Chemistry of NOx and HNO3 Molecules with Gas‐Phase Hydrated O.− and OH− Ions

Abstract The gas‐phase reactions of O. −(H2O)n and OH−(H2O)n, n=20–38, with nitrogen‐containing atmospherically relevant molecules, namely NOx and HNO3, are studied by Fourier transform ion cyclotron resonance (FT‐ICR) mass spectrometry and theoretically with the use of DFT calculations. Hydrated O. − anions oxidize NO. and NO2 . to NO2 − and NO3 − through a strongly exothermic reaction with enthalpy of −263±47 kJ mol−1 and −286±42 kJ mol−1, indicating a covalent bond formation. Comparison of the rate coefficients with collision models shows that the reactions are kinetically slow with 3.3 and 6.5 % collision efficiency. Reactions between hydrated OH− anions and nitric oxides were not observed in the present experiment and are most likely thermodynamically hindered. In contrast, both hydrated anions are reactive toward HNO3 through proton transfer from nitric acid, yielding hydrated NO3 −. Although HNO3 is efficiently picked‐up by the water clusters, forming (HNO3)0–2(H2O)mNO3 − clusters, the overall kinetics of nitrate formation are slow and correspond to an efficiency below 10 %. Combination of the measured reaction thermochemistry with literature values in thermochemical cycles yields ΔH f(O−(aq.))=48±42 kJ mol−1 and ΔH f(NO2 −(aq.))=−125±63 kJ mol−1.


Introduction
Heterogeneous reactions occurring on particles urfaces have attracted considerable attention owing to their environmental impact in several atmospheric processes. The most striking example is the conversion of reservoir speciesc ontainingh alogenatedm olecules on polar stratospheric clouds (PSCs) into photochemically actives pecies that participate in catalytic ozone depletion. [1] Atmospheric modelsp redicted that more than 90 %o ft he ozone depletion is induced by chlorine activated in heterogeneous reactions on PSCs. [2] In addition, heterogeneous chemistry has become af ocuso fi nterest for the conversion of atmospheric pollutantsi nt he troposphere. Some atmosphericp ollutants, such as nitrogen oxides (NO x ), short for nitric oxide (NO) and nitrogen dioxide (NO 2 ), exhibit efficient prooxidant activity in the reactionwith OHC or O 3 . [3] Ni-trogeno xides are removed from the atmosphere either by dry or by wet deposition, mostly leadingt oH NO 3 . [3a, 4] On the other hand, severalr eaction pathways have been suggested, in which nitric acid is recycled back to NO x (known as renoxification) including reactions on aerosols urfaces [5] and heterogeneous photochemistry. [6] Therefore, the heterogeneous chemistry involvingr eactions in aerosol particles is believed to have a significant influence on the NO x /HNO 3 balance of the atmosphere and greatlya ffects ozone concentration. [5b, 7] The importance of HNO 3 is also derived from the fact that PSCs of type I consist almostentirely of nitric acid hydrates. [1a, 8] Atmospheric aerosols consist of neutrals and ions, volatile and nonvolatile molecules,l iquid-a nd solid-phase particles, and various impurities. [9] The presence of impurities even at low concentrationsd ramatically influences aerosol properties and processes in the atmosphere. Particularly interesting is the influence of ions in atmospherica erosoln ucleation,e nhancing the nucleation rates owing to the long-rangec harge-dipole interactions between the core ions and the adsorbing polar molecules. [10] This was invoked to explaint he correlation between the global cloudiness and the intensity of cosmicr adiation. [11] Nowadays, the role of ions in aerosol formation is one of the most debated subjects in atmospheric chemistry. [12] Cosmic radiation is the principal source of ionization and free electrons in the upper atmosphere.T he chemistry of atmospherica nions is usually initiated by electron attachment to abundant molecules.I nt he gas phase, the key intermediates O 2 C À and OC À are formed by the electron attachment to O 2 and O 3 ,r espectively. [13] The primary anions then undergo ac ascade of ion-molecule reactions yielding NO 2 À ,N O 3 À ,a nd HSO 4 posphere and stratosphere. In these regions, uptake of single water molecules by anions is likely due to their high water affinity.H ydration might change the