Prediction of Reactive Nitrous Acid Formation in Rare‐Earth MOFs via ab initio Molecular Dynamics

Abstract Reactive gas formation in pores of metal–organic frameworks (MOFs) is a known mechanism of framework destruction; understanding those mechanisms for future durability design is key to next generation adsorbents. Herein, an extensive set of ab initio molecular dynamics (AIMD) simulations are used for the first time to predict competitive adsorption of mixed acid gases (NO2 and H2O) and the in‐pore reaction mechanisms for a series of rare earth (RE)‐DOBDC MOFs. Spontaneous formation of nitrous acid (HONO) is identified as a result of deprotonation of the MOF organic linker, DOBDC. The unique DOBDC coordination to the metal clusters allows for proton transfer from the linker to the NO2 without the presence of H2O and may be a factor in DOBDC MOF durability. This is a previously unreported mechanisms of HONO formation in MOFs. With the presented methodology, prediction of future gas interactions in new nanoporous materials can be achieved.


Introduction
Chemical separations are necessary to produce everyday products and services used throughout the world and account for about 40 %o fU Si ndustrial energy use. [1] 80 %o f worldwide energy production is still generated using fossil fuels. [2] Chemical separations are needed to treat flue gas streams which can contain parts per million levels of reactive NO x (NO 2 /NO), SO x ,CO 2 acid gases,along with humidity. [3][4][5] Thepresence of acid gas species in flue gas streams contribute to its toxicity.T hey also present challenges for separation materials since the intrinsic reactivity of acid gas species results in material poisoning and degradation of many adsorbents.M aterial degradation in the presence of acid gases also increases costs as current materials may only be applied once before losing separation capability.
To address these challenges,s ignificant research has focused on ac lass of nanoporous materials called metalorganic frameworks (MOFs), which have exhibited excellent qualities for chemical separations. [6][7][8][9][10][11][12] MOFs are synthesized through aj udicious selection of metal cluster elements and organic linker molecules,e nabling targeted framework compositions,p ore size,a nd ligand functional groups.F urthermore,M OF materials can be tailored to contain unique material characteristics for specific chemical environments.
One method for tuning MOF material properties is to choose am etal precursor with new chemical properties.T he development of MOF materials synthesized with lanthanide (Ln) and actinide elements provide unique advantages compared to traditional transition metal MOFs. [13][14][15] The inclusion of fb lock elements offer new electronic structures which can result in unique MOF topologies,and novel optical and magnetic properties.
Recently,anew series of rare earth 2,5-dihydroxyterephtalic acid (RE-DOBDC) MOFs have been synthesized with their crystal structure based on the Zr UiO-66 framework. [16,17] TheRE-DOBDC MOFs maintain asimilar framework that is approximate to UiO-66 but provide unique chemical and electronic properties attributed to rare earth elements.P revious DFT calculations have also shown consistencyw ith experimentally measured IR spectra when modelled as fully activated materials,m imicking the experimental conditions. [17,18] Theu nique electronic structures provided by Ln 4f electrons offer binding properties not exhibited by Zr. Utilization of the RE elements in the MOF metal centre enabled preferential binding of acid gases,s uch as NO x and SO x ,tothese frameworks. [19][20][21] In addition to the selective adsorption of acid gases,this series of RE-DOBDC MOFs have shown to be structurally stable under humid NO x environments,and both optically and magnetically responsive to NO x adsorption in humid environments. [20][21][22][23] Ther esponsiveness of the RE-DOBDC MOFs to NO x adsorption stems from two primary adsorption sites:i )a nu nsaturated metal centre and ii)t he carboxylates on the DOBDC organic linkers.R esulting chemical species in the MOF pore (posthumid NO x exposure) were experimentally identified as nitrate,nitrite,and nitro functional groups. [20] Previously published experimental work identified newly formed gas species and adsorption site competitions in RE-DOBDC MOFs. [20] However,the effect of species formation mechanisms or binding on MOF structural stability was not investigated. This is necessary in order to obtain atomic level insight into adsorption mechanisms and processes.S tatic density functional theory (DFT) simulations at 0K were performed and validated that H 2 Oismore strongly bound to the RE metal sites than NO x ,which strongly interacts with the DOBDC linkers. [20] While these previous DFT studies were able to shed some light on the adsorption process,s everal assumptions were made,i ncluding the concentration and binding