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1 Surfe Siene 603 (2009) Contents lists ville t SieneDiret Surfe Siene journl homepge: Ammoni synthesis n eomposition on Ru-se tlyst moele y first-priniples A. Hellmn,, K. Honkl,2, I.N. Remeikis,3, Á. Logóttir, A. Crlsson, S. Dhl, C.H. Christensen, J.K. Nørskov, * Hlor Topsøe A/S, Nymøllevej 55, DK-2800 Lyngy, Denmrk Center for Atomi-Sle Mterils Design, Deprtment of Physis, NnoDTU, Tehnil University of Denmrk, Builing 307, DK-2800 Lyngy, Denmrk Center for Sustinle n Green Chemistry, Deprtment of Chemistry, NnoDTU, Tehnil University of Denmrk, DK-2800 Lyngy, Denmrk rtile info strt Artile history: Aville online 20 Jnury 2009 Keywors: Density funtionl theory Monte Crlo simultions Ctlysis Surfe hemil retion Ruthenium NH 3 sunthesis A reently pulishe first-priniples moel for the mmoni synthesis on n unpromote Ru-se tlyst is extene to lso esrie mmoni eomposition. In ition, further nlysis onerning trens in mmoni proutivity, surfe onitions uring the retion, n mro-properties, suh s pprent tivtion energies n retion orers re provie. All oserve trens in tivity re pture y the moel n the solute vlue of mmoni synthesis/eomposition proutivity is preite to within ftor of 00 epening on the experimentl onitions. Moreover it is shown: (i) tht smll hnges in the reltive sorption potentil energies re suffiient to get quntittive greement etween theory n experiment (Appenix A) n (ii) tht it is possile to reproue results from the first-priniples moel y simple miro-kineti moel (Appenix B). Ó 2009 Pulishe y Elsevier B.V.. Introution In heterogeneous tlysis mmoni synthesis/eomposition shres the sme prigmti role s the hyrogen tom in tomi physis n it hs een use to evelop mny importnt onepts n ies routinely use nowys []. The importne of mmoni synthesis nees few rguments s it is the min tive ingreient in fertilizers, n ever neee prout s worl popultion inreses. Ammoni eomposition might turn out lso to e n importnt proess sine mmoni is n exellent hyrogen rrier [2]. The literture survey revels n enormous mount of stuies, where some entrl works re ollete in series of monogrphs [3 5]. Hene, it is nturl tht mmoni synthesis is the first lrgesle heterogeneous tlyti retion for whih omplete firstpriniples moel hs een evelope [6]. The moel is le to preit mmoni formtion on supporte tehnil tlyst with resonle level of ury [7]. Other first-priniples stuies hve fouse on esriing single rystl retivity of vrious tlyti retions, suh s ethylene hyrogention [8], ethylene oxition * Corresponing uthor. Tel.: ; fx: E-mil ress: norskov@fysik.tu.k (J.K. Nørskov). Present ress: Competene Centre for Ctlysis, Chlmers University of Tehnology, SE Göteorg, Sween. 2 Present ress: Deprtment of Chemistry, University of Jyväskylä, Nnosiene Center, P.O. Box 35, FIN-4004, Finln. 3 Present ress: Deprtment of Mterils, Siene n Tehnology, University of Crete, 7003 Herklion, Greee. [9 ], NO n CO reution [2,3], seletive tlyti reution of NO [4], zeolite tlysis [5], n CO oxition [6 9]. On the est elementry metl tlyst (Ru, Fe) the NH 3 synthesis proees long well-efine Lngmuir Hinshelwoo retion pth. Hene, the stepwise ition of sore H to the N-ompouns n e written s N 2 þ 2 2N N þh NH þ NH þh NH 2 þ NH 2 þh NH 3 þ NH 3 NH 3 þ H 2 þ 2 2H ðrþ ðr2þ ðr3þ ðr4þ ðr5þ ðr6þ where n X orrespon to n empty site n n sore X hemil ompoun, respetively. Although ruthenium (Ru) ws onsiere to e n interesting nite uring the lrge-sle sreening experiments of Mittsh [20] it ws not until the 970s [2,22] tht Ru ws reognize s the est elementry metl tlyst to proue mmoni [23,24]. Toy it is known tht Ru tlysts perform etter thn iron (Fe) tlysts, prtiulrly t low temperture n lose to the thermoynmi equilirium [24 28]. Moreover, Ru tlysts exhiit stronger response to promotion n etter resistne towrs poisoning. Ru tlysts hve een put to ommeril use [29 3], lthough Ru is onsierly more expensive thn Fe n the tlyst hs shorter tlyti lifetime ompre to the Fe tlyst /$ - see front mtter Ó 2009 Pulishe y Elsevier B.V. oi:0.06/j.sus

