ATMOSPHERIC CHEMISTRY

Reactive uptake of N2O5 by atmospheric aerosol isdominated by interfacial processesMirza Galib1 and David T. Limmer1,2,3,4*

Nitrogen oxides are removed from the troposphere through the reactive uptake of N2O5 into aqueousaerosol. This process is thought to occur within the bulk of an aerosol, through solvation and subsequenthydrolysis. However, this perspective is difficult to reconcile with field measurements and cannot beverified directly because of the fast reaction kinetics of N2O5. Here, we use molecular simulations,including reactive potentials and importance sampling, to study the uptake of N2O5 into an aqueousaerosol. Rather than being mediated by the bulk, uptake is dominated by interfacial processes due tofacile hydrolysis at the liquid-vapor interface and competitive reevaporation. With this molecularinformation, we propose an alternative interfacial reactive uptake model consistent with existingexperimental observations.

The reactive uptake of N2O5 in the atmo-spheric aerosol plays a key role in es-tablishing the oxidative power of thetroposphere and is a major factor in de-termining air quality and climate (1, 2),

In nighttime air, NO and NO2 are oxidized byO3 to formNO3 andN2O5 (3). Between 25 and41% of that tropospheric N2O5 is thought tobe subsequently removed by hydrolysis toHNO3 in aqueous aerosol (4, 5). Experimen-tally, only the overall reactive uptake of N2O5

gas to aqueous aerosol can be measured (6).However, a molecular-level understanding ofthat process is lacking, frustrating attempts torationalize variations in field measurements(7–11). We used state-of-the-art computationaltools, including machine learning–based re-active force fields (12, 13) and methods ofimportance sampling molecular dynamicssimulations, to determine that the hydrolysisof N2O5 in aqueous aerosol is fast and sub-sequently that interfacial processes dominateits reactive uptake. This finding is inconsistentwith traditional models of reactive uptake,which assume reaction-limited bulk hydrol-ysis and equilibrium solvation (6, 8, 10, 14).Rather, we showwith explicit simulations thatreactive uptake can be understood as a resultof competition between interfacial hydroly-sis and evaporation. This interfacial model ofN2O5 reactive uptake can reasonably reproducethe experimental reactive uptake coefficienton pure water droplets. This model also helpsto rationalize a number of existing experimen-tal observations, including the temperaturedependence of the uptake coefficient and thesimilarity between the uptake coefficients onice particles and liquidwater droplets, and can

be extended to consider the dependence onorganic and inorganic species.Under standard conditions, reactive uptake

is determined by the uptake coefficient, g,which is the fraction of N2O5 molecules thatcollide with an aerosol surface and are irre-versibly lost through reaction. Measurementsof g in pure water vary, with 0.01 ! g ! 0.08(8, 10). Uptake on pure water represents anidealized case of dilute solution conditionsas might be found in fog or cloud droplets,because contributions from surface-active or-ganics and soluble inorganic salts can changeuptake in complex ways (7, 8, 15, 16). The sizeof g and its dependence on solution compo-sition and thermodynamic state is currentlyrationalized with simplified kinetic models(6, 10, 17). Unfortunately, the basic physical andchemical properties of N2O5, like its solubilityand hydrolysis rate constant, which are neededto validate assumptions made in such modelsare not available. Therefore, a model capableof directly interrogating the molecular dy-namics that transfer an initially gaseous N2O5

molecule into its solution hydrolysis productsis needed.Molecular simulations can in principle be

used to gain microscopic insight into the re-active uptake of atmospheric gases into solu-tion (6). Classical force fields have been used tostudy the physical solvation of N2O5 (18, 19),where it is computationally tractable to use en-hanced sampling methods and represent largeinhomogeneous systems. However, existingpotentials are not suitable to model chemicalreactions, precluding a study of the hydrolysisreaction. Ab initiomolecular dynamics has beenused to study hydrolysis and halide substitu-tion reactions ofN2O5 inwater clusters (20–24).However, studying systems large enough torepresent inhomogeneous systems (25) or toevolve systems long enough to study rare eventsis difficult. To overcome these limitations, weusedmachine learning techniques to fit a high-dimensional reactive potential to ab initio train-

ing data. The resultant potential allows us toaccess larger length and time scales than typicalab initio simulations, butwith comparable accu-racy. In so doing we are able to use advancedsimulation methods to uncover a completepicture of the thermodynamics and reactivedynamics that lead to the uptake of N2O5.To simulate the hydrolysis of N2O5 in liquid

water, we developed a reactive force field capa-ble of describing a broad ensemble of solvationand bonding configurations. Specifically, weconstructed a model using ab initio referencedata fit to a flexible artificial neural networkfunctional. We used supervised and activelearning procedures on a range of condensed-phase and reactive-path structures (26). Theartificial neural networks are trained on refer-ence energies and forces computed from den-sity functional theory (27, 28), which providesan accurate description of aqueous solutionstructure and thermodynamics (29–32) andwhichwe additionally benchmarked for N2O5

gas-phase dissociation energies (table S1). Theresultant reactive force field accurately repre-sents the ab initio potential-energy surfaceof water and N2O5 (tables S2 and S3), but ata substantially reduced computational cost,enabling the systematic study of the thermo-dynamics and kinetics of solvatedN2O5 and itshydrolysis products (figs. S1 to S8).