location of the acid gas molecules in the structure. Furthermore,the simulations were unable to identify possible formation of secondary molecular species (both long lasting and temporary species), the effect of spatial confinement by the organic linkers on adsorption, and the role of temperature.S ince MOFs are comprised of flexible organic linkers, material motion and gas-framework interactions influence the separation capability and needs to be considered in investigations of acid gas separation. Ultimately,a nu nderstanding of the structure-property relationship between framework composition and durability is required for the design of MOFs toward applications in more complex, caustic environments.A bi nitio molecular dynamics (AIMD) simulations enable real world predictions toward that end.
AIMD combines accurate electronic structure calculations found in DFT and large scale classical molecular dynamic (MD) simulations by implementing DFT electronic structure optimizations at each time step along aM D trajectory.A IMD is computationally expensive but is offset by the level of insight into the energy and chemical behaviour of highly interacting gas-MOF environments.T his is true especially for systems containing NO x species which contain an unpaired electron. All calculations are spin unrestricted, [24] allowing for the spin to be taken into account. Previous AIMD work has been used to predict competitive adsorption and separations of O 2 versus N 2 in M 2 (DOBDC), [25] C6 alkane isomers, [26] and to describe the mechanisms of adsorption and desorption of H 2 Oi nM 2 (DOBDC). [27] Additionally,A IMD simulations have been applied to identify unique breathing modes found in MOF materials [28] and hydrogen uptake in MOF-74. [29] While these works attest to the insight and predictive capabilities of AIMD simulations,p revious work has stopped short of application of AIMD to the simulations of complex multicomponent mixed acid gases.
Theapplication of advanced computing simulations,such as AIMD,a re required to address the role of how acid gas mixtures react inside the RE-DOBDC MOF pores.Examples of this include studies of the formation of molecular species, binding energies between the acid gas species and the framework, and framework compensation for local defects. In particular,identification of chemical by-products in situ is very difficult experimentally given the fast time scales and high number of simultaneous interactions.U sing AIMD provides valuable atomistic mechanism information that cannot be achieved elsewise.
To overcome the inherent shortfalls of standard computational investigations we present, for the first time,a nA IMD investigation of separation of complex mixed acid gas environments in RE-DOBDC MOFs.T oi dentify the mechanisms that control the interactions of mixed acid gases with RE-DOBDC MOFs,2 4u nique dynamic AIMD simulations were performed for both single gas adsorption of NO 2 and H 2 Oa nd mixed gas compositions of NO 2 and H 2 Oi nR E-DOBDC MOFs (RE = Eu, Tb,Y ,Y b) at ambient temperatures.T he suite of AIMD simulations enabled the exploration of the effect of acid gas composition and concentration on the in-pore formation of various nitrous biproducts.These simulations enable the first computational investigation of this novel and stable RE-DOBDC MOF series in response to complex mixed acid gas environments,w ith the results providing mechanistic-based insights that can be used to predict the material response to even more complex acid gas mixtures.
Additionally,d etailed analysis focuses on the interaction between the RE-DOBDC MOF framework and NO 2 adsorbed gas molecules.P revious experimental results had identified multiple unique reactions occurring between humid NO x and RE-DOBDC MOFs including interaction between NO x and the DOBDC linker. [20] NO 2 adsorption or desorption at unsaturated RE metal sites,r eactions between NO 2 -DOBDC hydroxyl linkers,C -NO 2 nitro formation, N 2 O 4 formation, and HONO formation were all explored. The formation of HONO is highlighted as it is an important precursor to the hydroxyl radical, which is detrimental in atmospheric chemistry. [30] Furthermore,HONO has also been shown to reactively interact with UiO-66-NH 2 MOFs,r esulting in HONO being broken down into N 2 and H 2 O. [31] Thea pplication of AIMD allows for the simulation of spontaneous reactions between in-pore acid gas molecules, and between the acid gas molecules and the MOF framework. Through this complex AIMD simulation series,t he preponderance of HONO formation and its bonding to MOF frameworks is highlighted. Additionally,u nique chemical insights are presented from more realistic temperature affects as compared with static DFT calculations.I mportantly,t he use of AIMD enables the future design of novel and optimized nanoporous materials for selective adsorption and durability to more complex and industrially relevant acid gas stream.