2 732 A. Hellmn et l. / Surfe Siene 603 (2009) Investigtions performe on the mmoni synthesis/eomposition in the 930s showe tht the N 2 issoition/ssoition on Fe is the rte-limiting step, t lest uner inustril onitions [32,33]. In the lte 970s n erly 980s high qulity surfe siene stuies eme possile n revele more etils out the N 2 issoition proess [34 38]. From experiment [39 4] n theory [42 44] it ws onlue tht there exists iret link etween the results of the ultr low pressure surfe siene stuies n mmoni synthesis t on Fe t elevte pressure n temperture. The existene of similr iret link for Ru hs een estlishe through numer of theoretil [45,46] n experimentl [46 48] works. The results on Ru show tht (i) N 2 issoition is rte-limiting step uner inustril onitions [45,46,48] n (ii) the issoition preferentilly ours on steps or efets with B5 onfigurtion [49,50]. Reent works on mmoni eomposition show tht (i) the retion onitions hve pronoune effet on the overges of ifferent retion intermeites [28], n hene (ii) lterl intertions ply n importnt role [5]. Reently, we reporte the finl step towrs first-priniples esription of the mmoni synthesis [6,52]. We showe y mens of DFT lultions tht it is possile to onstrut first-priniples moel, n to iretly preit the mmoni proutivity s funtion of temperture n flow uner inustril onitions for retor fille with supporte Ru tlyst. The link etween the quntum hemil lultions n the retor t is one within miro-kineti frmework se on Monte Crlo (MC) simultions of the surfe overges. All tivtion energies, intertion energies n entropy ontriutions were lulte using DFT n the only input from the tlyst is the verge prtile size istriution etermine y high resolution trnsmission eletron mirosopy (HRTEM). The mmoni proutivity ws lulte to e within ftor of 2 20 from experiment t 00 r [6]. In ition, we provie n explntion why proutivity n e preite with suh goo ury, lthough tivtion energies of iniviul elementry steps re less urte. It turns out tht the network of onseutive retions is self-regulting in the sense tht the errors in the ifferent prts of the retion nel eh other. Tht is relte to the so lle ompenstion effet [53], whih gives hope tht one my more generlly e le to lulte tlyti rtes iretly from first-priniples n thus use DFT to evelop new tlysts; for reent exmple see Ref. [54]. In this pper, we riefly present the first-priniples moel. After tht we pply our moel to numer of new mesurements on mmoni proutivity t ifferent retion onitions n exten the moel into the relm of mmoni eomposition. Our mmoni synthesis moel shoul e pplile to eomposition euse this is reverse proess to formtion. Furthermore we present n extensive omprison etween mmoni synthesis/ eomposition t ifferent temperture, flow, rtio, n pressure. Surfe overges, pprent tivtion energy n retion orers re lso nlyze. The pln of the pper is s follows: Setion 2 gives rief ount of our first-priniples moel together with experimentl etils. Setion 3 presents lulte mmoni (nitrogen) proutivity ompre to mesurements. In Setion 4, results onerning surfe onitions re given, wheres Setion 5 give lulte mro-properties, suh s, pprent tivtion energies n retion orers t ifferent retion onitions. Finlly, the pper ens with the onlusions n n outlook for future work. 2. The first-priniples moel All the prmeters neee for the first-priniples moel of mmoni synthesis/eomposition suh s sorption potentil energies, virtionl frequenies, intertions, n tivtion rriers, re lulte y mens of DFT [55,56] s implemente in the plne-wve pseuo-potentil oe DACAPO [57]. 