natureo fr eactions, dramatically affectingt he electronic structure of transient anions. We have recently shown that electron attachment to HNO 3 /H 2 O particles predominantly lead to NO 3 À ,w hich is in contrast to the dissociative electron attachment (DEA) to gas-phaseH NO 3 , yieldingp rimarily NO 2 À . [14] In addition, the hydration of the electron to form ah ydrated electron and its reactiont oward gas-phase HNO 3 lead to another reactiony ieldingO H À and gaseous NO 2 . [15] Gas-phase reactions between HNO 3 andh ydrated anions are strongly influenced by the acid dissociation in water environment. For as eries of hydratedi ons, including O 2 C À (H 2 O) n and CO 2 C À (H 2 O) n , n = 31-70, the reactions of HNO 3 providedd irect evidencef or proton transfery ieldingN O 3 À . [16] Similarly,t he formationo fN O 3 À was observed in flow tube experiments even for the small oxygen hydrates, (H 2 O) n 3 X À (X = O, OD, O 2 ,D O 2 ,O 3 ). [17] Particularly interesting chemistry was found in the reaction of OC À (H 2 O) n , n = 1-50, with HCl, [18] in which ad riving force of the reaction is protont ransfer followed by evaporation of OHC from the cluster.H owever,i n some cases OHC remains in the cluster until as econd HCl molecule is picked up, resulting in Cl 2 C À (H 2 O) m and additional water evaporation.
As reviewed, [19] the ion-molecule reactiono fs trong acids (HNO 3 ,HCl) with anions in water clusters proceeded exclusively by proton transfer.However,s everal types of reactions were investigated in the case of oxides, particularly oxidationa nd charge transfer.T he effect of hydration on the reactivity of OC À (H 2 O) n , n = 0-2, was investigatedt oward several gaseous molecules in at emperature-controlled fast flow reactor, [20] in which the majority of molecules, namely CO, SO 2 ,C H 4 ,a nd N 2 O, followed the general trend with decreasing reactivity as the number of water molecules increased. In contrast, bare OC À did not exhibit any reactivity with O 2 and CO 2 ,b ut the oxidation reactionw as enabled upon hydration yieldingO 3 C À and CO 3 C À .P articularly interesting was its reactivity toward NOC leadingt oN O 2 À ,i nw hich addition of one water ligand to OC À enhanced the reaction rate, but addition of the second water suppressed it. Nevertheless,t he oxidation of NOC was found to proceeda taslightly higher degree of hydration with OC À (H 2 O) n , n 5. [21] However,v ery little is known about reactions of OC À on larger water clusters. Only the formation of OC À (H 2 O) n , n = 0-59, itself was investigated by using af low tube reactor. [22] One of the reasonsc ould be the instability of the OC À ion surrounded by water molecules and as ubsequent formation of OHCOH À . [23] Ab initio calculations have shown that, after sufficient hydration,b oth structures are energetically very closea nd most likely coexist. [24] We have recentlyi nvestigated the equilibrium between OC À and OHCOH À structures in the water clusters by means of infrared multiple photon dissociation spectroscopy, [25] in which evaporation of OHC was experimentally observed, indicating interconversion of OC À into OHCOH À .
In the present paper,w ec ombine Fouriert ransform ion cyclotron resonance (FT-ICR) mass spectrometry and density functional theory (DFT) calculations to find evidencef or or against heterogeneousr eactions betweenO C À (H 2 O) n / OH À (H 2 O) n , n = 20-38, anions, and nitrogen-containing atmospherically relevant molecules, namely NOC,N O 2 C,a nd HNO 3 .W e report the rate coefficients and reactione nthalpies derived from the experimentald ata.

Results and Discussion
The formation of the reactant ions, OC À (H 2 O) n and OH À (H 2 O) n , occurs in the reaction of anionic water clusters with N 2 Om olecules. First, OC À (H 2 O) n clusteri ons are formed as ap rimary product when the charge transfer occurs, yielding N 2 O À followed by the formationo ft he oxygen radical anion (Reaction 1). The reactioni se xothermic and leads to dissociation of water molecules. As recently shown, [25][26] the excess energy also induces an intracluster proton transfer reactiont oy ield OHCOH À (H 2 O) nÀ1 ,w hichc an subsequently evaporate OHC,y ielding OH À (H 2 O) nÀ1 (Reaction 2).