Results and Discussion
Thea pplication of AIMD allows for the simulation of spontaneous reactions between individual acid gas molecules inside the MOF pore,and between the acid gas molecule and the MOF framework. Ther esults allow for the evaluation of competitive adsorption between NO 2 and H 2 Oa tb oth the unsaturated metal centres and the DOBDC linkers.Pure and binary mixtures of H 2 Oa nd NO 2 were evaluated for identification of how competitive effects may impact adsorption and separation. Thec omplete data set of acid gas adsorption for all 24 structures are included in the SI (Tables S1,S2).

Selection of acid gas mixtures
At otal of 24 unique AIMD trajectories were designated as vital to determining the effects of MOF metal centre choice,g as selectivity in adsorption, including gas composition, gas pressure,a nd adsorption temperature.F irst, four different metal centres (RE = Eu, Tb,Y ,Y b) of the RE-DOBDC MOF were evaluated to identify their influence on adsorption. Next, single gas compositions were simulated for H 2 Oa nd NO 2 as ab enchmark for comparing with more complex gas mixtures.B inary gas mixtures (H 2 O:NO 2 )w ere then simulated to identify direct competitive effects between two different acid gases.The increase in complexity of the gas mixtures allows for the simulation of competitive effects between gas species in adsorption behaviour. Thef inal variable was gas concentration, with both low and high concentrations of each gas mixture being simulated (i.e.1NO 2 molecule versus 12 NO 2 molecules,1 :1 H 2 O:NO 2 versus 6:6 H 2 O:NO 2 ). Theratio and composition of acid gases simulated in all AIMD trajectories are included in Table 1. TheR E-DOBDC MOF structures contain 12 metal atoms in the unit cell, therefore am aximum of 12 acid gas molecules were included in the simulation. This enabled gas adsorption at 100 %o ft he metal sites.T he complete data set of acid gas adsorption for all 24 trajectories is included in the SI (Tables S1,S2) and an example RE-DOBDC structure is included in Figure 1.

Metal dependence of adsorption
Overall, limited variation in adsorption of H 2 Oa nd NO 2 at the metal centres in the RE-DOBDC MOFs were hypothesized, based on previously calculated DFT binding energies for H 2 Oa nd NO 2 in RE-DOBDC MOFs,w hich identified that H 2 Oi sb ound more strongly than NO 2 across the entire Ln-series. [32] Additionally,t he statically calculated binding energies for H 2 Oa nd NO 2 in RE-DOBDC MOFs reported by Vogel et al. [32] exhibited only a % 0.1 eV variation in binding energies in RE-DOBDC MOFs.H ere,m etal centre dependence of adsorption across all AIMD trajectories included 9total adsorption events at metal centres in the Eu-DOBDC trajectories,4in Tb-DOBDC,6in Y-DOBDC and 4 Yb-DOBDC,T able S2. Along the calculated AIMD trajectories,a dsorption at aR Em etal site is classified as gas adsorption to aR Ea tom without desorption. This trend in metal adsorption events closely follows the Ln contraction trend in ionic 3 + radii Eu > Tb > Y > Yb for RE elements. [33] Thedecreasing ionic radii size results in adecrease in unit cell size and RE-DOBDC MOF pore volume.This places the gas molecules in closer proximity to each other in the pore and increases the number of gas-gas and gas-DOBDC interactions. [24] Tb shows alower number of adsorption compared to the smaller Y. However,i tc an be contributed to the small number of events along the trajectory.Therefore,the trend in gas adsorption indicates that it is the volume of the unit cell, Table S3, and not necessarily the chemistry of the metal centre,that is causing increased metal site adsorption through more frequent competitive interactions.