4 The Ru step is moele y using Ru(00 0) n (5 2) unit ell where two tom rows re remove to give step, hene, the tive site onsists of n upper step (US) n lower step (LS) whih re inepenent of eh other, tht is, there re no lterl intertions etween US n LS. For further etils, see Ref. [6]. The retion rte per tive site is lulte oring to rðt; p N2 ; p H2 ; p NH3 Þ¼ð Þm X i P i ðp H2 ; p NH3 Þ expðe i =k BTÞp N2 h 2 where T is the temperture, p N2 ; p H2 ; p NH3 re the pressures of N 2 ; H 2, n NH 3, respetively, m is the preftor for N 2 issoition n h 2 the proility to hve two simultneously empty sites, one on the US n one on the LS. P i gives the onitionl proility for ertin lol environment, E i is the orresponing tivtion energy, ¼ p2 NH 3 mesures the pproh to equilirium, n K p N2 p 3 g is the gsphse equilirium onstnt. The proility of lol environment, H Kg 2 P i ðp H2 ; p NH3 Þ, is neessry s the DFT lultions show the tivtion energy of N 2 issoition to epen on speies sore in jent sites. As the issoition/ssoition of nitrogen moleules is the rte-limiting step, P i ðp H2 ; p NH3 Þ n e lulte using Monte Crlo (MC) tehniques [58]. The first-priniples moel shows tht the presene of n sorte next to the issoiting N 2 might hiner the retion [6]. It shoul e stresse tht the onitionl proilities, P i, in Eq. () re eyon the usul men-fiel ssumption sine the orreltion effets originting from the lterl pir intertions etween intermeites re inlue vi the MC simultions. Dynmil orreltions n e sfely ignore owing to the ft tht for this system there is very fst iffusion of the sortes [59,60], reltively low sorte overge uner inustril onitions [6,52], n the existene of well-efine rte-limiting step [45,46,48] tht mkes (R2) (R6) to e in qusi-equilirium. The tive site ensity, q is estimte in the following mnner. First we lulte the surfe energy of ll low Miller inex ðh þ k þ l < 4Þ Ru surfes. Using these energies we mke n tomisti Wulff onstrution for severl Ru prtiles with ifferent imeters. None of the ominnt fes in the Wulff onstrution ontins B5 sites. After inluing ege effets the B5 sites pper long the ð000þ=0 intersetion. Hene, we know the numer of tive sites per prtile size. The mrosopi size-istriution of the Ru-prtiles is otine y the use of HRTEM n is the only link etween the rel tlyst n our moel. q results from the numer of tive sites per prtile size n the mrosopi sizeistriution. Reently, more sophistite metho to lulte the tive site ensity ws pulishe y Gvnholt n Shiøtz [6]. It ws onlue tht the tive site ensity is not sensitive to temperture n tht the optiml luster imeter is pproximtely 3 nm. Our result is in resonle ggrement with tht of Gvnholt n Shiøtz [6]. We moel plug-flow retor y iviing the tlyst into N slies n ssume n equl istriution of the tlyst mss, thus 4 The Kohn Shm wvefuntions re expne using plne-wves with kineti energy utoff of 25 Ry. The ioni ores re esrie y ultr-soft pseuo-potentils [66] n the k-point smpling of the first Brillouin zone is preforme with 6k-point Chi Cohen gri [67]. We use the RPBE [68] exhnge-orreltion funtionl selfonsistently. The sl thikness is three lyers n the perioi imges re seprte y 2 Å in z-iretion vuum region. Asorption is llowe on one of the two sl surfes, n the eletrostti potentil is juste oringly [69]. The positions of surfe toms re relxe so tht fores ting on toms re less thn 5 ev/å. N 2 issoition is lulte y onstrining the N N on length n relxing the other egrees of freeom. By vrying the N N istne, we lolize the trnsition stte [59,45]. For the hyrogention steps, we use the nuge elsti n (NEB) metho [70 72] to etermine the omplex retion pth wys n their tivtion energy. ðþ