Thermodynamics of solvation and hydrolysis

Figure 1A shows a characteristic snapshot ofN2O5 and its surrounding solvation environ-ment generated from our neural networkforce field. The intramolecular structure ofthe solvated N2O5 is characterized by largefluctuations in the position of the center oxy-gen (fig. S9). These fluctuations manifest thetendency of N2O5 to spontaneously undergointramolecular charge separation, localizingexcess positive charge in an emergent NO2

d+

moiety and excess negative charge in anNO3d"

moiety, as a transient precursor to dissociation(19, 24). Despite the transient charge sepa-ration, we find that N2O5 is relatively weaklysolvated on average (fig. S10). Water forms lessthan one hydrogen bond with the outer oxy-gens on average and even fewer with the ni-trogens and bridging oxygen, resulting in anunstructured solvation shell. This is becausethe localization of the charge is primarily on thenitrogens, which are sterically inaccessible.The observed hydration structure is consist-

ent with N2O5 being sparingly soluble in water.To quantify the driving force for dissolvingN2O5 in water, we computed the solvationfree energy using thermodynamic perturbationtheory (tables S5 and S6). The resultant solva-tion free energy, Fs = 1.3 ± 0.5 kcal/mol, impliesa Henry’s law constant ofH = 0.4 ± 0.1 M/atm.H is smaller than has been inferred from pre-vious mass uptake experiments, which showeda range from 1 to 10 M/atm (33). However, the

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1Department of Chemistry, University of California, Berkeley,CA, USA. 2Kavli Energy NanoScience Institute, Berkeley, CA,USA. 3Materials Science Division, Lawrence Berkeley NationalLaboratory, Berkeley, CA, USA. 4Chemical Science Division,Lawrence Berkeley National Laboratory, Berkeley, CA, USA.*Corresponding author. Email: dlimmer@berkeley.edu

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interpretation of such experiments is difficult be-cause of the inability to separate solvation fromsubsequent hydrolysis. For a molecule with adipole, this solubility is relatively low, thoughit is only modestly smaller than that of less-reactive nitrogen oxides (34). The low solubil-ity reflects a subtle interplay between favorablelong-range electrostatic energetics and a largeunfavorable cavity formation entropy.The hydrolysis of N2O5 in liquid water is

thermodynamically favorable. We calculatedthe free energy for dissociating N2O5 usingumbrella sampling. Specifically, we computedthe free energy, F(R), as a function of the intra-molecular nitrogen–nitrogen distance, R. Thefree energy is shown in Fig. 1B and exhibits anarrow minimum at R = 2.6 Å and a broadplateau for R > 4 Å, separated by a barrier atR = 3 Å. The minimum at R = 2.6 Å reflectsthe intact N2O5 molecule, as shown in Fig. 1A,whereas the plateau for R > 4 Å manifests itsdissociation. We find that at large R, it is ther-modynamically favorable to form two equiv-alents of HNO3 (Fig. 1A). The barrier region iswide, because large separations are neededto solvate the separated nitrogens. A barrierof nearly 4 kcal/mol implies that hydrolysis isa rare event and that N2O5 can be dynamicallydistinguished from its eventual hydrolysisproducts. The free energy difference betweenthe reactant and product basin results in a dis-sociation constant of 1.3 ! 104M. The low solu-bility of N2O5 implies that nearly all solvatedN2O5 in pure water is transformed to HNO3.After hydrolysis, it is thermodynamically

favorable for the nascent nitric acid to disso-ciate into an excess proton and NO3

". Wecomputed the free energy to deprotonateHNO3

bymonitoring a continuous coordination num-ber, nh, between the oxygens on theNO3moiety

and a hydrogen (26). The free energy, F(nh), canbe estimated directly from simulations and isshown in Fig. 1C. The free energy difference forremoving a proton corresponds to a pKa valueof "1.1 (where Ka is the acid dissociation con-stant), which is reasonably close to the exper-imental value of "1.35 (35).Taken together, the calculated thermody-

namics of N2O5 solvation and subsequenthydrolysis in water are consistent with exper-imental observations that its accommodationinto aqueous aerosol is largely irreversible (6).Though weakly soluble, in water N2O5 willundergo hydrolysis to form two HNO3, whichwill subsequently deprotonate. Under highnitrate concentrations, or in low-humiditydroplets, this equilibrium could be shiftedback toward an intact N2O5. Indeed, low–water content droplets are observed to havesmaller reactive uptake coefficients, and dis-solved nitrate salts can reduce the reactiveuptake by more than an order of magnitude(8, 34).

Kinetics of N2O5 hydrolysis

The mechanism of N2O5 hydrolysis involvesan interplay between intramolecular chargeseparation and stabilization from the surround-ing water. To understand this interplay, weidentified a reaction coordinate that encodesthe microscopic details relevant to hydrolysisin solution. An appropriate reaction coordinateis one that is capable of both distinguishingthe intact N2O5 from its dissociation productsas well as characterizing the transition-stateensemble of configurations, which are thoseconfigurations that have equal probability ofcommitting to either the reactant or productstates (36). Although the nitrogen–nitrogendistance in Fig. 1B is capable of the former, it

fails in the latter. Configurations taken at fixedvalues of R are overwhelmingly committed toeither the reactant or product basins of attrac-tions. This is becauseR lacks direct informationabout the surrounding water, which is pivotalin describing hydrolysis.We have found that an appropriate reaction

