Formation of HONO from the NH₃-promoted hydrolysis of NO₂ dimers in the atmosphere

Since first reported by Finlayson-Pitts et al. (19), the asymmetric isomer ONONO₂ has been considered as an intermediate in the hydrolysis of NO₂. Recent spectroscopic evidence reported by Stanton and coworkers (34) confirms the formation of asymmetric ONONO₂ from the dimerization of NO₂ in the gas phase. It has also been observed that symmetric N₂O₄ converts to asymmetric ONONO₂ with a very short lifetime, even on an ice surface at 130 K (35). Hence, among the nitrogen oxides in the atmosphere, ONONO₂ is selected as a starting point to study the hydrolysis of NO₂ in the presence of NH₃. For brevity, the N₂O₄ + (H₂O)_n + NH₃ systems considered here are denoted monohydrate, dihydrate, trihydrate, and tetrahydrate systems with n = 1–4, respectively.

First, we performed 100-ps Born–Oppenheimer molecular-dynamics (BOMD) simulations for the dihydrate, trihydrate, and tetrahydrate systems to obtain a set of stable structures. These structures (Fig. 1A) were then used for the initial state of metadynamics simulations to explore possible reaction paths. For the monohydrate, a hand-built structure was used. The height and width of the Gaussian functions used in the metadynamics simulations were 0.003 eV and 0.1 Å, respectively; a new Gaussian was added every 30 steps. These parameters aim to preserve accurate small barriers for the tetrahydrate system, while ensuring that the reaction occurs within 10 ps for the higher barrier reactions in the monohydrate system (SI Appendix, Fig. S1). The N–H distance (d_N-H, noted in Fig. 1A) is used as the collective variable. A quadratic wall is applied when d_N-H > 2.5 Å to narrow the sampling space. Note that all metadynamics simulations were stopped when a reaction was detected. Although convergence of the free-energy surface is not always guaranteed in metadynamics, our approximate free-energy surfaces allowed for the identification of possible reaction paths that were subsequently investigated in detail using both the climbing-image nudged elastic band (CI-NEB) and thermodynamic integration methods.

In Fig. 1 and SI Appendix, Fig. S2 (and Movies S1–S4), the simultaneous formation of NH₄⁺ and HONO is observed from the metadynamics simulations in all four systems following two different reaction mechanisms. Fig. 1B displays the variation in the N₁–O₁, N₂–H₂, and O₂–H₁ bond lengths for the dihydrate system and the N₁–O₁, O₁–H₁, and N₂–H₁ bond lengths for the tetrahydrate system during the metadynamics simulations. The corresponding bond length variations for the monohydrate and trihydrate systems are shown in SI Appendix, Fig. S2. In the dihydrate system, the reaction follows a loop-structure mechanism involving two water molecules, as reported in our previous paper (26). In Fig. 1B, two H₂O molecules (in red) bridge ONONO₂ and NH₃ via the electrostatic interaction of N₁–O₁ and hydrogen bonding of H₁–O₂ and H₂–N₂, forming a loop structure. Initially (<9.47 ps), the N₂–H₂ length (the collective variable) fluctuates between 1.20 and 2.64 Å. At ∼9.47 ps, a hydrogen atom in the H₂O molecule at the NH₃ end shifts toward the NH₃ molecule, and the N₂–H₂ distance decreases to 0.95 Å, suggesting the formation of NH₄⁺. Simultaneously, the H₂O close to the NO motif donates the H₁ atom to the oxygen atom in the H₂O at the NH₃ end, which shortens the H₁–O₂ distance to ∼0.96 Å, and a new H₂O molecule is generated. The remaining OH group combines with the NO motif to yield the HONO species, corresponding to shortening of the N₁–O₁ distance from 2.47 to 1.46 Å. This mechanism involves splitting the two H₂O molecules that bridge ONONO₂ and NH₃, and is thus denoted the dual-water mechanism. Similar to our previous report (26), the two water molecules (in red) act as a reaction center with the oxygen atom as the proton transporter. The dual-water mechanism is also observed in the trihydrate system. In SI Appendix, Fig. S2, Lower, the two water molecules (in red) in the reaction center directly participate in the reaction, whereas the third water molecule more likely acts as a “solvent” molecule. The addition of this solvent molecule lowers the barrier from 7.5 to 4.3 kcal/mol (SI Appendix, Fig. S1), which will be further confirmed with the CI-NEB.