3 A. Hellmn et l. / Surfe Siene 603 (2009) we get the following expression for the overll retion rte through the retor: X N x¼0 r x ðt; p N2 ðxþ; p H2 ðxþ; p NH3 ðxþþqm=n; where m is the tlyst mss, N the numer of slies, p N2 ðxþ; p H2 ðxþ; p NH3 ðxþ, re the prtil pressures in slie x, respetively. The mmoni proutivity is tken here to e the prtil pressure of mmoni t the outlet. The preprtion n the mmoni synthesis tivity mesurements of the Ru tlyst hs een esrie erlier [6,47]. The tlyst onsists of. wt% Ru supporte on n luminum mgnesium spinel rrier with surfe re of 52 m 2 /g. The mmoni synthesis tivities were etermine using plug-flow retor n wie rnge of proess onitions. The shre numer of experimentl t-points for the mmoni synthesis/eomposition mounts to totl of 3 inepenent mesurements. 3. Results In this setion, we present results otine from the first-priniples moel, suh s, mmoni n nitrogen proutivity, surfe omposition, turn-over frequeny (TOF), pprent tivtion energy n retion orer. Comprison with experiment is onute when possile. 3.. Ammoni n nitrogen proutivity Fig. ompres lulte n mesure mmoni n nitrogen proutivities for mmoni synthesis n eomposition. ð2þ The sme externl onitions, suh s prtil pressure, flow, n temperture, re pplie in the first-priniples moel s in experiments. For instne, the temperture rnge is K n the flow rnge ml/min (STP). In Fig. totl pressure is 00 r n the H 2 : N 2 rtio 3:. The ifferene etween the lulte n the mesure proutivities vry y ftor of At 50 r, in Fig., we lso vry the N 2 : H 2 rtio from 4: to :5. At these onitions the ifferene in proutivities etween the moel n the mesurements is ftor of 2 5. The lowest totl pressure we onsier is r (using only the stoihiometri H 2 : N 2 rtio), see Fig. for the omprison etween the proutivities. In this se the lulte n mesure proutivities iffer y ftor of 8. Finlly, we isply the results for mmoni eomposition in Fig.. Here, the totl pressure is r n the H 2 : NH 3 rtio vrying from : to :55. The lulte n the mesure proutivities gree very well t high N 2 onversion (owing to tht equilirium is rehe) ut iffer y ftor of 00 t the low onversion. Although the 45 -log log plots show n overll goo greement with experiment, they re too orse to isply temperture, flow n rtio epenene. Therefore, in Fig 2, we plot oth lulte n mesure mmoni proution ginst () temperture, () flow n () H 2 : N 2 rtio. In generl, the figure repets the goo greement etween theoretil n mesure results lrey seen in Fig Surfe onitions uring the tlyti retion In Figs. 3 5 surfe overges on oth US n LS s funtion of istne in the plug-flow retor re presente. In ition, the lulte TOF is isplye in the sme mnner. Eh figure gives Moel mmoni output (NH 3 -%) Experimentl mmoni output (NH 3 -%) Moel mmoni output (NH 3 -%) Experimentl mmoni output (NH 3 -%) Moel mmoni output (NH 3 -%) Experimentl mmoni output (NH 3 -%) Moel nitrogen output (N 2 -%) Experimentl nitrogen output (N 2 -%) Fig.. The lulte NH 3 proutivity ompre with the mesure one t totl pressure () 00 r, () 50 r, () r n finlly N 2 proutivity, i.e. NH 3 eomposition t () r. A omplete greement woul men tht the t points shoul e ontop of the igonl line. The etils of the retion onitions re given in the text.