The whole process is extremelyf ast, taking place within a few picoseconds, [23] and occurs in the cluster source of the present experimental setup. The branching ratio between OC À / OH À ions can be controlled by tuning the source conditions such as laser power, timing of the laser pulse, N 2 Op ressure in the pickup cell, opening of the piezovalve controlling the gas flow,e tc.T he present branching ratios are in the range from 4:3t o2:3 for the OC À to OH À ratio, as shown for initial conditions in Figure 1a,d.
Oxidation in the reaction of NO x with OC À À (H 2 O) n ions Although hydratedO C À ions show product formation with NOC and NO 2 C,t he hydrated OH À ions are largely unreactive toward any of the NO x species. Representative mass spectra for both reactions are displayed in Figure 1. Let us first discuss the reaction with NOC.A ti nitial 0s (Figure 1a), the mass spectrum exhibits two intense cluster series, namely OC À (H 2 O) n and OH À (H 2 O) n ions corresponding to the reactants with ab ranching ratio of approximately 4:3. Onlyt races of NO 2 À (H 2 O) n ions below 2% of the total intensity are found owing to reactive collisions during the ion accumulation (2 s) in the ICR cell. The intensity of the NO 2 À (H 2 O) n ions increases with the reaction time and after 5s (Figure 1b), represents around 15 %o ft he total ion intensity.I np arallel, intracluster reactiono fO C À (H 2 O) n (Reaction 2) occurs with respective OH À formation.Atemporal evolution of ion intensities as af unction of the reaction time is shown in Figure 1c.T he NO 2 À (H 2 O) n is formed either by oxidation of NOC by OC À (H 2 O) n (Reaction3), or through radical-radical recombination of NOC with OHC followed by proton transfer (Reaction 3'), as OC À (H 2 O) n is in equilibrium with OH À (OHC)(H 2 O) nÀ1 . [25] Both mechanistic pathways lead to the same product. At longer times, the clusters ize distribution shifts to smaller sizes owing to loss of water molecules upon blackbody infrared radiative dissociation (BIRD). Neither forma-tion of HONOC À (H 2 O) n ions nor loss of ion intensity of OH À (H 2 O) n clusteri ons are observed. Therefore, there is no evidence for the reactionb etween NOC and OH À (H 2 O) n (Reaction 4).
To determine the reactionr ate, the time evolution of ion intensities is fitted according to pseudo-first-order kinetics. Reaction (3) proceeds with k abs (3) = 5.0 AE 1.5 10 À11 cm 3 s À1 .T he measured experimental rate coefficient k abs (3) is compared with the calculated collisionr ates to determine the reactione fficiency.T he collision rates for n = 25 are estimated as k HSA = 9.9 10 À10 cm 3 s À1 , k SCC = 2.0 10 À9 cm 3 s À1 ,r esulting in al ow efficiency of 3.3 %.
The plot of mean cluster sizes as af unction of time, see Figure S1(b) in the SupportingI nformation, shows as ignificant shift in ion distribution of NO 2 À (H 2 O) m to smaller cluster sizes relative to that of the OC À (H 2 O) n .The loss of water molecules indicatesa nexothermic reaction. Wet herefore applied nanocalorimetry, in which the thermochemistry of the reactioni sd eterminedf rom the average number of evaporated water molecules. An anocalorimetric fit reveals that the oxidation leads to the evaporation of 6.1 AE1.1 water molecules, which correspondst oas trongly exothermic reaction with an enthalpy of The high exothermicity of reaction (3) is ac onsequence of covalentb ond formation between OC À and NOC.T he evolution of energies with the increasingn umber of water molecules is shown in Figure 2. In the gas phase, the enthalpy of reaction (3) is calculated to be À400 kJ mol À1 ,t his value is,h owever,l owered by the higher hydration energy of OC À compared with NO 2 À .T he averageh ydratione nthalpies for al ow number of water molecules differ substantially,c alculated to be À99 and À70 kJ mol À1 for OC À and NO 2 À ,r espectively,h ydrated by one to four water molecules. The calculated average enthalpy of À253 kJ mol À1 for reaction (3) with 7-11w ater molecules agreesw ithin error limits with the experimentally obtained value (Table 1). Interestingly,r eaction (4) is predicted to be markedly exothermicf or al ow number of water molecules (Figure 2), with a reactione nthalpy of À125 kJ mol À1 for the reactioni nt he gas phase, forming an ON···OH À complex with ad istance between both moieties of 1.86 .D ifferences in hydration enthalpy of OH À and [HONO] À ,h owever,l ower this value to À9kJmol À1 for 7-11w ater molecules (Table 1). This low value is comparable to the NOC hydration enthalpy on water clusters (À7kJmol À1 for 1-11w ater molecules) and explains why the reactionisn ot observed in the experiment.
