Reaction of a charge-separated ONONO 2 species with water in the formation of HONO: an MP2 Molecular Dynamics study †

The reaction of (NO + )(NO 3 (cid:2) ) with water is modelled in ONONO 2 (cid:3) (H 2 O) 4 clusters. Molecular Dynamics simulations using second-order Møller–Plesset perturbation (MP2) theory support the feasibility of the reactionof acharge-separatedspeciestoproduceHONOandnitricacid. It is well known that nitrous acid (HONO) plays a major role in the chemistry of the atmosphere, e.g. as a source of hydroxyl (OH) radicals. 1,2 While heterogeneous reactions of NO 2 with water on tropospheric surfaces are believed to be important in generating HONO, the actual mechanisms involved are not known with certainty. On a chemical basis, the involvement of the NO 2 dimer seems reasonable, 3 although other mechanisms have been proposed for production of HONO both in the dark and under irradiation. 4–11 Initial steps of one proposed mechanism 3 include NO 2 dimerization to form N 2 O 4 and autoionization of asymmetric N 2 O 4 , i.e. ONONO 2 , to form (NO + )(NO 3 (cid:2) ). Reaction of the (NO + )(NO 3 (cid:2) ) ion pair with water to form HONO and nitric acid (HONO 2 ) is the final step.

It is well known that nitrous acid (HONO) plays a major role in the chemistry of the atmosphere, e.g. as a source of hydroxyl (OH) radicals. 1,2 While heterogeneous reactions of NO 2 with water on tropospheric surfaces are believed to be important in generating HONO, the actual mechanisms involved are not known with certainty. On a chemical basis, the involvement of the NO 2 dimer seems reasonable, 3 although other mechanisms have been proposed for production of HONO both in the dark and under irradiation. [4][5][6][7][8][9][10][11] Initial steps of one proposed mechanism 3 include NO 2 dimerization to form N 2 O 4 and autoionization of asymmetric N 2 O 4 , i.e. ONONO 2 , to form (NO + )(NO 3 À ).
Reaction of the (NO + )(NO 3 À ) ion pair with water to form HONO and nitric acid (HONO 2 ) is the final step.
(NO + )(NO 3 À ) + H 2 O -HONO + HONO 2 (2) A number of studies have addressed the formation of NO 2 dimers in both the symmetric (with a central NN bond) and asymmetric (ONONO 2 ) forms, and the interconversion between the two. [12][13][14][15][16][17][18] While the symmetric form of the dimer is favoured, there are pathways that can generate the asymmetric trans-ONONO 2 form that is the most likely precursor to the ion pair and subsequently HONO. 12,13,15,16,18 de Jesus Medeiros and Pimentel, in a study of the dimerization of NO 2 and the symmetric to asymmetric isomerization of the dimer in water clusters, predicted direct HONO formation from the NO 2 Á(H 2 O) n + NO 2 reaction and from the transition state for symmetric to asymmetric isomerization. 15 These modifications of the proposed mechanism described above bypass formation of (NO + )(NO 3 À ) through autoionization or, in the case of the NO 2 Á(H 2 O) n + NO 2 reaction, formation of the NO 2 dimer. Further exploration of the (NO + )(NO 3 À ) path will allow for comparison between potential routes and provide additional insight into the detailed mechanism that converts NO 2 in the presence of water to HONO. This is particularly useful for understanding other important reactions of NO 2 on surfaces in the presence of water, such as the reaction with HCl to form ClNO, since such chemistry likely shares common intermediates with NO 2 hydrolysis. [19][20][21] In ab initio Molecular Dynamics [AIMD], the reaction trajectory is propagated classically on the ab initio potential surface providing a means for studying reactive processes and the influence of the immediate environment. 22 The system wave function or electron density is calculated at each time step, i.e. on-the-fly, for determination of the energy, the interatomic forces and other properties. Partial charges are an obvious metric to investigate charge separation in the reaction of an ion pair as charge characteristics can indicate a shift in the nature of the interaction that would be less obvious from a slight change in structural parameters. Following the changes in partial charges with time, or the charge trajectory, is a very useful tool for understanding the mechanism of the reaction studied here.