4 734 A. Hellmn et l. / Surfe Siene 603 (2009) Proutivity (NH 3 -%) 0. Mesure Clulte Mesure Clulte 0. Mesure Clulte Temperture (K) Flow (ml/min [STP]) 4: : :3 :5 Rtio (N 2 :H 2 ) Fig. 2. Ammoni proutivity s funtion of () temperture, () flow, n () rtio. The synthesis onitions re () N 2 : H 2 ð : 3Þ, 30 N ml/min (STP); () 73 K, N 2 : H 2 ð : 3Þ; () 73 K, 30 N ml/min (STP), ll t totl pressure of 50 r. Temperture 73K Temperture 593K Coverge US θ NH θ 2 NH 2 Coverge LS e 5.0 f 2 x0 5.0 TOF (/s) Distne in retor Distne in retor Fig. 3. The overge of ifferent retion intermeites on the US n LS n the TOF plotte s funtion of the retor length t 73 n. The other synthesis onitions re N 2 : H 2 ð : 3Þ, 30 N ml/min (STP), 50 r. results for oth low n high temperture. The totl pressure for mmoni synthesis in Figs. 3 n 4 is 50 r n r, respetively. Ammoni eomposition, Fig. 5, is simulte only t totl pressure of r. At the totl pressure of 50 r we oserve high overge of hyrogen toms, see Fig. 3, espeilly t low temperture. As the proution of mmoni proees more stle retion intermeites (NH 2 ) eome more unnt on the US. The sorption

5 A. Hellmn et l. / Surfe Siene 603 (2009) Temperture 73K Temperture 593K θ H Coverge US θ NH2 θ NH 2 Coverge LS e 5.0 f 2 x0 5.0 TOF (/s) Distne in retor Distne in retor Fig. 4. The overge of ifferent retion intermeites on the US n LS n the TOF long the retor length t r n t tempertures 73 n. The other synthesis onitions re N 2 : H 2 ð : 3Þ, 30 N ml/min (STP). energy of the retion intermeites [6] mkes the overge on the LS to e unffete y the proution of mmoni, t lest uner these onitions. Fig. 3e (high temperture) shows tht there is rpi erese in TOF s the overge of free sites on the US is erese. For the low temperture se, Fig. 3f, the erese in TOF is less pronoune s ompre to the high temperture se. Although not presente here, the sme nlysis pplies for mmoni synthesis t the totl pressure of 00 r. Figs. 3 n 4 show tht the overge of hyrogen toms is muh lower t r thn t 50 r. Atully, free sites oth on US n LS re most unnt, espeilly t high temperture. For Fig. 3e n f we note tht erese in totl pressure own to r still keeps the orer of mgnitue of the TOF equl to tht lulte t high pressure (ompre Figs. 3e n f & 4e n f). Uner eomposition onitions, see Fig. 5, the ominnt surfe intermeites re H (US), NH 2 (US) n H (LS). There re lso some nitrogen toms t the LS. As the proution of nitrogen proees, i.e. the prtil pressure of mmoni ereses, the overge of NH 2 ereses n the overge of nitrogen toms goes to zero Apprent tivtion energy n retion orers Apprent tivtion energy n retion orers re quntities often use to hrterize the overll kinetis of tlyti retion. The pprent tivtion energy, E pp, is efine s E pp ¼ RT 2 lnðr þ Þ T where R is the gs onstnt n r þ is the forwr rte in Eq. (). The TS energies of the RDS n pprent energy require to rete free sites omprise the ifferent ontriutions of E pp [62]. As the firstpriniples moel inlues lterl two-oy intertions, it introues onitionl proilities into Eq. () n prevents the erivtion of n nlytil expression for the pprent tivtion energy n retion orers [62]. To etermine the retion orers we look t the epenene of rte on the prtil pressures of retnts n prout. Negtive retion orer mens hinering the retion n positive elerting. The retion orers for mmoni synthesis, ðn 2 Þ; ðh 2 Þ, n ðnh 3 Þ re efine s r þ ¼ kp ðn 2Þ N 2 ð3þ p ðh 2Þ H 2 p ðnh 3Þ NH 3 : ð4þ