coordinate for hydrolysis is a linear combina-tion of the nitrogen–nitrogen distance, R, anda continuous coordination number betweenthe nitrogen atoms in N2O5 and the surround-ing water molecules, denoted nw (26). Thecoordination number acts as collective sol-vent coordinate and describes ion pairing andsolvation dynamics in solution (37). Figure 2Ashows the corresponding free energy surface,F(nw, R), computed using umbrella sampling.A line nw = 3R + 9.6 defines a separatrix dis-tinguishing the reactant and product basins.The direction orthogonal to the separatrix actsas the reaction coordinate, x. For small R, theweak hydration structure of N2O5 is evident bythe low value of nw. The NO3

d" and NO2d+ pair

generated at large R but nw = 0 is not thermo-dynamically stable. The hydrolysis products,which are two equivalents of HNO3, at large Rhave an increased coordination number,nw# 1,reflecting the altered bonding arrangementupon abstracting a watermolecule. The saddlepoint of the surface, which we denote x*, islocated at an intermediate coordinationnumbernw = 0.4 and intermediate nitrogen–nitrogendistance R = 3.1 Å, with a free energy barrierF(x*) = 3.8 kcal/mol. The thermodynamicallymost likely reactive path follows the simulta-neous increase in the nitrogen–nitrogen dis-tance and coordinationnumber. The increasingdistance correlates with the lengthening of aN–O bond and accompanying charge reorgan-ization, which is thermodynamically stabilizedby a solvent fluctuation that alters the coordi-nation number.We used the Bennett-Chandler method (38)

to quantify the rate constant for hydrolysis.Specifically, we computed the rate, kh, as aproduct of the transition-state theory estimateand the transmission coefficient, k(t), wheret is lag time. The transition-state theoryestimate of the rate is computable from thefree-energy surface. The transmission coeffi-cient corrects transition-state theory for dy-namical effects at the top of the barrier andis given by the plateau region of the flux-sidecorrelation function. The transmission coeffi-cient is shown in Fig. 2C. Taken together, wefind the rate of hydrolysis kh = 4.1 ns"1, im-plying an average lifetime of N2O5 to be nearly240 ps. This time is in excellent agreementwith that estimated from reactive trajecto-ries propagated with direct dynamics.Figure 2, D and E, show representative

snapshots taken along typical hydrolysis path-ways. Subsequent to passing through the tran-sition state, we find that the ensemble of

Galib et al., Science 371, 921–925 (2021) 26 February 2021 2 of 5

Fig. 1. Solvation and hydrolysis thermodynamicsin bulk water. (A) Representative snapshots ofsolvated N2O5 and HNO3 in bulk water from moleculardynamics simulations. The red, blue, and whitespheres denote oxygens, nitrogens, and hydrogens,respectively. (B) Free-energy profile for N2O5 hydrolysisreaction as a function of intramolecular nitrogen–nitrogen distance. (C) Free-energy profile for thedissociation of HNO3 as a function of a continuouscoordination number between an O in the NO3 moietyand a hydrogen, nh (left). A characteristic snapshot of dissociated HNO3 from molecular dynamicstrajectory is shown, where the excess proton is highlighted in yellow (right).

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reactive pathways bifurcate, resulting in twodifferent product states. In one pathway (Fig.2D), two nitric acids are formed through theconcerted ionization of water and additionof the OH" to the NO2

+ moiety, followed byproton transfer to theNO3

"moiety. In the otherpathway (Fig. 2E), one HNO3 and one NO3

"

are formed. This process proceeds throughthe ionization of water and addition of theOH to the NO2

+; however, the H3O+ generated

does not have an existing hydrogen-bond wireto enable the subsequent donation of theproton to the NO3

". In our ensemble of tra-jectories, 20% of those follow the first pathwayand 80% follow the latter one. These observa-tions are similar to previous calculations forwater clusters (21). During hydrolysis, we findthat NO2

+ is only formed transiently, with anaverage lifetime of 4 ps, and is better charac-terized by a hydrated H2ONO2

+ species. Oncean HNO3 molecule has its own independentsolvation shell, we find that dissociation occurson average within 60 ps, or with a reactionrate of 15.4 ns"1. The Grotthuss diffusion of theexcess protons are well reproduced with ourforce field.We find a relative diffusivity ofH3O

+

to OH" of 2.2 compared with the 1.9 measuredexperimentally (39).Previous estimates of the hydrolysis rate for

N2O5 in solution place it on the order of 10"3

to 10"4 ns"1, or three to four orders of mag-nitude slower than our computed rate (40).However, like the solubility of N2O5, this rate

has been inferred indirectly frommass transfermodels and has not been measured indepen-dently. The model that is most commonly in-voked assumes equilibration between thevapor and bulk solution and is valid whenuptake is reaction limited (6). Given the shortlifetime of N2O5 in solution, this equilibriumassumption requires reevaluation. Indeed, thereaction diffusion length is small, defined aslD !

!!!!!!!!!!!D=kh

p, where D is the self-diffusion

constant of N2O5. Within our model, lD # 1 nm(table S4). As a consequence, we expect thatN2O5 does not diffuse away from the inter-facial region before reacting. This suggests thatrather than being mediated by bulk solvationand subsequent reaction, reactive uptake ofN2O5 is determined directly at the air-waterinterface, through a process of interfacial ab-sorption and reaction. This is in agreementwith some measurements on the particle sizedependence of reactive uptake, but not all(40, 41).