The reactions with NO 2 C as an eutralr eactant occur in as imilar fashion to that of NOC molecules, in which oxidation of NO 2 C by OC À is observed( Reaction (5)). Again, if OC À (H 2 O) n rearranges to OH À (OHC)(H 2 O) nÀ1 ,r adical-radical recombination followed by proton transfer yields the same product (Reaction (5')). The hydrated OH À ion is largely unreactive, with an upper limit for the rate of k abs < 10 À12 cm 3 s À1 .T he representative mass spectra are shown in Figure1d, e. The mass spectrum taken at 0s (Figure 1d)i sd ominated by both reactanti ons with ab ranching ration 3:2f or OH À ,h owever,a lready at the initial time, one can observe as mall amount ( % 5%)o fN O 3 À as ap roduct ion.
Traces of NO 2 À are also observed, which are assigned to NOC as an impurity in the NO 2 C gas bottle.T emporal evolution of the ion intensities with the reaction time is showni nF igure 1f. After 4s of reaction, the abundanceso fr eactant OC À ions and product NO 3 À ions are almost exactly equal. In the further courseo fr eaction, the abundanceo fN O 3 À increases until the OC À ion intensity disappears.
The calculated average reaction enthalpyo fr eaction (5) is À286 kJ mol À1 for7 -11w ater molecules, again in perfect agreement with the experiment. Similarly as for reaction(3), there is av ery high reactione nthalpy in the gas phase (À466 kJ mol À1 ), which is reduced upon hydration owing to the differencei nt he solvation energies of OC À and NO 3 À .T he computation reveals reaction (6) to be only mildly exothermic with the average enthalpy of À17 kJ mol À1 ,s imilarly to the calculated adsorption enthalpy of NO 2 C on aw ater clusters (À12 kJ mol À1 for 1-11w ater molecules). In the gasp hase, the formed OH À ···NO 2 moiety with the O-N distance of 2.24 is stable (À177 kJ mol À1 ), the relative hydration energy of OH À and the [OH···NO 2 ] À moiety makes the reactions ignificantly less exothermic.
Although both reactions are accompanied by high exothermicity,t hey are quite inefficient, occurring at 3.3 %o ft he collisions for NO and 6.5 %f or NO 2 .Apparently,the low reaction efficiency might be ac onsequence of two complementary processes: (i)NO x hydrophobicity towards water clusters and (ii) suppression of OC À reactivity upon hydration.Asignificantly smaller sticking coefficient for collisions of NO x with large water clusters comparedw ith hydrophilic molecules like water or methanol was found in pick-up experiments. [27] For instance, the values reported by Ahmed et al. [27a] showedt hat the stick-  ing coefficients of NOC and NO 2 C are smaller by factors of 11 and 20 compared with methanol, indicating av ery low pick-up efficiency.A nadditional effect might be the influence of hydration on the reaction between NO x and hydratedO C À ions, as observed in af ast flow reactor. [20][21] In thesee xperiments,adecreasingr eactivity as af unction of cluster sizew as observed. Viggianoe tal. [20] reportedt hat the rate coefficients decreased two times upon addition of one water molecule to the OC À (H 2 O) cluster. However,a lthough the number of water molecules affects OC À (H 2 O) n reactivity with n 2, no such influence was found in the range of n = 2-5 and the rate coefficients were around1 .8 10 À10 cm 3 s À1 ,r epresenting about 30 %r eaction efficiency. [21] Our experimental rate coefficient for OC À + NOC in large water clusters is about af actor of 3.6 lower than the rate coefficients reported for small ones. Our observations indicatet hat the uptake of NO x onto the aerosolp articles and their subsequento xidationo nt he particles urface do not significantly contribute to the formation of the atmospheric NO 3 À ,w hich is rather formed through gas-phase oxidation of NO x yielding gaseous HNO 3 , [3a] followedb yi ts uptakeo nto the aerosolparticles.