6 736 A. Hellmn et l. / Surfe Siene 603 (2009) Temperture 773K Temperture 623K θ * θ NH 2 Coverge US θ NH 2 TOF (/s) Coverge LS e 2 x0 θ N θ N f Distne in retor Distne in retor Fig. 5. The overge of ifferent retion intermeites on the US n LS n the TOF plotte long the retor length. The left n right figures re t tempertures, 773 n 623 K, respetively. The rest of the eomposition onitions re NH 3 : H 2 ð3 : 2Þ, 20 N ml/min (STP), r. ðn 2 Þ is one uner ll onsiere onitions, whih grees well with the ft tht N 2 issoition is onsiere the RDS. The E pp of the first-priniples moel is lulte throughout the plug-flow retor n presente in Fig. 6. The vlues of E pp t the inlet rnge etween 00 n 60 kj/mol epening on totl pressure ( high pressure results in high E pp ). There is n inrese in E pp s the proution of mmoni proees. The lulte retion orers re lso presente in Fig. 6. Note tht sine ðn 2 Þ is more or less onstnt it is exlue from Fig. 6. All retion orers re negtive throughout the plug-flow retor. However, ðnh 3 Þ is initilly zero ut turns negtive s the mmoni proution proees, wheres ðh 2 Þ strts t negtive vlue lose to n turns less negtive t higher mmoni onversion. 4. Disussion From Fig. n it is ler tht our moel unerestimtes mmoni proution t ll retion onitions n tht the isrepny is lrger t low mmoni onversion. For mmoni synthesis t r, Fig., the isrepny is proly relte to experimentl iffiulties, suh s prolems to tret pressure rop orretly in the plug-flow retor. Our moel lso unerestimtes mmoni eomposition t most retion onitions, espeilly t low onversion, see Fig.. Exmining the results in more etil it is foun tht the lulte mmoni n nitrogen proutivity evites from the mesure one y ftor of 00. Note tht no fitting is one n ll the prmeters otine from the DFT lultions re use s suh. The iniviul evitions re not sensitive to ifferent flows n N 2 : H 2 rtios. Inste it is the low temperture onitions tht give rise to the lrgest errors. The verge evition inluing ll mesurements is only ftor 6. A proper sttistil evlution of the sensitivity remins s future tsk [63]. As seen from Fig. 2 n inrese in temperture inevitly les to n inrese in proutivity, s the higher temperture inreses oth the rte, Eq. (), n the numer of empty sites. A erese in flow, see Fig. 2, implies tht the tlyst hs more time to intert with surrouning gs leing lso to higher proutivity. In Fig. 2 we see tht erese in the N 2 : H 2 rtio of the inlet gses will inhiit the proutivity s the higher prtil pressure of H 2 les to

7 A. Hellmn et l. / Surfe Siene 603 (2009) Apprent tivtion energy (kj/mol) 73 K Retion orers (NH 3 ) 73 K (H ) K (NH 3 ) 73 K (H 2 ).0.5 e K f (NH 3 ) 73 K Distne in retor.0 (H 2 ) 0.5 Distne in retor Fig. 6. The pprent tivtion energy t () 00 r, () 50 r, (e) r, n the retion orers ðh 2Þ, n ðnh 3Þ t () 00 r, () 50 r, (f) r. Here, in x-xis mens the inlet of the retor n.0 is the outlet of the retor. higher overge of sore H on the surfe, i.e. less free sites. An inrese in the N 2 : H 2 rtio will hve twofole effet towr higher proutivity: iretly vi the rte Eq. (), where the prtil pressure of N 2 is expliitly use n vi more free sites s lower H 2 prtil pressure implies less sore H loking the tive sites from N 2 issoition. From the first-priniples moel further informtion of the etils of the mmoni synthesis/eomposition n e gine. Prtiulrly interesting is to look for the reltions etween retion intermeite overges n mrosopi properties. At totl pressure of 50 r ifferent retion intermeites ompete with eh other for the ville surfe sites, Fig. 3, n hene the low numer of free sites hiners the retion. The extent of the mmoni onversion fully etermines the surfe omposition: At smll onversion, whih tkes ple t low temperture n/or t the inlet of the retor, the B5 sites re minly oupie y hyrogen, wheres t higher onversion the other retion intermeites pper on the surfe therey moifying the surfe omposition. Prtiulrly this is true for NH 2 on the US, ue to its high sorption potentil energy n the ttrtive intertion with sore H [6]. Fig. 3e n f shows rpi erese in turnover frequeny (TOF) s the numer of free sites erese on the US. The effet of lol environment is lerly seen in Fig. 3e where the TOF rops y ftor of 5 wheres the numer of free sites, given in Fig. 3 n only hnge with ftor of 2. The itionl erese in TOF follows from the inrese in N 2 tivtion rrier in the presene of NH 2 on the US [6]. Deresing the totl pressure to r hs lrge impt on the surfe omposition, see Fig. 4. In generl the overge of H is muh reue resulting in n inrese of ville free sites, espeilly on the LS. The overge of hyrogen is more or less inepenent to the extent of mmoni onversion, wheres the overge of NH 2 n free sites re iretly linke to eh other. The TOF hnges only y smll mount when eresing the totl