Interfacial model for N2O5 reactive uptake

The canonical kinetic model for the reactiveuptake of N2O5 is the so-called resistor model(6, 14, 17, 42). This model assumes that the gasmolecule is first accommodated at the surface,with probability a, and then diffuses from thesurface to the bulk where the reaction takesplace. The bulk reaction with rate kh shouldbe slow enough that an equilibrium can beestablished between the gas and the liquid

phases, with concentrations determined byHenry’s law constant H. Under these assump-tions for themass transfer kinetics, the reactiveuptake coefficient, g, can be estimated from

g ! 1a" v

4kBTH!!!!!!!!!Dkh

p" ##1

where v is the thermal velocity, kBT is theBoltzmann constant times temperature (T).Measurements suggest a value of a #> 0.4(43); however, as discussed above, neither Hnor kh can be independently measured. Pre-vious work has assumed the value of H to be5.0 M/atm, which was taken from extrapolat-ing the known solubilities of a series of otherNOx compounds (34). Inverting the expressionfor g and setting it equal to 0.03, which is themiddle of the range of experimental estimates,provides an estimate of the reaction rate on theorder of 105 s"1 for N2O5 hydrolysis. This anal-ysis is internally consistent, because it predictsa reaction-diffusion length much larger thanthe width of the interface, lD # 80 nm, but thesolubility and hydrolysis rate are dramaticallydifferent from those computed ab initio. Usingour computed values ofH and kh, we arrive atg = 0.6, which is much higher than observed.This inconsistency can be resolved by formu-

lating an alternative to the standard resistormodel that envisions the reactive uptake ofN2O5 as an interfacial process. Specifically,assuming all incoming N2O5 molecules stick

Galib et al., Science 371, 921–925 (2021) 26 February 2021 3 of 5

Fig. 2. Kinetics andmicroscopic reactionmechanisms forthe hydrolysis of N2O5

in bulk water. (A) Freeenergy as a functionof the intramolecularnitrogen–nitrogendistance and a continuouswater coordinationnumber, nw. Lines arespaced 1 kcal/mol apart,and the dashed lineplots the separatrix. Thecircles indicate theapproximate location ofconfigurations in (D) and(E). (B) Distribution ofcommitment probabilitiesto the product basin,pB, for configurationstaken along the separatrixin (A). (C) Transmissioncoefficient, k(t),as a function of time.(D) Representativesnapshots along a molecular dynamics trajectory in which two protonated nitric acids are formed through the concerted ionization of water and addition of the OH! tothe NO2

+ moiety, followed by proton transfer to the NO3! moiety. (E) Representative snapshots along a molecular dynamics trajectory in which hydrolysis of N2O5

into one HNO3 and one NO3! proceeds through the concerted ionization of water and addition of the OH! to the NO2

+ moiety.

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to the interface and do not diffuse away, thereactive uptake is given by a competition be-tween hydrolysis of N2O5 at an interface (21)and its reevaporation. If ksh is the reactionrate at the surface and ke is the evaporationrate, then the reactive uptake coefficient canbe computed from

g ! kshksh " ke

which, in the limit that g is small, reduces tog ! ksh=ke (44). This competition is illustratedin Fig. 3 with accompanying simulation snap-shots and contrasts it with the processes ofsolvation and bulk hydrolysis included in thestandard resistor model. This interfacial modelis analogous to an older perspective on N2O5

uptake (41). Using molecular dynamics simu-lations, we have tested the assumptions of thismodel and explicitly computed g by estimatingksh and ke.We computed the reaction rate at the air-

water interface to beksh = 0.95 ns"1 from directmolecular dynamics simulations. The distribu-tion of waiting times for hydrolysis are shownin Fig. 3. This rate is slower than the corre-sponding rate in the bulk by a factor of fourand predominantly follows a pathway that gen-erates two protonated HNO3 molecules. This isconsistent with previous reports of the weakeracidity of HNO3 and HCl at the air-water in-

terface (45, 46). We estimated the evapora-tion rate by first computing the free energyof adsorption to the interface from the vaporusing thermodynamic perturbation theory andthen assuming that evaporation is barrierless.We obtained a free energy of adsorption Fs =3.4 kcal/mol, which is lower than the corre-sponding solvation free energy, as shown inFig. 3. This indicates that N2O5 is preferen-tially solvated at the interface (fig. S11), whichis consistent with previous studies using em-pirical potentials (18, 19) and the weak hydra-tion observed in our bulk simulations. Fromthis, we estimate an evaporation rate ke =12.5 ns"1. The reactive uptake coefficient com-putable from these two rate processes yieldsg = 0.07, which is on the high end of the mea-sured experimental range (8, 10).An interfacial model of N2O5 reactive uptake

helps rationalize a number of existing exper-imental observations and opens additionalquestions for further examination. For exam-ple, it has been noted that the temperaturedependence of N2O5 uptake is weakly nega-tive (47, 48). The similar activation energies forinterfacial hydrolysis and evaporation resultin both processes decreasing with tempera-ture, though the larger energy of hydrolysis isconsistent with a negative temperature depen-dence. Further, measurements of the reactiveuptake on ice particles are close to those forliquid particles (49). The importance of surface

processes elucidated in our work clarifies thiscoincidence, as diffusion into the bulk of thesolid is prohibitively slow, yet interfacial hy-drolysis can still proceed. Finally, it is knownthat uptake can be suppressed at high nitrateconcentrations (8). Fromadditional simulationswith excess nitrate, we find that the stabiliza-tion of N2O5 in the presence of NO3