A computational study of the minimum energy path for HONO formation by Luo and Chen used a trans-ONONO 2 Á(H 2 O) 2 reactant cluster and accounted for additional solvation through use of an empirical force field. 23 In the present study of the ion pair reaction, a trans-ONONO 2 Á(H 2 O) 4 cluster was chosen as the model system to examine the influence, and participation, of the surrounding water. The ab initio treatment of additional water molecules allows for greater flexibility in the reaction dynamics explored in these simulations. Both experimental and theoretical studies confirm that while certain water configurations promote the formation of HONO in the (NO + )Á(H 2 O) 4 cluster, the reaction does not proceed in (NO + )Á(H 2 O) n clusters for n r 3. [24][25][26] This previous work on HONO formation in absence of the NO 3 À anion motivated the choice of water cluster size and configuration in the present study. In previous work by Miller and Gerber, a similar cluster model was employed in studies of N 2 O 4 autoionization as well as proton recombination with the NO 3 À anion. 27,28 In choosing a method for calculation of the energy and interatomic forces for an AIMD study, or any computational study, computational cost and chemical accuracy must be weighed. Treatment using density functional theory 15,21 or a small basis set 27 may be necessary in a dynamics study where thousands of gradient calculations are required for each picosecond (ps) simulated. However, in a study of the N 2 O 4 potential surface, the B3LYP density functional was found to overestimate the stability of (NO + )(NO 3 À ) predicting a stable ion pair, while the more accurate ab initio methods found this structure to be a transition state. 18 Additionally, the sensitivity of the interaction between the NO + cation and water to the level of correlation, i.e. MP2 vs. CCSD, has been noted previously. 26,29 We found that the description of the relevant portions of the ONONO 2 Á(H 2 O) 4 potential surface is qualitatively incorrect when B3LYP, an insufficient basis set or MP2 without spin-component scaling are employed (see ESI †). We have selected the MP2 method with scaling of opposite spin and a basis set with diffuse functions to efficiently and accurately describe the region of the ONONO 2 Á(H 2 O) 4

potential surface of interest.
A trans-ONONO 2 Á(H 2 O) 4 cluster with a branched water configuration similar to that of the reactive (NO + )Á(H 2 O) 4 cluster 26 was identified, as well as a lower energy isomer with a square water configuration. In Fig. 1 Table 1. While the branched configuration, Fig. 1(b), is approximately 3 kcal mol À1 above the trans-ONONO 2 minimum with a square water configuration, the branched configuration promotes reactivity of ONONO 2 as seen in the lengthening of the distance between the NO and NO 3 fragments. The ON-ONO 2 distance extends from 1.76 Å in the cluster with a square water configuration, Fig. 1(a), to 1.84 Å in the cluster with a branched water configuration, Fig. 1(b), prior to insertion of the reacting water between the NO and NO 3 fragments, Fig. 1(c) and (d).
In the minimum energy cluster, the partial charge on the NO and NO 3 fragments are d(NO) = 0.46 and d(NO 3 ) = À 0.45 for a charge separation, d(NO) À d(NO 3 ), of 0.9. In the cluster with a branched water configuration, the charge separation increases to 1.1 with a partial charge of 0.55 on the NO fragment and À0.54 on the NO 3 fragment. Below, the charge separation will be used to describe the nature of the reactant and as one of the metrics indicating product formation.