To clarify the mechanism of the intracluster reaction, we have carried out molecular dynamics simulations and optimized structures with NOC and NO 2 C on different positions with respectt ot he OC À (H 2 O) n cluster.W eh ave found that the impactingr adicals react only when the orientation favors the direct contact with the OC À anion. Otherwise, they might stay on the surface and eventually react. The adsorption energy, however, is small, on neat water.Wecalculated the average adsorptione nthalpy on (H 2 O) n , n = 7-11, as À7kJmol À1 and À12 kJ mol À1 for NOC and NO 2 C,r espectively.O ur calculations thus corroborate the low rate coefficient measuredi nt he experiment in aq ualitative way.
We have previouslys hown that the thermochemistry derived from our cluster studies is compatible with bulk aqueous solutions. [15,28] The enthalpy of reaction (5) combined with literature thermochemistry [29] yields the heat of formation of the OC À radical in aqueous solution of DH f (OC À (aq.)) = 48 AE 42 kJ mol À1 ,s ee the Supporting Information sectionS 2.2 for details. Combining this value with literaturet hermochemistry and the enthalpy of reaction (3) measured here yields the heat of formationo ft he nitrite ioni na queous solution, DH f (NO 2 À (aq.)) = À125 AE 63 kJ mol À1 .
Proton transfer in the reaction of HNO 3 with OC À À (H 2 O) n and OH À À (H 2 O) n ions In contrastt oN O x molecules,g aseous HNO 3 reacts with both OC À (H 2 O) n and OH À (H 2 O) n , n = 22-38. The respective mass spectra are shown in Figure 3. At first glance, experimentsw ith HNO 3 exhibit higher complexity than in the previous cases with NO x molecules. The reaction results in intense NO 3 À (H 2 O) m formation, but av ery small abundance (< 2%)o f NO 3 À (OHC)(H 2 O) m is also observed. Traces of NO 2 À (H 2 O) m are presento wing to decomposition of HNO 3 on the apparatus walls, which leads to HONO. Figure 3a exemplifies an initial distribution of clusters at an ominal time of 0s,i nw hich a small amount of 5% of NO 3 À as ap roduct ion is already present owing to reactions occurring during the accumulation process. The results indicatet hat the primary reaction is proton transfer to hydratedO C À and OH À ions, yieldingN O 3 À (Reactions (7), (7'), and( 8)). The NO 3 À (OHC)(H 2 O) m product at some point loses OHC (Reaction (7'')). After 5s of reaction time (Figure 3), the NO 3 À moiety dominates the mass spectrum and uptakeo fa dditional HNO 3 is also found (Reaction (9)). At longert imes (Figure 3c), multiple pick-up of HNO 3 andt he significant effect of BIRD take place, leading to complete water The kinetic analysis is complicated by severale ffects:r eactions (7'')a nd (8) lead to the same product;O H C radicals statistically evaporate from the product of reaction(7) or (7'), leading to hydrated nitrate with ad elay that dependso nc luster size;r eactions (9) and (10) lead to products of the same nominal mass as OH À (H 2 O) n and NO 3 À (H 2 O) m ,r espectively,w hicha re only partially resolved. Secondary reactions analogous to (9) and (10) may occur whilet he OHC is still present. The relative intensitiese xtracted for the fit in Figure 3d are therefore associated with significant uncertainties. To get an estimate for the rate of HNO 3 uptake by the clusters, we fitted the data assuming pseudo-first-order kinetics, and by combining reactions (7)/ (7')a nd (7'')i nto as ingle step. In other words, all OHC-containing products are neglected in the fit, as their intensity cannot be extracted from the data. As an aqueous7 0% HNO 3 solution is used in the experiment, which is close to the azeotropic point, we assume that the composition of the binary HNO 3 / H 2 Om ixture in the gas phase is the same as in solution. Therefore, the partial pressure of HNO 3 is estimated as 70 %o ft he total measured pressure. Then, we obtain the rate coefficients k abs (7 + 7'') = (2.0 AE 0.6) 10 À10 cm 3 s À1 and k abs (8) = (2.3 AE 0.7) 10 À10 cm 3 s À1 ,w hich correspond to 8.2 %a nd 9.4 %c ollisional efficiency,r espectively.