Unlike the dihydrate and the trihydrate systems, the reaction occurring in the monohydrate and tetrahydrate systems follows a single-water mechanism. In the monohydrate system, a loop structure is formed with a water molecule bridging the ONONO₂ and the NH₃. With the approach of NH₃, the H₂O molecule splits into an OH and an H (in gray) that bind with the NO motif in the ONONO₂ and the NH₃ molecules, respectively, thus leading to the formation of the HONO species and NO₃⁻ and NH₄⁺ groups (SI Appendix, Fig. S2, Upper, and Movie S1). Similarly, in the tetrahydrate system, only one water molecule is directly involved in the HONO formation reaction. In Fig. 1B, ONONO₂ and NH₃ are bridged through one water molecule (in red) with the other three water molecules surrounding them. At ∼1.21 ps, the N₂–H₁ distance decreases to ∼1.00 Å and is accompanied by an increase in the O₁–H₁ distance, which suggests the formation of NH₄⁺ and the dissociation of the water molecule. Simultaneously, the N₁–O₁ distance is shortened to ∼1.47 Å, leading to the formation of the HONO species. During the whole process, no bond breaking and formation are observed in the other three surrounding water molecules. In both the monohydrate and the tetrahydrate systems, the water molecule bridging ONONO₂ and NH₃ is the only one that dissociates and directly participates in HONO formation. As such, this mechanism is denoted the single-water mechanism. The reaction barriers involved in this process are 5.2 and 1.8 kcal/mol for the monohydrate and tetrahydrate systems (SI Appendix, Fig. S1), respectively.

To gain more insight into the two mechanisms illustrated above, we located the transition state (TS) for all four systems, following both the single- and dual-water mechanisms; the energy profiles are presented in Fig. 2. For the monohydrate system, only the single-water mechanism is considered since only one H₂O molecule is involved. Note that the energy of the reactant states (RSs) shown in Fig. 2 are the average binding energies relative to gas-phase H₂O, N₂O₄, and NH₃ molecules, which is calculated as follows:where n and m represent the number of water molecules and the total number of molecules in the system, respectively. $E_{\text{system}}$ is the energy of the monohydrate, dihydrate, trihydrate, or tetrahydrate system. $E_{{\mathrm{N}}_2{\mathrm{O}}_4}$, $E_{{\mathrm{H}}_2\mathrm{O}}$, and $E_{\mathrm{N}{\mathrm{H}}_3}$ represent the energies of the N₂O₄, H₂O, and NH₃ molecules, respectively. The average binding energy reflects the variation in the binding strength within the system. The energies of the TS and the product state (PS) are calculated relative to the corresponding RS. All energies presented in Fig. 2 are the calculated electronic energies with a zero-point energy (ZPE) correction at the B3LYP/6-311++G(3df,2p) level.

Clearly, for both mechanisms, the energy barrier decreases with an increasing number of water molecules in the system. Such an effect is particularly significant for the single-water mechanism. In Fig. 2, Left, for the monohydrate system, the single-water mechanism is associated with a barrier as high as 14.4 kcal/mol. The addition of one more water molecule reduces the barrier by ∼74% (3.7 kcal/mol for the dihydrate system). The trihydrate and tetrahydrate systems have even lower energy barriers of 1.8 and 0.6 kcal/mol, respectively. The reduction in the barrier with the addition of water molecules is likely due to solvation and stabilization effects of water molecules. A comparison of the RSs in the monohydrate and tetrahydrate systems show that the additional water molecules weaken the π-orbital coupling between the NO motif and the NO₃ groups, as indicated by the highest occupied molecular orbitals in the ONONO₂ molecules (SI Appendix, Fig. S3). Additional direct evidence is the increase in the bond length between the NO motif and NO₃ group from 1.933 to 2.092 Å and an increased charge separation of the ONONO₂ molecule. The charges of the NO₃ group and the NO motif are −0.54/0.45 and −0.63/0.38 |e| for the monohydrates and tetrahydrates (SI Appendix, Table S1), respectively, suggesting a larger ionization extension of the ONONO₂ molecule, which leads to the formation of a more active NO⁺/NO₃⁻ ion pair. In addition, the net charge of the ONONO₂ becomes more negative in the TS (−0.35, −0.38, −0.21, and −0.45 |e| for the monohydrates, dihydrates, trihydrates, and tetrahydrates, respectively), suggesting increased charge transfer between the ONONO₂ and nH₂O + NH₃ groups. The charged ONONO₂ group in the TS can be effectively stabilized by the solvation effect of the nH₂O + NH₃ group, a well-established fact in the gas-phase clusters (36–39). The addition of extra water molecules (indicated by green arrows in SI Appendix, Fig. S4A) around the reaction center enhances such stabilization, leading to a decrease of the energy barrier. SI Appendix, Fig. S4A clearly shows an enhancement in the hydrogen bonding formed by the surrounding water molecules. For example, in the dihydrate system, the length of the hydrogen bond decreases from 2.019 and 1.866 Å to 1.817 and 1.734 Å in the TS (SI Appendix, Fig. S4A). In the trihydrate and tetrahydrate systems (SI Appendix, Fig. S4 C and B), the average length of the hydrogen bonds in the TSs is reduced by 0.11 and 0.08 Å compared with that in the corresponding RSs, respectively. As such, the promoted ionization due to the solvation and stabilization effects of the TS cooperatively enhances the reactivity of the NH₃ + ONONO₂ + nH₂O system with increasing n.

