AutomaticReactionMechanismGenerationwithGroupAdditiveKineticsRichardH.West, JoshuaW.Allen, and WilliamH.GreenMassachusettsInstituteofTechnology, DepartmentofChemicalEngineering,77MassachusettsAvenue66-270, CambridgeMA 02139

Abstract

Thekeychallengeinmakingchemicalmechanismdevelopmentpredictiveisbeingabletoaccu-ratelyestimateanypossibleratecoefficient k(T ) eveniftherearenoexperimentaldata. ReactionMechanismGenerator (RMG) isanopen-sourcesoftwareproject thatcanbuilddetailedkineticmodels forchemical reactingsystems (http://rmg.sourceforge.net). Itusesadatabaseof rules toproposeelementarychemicalreactionsandtoestimatethenecessarythermochemicalandkineticparameters. Wearemodifyingthealgorithmusedtoestimatekineticdatatomaketheestimatedreactionratesmorereliableandeasiertodocumentincaseswheretheyareestimatedfromsparsedata. WepresentabriefoverviewofRMG,adiscussionof thekineticsestimationoptions, anexplanationofthechosenalgorithm, andanassessmentofitsperformance.

Introduction

Kineticmodels forgas-phase reacting systems, suchasatmosphericchemistryandcombustion,oftencontain thousandsofspeciesandreactions. Researchers in thesefieldshavedevelopedanumberoftoolstohelpthemgeneratethesedetailedmodels[1–5].

ReactionMechanismGenerator(RMG) isanopen-sourcesoftwareprojectthatcanbuilddetailedkineticmodelsforreactingsystems[4–7]. Toestimatereactionrateexpressions, RMG usesagroup-basedapproach. Thecurrentalgorithmworkswellwhenthedatabaseofrate-estimationrulesandassociatedgroupvaluesiscomplete, butperformspoorlywhenkineticdataaresparse. Wearemodifyingthealgorithmtomaketheestimatedreactionratesmorereliableandeasiertodocumentincaseswheretheyareestimatedfromsparsedata.

AutomatickineticmodelgenerationwithRMG

Givensomestartingspecies(e.g.methaneandoxygen)andsomereactionconditions(temperatureandpressure)itwillcreateakineticmodelofthereactionmechanismconsistingofmany(uptothousands)elementaryreactionsbetweenintermediatespecies. Insidethesoftwaremoleculesarerepresentedasgraphs, withatomsasnodesandbondsasedgesconnectingthenodes. Standardgraph-theorymethodsareusedtoidentifyequivalentgraphsandensureuniqueness. RMG uses“reactionfamilies”togenerateallthepossiblereactionsthataspeciescanundergointhepresenceoftheotherspeciesinthechemicalmechanism. Everyreactionfamilyrepresentsaparticulartypeofelementarychemicalreaction, suchasbond-breaking, orradicaladditiontoadoublebond. Eachreactionfamilyhasarecipeformutatingthegraph, andalibraryofrateexpressionsfordifferentreactingsites.

Becausethemodelcancontainthousandsofspeciesandrates, theestimationofthermochemicalandkineticparametersmustbeveryfast. Aswithmostmechanismgeneratingtools, RMG usesadatabaseofknownvalueswhereverpossibletofindthermochemicaldataforspecies, butusuallythedataareunknownanditestimatesparametersusingagroupcontributionmethod. ThermochemistryestimatesarebasedonBenson’sgroupadditivitymethodforstandardenthalpiesofformation[8, 9].Thefunctionalgroupsarerecognizedusingagraph-theorymatchingalgorithm. A similarmethodisused toestimate the ratecoefficients for the reactions: functionalgroupsare identifiedusinggraph-matchingandtheratesareestimatedfromadatabaseofrules.

RMG usesarate-basedterminationcriterion; thereactionnetworkisexpandeduntiltheratesofall reactions going to species not included in thenetwork fall belowa certain threshold. Thishelpstoincludeimportantpathwayswithoutunnecessarilyexploringslowerpathways, ratherthanterminatingtheexpansionafterasetnumberofgenerations[10].

Rateestimationmethods

Theratecoefficientofareactionislargelydeterminedbytheatomsintheregionarounditstransitionstate. This region, containingseveralpolyvalentatoms, canbecalleda“supergroup” [11, 12].Identifyingthesupergroupallowsonetoestimatethereactionratecoefficient.

Thesupergroupcanbedecomposedintocomponentgroups. Forexample, inH-abstractionreac-tions

XH+ Y· −→ X·+ YH (1)

thecomponentgroupswouldbetheabstractinggroup(Y) andthegroupfromwhichahydrogenisabstracted(X).

CurrentlyinRMG,thegroupsX andY areusedonlytolocatethetransitionstatesupergroupXHYinthedatabase. WhenarateexpressionisnotavailableforXHY,theratesofsupergroupsclosetoitinthedatabasearecurrentlyaveragedusingacomplicatedschemethatcanunfortunatelyleadtopoorestimatesandobfuscatethesource(s)ofthefinalreactionrateexpression.

Inthenewgroupadditiveapproach, theeffectonthekineticexpressionfromthecomponentgroupsX andY areseparatedandassumedtobeindependentandadditive. Forexample, theeffectofchangingY fromaprimarytoasecondarycarbonisindependentofthegroupX [13].

Wetrainourgroupvalueswithalargedatabaseofreactionratestakenfromtheliteratureand abinitio calculations. Weorganizethegroupsinahierarchicaltreestructurewherechildnodesaremorespecificinstancesoftheirparentnode. AnexampleisgiveninFigure 1. Thegroupvaluesforeachnodearefitted toall thekineticdata thatmatchthatnode, including those thatmatchitsdescendants. Thegoodnessofthisfitisalsostored. Whenestimatingtheratecoefficientforareaction, themostspecificinstanceofeachgroupisidentified. Ifvaluesaremissingforthatgroupthenitsparentnodeisused, continuingupthetreeuntilanodewithdataisfound. ThiswillallowsomeindicationofthefittingerrorsateachnodeandmakeitclearerhoweachratecoefficientwasestimatedinRMG.