" resultsfrom a weakened solvation structure of N2O5,which makes it difficult for water to stabilizenascent charge separation, suppressing thehydrolysis rate (fig. S12). Such a mechanism ofsuppression could be quite general and high-lights the need for future research with morecomplex solutions. Suppression of the hydrol-ysis rate below 105 s"1 should restore the ca-nonical bulk reactionmodel. Tomove beyondidealized compositions and conditions, weimagine our framework can be incorporatedinto existing reaction diffusion models wheremolecular mechanisms and chemical data areknown. For example, the suppression of uptakeby surface-active organics can be incorporatedby parameterizing rates to accommodate,reevaporate, and react with surface cover-age. In cases wheremolecularmechanisms areunknown, additional neural network–basedsimulations can be used. For example, to un-derstand the origin branching ratio to nitrylhalides (50), models capable of the SN2 reac-tion between Cl"with N2O5 at the liquid-vaporinterface can be developed and studied.

Galib et al., Science 371, 921–925 (2021) 26 February 2021 4 of 5

Fig. 3. Elementary physical and chemical steps involved in the reactiveuptake of N2O5 in a pure-water droplet. Red denotes our proposed interfacialmodel, and blue refers to the standard bulk model. The images show an incomingN2O5 molecule first adsorbed at the liquid-vapor interface, which then eitherreacts to form HNO3 or evaporates back into the gas phase. Diffusion into the bulkof the droplet is comparatively slow, but once in the bulk, N2O5 can undergo

hydrolysis. In either case, deprotonation of HNO3 occurs after solvation intothe bulk. The blue surface in the top images represents the location of the liquid-vapor interface. The probability distribution of the lifetime time of a N2O5

molecule, P(t), at the air-water interface and in bulk water is shown at the topright. Solvation free energies of N2O5 at the air-water interface and in bulkcompared with the gaseous N2O5 are shown at the bottom left.

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ACKNOWLEDGMENTS

We thank T. Bertram, B. Gerber, A. Goetz, and G. Nathanson forstimulating discussions and B. Hirshberg for initial solvated N2O5configurations. Funding:This work was funded by the National ScienceFoundation through the National Science Foundation Center forAerosol Impacts on Chemistry of the Environment (NSF-CAICE) undergrant no. CHE 1801971. This research used resources of the NationalEnergy Research Scientific Computing Center (NERSC), a U.S.Department of Energy Office of Science User Facility operated undercontract no. DE-AC02-05CH1123. Author contributions: M.G. andD.T.L. designed the numerical simulation setup, analyzed the data, andprepared the manuscript. M.G. ran the simulations, and D.T.L.supervised the project. Competing interests: The authors declare nocompeting interests. Data and materials availability: All data areavailable in the manuscript or supplementary materials.

SUPPLEMENTARY MATERIALS

science.sciencemag.org/content/371/6532/921/suppl/DC1Materials and MethodsFigs. S1 to S12Tables S1 to S6References (51–66)

10 July 2020; accepted 22 January 202110.1126/science.abd7716

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by atmospheric aerosol is dominated by interfacial processes5O2Reactive uptake of NMirza Galib and David T. Limmer

DOI: 10.1126/science.abd7716 (6532), 921-925.371Science

, this issue p. 921Sciencesome existing experimental observations.inverse: Interfacial hydrolysis is followed by solvation into the interior. Their reactive uptake model is consistent with

used molecular simulations to show instead that the mechanism is theet al.because of the fast reaction kinetics. Galib solvation and subsequent hydrolysis in the bulk of the aerosol. However, this mechanistic hypothesis was unverifiable

from the atmosphere by aqueous aerosols was long thought to occur by5O2The uptake and hydrolysis of NOn the surface

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Supplementary Materials for

Reactive uptake of N2O5 by atmospheric aerosol is dominated by interfacial processes

Mirza Galib and David T. Limmer*

*Corresponding author. Email: dlimmer@berkeley.edu

Published 26 February 2021, Science 371, 921 (2021)

DOI: 10.1126/science.abd7716

This PDF file includes:

Materials and Methods Figs. S1 to S12 Tables S1 to S6 References

2

Materials and Methods S1. Machine learning ab initio potential

We have used the smooth version (12) of the DeePMD-kit (51) to learn the many body interatomic potential energy and forces generated at the DFT level of theory. The primary data sets for the training were generated from ab initio molecular dynamics simulations using the Gaussian Plane Wave implementation in CP2K (52). All ab initio molecular dynamics simulations were carried out in the canonical ensemble at ambient temperature and density using the revised version of PBE functional (25) along with empirical dispersion correction (Grimme D3) (26). We used a molopt-DZVP basis set and a plane wave cut-off of 300 Ry. The core electrons were described with GTH pseuodopotential (53). We also carried out metadynamics simulations (54) and umbrella sampling (55, 56) to generate reactive structures along the hydrolysis pathway. With the primary data set generated by molecular dynamics and metadynamics simulations, we first trained two independent machine learned potentials that were then followed by active learning to improve both models. The disagreement in force between the two models was used to select the new data sets for active learning. Final convergences for testing errors in the energy were 0.2 meV/atom and in the force were 50 meV/ Å -atom.