In comparison with the single-water mechanism, the dual-water mechanism generally entails higher energy barriers. Additionally, the RSs associated with the dual-water mechanism exhibit a weaker binding strength due to their slightly higher average binding energies than those of their single-water counterparts. In Fig. 2, Right, H₂O acts as the proton acceptor in the formation of an H₃O⁺ group in the TS, rather than NH₃, as observed in the single-water mechanism. Given the more basic properties of NH₃, it is considered a better proton acceptor than H₂O. Thus, the dual-water mechanism with H₂O as the first proton acceptor is less favorable than the single-water mechanism where NH₃ acts as the first proton acceptor. However, we previously reported that the dual-water mechanism is very important in the hydrolysis process of SO₃. The difference is due to the different hydrophilic abilities of SO₃ and ONONO₂, that is, SO₃ is more hydrophilic than ONONO₂ and can bind with H₂O via a stronger S–O interaction. This stronger binding offsets the unfavorable H₂O as the first proton acceptor. Hence, a future study of the dependence of both mechanisms on the hydrophilic ability of various reactant candidates will be insightful.

In addition to the energy barrier, the probability of forming a specific RS structure, which is required for a specific reaction mechanism to occur, is another key factor that affects the activity. The single-water mechanism requires preformation of a structure with one water molecule bridging the NO motif and NH₃ molecule, whereas the dual-water mechanism requires an initial structure where two water molecules act as the bridge connecting the NO motif and the NH₃ molecule. The isomer structure with the former feature is denoted by “S” and the latter by “D.” In SI Appendix, Fig. S6, the notations 2D-i and 2D-ii represent the isomers of the dihydrate with the D feature but different arrangements of the remaining molecules. A comparison of the ZPE-corrected electronic energies suggests higher stability for the S-featured isomers for all systems considered here. However, the analysis of the snapshot structures from the BOMD simulations shows that the probability distribution of both structures depends on the number of water molecules in the system as shown in Fig. 3. For the dihydrate system, the D-featured isomers exhibit the highest population (74% and 22% for 2D-i and 2D-ii, respectively). Only 5% of the isomers exhibit S features. For the trihydrate system, the most populated isomers still exhibit the D feature with a total population of 53%. However, the population of the S-featured isomer (isomer 3S) increases to 18%, and isomers (3T) with three water molecules bridging the NO motif and NH₃ are present. Notably, the favorability of the population of the S- and D-featured isomers is inverted in the tetrahydrate system, where the S-featured isomer is most populated, and the D-featured isomer has a population percentage of less than 9%. Notably, more than one-half of the isomers exhibit the well-defined structure of the RS that has been proven highly active with low barriers, based upon both metadynamics simulations and reaction path calculations.