The reactione fficiency for HNO 3 is about af actor of 2.5 greater than for NOC,i nl ine with the relative sticking efficiencies determined by Whiteheada nd co-workers [27a] where the ratio of the HNO 3 to NOC coefficients is around 3, albeit for neutralw ater clusters. As ignificant discrepancy between our reactione fficiency and stickinge fficiency is found only when the reaction with HNO 3 is compared to NO 2 C.A lthough the adsorptione fficiency of HNO 3 to water cluster is almost six times larger when compared with NO 2 C,t he ratio of reaction efficiencies of the HNO 3 to NO 2 C in our clusters is only approximately 1.2. The most straightforwarde xplanation is that in the present experiment, ac hemical reaction occurs between the incoming neutralm olecule and the charged reactive speciesi nt he water cluster,a nd this changes the nature of the event completely, compared with neat neutral water clusters.

Conclusion
The hydrated OC À oxidizes NOC or NO 2 C to NO 2 À and NO 3 À , whereas OH À is found to be unreactive to NO x .D FT calculations indicate that OH À reactivity toward NO x is thermodynamically hindered, whereas the oxidationr eaction with OC À is strongly exothermic. Despite high heat releaseo wing to ac ovalent bond formation,t he oxidation has slow kinetics with collisionefficiencieso f3 .3 %and 6.5 %.
In contrast to NO x ,H NO 3 exhibits reactivity towardb oth hy-dratedO C À and hydrated OH À .O ur molecular dynamics simulations reveal that nitric acid is efficiently picked-up by the water cluster and undergoes ionic dissociation,f orming a H 3 O + ···NO 3 À ion pair structure.T he protont hen almost immediately reacts with OC À /OH À ,w hich therebyl eaves the cluster where NO 3 À remains. The mass spectra also demonstrate an ef-ficientH NO 3 adsorption on the surface of water clusters by observation of (HNO 3 ) 2 NO 3 À clusters. However,t he overall kinetics of the proton transfer from HNO 3 to the anionse xhibits comparable slow kinetics as measured for NO x .

Experimental Section Experimental methods
The experiments were performed by using a4 .7 TF T-ICR mass spectrometer,e quipped with al aser vaporization cluster source, [30] which has recently been modified, providing the capability of generating large hydrated cluster ions, for example, OC À (H 2 O) n .T he reactant cluster ions are generated in at wo-step process. First, the hydrated electrons (H 2 O) n C À are formed by laser vaporization of a solid zinc target and jet expansion of the hot plasma in ah elium/ water gas pulse. [31] Then, the anionic water clusters are passed through the expansion channel of the source, where they are mixed with N 2 O, yielding hydrated OC À and OH À cluster ions. [25][26] The skimmed cluster beam of OC À (H 2 O) n and OH À (H 2 O) n ions is transferred through an electrostatic lens system through differential pumping stages into the ultra-high vacuum (UHV) region of the mass spectrometer,w ith ab ackground pressure below 4.8 10 À10 mbar,a nd is stored in the ICR cell. We avoid kinetic excitation of the ions by not using the so-called side-kick, avoltage difference in the entrance electrode of the infinity cell. The trapping potentials are in the range of 1.5 V, posing an upper limit to the kinetic energy of the cluster ions. However,w ek now from many experiments with ionic water clusters that collisions do not significantly enhance the BIRD rate of water evaporation, which indicates that the available kinetic energy in the center of mass frame of clusters and reactant gas is negligible. Nanocalorimetry yields realistic thermochemical values, [28] indicating that the kinetic energy of the cluster ions is near-thermal. Reactant gas (e.g.,N O C,N O 2 C,a nd HNO 3 )i si ntroduced into the UHV region of the mass spectrometer through al eak valve at constant pressures in the range 1.0-8.0 10 À8 mbar.A st he presence of impurities in the samples might interfere with the results, substantial effort has been devoted for their purification. Both gaseous samples, nitric oxide (98.5 %, Sigma-Aldrich) and nitrogen dioxide (! 99.5 %, Sigma-Aldrich) were used directly from the lecture bottle. Before introducing NOC to the ICR cell, it was flowed through ag as purifier-a glass trap in an ethanol bath at around À50 8Ct of reeze-out the residual NO 2 C.N os uch purification method was used for the NO 2 C sample. The nitric acid liquid sample (70 %, Sigma-Aldrich) was stored in a glass ampule under vacuum and degassed by several freezepump-thaw cycles to remove gaseous impurities.