8 738 A. Hellmn et l. / Surfe Siene 603 (2009) pressure from 50 r to r, see Fig. 4e f. A iret omprison of TOF t n 50 r pressures n t low temperture shows tht the TOF is more thn ftor of 2 lrger in the former thn in the ltter se. At first sight this might look like ontrition s Eq. () implies tht erese in N 2 prtil pressure lso reues the TOF. However, Eq. () is lso epenent on the surfe omposition n tht ompenstes for the reution in prtil pressure of N 2. The surfe overge of ifferent retion intermeites is ifferent uner mmoni eomposition s ompre to synthesis onitions, Fig. 5. The prtil pressure of NH 3 results in muh higher overge of NH 2 on the US n on the LS there is tully even overge of N, t lest lose to the inlet. The high TOF, Fig. 5e n f, results from oth high temperture n lrge pplie NH 3 : H 2 rtio (3:2). Note tht for mmoni eomposition higher temperture is use (773 n 623 K) s ompre to the ses of mmoni synthesis (73 n ). However, s the eomposition proees the prtil pressures of N 2 n H 2 inrese reuing the NH 3 : H 2 rtio n eresing the TOF. The lulte E pp for the first-priniples moel, Fig. 6, shows strong epenene to the extent of mmoni onversion. This mrosopi ehvior is the result of severl ontriutions in the firstpriniples moel. For instne: (i) the lulte retion energy lnspe [6] showe tht the trnsition stte energy of N 2 issoition epens on wht type of retion intermeite is sore lose to the B5 site. Therefore, the ontriution of the RDS to n pprent tivtion energy is weighte verge of severl N 2 TS energies n their lol environments. (ii) As the surfe omposition hnges uring mmoni synthesis, shown in Figs. 3 n 4, it is ler tht E pp will vry n epen rther sensitively on the overges of H n NH x ; x ¼ 0; ; 2; 3. From previous figures n Fig. 6 the following generl fetures of the pprent tivtion energy n e rwn (i) t the inlet H overge totlly etermines the pprent tivtion energy n (ii) s the mmoni synthesis proees long the retor the E pp inrese rpily ue to the higher overge of NH 2. Negtive ðh 2 Þ inites tht the synthesis of NH 3 is hinere y sore H, whih is nturl onsequene of the high overge of H. As shown erlier [6], n lso in the Appenix B, smll hnge in H sorption potentil energy is enough to give full greement etween the lulte n mesure NH 3 proutivities. The negtive vlue of ðh 2 Þ essentilly shows the sme thing. The zero retion orer in NH 3 t the inlet of the retor is expete s no NH x ; x ¼ 0; ; 2; 3 intermeites re present. As the NH 3 synthesis proees through the retor the retion orers of oth H 2 n NH 3 hnge: ðh 2 Þ eomes less negtive s NH 2 reples the sore H, wheres ðnh 3 Þ turns negtive for the sme reson, see Fig. 6,, n f. The lulte pprent tivtion energies n retion orers, given in Fig. 6, gree with mesurements of Béue et l. [64], lthough, the mesurements were performe uner ifferent onitions. Interestingly Béue et l. [64] foun tht their lest tive tlysts were inhiite y hyrogen, i.e. in goo greement with our results. 