These simulations explore the ion pair reaction given that the system has sufficient energy to reach one of two proton transfer transition states. Thus it is important to accurately determine the energy barrier relative to the trans-ONONO 2 Á(H 2 O) 4 configurations. The SOS-RIMP2 30,31 method and the SVP 32,33 basis set with added diffuse functions 34,35 [aSVP] were chosen for a sufficient qualitative description of the relative energies along the reaction path. For a more accurate determination of the energies, the structures were optimized at the SOS-RIMP2 level of theory with a larger basis set, the Dunning aug-cc-pVTZ [34][35][36] [aTZ] basis set, followed by single point calculation at the CCSD 37 level. Following optimizations at the SOS-RIMP2 level with the aug-cc-pVDZ basis set, the CCSD(T) 38 energy was calculated. The CCSD/ aTZ//SOS-RIMP2/aTZ and the CCSD(T)/aDZ//SOS-RIMP2/aDZ energies are included in Table 1 alongside the SOS-RIMP2/aSVP energies. The energetic ordering of the isomers is correctly predicted at the lower level of theory with the exception of the products. The energy of the products relative to the ONONO 2 Á(H 2 O) 4 minimum is more sensitive to the basis size and method (see ESI †). However, the SOS-RIMP2/aSVP approach gives a qualitatively correct description of the reactant and TS energetics and the formation of the products from the transition states is sufficiently exothermic to prevent the reverse reaction in the short simulations presented here. The branched reactive cluster is predicted to be approximately 3 kcal mol À1 above the minimum energy trans-ONONO 2 Á(H 2 O) 4 cluster and the transition states roughly an additional 2 to 3 kcal mol À1 higher at the higher levels of theory. To study the charge characteristics of the clusters during the evolution of this reaction, the charge separation, determined through Natural Population Analysis, 39 was monitored in AIMD simulations 40 in addition to bond distances. Beginning from the proton transfer transition states, trajectories were propagated forward and reversed to connect the reactants and products. Results of a simulation beginning from the transition state for proton transfer to the nitrate anion (Fig. 1c) are presented in Fig. 2. The charge separation of the NO and NO 3 fragments, d(NO) À d(NO 3 ), is plotted in the upper panel (a) and in the lower panel (b) the central NO distance of HONO is plotted showing bond formation. In Fig. 2a, the charge separation of the reactant (Fig. 1b) and product (Fig. 1e) clusters are given for reference as red and blue dashed lines respectively. In Fig. 2b, the HO-NO distance in the product cluster is given for reference as a blue dashed line.
As the trajectory is propagated forward in time from 0 ps, the charge separation quickly drops from approximately 1.1 at the transition state to oscillate about the value determined for the cis-HONO product cluster, just less than 0.7. The change in the plotted distance showing formation of the central HO-NO bond also indicates quick association to form HONO and oscillation about the value of the cis-HONO cluster (1.4 Å). When the initial velocities are reversed and propagated from the transition state, the plotted NO distance, which on the reactant side is the distance between the NO fragment and the reacting water, gradually increases as the reacting water migrates away.
On the reactant side, 0 ps to À3 ps, the charge separation increases to a maximum greater than 1.5 before decreasing to eventually oscillate near the value determined for the branched reactant cluster, approximately 1.1. This charge trajectory indicates a passage through a more charge-separated form of ONONO 2 between reactant cluster and transition state. While the charge trajectory does demonstrate the role of a chargeseparated species, formation of a true (NO + )(NO 3 À ) ion pair with d(NO + ) À d(NO 3 À ) of 2 does not occur here. Charge separation of approximately 1.5 corresponds that of a local minimum with an ON-ONO 2 distance of 2.4 Å and an H 2 O-NO distance of 1.9 Å. This structure is 1.8 kcal mol À1 at the SOS-RIMP2/aSVP level (1.5 kcal mol À1 at the CCSD/aTZ level) above the branched reactant cluster (Fig. 1b), which has an ON-ONO 2 distance of 1.8 Å and an H 2 O-NO distance of 2.5 Å. While harmonic frequency analysis confirms that this is a local minimum (zero imaginary frequencies), it may not be considered a true intermediate as there is not a significant barrier between this (NO d+ )(NO 3 dÀ )Á(H 2 O) 4 cluster and the branched water configuration of trans-ONONO 2 Á(H 2 O) 4 . The charge separation for the minimum energy trans-ONONO 2 Á(H 2 O) 4 cluster with a square water configuration is just under 0.9. In these short simulations, the cluster did not isomerize to the lower energy configuration and the charge separation only briefly dropped below 1.0 on the reactant side at approximately À2.7 ps. The branched water configuration promotes a greater (NO d+ )(NO 3 dÀ ) charge separation and places a water molecule in closer proximity to the NO fragment for reaction.