S1.A Gas phase dissociation energies for N2O5 We have computed the dissociation energy difference and the energy barrier for the gas phase dissociation reaction (N2O5 -> NO3 + NO2

+ ) at the revPBE-D3 level of theory (25, 26) and compared

those to B3LYP (57, 58) and MP2 (59). These are shown in Table S1, in which we find that revPBE functional can satisfactorily reproduce the gas phase dissociation energies relative to a hybrid functional and higher level electronic structure theory. S1.B Training Data set The training data set includes structures generated by ab initio molecular dynamics with three dimensional periodic boundary conditions for solvated N2O5 and bulk ambient water. We have included representative structures from the following simulations in a 19.73 x 19.73 x 19.73 Å simulation box:

1. pure water box with 256 water molecules 2. solvated N2O5 with one N2O5 molecule solvated by 253 water molecules 3. solvated HNO3 with one HNO3 molecule solvated by 253 water molecules 4. solvated NO3

- and H3O+ with one NO3

- and one H3O+ molecules solvated by 252 water molecules

5. solvated H3O+ and OH- with one H3O+ and one OH- molecules solvated by 254 water molecules 6. solvated N2O5 at the surface of a liquid vapor interface with one N2O5 and 522 water molecules in

a 25 x 25 x 25 Å slab and 20 Å vacuum on both sides. We also included structures along the hydrolysis pathway into our training sampled from metadynamics (54) simulations in conjunction with AIMD using CP2K (52). Our final data set to train the bulk solvated N2O5 model contained 10000 data points and the slab model contained 20000 data points. S1.C Training accuracy We trained our neural network (NN) model using a deep neural network architecture with 3 layers each having 600 nodes as implemented in DeePMD-kit (49). We used a cutoff distance of 8 Å to represent the local internal structure around any atom in our training data set. We defined the loss function as the sum of mean square deviations in energy and force, which was minimized during the training process. For the slab model, we also included mean square deviation in virial in the loss function. At the end of the training, the accuracy of the model was 2.0 meV in energy/atom and 0.05 eV/Å in force/atom. Correlation plots for the testing and training data for the force predicted by the neural network relative to that

3

computed from DFT are shown in Fig.S1 and S2. Summary errors are presented in Table S2 and Table S3. S1.D Active learning We trained two independent models, each with the same primary data set but with different initial parameters and different structures of the hidden layers. Both models were trained with a neural network architecture having 3 layers, but one having 600 nodes in each layer and the other having 400 nodes in each layer. We then followed active learning procedure to improve both models (60). The disagreement in force between the two models was used to select the new data sets for active learning. The force-force correlation between these two models is used to determine finally whether the training data set is large enough to achieve a converged result. This data is shown in Fig. S3 and yielded a mean squared deviation of 45 meV/Å-atom. S1.E Validation of the NN model We have checked the accuracy of our model by comparing various structural and dynamic properties with DFT data and also the consistency between the two independent NN models. We report the structural calculations in Figs.S4-S10. We have calculated the diffusion constant of N2O5, H3O+ and OH- in bulk water from the mean squared displacement of the solvated molecule in a molecular dynamics trajectory. This is detailed in Table S4. S2. Molecular dynamics simulations

To investigate the hydrolysis reaction of N2O5, we carried out molecular dynamics simulations at ambient temperature and pressure with 0.5 fs timestep. All of our studies were performed at ambient conditions with temperature T = 298K and pressure p = 1 atm. The integrator used a Langevin thermostat, with characteristic time constant of 1 ps. The bulk system contained one N2O5 molecule solvated by 253 water molecules in a 19.73 x 19.73 x 19.73 Å box with periodic boundary conditions in all three dimensions. An equilibration molecular dynamics simulation of 5 ns was carried out by classical molecular dynamics that was followed by another equilibration MD simulations for 400 ps with machine learned force field. During the equilibration, the N-N distance was constrained to 2.6 Å to prevent the hydrolysis reaction taking place. We sampled the initial configurations from a 1 ns constrained molecular dynamics simulation and then carried out unconstrained molecular dynamics simulations for an ensemble of 50 trajectories, each for 1 ns. To investigate the hydrolysis reaction of N2O5 at the air-water interface, we prepared a slab model with thickness of 25 x 25 x 25 Å, having free interface and an additional 20 Å vacuum on each side. We employed periodic boundary conditions in all three dimensions. The slab model included 1 N2O5 molecule and 522 water molecules. The z-position of the N2O5 molecule was constrained at the Gibbs diving surface of the slab. The initial configuration was generated from an equilibrated water box. An equilibration of 10 ns was carried out by classical molecular dynamics simulations with SPC/E water and GAFF force field (18), which was then followed by another equilibration MD simulations for 500 ps with the machine learned force field. During the equilibration, the N-N distance was constrained to 2.6 Å to prevent the hydrolysis reaction taking place. We sampled the initial configurations from a 1 ns constrained molecular dynamics simulation and carried out molecular dynamics simulations for an ensemble of 28 trajectories, each for 3 ns. S3. Free energy and rate calculations We used umbrella sampling (55) to estimate the reaction free energies for the hydrolysis reaction of N2O5 in the bulk water. Harmonic biases were employed for both nw and R, and each of 26 windows were simulated for 1 ns. The free energies were then estimated using WHAM (56). In order to calculate the correction to the transition state theory rate we computed the transmission coefficient from an ensemble of 2000 unbiased trajectories. The commitor probability was computed from an ensemble of 1000 unbiased trajectories, each starting from constrained configuration at the dividing surface with a random