Gas adsorption dependence on concentration
Gas adsorption at metal sites is the primary mechanism of adsorption in MOF materials and occurs in all AIMD trajectories.W hena nalysing the effects of gas concentration in the RE-DOBDC MOF analogues,c omparison of adsorption behaviour between low and high concentration gas mixtures shows aclear distinction. In low gas concentrations containing as ingle H 2 Om olecule adsorption at am etal site occurs only in the Y-DOBDC MOF.H owever, high concentration H 2 Og as mixtures (12 H 2 O) account for 95 %o fa ll identified metal site adsorption events along the AIMD trajectories, Figure 2, with adsorption occurring in the Eu, Tb, Y, and Yb -DOBDC MOFs.A tl ow concentrations,t he individual acid gases were observed to interact with the DOBDC linkers,h indering their ability to diffuse to an unsaturated metal site,r esulting in minimal adsorption. The

Angewandte Chemie
Forschungsartikel formation of new chemical species is also concentration dependent, with increased formation of new chemical species and increased gas adsorption along the AIMD trajectories, Figure 2a nd Table S1.

Gas adsorption dependence on composition
Identification of competitive adsorption is investigated through comparisons of high concentration single and binary H 2 Oand NO 2 gas mixtures.Initially focusing on pure NO 2 gas, limited gas-metal adsorption in the 12 NO 2 trajectories was observed, with atotal of 4adsorption events.The low number of adsorption events highlights the weak adsorption energy of NO 2 at unsaturated metal sites in RE-DOBDC MOFs compared with H 2 Oo rm ixed H 2 O + NO 2 gases.I n comparison to pure NO 2 ,the 12 H 2 Otrajectories show atotal of 9adsorption events and indicates astronger interaction of H 2 Oa tt he metal sites.T his finding is in agreement with previous static DFT calculations in RE-DOBDC MOFs which identified abinding energy trend of H 2 O > NO 2 across the RE-DOBDC MOF series at unsaturated metal sites. [32] NO 2 is known to adsorb to both metal centres and ligands, [20] which may be affected through competition with H 2 Oadsorption. In the binary 6NO 2 + 6H 2 Ogas mixture,the NO 2 adsorption is reduced compared to pure 12 NO 2 .I na ll mixed gas trajectories,N O 2 is the least common molecule bound to am etal centre,a ccounting for only 25 %o ft he bound species in the 6NO 2 + 6H 2 Ot rajectories,i ndicating competitive metal site adsorption between NO 2 and H 2 O. The new competing interactions are hypothesized as NO 2 -H 2 O gas-gas interactions and H 2 O-metal adsorption. However,a s the number of NO 2 adsorption events decreased following the introduction of H 2 Ointo the AIMD trajectories,from 4to2, the total number of gas adsorption events at metal centres increased, from 4to8.T he increased metal site adsorption is due specifically to H 2 Oa dsorption, highlighting the stronger H 2 Oi nteraction when directly competing with NO 2 .A st he H 2 Op referentially binds at the metal sites,N O 2 begins to adsorb in adifferent pore location.
Despite the energetic preference for H 2 Oa dsorption at the metal centre and the high adsorption of NO 2 on the linker, metal site adsorption of NO 2 was still identified. TheA IMD trajectories highlighted aseries of conditions which allow the NO 2 to adsorb at an unsaturated metal site and are detailed later in this manuscript.

Formation of secondary molecular species in MOFs
In complex gas mixtures,newly formed by-product species play ar ole in competitive gas-MOF interactions.I ns tudying the effects of competitive gas adsorption, the data shows five new species observed across the AIMD subset:HONO,N 2 O 4 , nitrate groups,n itro groups,a nd H 3  Them ost reactive gas species identified in the AIMD trajectories was NO 2 ,a si tw as calculated to adsorb at metal sites and resulted in by-product species within the RE-DOBDC MOFs.Inthe data set, all of the AIMD trajectories that contained NO 2 resulted in the formation of nitrogen based gas-MOF interactions that were not present the beginning of AIMD trajectories,F igure 3. Adsorption data identifies 5NO 2 binding events at metal centres,5 NO 2 binding events to ligands,3 2HONO molecules formed, 4N 2 O 4 molecules formed, 4nitro (R-NO 2 )g roups formed, and 1nitrate (R-ONO 2 )f ormed across the 4RE-DOBDC MOFs studied.
Theformation of aHONO,nitro,ornitrate species in all calculated RE-DOBDC structures indicates as trong interaction of NO 2 with multiple parts of the MOF framework. Specifically,t he formation of HONO,n itro,a nd nitrate all result from aN O 2 -DOBDC linker interaction. However, following the introduction of H 2 O, the predominance of HONO is slightly reduced and the formation of nitro and nitrate groups are not seen. This indicates ac hange in how NO 2 interacts with the DOBDC linkers.T he changes are hypothesized to be attributed to NO 2 -H 2 Oi nteractions and H 2 O-DOBDC interactions,t hat can interfere with HONO, nitro,a nd nitrate formation. Thec oncentrations and mechanism of formation of these by-products are discussed in detail below.