Six additional trajectories from the same starting geometry with the same total energy and alternate random initial velocities were propagated to À1 and 1 ps. Five of the six additional trajectories showed similar behaviour. In the sixth additional trajectory, products rapidly formed as the velocities were reversed as well as for the forward trajectory. While seven trajectories are not sufficient to obtain quantitative rates, the consistent result for several trajectories supports a qualitative description of the mechanism and timescale of this reaction (see ESI † for additional trajectories).  Results from a simulation begun at the transition state for proton transfer to the nearby water (Fig. 1d) are presented in Fig. 3. The results are quite similar to those in Fig. 2 with the largest difference being the charge separation (Fig. 3a) on the product side. The partial charge on the NO fragment drops to 0.16 upon formation of HONO, but the partial charge for the NO 3 anion is À0.86 in the trans-HONOÁ(NO A trajectory from a similar simulation, with the same starting structure but greater total energy, is also included in Fig. 3. On the reactant side of Fig. 3a, the time spent in the configuration of greater charge separation is significantly shorter than in the lower energy simulations and oscillations in charge separation have much greater amplitude. However, it is the product cluster on which the greater energy has a more significant effect. Just after 1 ps, the charge separation decreases to below the value determined for the trans-HONOÁ(NO 3 À )Á(H 3 O + )Á(H 2 O) 2 product cluster (1.0) and remains at a value similar to that of the cis-HONOÁHONO 2 Á(H 2 O) 3 product cluster (less than 0.7). This indicates that further proton transfer occurred along a ''water wire'' 41,42 to form trans-HONOÁHONO 2 Á(H 2 O) 3 . With one bridging water between the H 3 O + and NO 3 À ions, concerted transfer of two protons occurs to form nitric acid. For this higher energy simulation, three of the six additional trajectories (See ESI †) reproduced the initial result seen here. This work demonstrates the feasibility of the ion pair reaction with water in the formation of HONO following autoionization of trans-ONONO 2 . This reaction could proceed through diffusive separation of the ions followed by reaction of NO + with water in absence of the counter ion. However, in the current simulations the water configuration that promotes charge separation and the reaction with water also leads to the nearly immediate formation of HONO making diffusive separation unlikely. The many studies indicating a preference for the molecular form of nitric acid at a water surface rather than the deprotonated NO 3 À anion offer an additional driving force for reaction immediately following autoionization. 6,[43][44][45][46][47] Based on gas phase calculations, Liu and Goddard suggest that NO 2 hydrolysis likely occurs through direct formation of the cis asymmetric dimer followed by isomerization to the trans isomer circumventing the high symmetric to asymmetric barrier. 18 They found no barrier for formation of the cis isomer and the barrier for the cis-trans isomerization was predicted to be 3 kcal mol À1 above the cis minimum. Direct formation of the asymmetric isomer in the gas phase and deposition on a water surface could proceed to HONO formation through the transition states presented here.

Conclusions
In the current work the reaction of an (NO + )(NO 3 À ) ion pair with water was studied using a cluster model, the opposite-spin scaled variant of MP2 and a suitable basis set. The simulations presented here predict essentially simultaneous production of HONO and HONO 2 and support the feasibility of the ion pair reaction, or rather, passage through a significantly charge-separated species, as a major step in the hydrolysis of NO 2 through the asymmetric dimer ONONO 2 . There is considerable evidence for the accuracy of MP2 in describing water clusters in many cases. The merits of MP2 were enhanced here by using scaling of opposite-spin components and an adequate basis set. As the calculations are not too demanding computationally, we suggest the use of SOS-RIMP2 for MD simulations of other reactions in water clusters.