4

velocity taken from Maxwell-Boltzmann distribution. We have computed the free energy to dissociated HNO3 in bulk water from an ensemble of molecular dynamics trajectories having one HNO3 molecule solvated by 255 water molecules in a 19.73 x 19.73 x 19.73 Å box. Since deprotonation occurs frequently, we have computed the free energy by monitoring nh. We have computed the solvation free energy of N2O5 using thermodynamic perturbation theory. For computational efficiency, we first used an empirical nonreactive reference potential and constructed a reversible work path by pulling a molecule of N2O5 initially in the vapor through a liquid-vapor interface and into the bulk using a slab geometry. We used the SPC/E water model and a GAFF force field for the N2O5 with partial charges parametrized to reproduce the ab initio electrostatic potential (18). We then estimated the free energy difference between the empirical model and our neural network potential model, by linearizing the relative Boltzmann weights collected from 20,000 configurations of the solvated classical model. An analogous calculation was used to compute the absorption free energy at the interface. S3.A Free energy of N2O5 hydrolysis We employed umbrella sampling to calculate the free energy of N2O5 hydrolysis, as a function of two reaction coordinates, i) the distance between the two nitrogen atoms within the N2O5 molecule (R) and ii) the water coordination number nw. The coordination number was computed from (62)

where rij is the distance between atoms i and j, and rc = 2.4 Å. We employed harmonic potentials of the form,

with 26 windows are equally spaced along the distance coordinate, 2.4Å ≤ R0 ≤ 5.0Å and 10 windows along the coordination number coordinate, 0 ≤ n0 ≤ 1.0. We used spring constants of kR = kn =15.0 kcal/mol-Å2. Each of the windows was run for 1 ns. S3.B HNO3 dissociation To compute the free energy for dissociation of HNO3, we monitored a continuous coordination number, nh, between the oxygens on the NO3 moiety and the hydrogens, defined as

with rc = 1.2Å. Using an ensemble of 10 trajectories, each for 4 ns we were able to converge a distribution of nh and also the characteristic time for HNO3 dissociation. S3.C Bulk and interfacial solvation free energy of N2O5 In order to computer the free energy of solvation, we employed thermodynamic perturbation theory using a classical fixed charge reference potential. We have computed the free energy profile for the transfer of a N2O5 molecule from the gas phase to the bulk through the air-water interface in slab simulations using umbrella sampling (55). We employed SPC/E water model (63) and the GAFF force field (64) for the N2O5 with partial charges parametrized to reproduce the ab initio electrostatic potential (18). We employed a real-space cutoff of 9.0 Å to non-bonded interactions and the long range electrostatics was computed by Particle Mesh Ewald summation. The bonds involving hydrogen atoms were constrained using the SHAKE algorithm (65). The temperature was kept at 300 K using Langevin

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UB = kR(R�R0)2 + kn(nW � n0)

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dynamics with a collision frequency of 5.0 ps-1 and a time step of 1 fs was used as employed by LAMMPS (66). The free energy profile is obtained from a set of umbrella sampling using distance between the COM of a water slab and the N2O5 molecule. The bias potential was of the form

where we took 50 windows equally spaced along the z-coordinate from 0.0 ≤ zo ≤ 25.0 Å, and employed kz =5.0 kcal/mol-Å2. Each of the windows was run for 4 ns. The free energy as a function of z, F(z), is shown in Fig. S11. We define a bulk N2O5 as z < 4Å and an interface N2O5 as 10 ≤ z ≤ 17Å. To compute the solvation free energy within the NN model from the empirical model, it is sufficient to compute the additional free energy to transform the gaseous N2O5 from the NN model from the empirical model and the solvated N2O5 NN model from the empirical model. The free energy to transform the system from the empirical model described by energy function EE to the NN model described by energy function ENN is given exactly by (55),

where FNN, FE are the free energies in the NN model and empirical model respectively, and <...> denotes ensemble average. If the energy difference between the two representations is small, the expression above can be expanded to first order, yielding,

which is an approximation that can be checked a posteriori. For the solvation free energy in the bulk and at the interface, we must compute free energy changes for the gases N2O5 as well as the two differently solvated species. For the empirical model, we have computed the average energies for these three species from a 10 ns long molecular dynamics trajectory, and averaged potential energy from a 4 ns long molecular dynamics trajectory from the NN model. These differences, as well as their implied free energies are shown in Tables S5 and S6. Note that the first order perturbation theory assumes identical entropic contribution to the free energy, which given the small changes in energy, on the order of kBT, seem self-consistent. S4. Generalization of the interfacial uptake model