Identification of NO 2 interactions with the MOF
As previously stated, the strong NO 2 -DOBDC interactions allow for the formation of new chemical species, including new NÀOo rN ÀCc hemical bonds in the RE-DOBDC pore.The formation of NÀObonds can occur at the

Angewandte Chemie
Forschungsartikel DOBDC anchoring carbonyl Oa toms or at aD OBDC hydroxyl group,a st hey are the most available Of ramework atoms.The interactions with linker Oatoms can result in one of two chemical reactions:either the breaking aRE À Obond at an anchoring carbonyl or the deprotonation of ah ydroxyl group.N ew NÀCb onds are created during the formation of nitro groups,which forms aN ÀCbond between the NofNO 2 and an alpha carbon relative to the DOBDC hydroxyl group, Scheme S2.
Thef ormation of new Nb onds,s pecifically N À Ob onds, indicate the reactive effects of MOF-gas interactions within the material. Then ew functional groups,c ombined with adsorption of NO 2 at RE metal sites,provide insight into the possible capture of NO 2 in competitive gas environments. Such complex reactions could result in degradation of the MOF and require multiple interactions to occur simultaneously.

HONO formation from NO 2 + H 2 Ointhe MOF framework
Thed irect comparison between pure NO 2 and pure H 2 O in the RE-DOBDC framework showed the formation of HONO occurs more readily in dry NO x gas environments than with humid NO x .While HONO can form in both dry and humid environments,H 2 Owas observed to also interact with DOBDC hydroxyl groups which creates competition at linker sites with NO 2 .T he interaction of H 2 Ow ith DOBDC hydroxyl groups can result in H 3 O + formation, Scheme S3, but does not form new bonds with the linker.T he effect of humidity is areduction in the number of interactions NO 2 can experience with DOBDC hydroxyl Hatoms.Even accounting for HONO formation, through proton transfer along ac hain of water molecules,d oes not offset the ability for NO 2 to deprotonate the DOBDC linker.T he spontaneous formation of HONO exemplifies the NO 2 -MOF interaction found within RE-DOBDC MOFs.H owever,f ormation of HONO in ad ry environment is unique,a sk nown mechanisms for HONO formation involve H 2 O. [34,35] HONO formation has also been identified in atmospheric mixtures of NO 2 ,SO 2 ,and H 2 O; this is the only known environment which shows favourable formation of HONO with the inclusion of H 2 O. [36] Detailed Analysis of AIMD simulations Thec ommonality found in the HONO formation of RE-DOBDC MOFs indicates this is ap redominant occurrence. Them echanisms of HONO formation are essential to reactive gas species formation in MOFs.T his chemical reaction has never been observed experimentally in RE-DOBDC MOFs and is only isolated through the power of AIMD simulations.Therefore,adeep dive into the simulation results is necessary to understand mechanisms of formation that can be applied in future material design. Below is ad etailed accounting of the mechanistic results of AIMD simulations and analyses of (i)HONO formation, (ii)HONO formation conditions,( iii)N O 2 adsorption in an exemplar RE-DOBDC MOF (RE = Y), and (iv) the formation of secondary nitrogen species.
(i)AIMD simulations for astep by step formation timeline of HONO formation Mechanisms of HONO formation in RE-DODBC MOFs were found to occur primarily via the binding to am onodentate DOBDC hydroxyl group.P ublished RE-DOBDC crystal data identified two linker coordinations,monodentate and bidentate,a t3 3% and 67 %i nt he original unit cell, respectively. [16] Thecoordination is indicative of native defect sites in MOF materials, [18,37] which can be formed due to crystallization kinetics and allows both linker coordinations to exist, Scheme S4. Thed efect allows for am ore flexible coordination within the MOF that can enable metal cluster and linker rotation, known to exist in certain MOFs. [38,39] The monodentate linkers also result in an extra hydroxyl group on one third of the organic linkers in RE-DOBDC MOFs,which serve as reactive sites in the material.
From the AIMD trajectories,itwas observed that as NO 2 approaches the hydroxyl group of am onodentate linker, astrong hydrogen bonding interaction forms.T he Hatom of the hydroxyl then begins to transfer between the NO 2 and the hydroxyl Oa tom. While all DOBDC linkers have hydroxyl groups,itisthe extra neighbouring hydroxyl group found only on monodentate coordination which assists in the formation of HONO.T he neighbouring hydroxyl allows aHto be shared between two hydroxyl groups,a llowing NO 2 to take the Ha nd form HONO,S cheme 1.
Thetransfer of aDOBDC hydroxyl Hatom can also occur in two less frequent mechanisms.I nt he first mechanism, abidentate coordinated linker can produce HONO following as pecific mechanism in which an NO 2 interacts with the DOBDC hydroxyl group and as econd NO 2 molecule approaches the Ot of orm an itrate or provide aHatom, Scheme S1. In both cases of Hr emoval from the linker, as econdary interaction is provided to assist the mechanism. In the second mechanism, aH 2 Odeprotonates the linker and then transfers the Ha tom to an earby NO 2 .T he resulting HONO molecular formations include all isomers of the molecule: trans-HONO, cis-HONO,a nd isonitrous acid (HNO 2 ), [40] with the trans-HONO molecule as the primary isomer.T he distribution of the HONO isomers is included in Figure S1. Thef requent generation of HONO species across the majority of trajectories identifies the strength of interaction in highly competitive environments.I twas hypothesized and validated that NO 2 interacts with the DOBDC Scheme 1. Mechanism of HONO formation via NO 2 interacting with amonodentate DOBDC hydroxyl group, facilitated by neighbouring hydroxyl.