To determine the rate coefficient, reactions are monitored by recording mass spectra as af unction of time. The intensities of reactant and product clusters in the mass spectra are summed over all cluster sizes. The kinetic fit yielded ap seudo-first-order rate coefficient (k rel /s À1 ), which is converted to ap ressure-corrected absolute rate coefficient (k abs /cm 3 s À1 ). The perfect pseudo-first-order behavior also indicates that rate coefficients are largely independent of the cluster size. Ar elative error of AE 30 %i sa ssumed, determined by the uncertainty of the pressure calibration. The absolute rate coefficient k abs is then compared with calculated collision rates to determine the reaction efficiency, F. The reaction efficiency can be estimated by using the hard sphere average dipole orientation (HSA) and the surface charge capture (SCC) models through Equation (11). [32] As previously shown, the actual collision rate of ionic water clusters lies between the models. [28,33] If applicable, evaporation of OHC,w hich converts OC À (H 2 O) n into OH À (H 2 O) nÀ1 ,w as included in the fits.
F ¼ 2k abs =ðk HSA þ k SCC Þð 11Þ Thermochemistry was investigated by using nanocalorimetry. [28, 30b] The heat released during the reaction is extracted by quantitative modeling of the average size of reactant and product clusters as a function of time, taking into account blackbody infrared radiative dissociation (BIRD). [34] To extract the reaction enthalpy from the mass spectra, the mean cluster sizes of reactants and products are calculated. The results are fitted with ag enetic algorithm by using the following differential equations [Eq. (12), Eq. (13)]: dN P ¼ Àk f ðN P ÀN 0,P Þdt þðN R DN vap ÀN P Þðk Á I R =I P Þdt ð13Þ Equation (12) and the first term in Equation (13) describe BIRD of water clusters, with k f describing the linear dependence of the unimolecular BIRD rate on cluster size. The parameters N 0,R , N 0,P account for the contribution of the ionic core to the IR absorption cross sections. The second term in Equation (13) describes the evaporation of water molecules owing to the reaction enthalpy released in the water cluster.T he average number of evaporated water molecules DN vap is the key result of the fit. Assuming the energy of 43.3 AE 3.1 kJ mol À1 required to evaporate as ingle water molecule from the water cluster [35] and minor thermal corrections (see the Supporting Information), this translates to the reaction enthalpy D r H exp (298 K).

Computational methods
Clusters were calculated at the B3LYP/TZVP level of theory with dispersion correction as suggested by Grimme, [36] further denoted as B3LYP + D2/TZVP.S tructures from our recent article [25] were used as the initial point for the search of possible conformations. For hydrated NO 3 À HNO 3 and NO 3 À (HNO 3 ) 2 clusters with four or more water molecules, al arger conformational space can be expected. Therefore, we ran molecular dynamics at 300 Kf or 15 ps on the BLYP/SVP potential energy surface with at ime step of 30 a.u. ( % 0.73 fs). From the last 10 ps, 16 structures were taken and optimized at the B3LYP + D2/TZVP level of theory.
The Gaussian software suite [37] was used for all quantum chemical calculations included in the present manuscript. For molecular dynamics, the ABIN code was used. [38]