S4.A. Temperature dependence of reactive uptake

Within the interfacial model we propose for pure water, to first order in the temperature change around 300 K, the temperature dependence results from the difference in activation energies of the two competing rate processes. Specifically, assuming that the kinetic prefactors scale linearly with temperature to first order the relative change in the uptake is given by

where the change will be negative if the activation energy of hydrolysis (ΔEh) is larger than the activation energy for evaporation (ΔEe). In our calculations, the free energies both have significant energetic and entropic contributions and decoupling this two is difficult. However, in Table S6 we have an estimate of the activation energy to evaporate 8.2 kcal/mol, and in Table S1 we have the gas phase value of the activation energy for breaking the NO bond be 13.8 kcal/mol, leading to a slope that is negative though

UB = kz (z � z0)2

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small. Increasing the temperature from 300 K to 310 K would yield a corresponding change to the uptake from 0.07 to 0.05. S4.B. Role of nitrate ions on reactive uptake

With our existing intermolecular potential, we can gain indirect insight into the suppression of reactive uptake in aqueous aerosol with added nitrate by performing additional bulk molecular simulations at 1 M concentration of HNO3. We find that the presence of NO3

- in the vicinity of N2O5 supresses the local solvation structure of N2O5, making it more difficult for water to stabilize the nascent charge separation, and affecting a suppression of the hydrolysis rate. Figure S12 compares the radial distribution function between nitrogen of N2O5 and oxygens of the water molecules for a single N2O5 solvated by waters to that for a system where a NO3- ion was biased to remain in the first solvation shell of the N2O5 molecule with a constraint on distance between the excess nitrate and the average Ns of the N2O5 to lie within 4 Å. We find that NO3

- and N2O5 spontaneously cluster and employ the constraint to aid in gathering statistics. The radial distribution function shows clearly that N2O5 is less solvatedbywatermoleculeswhenNO3-isinproximity to the N2O5. Integrating the radial distribution function to 5 Å, we find a decrease in water coordination number of 2.8 molecules for N2O5 in the presence of NO3

- relative to its neat solution value. This reduction in coordination reduces the likelihood that a solvation fluctuation results in hydrolysis.

7

Fig. S1. NN model prediction vs DFT results for the x-component of the force over a data set that was included in the training.

8

Fig. S2. NN model prediction vs DFT results for the x-component of the force over a data set that was not included in the training.

9

Fig. S3. NN model prediction between two independently trained models for the x-component of the force over a data set that was not included in the training.

10

Fig. S4. O-O radial distribution function for bulk water at ambient temperature and pressure

11

Fig. S5. O-H radial distribution function for bulk water at ambient temperature and pressure

12

Fig. S6. Probability distribution of N-O-N angle of solvated N2O5 in bulk ambient water.

13

Fig. S7. H-H radial distribution function for bulk water at ambient temperature and pressure.

14

Fig. S8. Probability distribution of the terminal O-N-O angles of solvated N2O5 in bulk ambient water.

15

Fig. S9. Probability distribution of the difference between two N-O distances of solvated N2O5 in bulk ambient water.

16

Fig. S10. Nitrogen-water oxygen radial distribution function for solvated N2O5 in bulk water at ambient temperature and pressure.

17

Fig. S11. Potential of mean force for the transfer of a N2O5 molecule from gas phase to bulk of the liquid. Gibbs dividing surface is at 12 Å and gas phase is in the right hand side of the dividing surface.

18

Fig. S12. Radial distribution function between the nitrogen of N2O5 and oxygens of water molecules (left), and between the nitrogen of N2O5 and hydrogens of water molecules (right). Red line represents solvated N2O5 system, and black line represents solvated N2O5

with excess NO3- where a NO3

- was biased at a distance of 4 Å from average of the two nitrogen atoms of N2O5.

Table S1.

19

Calculated energies (kcal/mol) for the gas phase dissociation of N2O5 into NO3- and NO2

+.

Method ȟ� ȟ�†

MP2/6311++G(2d,2p) 147.33 12.21

B3LYP/6311++G(2d,2p) 155.85 14.00

revPBE/6311++G(2d,2p) 151.74 13.78

Table S2.

20

RMS error in the NN model for the bulk system.

Training data set Test data set

Energy (meV/atom) 0.2 0.25

Force (meV/Å-atom) 50 60

Table S3.

21

RMS error in the NN model for the slab system.

Training data set Test data set

Energy (meV/atom) 0.2 0.25

Force (meV/Å-atom) 60 70

Virial (meV/atom) 3.0 3.0

Table S4.

22

Diffusion constant, units are in 10 9 m2/s.

Simulation ���������� (37, 58)

N2O5 0.55 0.10

H3O+ 7.8 9.4

OH- 3.6 5.2

Table S5.

23

Enthalpy and entropic contribution to the solvation free energy computed from the empirical potential. Units are in kcal/mol. The statistical sampling error of the calculated free energy values �ǻF) is approximately ± 0.1 kcal/mol and that for the energetiF� FRQWULEXWLRQ� �ǻU) is ± 1.0 kcal/mol.

ȟ ȟ� -T ȟS

Gas 0.0 0.0 0.0

Surface -2.7 -7.5 4.8

Bulk -1.55 -9.2 7.65

Table S6.

24

Solvation free energy obtained from the NN model employing thermodynamic perturbation method. Units are in kcal/mol. The statistical sampling error of the calculated energetic contribution �ǻU) is ± 1.0 kcal/mol.

ȟ ȟ� -T ȟS

Gas 0.0 0.0 0.0

Surface -3.4 -8.2 4.8

Bulk -1.3 -8.95 7.65

25

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