Angewandte Chemie
Forschungsartikel linker,b ut the identification of new HONO products, compared to nitro and nitrate formation, is anew mechanism not formerly identified.
Thenew species formed from strong NO 2 interactions are identified for all RE metals simulated. As previously stated, there is no clear trend between strong NO 2 interactions and the RE metal in the MOF.G iven the non-metal dependent relationship,a sw ell as established similarity in adsorption across the Ln series,the Y-DOBDC material has been chosen for use in an exemplary trajectory for in depth analysis.T he identification and analysis of NO 2 interactions in Y-DOBDC are expected to be representative for the same interactions in all RE-DOBDC MOFs.

(ii)A IMD analysis of HONO formation conditions
Theprimary HONO formation mechanism is identified to be aN O 2 molecule deprotonating am onodentate bound DOBDC hydroxyl, as shown in Scheme 1. Thea toms and bonds of the NO 2 and DOBDC hydroxyl are presented in Figure 4.
AH ONO molecule containing N1, O1, O2, and H1 is shown interacting with ap reviously deprotonated DOBDC hydroxyl Oatom, O3. As the bond between the NO 2 and H1 (B1) reaches 1 ,t he HONO molecule is formed. The originally deprotonated Oa tom (O3) is protonated. This proton comes from an eighbouring hydroxyl group,w hich is only available on monodentate coordinated DOBDC linkers and identifiable via AIMD.
Determination of when the HONO species forms are identified through calculated interatomic distances,F igure 5. At the beginning of the trajectory,t he HONO Ha tom transfers from the original DOBDC hydroxyl group near time 0.18 ps,a ss een in Figure 5. Ther ed and blue H À Ob ond distances in Figure 5c orrespond to the B1 and B2 bonds visualized in Figure 4, respectively.Note that in the snapshot of Figure 4, the deprotonated hydroxyl O( O3) has as trong interaction with an eighbouring DOBDC hydroxyl group. This is possible due to the intrinsic defect in the RE-DOBDC materials where the anchoring carboxyl Oa toms do not all coordinate to metal sites.
After 0.25 ps,t he Ha tom maintains the expected bond distance of % 1 with the NO 2 molecule (red), completing the formation of the HONO molecule.After the formation of HONO is complete at 0.25 ps,the atomic distances in Figure 5 (blue) corresponds to the relative distance between the HONO molecule and the deprotonated DOBDC hydroxyl group.T he calculated distances range between 1.5-4.8 as the HONO molecule moves away from the DOBDC.T he distances are subsequently used to identify the relationship between interaction energy and distance of the formed HONO molecule.T he interaction energy of the HONO molecule within the system was calculated for two time periods along the trajectory from 0-0.5 ps and 2.2-2.8 ps. These two segments of the trajectory capture the energy of the final Htransfer between the DOBDC linker and NO 2 and the HONO molecule dissociating from the deprotonation site.
In the 0-0.5 ps trajectory segment, the HONO molecule is formed both from 0-0.125 ps and again from 0.375-0.5 fs.The average calculated binding energies of HONO with the deprotonated site for these time steps are À0.86 eV and À0.65 eV,r espectively.T he calculation of time dependent binding energies is defined in the SI. Thed ecreased interaction strength of the HONO with the framework is highly dependent on the distance from the deprotonation site.F or example,t he average distance from the deprotonated O grows from 1.51 in the 0-0.125 ps range to 1.66 in the 0.375-0.5 ps range.A st he HONO molecule finalizes its dissociation from the deprotonation site in 2.6-2.8 ps,t he interaction energy weakens to an average of À0.47 eV.T he calculated time dependent binding energy of the HONO molecule shows an increase as the time approaches 2.8 ps. However,this is due to the HONO beginning to interact with an ew part of the MOF pore.I nu sing the time dependent interaction energies from the final formation of HONO at 3.75 ps to the final dissociation near 2.8 ps,t he change in energy is % 0.2 eV.N ear 0.2 eV the interaction can be