5. Conlusion We onlue tht mmoni synthesis/eomposition n e preite solely from first-priniples. The solute proutivities re in semi-quntittive greement with experimentl t mesure over n inustril, high-surfe tlyst t vrious tempertures, flows n rtios. For reltive epenene of flow, temperture, n H 2 : N 2 rtio, the first-priniples moel even provies quntittive greement with experimentl t. Anlyzing surfe overge, pprent tivtion energy n rte orers of H 2 n NH 3 shows tht t the inlet of plug-flow retor these properties re minly ffete y sore H toms, wheres for lrger mmoni onversion sore NH 2 eomes more importnt. Clulte pprent tivtion energies n rte orers re in semi-quntittive greement with experimentl t. The ft tht, we n moel mmoni synthesis/eomposition with suh high ury using firly inexpensive quntum hemil metho like ensity funtionl theory shows tht in the ner future omputtionl sreening will e ompetitive metho for serh of new tlysts. For instne, it is possile to lulte ll the energies neee in the first-priniples moel in few ys on, sy, luster of 24 Pentium IV PC s. As there is liner orresponene etween the omputtionl power n the numer of mterils we oul sreen together with the historil inrese in ville omputer power it is ler tht omputtionl sreening is very ompetitive metho for fining new tlysts. Aknowlegement We thnk Dnish Center for Sientifi Computing for omputer resoures n eonomi support y EU Projet No. HPRN-CT Appenix A While the overll rte of mmoni synthesis is not very sensitive to the errors in the solute sorption potentil energies it oul epen more sensitively on the reltive errors in sorption potentil energies of ifferent sortes. To test this, we hve erese H sorption potentil energy y 6 ev. The otine results re shown in the Fig. 7, where we ompre the proutivity lulte using the originl DFT energies n the proutivity otine with moifie H sorption energy. Clerly smll hnge in the reltive energies is enough to give quntittive greement etween theory n experiment t ll tempertures n flows. Hene from funmentl point of view further evelopment in the exhnge-orreltion funtionl shoul e irete towr n inrese in the ury of reltive energies etween retion intermeites. Appenix B Reent stuies show tht inluing the lterl two-oy intertions etween retion intermeites into the moel inreses the mmoni proutivity t lest y orer of mgnitue Moel mmoni output (NH 3 -%) Experimentl mmoni output (NH 3 -%) Fig. 7. The lulte mmoni proutivity with moifie H sorption potentil energy ompre with the mesure mmoni proutivity. The 00 r, 50 r n r t re represente y plus, ross, n str symols, respetively.

9 A. Hellmn et l. / Surfe Siene 603 (2009) Moel mmoni output (NH 3 -%) 0 0. [6,65]. This woul inite tht most of the stuies, where intertions re ignore the results might e quntittively wrong. However, we will show in this ppenix tht quntittive greement with MC results n simple miro-kineti moel n e hieve. The im is to reproue our results using the first-priniples moel with simple miro-kineti moel using the site pproximtion. The miro-kineti moel will only serh for two empty sites, hene, ompletely ignore ny effets from the lol environment roun the tive sites. Hene, the retion rte per tive site is rðt; p N2 ; p H2 ; p NH3 Þ¼ð Þm expðe =k B TÞp N2 h 2 where E is single effetive tivtion rrier. We otin it y verging over ll tivtion energies for eh lol environment tht pper in the MC simultion P E i ¼ k B T ln P i expð E i =k B TÞ P i P ð6þ i It shoul e note tht in this fshion the effetive energy not only rries the informtion of the height of ertin tivtion rrier ut lso the proility for this lol environment. From Fig. 8 we see tht it is inee possile to reproue the first-priniples results with muh simpler miro-kineti moel. This explins why erlier use of miro-kineti moel hve one so well. Referenes Experimentl mmoni output (NH 3 -%) Fig. 8. The lulte mmoni proutivity for 00 r using the simplifie kineti moel introue in Appenix B ompre to the results from the first-priniples moel. [] M. Bourt, Top. Ctl. (994) 405. [2] C.H. Christensen, T. Johnnessen, R.Z. Sorensen, J.K. Nørskov, Ctl. Toy (2006) 40. [3] J.R. Jennings (E.), Ctlyti Ammoni Synthesis: Funmentls n Prtie, Funmentl n Applie Ctlysis, Plenum Press, New York, 994. [4] M. Gunze, in: D.A. King, D.P. 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