Having obtained the most probable structures, we evaluated the relative free-energy variation along the selected reaction coordinates for the monohydrate and tetrahydrate systems using thermodynamic integration. For both systems, the reaction coordinate (also referred to as the collective variable) is chosen as the sum of the N–H and N–O distances. For comparison, we also computed the relative free energy along with the variation in the N–H distance for the dihydrate and pentahydrate systems without the NH₃ molecule. The NH₃-free dihydrate and pentahydrate systems are considered the counterpart of the NH₃-containing monohydrate and tetrahydrate systems, respectively. The free-energy surfaces calculated for all four systems are shown in Fig. 4. The reaction coordinates are normalized with the equation below:where $R_{\max }$, $R_{\min }$, and $R_{\mathrm{i}}$ are the maximum, minimum, and instantaneous value of the collective variable at each point. As shown by the gray line in Fig. 4, without the NH₃ molecule, a relatively high free-energy barrier of 8.2 kcal/mol is encountered for the formation of the HONO species, solely from one N₂O₄ and two H₂O molecules, and the reaction is endergonic by 4.3 kcal/mol, suggesting that HONO formation is unfavorable. The addition of three water molecules reduces the free-energy barrier to 5.6 kcal/mol, but the reaction remains endergonic by 1.2 kcal/mol. In contrast to the NH₃-free systems, HONO formation in the NH₃-containing monohydrate and tetrahydrate systems has a lower free-energy barrier, and the reaction is exergonic. Compared with the NH₃-free dihydrate system, the NH₃-containing monohydrate system can be viewed, simply, as replacing one H₂O with one NH₃ molecule. However, the reaction becomes exergonic by 5.8 kcal/mol, and the free-energy barrier is lowered to 5.8 kcal/mol, in contrast to the endergonic and high-barrier reaction associated with the NH₃-free dihydrate system. The addition of three more H₂O molecules to the NH₃-containing monohydrate system further reduces the free-energy barrier to 3.4 kcal/mol, ∼2.2 kcal/mol lower than that of the NH₃-free counterpart (the pentahydrate system). Moreover, the resulting HONO and NH₄NO₃ species are stabilized by 5.3 kcal/mol. Therefore, the more basic NH₃ molecule helps stabilize the hydrated HONO + NO₃ system and reduces the free-energy barrier of the reaction, thereby promoting the formation of HONO.

In addition to clusters in the atmosphere, water can also exist in the liquid phase as water droplets and solvents in, or surrounding, aerosol particles. The water content and the air–water interface in these systems have been shown to have a catalytic role toward various chemical reactions (26, 40–42). Here, we further investigated the reaction of ONONO₂ and NH₃ on the surface of a water droplet via both BOMD and thermodynamic integration. The formation of HONO is directly observed in the BOMD simulation via a single-water mechanism (Movie S5) with a free-energy barrier as low as 0.5 kcal/mol. In Fig. 5A, before 3.6 ps, the N₁–O₁ and N₂–H₁ distances vary from 1.98 to 2.70 and 1.47–2.20 Å, indicating the relative stability of the N₂O₄ and NH₃ compounds on the droplet surface. The O₁–H₁ distance fluctuates by ∼1 Å, suggesting that no water splitting occurs. At 3.6 ps, the elongation of the O₁–H₁ bond length in the water molecule bridging ONONO₂ and NH₃ emerges, accompanied by a shortening of the N₁–O₁ and N₂–H₁ bond lengths. Upon summiting a TS, as shown in the second Inset images in Fig. 5B, the water molecule dissociates into a H atom and a OH group, corresponding to an elongation in the O₂–H₁ bond length from 1.00 to 1.60 Å. Simultaneously, the resulting H atom binds to NH₃, and the OH group binds to the NO motif, leading to the formation of the NH₄⁺ ion and the HONO species. During the whole process, bond breaking only occurs on one water molecule, suggesting that the single-water mechanism is the same as that in the tetrahydrate system. Following the single-water mechanism, the free-energy barrier is 0.5 kcal/mol, much lower than in the tetrahydrate system (3.4 kcal/mol). The reaction is also over twice as exergonic (15.3 kcal/mol) than the tetrahydrate system (5.3 kcal/mol). The extremely low barrier and the high exergonic property of the reaction on the water droplet surface result from the existence of a complex hydrogen-bond network. Compared with the RS, the TS and the PS show more ionic properties and can be further stabilized by the complex hydrogen-bond network due to the formation of the solvation shell around ionic chemicals (i.e., NO₃⁻ and NH₄⁺) (36–39). Hence, we have demonstrated that water droplets promote the formation of HONO from the reaction between ONONO₂ and NH₃ with a free-energy barrier comparable to k_BT at room temperature.

In conclusion, we have studied the role of gaseous NH₃ molecules in the formation of HONO from N₂O₄ and H₂O using several theoretical methods. Two distinctly different mechanisms, the single- and the dual-water mechanisms, are identified from metadynamics simulations. CI-NEB calculations confirm that the single-water mechanism is generally more favorable than the dual-water mechanism. Solvation effects from additional water molecules in the systems further lower the energy barrier, promoting the formation of HONO. The configuration statistics from the BOMD simulations show that the dihydrate and trihydrate systems preferentially form the RS structure (the structure with the D feature) of the dual-water mechanism, whereas the structure with the S feature required for the single-water mechanism has the highest population in the tetrahydrate system. Overall, the formation of HONO in the monohydrate and tetrahydrate systems tends to follow the single-water mechanism, whereas the dual-water mechanism appears to be more favorable in the dihydrate and trihydrate systems.