Angewandte Chemie
Forschungsartikel 11620 www.angewandte.de classified as physisorption of aH ONO molecule with the MOF framework. Otherwise,the average total energy during the final formation of the HONO species changes by À0.2 eV, indicating as tability of the HONO formation.

(iii)AIMD simulations of NO 2 adsorption in Y-DOBDC
Thef irst spontaneous reaction analysed along the Y-DOBDC + 12 NO 2 AIMD trajectory is desorption at an unsaturated Ymetal site.
Examination of asingular NO 2 molecule that experiences desorption along the AIMD trajectory,F igure 6, shows three phases associated with the MOF-NO 2 interaction. First, aNO 2 molecule is initially adsorbed to an unsaturated metal site (blue box) and then desorbs into free pore space (green box), seen in Figure 6. Thec alculated interaction energies of each of the NO 2 locations within the MOF framework is presented in Figure 6, with corresponding snapshots along the AIMD trajectory.
Thei nitial NO 2 adsorption event shows that the NO 2 molecule is in physisorption distance of an unsaturated Y metal site;i td oes not have any secondary interactions with neighbouring linkers or gas molecules.Asthe NO 2 desorbs off the MOF framework and into the pore,the interaction energy weakens.I to nly strengthens again when it an ew binding interaction with aD OBDC hydroxyl group.A st he NO 2 approaches the DOBDC linker,the interaction energy again increases to around À1eV. Interestingly,t his interaction energy of NO 2 with the linker is stronger than the binding energy between NO 2 adsorbed to the metal site.
Thei nverse of the desorption interaction (adsorption of an NO 2 molecule to an unsaturated metal site) is also identified along the same trajectory.Inthis adsorption event, an NO 2 molecule interacts with aD OBDC hydroxyl group before adsorbing.Inset snapshots along the AIMD trajectory are presented in Figure 7, along with the corresponding interaction energy.
Thei nitial interaction between NO 2 and the hydroxyl group is shown to be in the same energy region, À0.6 to À1.1 eV,a st he previously described NO 2 -DOBDC interaction. As the NO 2 nears the DOBDC,aHONO molecule forms 0.7 ps into the interaction with the deprotonation of the DOBDC hydroxyl group.During this interaction, the Hatom is transferred back and forth between the NO 2 and DOBDC. As the DOBDC hydroxyl does not have any neighbouring hydroxyl groups which could pass another proton, the NO 2 and DOBDC are reformed and the NO 2 binds at an earby unsaturated metal site.I nt his trajectory,t he adsorption energy of the NO 2 is stronger than what was calculated for the desorption event. Theadditional hydrogen bond formed with the adsorbed NO 2 strengthens the NO 2 binding energy.
Prior to permanent NO 2 adsorption at an unsaturated metal site,t he following criteria were met:1 )N O 2 hydrogen bonded with DOBDC hydroxyl, 2) no neighbouring hydroxyl group were located nearby to donate aproton, 3) NO 2 was in close proximity to an unsaturated metal, and 4) the continued H-bond interaction formed with the adsorbed NO 2 .T hese steps have been identified to achieve sustained adsorption. Other NO 2 trajectories were observed to show NO 2 -metal interactions;however,all are short lived and desorbs quickly without any secondary framework interaction.
(iv) AIMD simulations of the formation of the secondary nitrogen species Species such as nitro,n itrate,a nd nitrite groups,w hich form on the DOBDC linkers,were confirmed experimentally by FTIR [20] and have been identified in current AIMD trajectories.O ne of them, an itro group (NO 2 )h as been further analysed along the Y-DOBDC + 12 NO 2 trajectory. Along the first 1psofthe trajectory,the interaction energy of NO 2 [20] has been plotted as with the C À Nb ond distance, Figure 8.
