate the contribution of interfacially generated HONO to particulate-phase nitrosamine formation, we investigated the reaction of DMA with HONO at the air–water interface using BOMD and MetaD simulations. DMA was selected as the representative amine due to the substantially higher atmospheric abundance of NDMA compared to NMA in field observations, as well as the extensive data available for DMA-driven nitrosamine formation in kinetic models (Karl et al., 2012; Choi et al., 2021, 2025b). Consequently, while MA is also a relevant precursor, the current study focuses specifically on the DMA system to align with these dominant atmospheric observations. As shown in Fig. 4a, b, HONO first undergoes N–O bond cleavage to form an OH⁻ / NO⁺ ion pair. Concurrently, the N–H bond of DMA dissociates; the released proton (H⁺) neutralizes OH⁻ to form an H₂O molecule, while electrophilic NO⁺ attacks (CH₃)₂N⁻ to yield NDMA. The calculated energy barrier for this process is 7.65 kcal mol⁻¹ (Fig. 4c), corresponding to an interfacial rate constant of 1.67 × 10⁷ M⁻¹ s⁻¹ at 300 K based on transition state theory (TST). Computational details are provided in Sect. S4 of the Supplement. Although HONO-mediated nitrosation is kinetically feasible at the air–water interface, it is predicted to be less efficient than the direct N₂O₄-mediated pathway under the conditions investigated in this work. However, previous atmospheric kinetic models have also identified N₂O₃ as a potentially important nitrosating agent, in addition to HONO and N₂O₄. The N₂O₃-mediated pathway was not considered in the present study because, under typical nighttime atmospheric conditions, N₂O₄ is generally expected to be substantially more abundant than N₂O₃. This difference is attributed to the rapid consumption of NO by ozone, which suppresses N₂O₃ formation, whereas NO₂ readily undergoes dimerization to form N₂O₄ (Brown and Stutz, 2012; Roscoe and Hind, 1993). Nevertheless, N₂O₃-mediated interfacial nitrosation may also contribute under conditions where sufficient N₂O₃ is available. Further studies on N₂O₃-mediated interfacial reactions are therefore needed to evaluate their potential role in atmospheric nitrosamine formation.

Although the HONO-mediated nitrosation pathway is kinetically less favorable than the direct N-nitrosation by N₂O₄ under the investigated conditions, this pathway may become environmentally relevant under specific atmospheric scenarios. In particular, aged aerosols with prolonged atmospheric residence times and nighttime HONO-rich environments may provide favorable conditions for this secondary pathway, because heterogeneous HONO production and accumulation can increase the availability of HONO at aqueous aerosol surfaces, whereas the concentration of highly reactive N₂O₄ may decrease during aerosol evolution. Under such conditions, interfacial HONO may serve as an important reactive nitrogen reservoir, linking inorganic nitrogen species with particulate organic nitrogen formation through subsequent reactions with amines. Therefore, the HONO-mediated pathway should not be considered merely as a kinetically minor reaction, but rather as a potentially important complementary pathway that contributes to particulate nitrosamine formation under specific atmospheric conditions.

Considering that both the HONO- and N₂O₄-mediated pathways originate from reactive nitrogen species in the atmosphere, their relative importance should be evaluated within the broader context of previous molecular studies, particle-phase observations, and atmospheric kinetic models. Previous theoretical studies have provided important insights into the intrinsic reactivity of DMA toward N₂O₄. Lv et al. (2008) systematically investigated the nitration and nitrosation pathways of DMA with N₂O₄ and identified asymmetric ON–ONO₂ as the key reactive isomer responsible for N-nitrosation. Their calculations demonstrated that ON–ONO₂ can undergo a nearly barrierless concerted reaction with DMA in both the gas phase and an implicit aqueous environment, establishing the molecular feasibility of N₂O₄-mediated nitrosamine formation. These findings provided a mechanistic basis for understanding the role of N₂O₄ as an effective nitrosating agent in aqueous environments.

Beyond these theoretical investigations, recent experimental studies have demonstrated that amines in the particulate phase can undergo heterogeneous reactions with reactive nitrogen species under atmospheric conditions. Chen et al. (2022) investigated the transformation of particulate DMA under NO_x exposure and reported the formation of both nitramine and nitrosamine products through experimental measurements and theoretical analysis. They further suggested that reactive nitrogen oxide species, including N₂O₄ and N₂O₃, may contribute to DMA transformation through interactions with the nitrogen center of the amine. However, the specific reactive intermediates and molecular pathways controlling N₂O₄-driven nitrosation at the air–water interface of aqueous aerosols remain poorly constrained.

Building upon these theoretical insights and atmospheric observations, the present study reveals how the air–water interface regulates N₂O₄-mediated nitrosation under realistic heterogeneous conditions. Consistent with the findings of Lv et al. (2008), our BOMD simulations identify t-ONONO₂ as the active nitrosating species. However, unlike what is captured in previous gas-phase and continuum-solvent models, the explicit aqueous interface introduces dynamic solvent organization, interfacial hydrogen-bond networks, and adsorption-dependent collision configurations that regulate the reaction pathway. Therefore, this work extends previous descriptions of N₂O₄-mediated nitrosation from intrinsic molecular reactivity to heterogeneous atmospheric chemistry by demonstrating that aqueous aerosol interfaces can facilitate nitrosamine formation through interface-mediated reaction dynamics.

The atmospheric implications of the proposed mechanism can be further considered in the context of existing kinetic models. Previous atmospheric chemistry models, including the SINTEF mechanism developed by Karl et al. (2012) and the box-model study of Choi et al. (2021, 2025b), represented DMA nitrosation by HONO, N₂O₃, and N₂O₄ using parameterized reaction pathways and effective rate coefficients. Although these mechanisms provide an important framework for evaluating secondary nitrosamine formation, the associated kinetic parameters remain subject to uncertainty. Importantly, the box models developed by Choi et al. (2021, 2025b) did not incorporate heterogeneous reactions, primarily due to the limited kinetic data available at the time. Consequently, aerosol interfacial nitrosation pathways remain absent from current atmospheric kinetic models, despite their potential atmospheric relevance. Furthermore, the molecular mechanisms underlying N₂O₄-mediated nitrosation, particularly at the air–water interface of aqueous aerosols, remain poorly understood. As a result, many of the kinetic parameters adopted in current atmospheric models are based on indirect estimates, analogous systems, or empirical parameterizations rather than explicit molecular-level reaction mechanisms.

Moreover, the interfacial pathway identified in this study exhibits rapid kinetics, with the N₂O₄-mediated reaction producing nitrosamine cations within picoseconds, while the HONO-mediated interfacial pathway also proceeds efficiently. Although the quantitative influence of this interfacial pathway on atmospheric nitrosamine budgets requires future model implementation, our findings highlight the need to incorporate aerosol interfacial chemistry into future parameterizations of heterogeneous nitrosamine formation.