More importantly, a comparison of the free energy of HONO formation from the NH₃-free and NH₃-containing hydrated N₂O₄ systems demonstrates the promoting role of NH₃ toward HONO formation. The involvement of NH₃ molecules in the system leads to a stabilization of the PSs, making HONO formation exergonic rather than endergonic, as observed in NH₃-free systems, while notably lowering the free-energy barrier required for HONO formation. The free-energy barrier is as low as 3.4 kcal/mol in the NH₃-containing tetrahydrate system. Moreover, the free-energy barrier can be further reduced to 0.5 kcal/mol when the formation of the HONO species is on the surface of a water droplet, confirming the important role of water droplets in promoting atmospheric chemistry. Hence, the NH₃-promoted HONO formation from hydrated N₂O₄ is an important source of HONO in the atmosphere. In highly polluted areas where NH₃ is relatively abundant, its contribution is even more important, a conclusion consistent with previous field observations.

The Gaussian and plane-wave (GPW) method implemented in the CP2K Quickstep package (43) is used in the BOMD simulations, metadynamics simulations, and thermodynamic integration methods. The wave functions expanded in a triple-ζ Gaussian basis set with additional auxiliary basis sets are used to treat the valence electrons (44, 45), whereas the Goedecker–Teter–Hutter (GTH) norm-conserved pseudopotentials are adopted to model the core electrons (46). The energy cutoffs for the finest grid level and Gaussian wave are set as 300 and 40 Ry, respectively. The Becke–Lee–Yang–Parr (BLYP) functional method (47, 48) and Grimme’s dispersion correction method (49) are employed to describe the electron exchange and correlation and the London dispersion interaction, respectively (denoted the BLYP-D method). For all BOMD simulations (including those involved in the metadynamics simulations and thermodynamic integration methods), the constant-volume and constant-temperature (NVT) ensemble is adopted, and the time step is set as 0.5 and 1 fs for the cluster and droplet models, respectively. Temperature is controlled at 300 K using the Nosé–Hoover chain method (50, 51).

A large supercell (20 × 20 × 20 ų) is chosen to minimize the interaction between two neighboring clusters for the NH₃ + N₂O₄ + nH₂O systems (n = 1, 2, 3, and 4). A (20 × 20 Ų) water slab (as shown in the Inset image of SI Appendix, Fig. S7) with a thickness of ∼15 Å is used to simulate the water droplet system. The initial structure is first stabilized with classic force field methods for ∼100 ps and is followed by an ∼20-ps BOMD simulation at 300 K. The tetrahydrate (NH₃ + N₂O₄ + 4H₂O) structure from the ∼100-ps MD simulation is placed onto the surface of the prestabilized water slab. The structure is further stabilized with the BOMD simulation for an additional 15 ps by fixing the reaction center (highlighted in the Inset images of SI Appendix, Fig. S7). The obtained structure is used for further BOMD simulations with all atoms free to move. To narrow the sample space, a quadratic wall is applied with a force constant of 20 kcal/mol when the sum of the N₁–O₁ and N₂–H₁ lengths (as labeled in Fig. 5B) is larger than 4.5 Å.

For the reaction path search, we use the CI-NEB method (52), implemented in the TSASE toolkit. The B3LYP functional with the 6-311++G(3df, 2p) basis sets (48, 53) and Grimme’s dispersion correction, implemented in the Gaussian 09 package, are used to evaluate the force and energy of each image. The convergence criterion for the force on each image is set to be 0.02 eV/Å. The vibrational frequencies for each TS are computed to confirm that only one imaginary frequency exists. The ZPE correction is included in the energy profile. To validate the parameters used here, we compute the heat of reaction for the reaction 2NO₂ + H₂O → HONO + HNO₃ using both the CP2K and Gaussian 09 packages. The obtained values are −5.75 and −7.32 kcal/mol, which are acceptable compared with the experimental value of −6.7 ± 0.6 kcal/mol (54). We also compute the energy barrier for the reaction ONONO₂ + H₂O → HONO + HNO₃ with presence of one NH₃ molecule. The obtained energy barriers of 12.26 and 14.35 kcal/mol based on the CP2K and Gaussian 09 packages, respectively, are comparable.

Calculations were done at the University of Nebraska Holland Computing Center, the National Energy Research Scientific Computing Center, and the Texas Advanced Computing Center. This work was supported by National Science Foundation Grant CHE-1665325 and the Welch Foundation (F-1841).