Initially the NO 2 molecule is located in the MOF pore and % 3.5 from the nitro-C atom bond;the average interaction  energy of the NO 2 is approximately À0.15 eV.Asthe distance of the C À Nbond shortens,the interaction energy of the NO 2 with the Cs trengthens and reaches av alue close to À1.5 eV. This interaction energy agrees with the experimental evidence of NO 2 preferring NO 2 -DOBDC interactions as compared to the NO 2 -Ln metal where the energy of adsorption is close to À0.2 eV.What is also of interest in this interaction is the deprotonated state of the DOBDC linker. As can be seen in the inset geometry of Figure 8. the DOBDC hydroxyl group next to the nitro-C has been deprotonated via another gas molecule.I mportantly,t he deprotonation of the neighbouring hydroxyl is not required for nitro formation but was observed in the majority of cases.The unique interaction of NO 2 binding directly to the MOF DOBDC linkers has previously been identified in M-MOF-74. [11,12] It was then further confirmed to occur in RE-DOBDC MOFs. [20] Similar binding was seen in av ariety of Zr-based MOFs,w hich at times resulted in occurrences of material degradation. [41] Conclusion An extensive set of ab initio molecular dynamics (AIMD) simulations were used for the first time to evaluate competitive adsorption of mixed acid gases (NO 2 ,H 2 O) in aseries of RE-DOBDC MOFs.T he dynamically evolving trajectories allow for evaluation of spontaneous formation of secondary molecular species in the MOF.These simulations account for the effects of confinement by organic linkers and resulting changes in adsorption that cannot be analysed through static density functional theory (DFT) calculations alone.
Analysis of competitive adsorption identified that the gas composition had as tronger influence on gas adsorption than the specific metal centre (Eu, Tb,Y ,Y b). Furthermore, adsorbed H 2 Oi sm ore frequently bound to metal centres, while NO 2 can bind with both metal centres and the linker. Additionally,the AIMD trajectory identified the formation of secondary molecular species,including HONO,N 2 O 4 ,nitrate groups,nitro groups,and H 3 O + .
Of those secondary molecular species formed, the most common is HONO,w hich is readily formed as ar esult of deprotonation of the MOF DOBDC organic linker,a nd not from the interaction between NO 2 and H 2 Ointhe pore space. This is ap reviously unreported mechanism of HONO formation in MOFs that was discovered, and is reported herein, through this unique application of AIMD methodologies.T he unique DOBDC coordination found specifically in RE-DOBDC MOFs allows for proton transfer from the linker to the adsorbed NO 2 without the presence of H 2 O. Additionally,s everal proton transfer events occur prior to HONO formation.
Through the combination of AIMD simulations and validation from previous experiment, unprecedent insight into mechanisms of acid gas separation can be developed not only in MOFs but across porous organic systems.T he AIMD simulations provide step-wise improvement in accuracy of computational results including temperature effects and spontaneous reactions.I dentification of individual strong MOF-gas interactions in RE-DOBDC MOFs provides fundamental understanding of the separation capability and maintained stability of RE-MOFs under acid gas conditions. Further application of AIMD to simulated mixed acid gas adsorption in MOFs will allow for identification of mechanisms that control competitive adsorption processes with even more complex gas streams.T his will also enable future computational design of materials around these adsorption mechanisms.