Thisprocedurecanbemadeautomatic, sothatallthegroupvaluescanbeeasilyrefitwhenevertheuserhasaddednewdataon individual reactionrates, making itmorepractical tokeep therate-estimationrulesup-to-datewiththelatestinformation.

Inspecting thefittedvaluescansuggestmodifications to the tree structure. Forexample, in thebottomleftcornerofthe Y · treeinFigure 1 molecularoxygen O2(

3Σ−g )isasiblingof C2(X

1Σ+g )

althoughtheirreactivitiesareverydifferent.

X-­H  +  Y.    X.  +  Y-­Hrates  contributing:  (233)log10(kf  @  1000K):  9.23

H2 C H

X H

O HCC H CO HCC H

(19)-­0.59

(120)+0.18

(25)-­0.55

(5)-­2.31

(22)+0.79

(34)-­0.05

CH4 CH3 CH2 CH

(16)-­0.45

(47)+0.16

(28)+0.18

(29)+0.56

O CH3C CH3 CC CH3 CO CH3CC CH3

(23)+0.05

(17)-­0.12

(2)+1.83

(1)+2.09

(3)+1.42

(1)+3.52

.C C.

(12)-­7.82

.O O. C.H3 C.H2 C.H C.

(23)+0.54

(34)-­0.69

(23)-­0.96

(17)-­1.11

R: R.

Y.

(13)+1.68

(218)-­0.09

H. C. O.C.C C.OC.C

(23)+2.21

(13)-­7.01

(97)-­0.56

(26)+1.02

(7)+2.62

(37)+0.77

(12)-­1.13

.R R.:CH2

(4)+0.13

O:

(9)+2.40

Figure 1: Part of a pair of trees for hydrogen abstraction reactions, showing the number of re-actionratescontributingto the training(inparentheses)andthefittedgroupvalue forlog10 (kf @1000 K)

Example

Figure 1 showspartofapairoftreesforthehydrogenabstractionreactionfamily. Inthiscasethedatausedare thebase-10 logarithmsof the forward reaction ratecoefficientsat1000 K,perHatom. 223reactionrateexpressionswereusedinfittingthegroups, andtheoverallaverageratewas 109.23 cm3/mol/s. Forthereaction C2H6 + HCO −→ C2H5 + CH2O, wecanestimatetheratecoefficientat1000 K byidentifyingthe X−H and Y · groupsinthetreeasfollows:

C CH3

-­0.129.23

Base TotalC.O

-­1.13 =+ + 7.98

There are 6 equivalent H atoms to abstract so the total rate coefficient is 6 × 107.98 = 5.6 ×108 cm3/mol/s, whichcompareswellwitha 7.0× 108 cm3/mol/sestimatebyTsang etal.[14].

Methodcomparison

Totestthemethodsweextracted888rateexpressionsforhydrogenabstractionreactionsofspeciescontainingonlycarbon, hydrogenandoxygen(ascoveredbyourrules)fromthePrIMeKineticsdatawarehouse[15]andcomparedthemwithestimatesmadeusingtherulesandgroupvalues.Thetestsetincludesalltheavailabledata, notjustthecurated, checked, andapprovedvalues.

Foreachreactionthereactingfunctionalgroups X−H and Y · areidentified. Sometimeswehavearule for thatexactcombinationofX andY, inwhichcaseweuse it toestimate the rate. ThecomparisonofpredictedvsPrIMe k(1000 K) for thesecases is shown inFigure 2. Thekineticsestimationschemeworksquitewell. The95%confidenceintervals(shownbythedashedlines)are±1.13 in log(kf ) andmostoftheoutliersaremistakesinthetestdatafromthePrIMedepository. 1

976

820

PrIMe database rate coefficient (cm³/mol/s)

Pre

dic

ted r

ate

coeffic

ient

(cm

³/m

ol/s)

Figure 2: Parityplotcomparingpredicted k(1000 K) withdatafromPrIMedatabase, forhydrogenabstractionreactionsreactionsthatmatchaknownruleforXHY.

WhenthereisnoruleavailablefortheidentifiedcombinationofX andY,theratemustbeestimatedusingtherulesthatareavailable. ThepreviousmethodusedinRMG softwarewastoaveragetheratesofrules“nearby”inthetrees. Whentheneighboringpairsofgroupsarealsomissingthiscanleadtocomplicatedexpressionswhicharehardtounderstandandcangivepoorestimates. 2 The

1Checkingtheoriginalsourcesforpoints820and976inFigure 2 revealserrorsintheactivationenergiesof −6.1and −9.6 kcal/molrespectively. Theoutlyingpoint877inFigure 3 signifiesanothermistakeininterpretingthePrIMedatabase: the n inthemodifiedArrheniusexpressionrepresents (T/298 K)n not (T/1 K)n.

2Thereaction HC−−−C · + H2O −−→ HC−−−CH + HO · (point893inFigure 3)matchesthepairofgroups(O-pri, Ct-rad), butthatruleisunknown. Usingtheoldschemeitisestimatedas: (Averageof: (Averageof: (Averageof: (O-priO2b)&Averageof: (O/H/NonDeC O2b)&O-priH-rad&Averageof: (O/H/NonDeC H-rad&O/H/OneDeH-rad)&Averageof: (O-priC-methyl&Averageof: (O-priC-rad/H2/Cs))&Averageof: (O/H/NonDeC C-methyl&Averageof:(O/H/NonDeC C-rad/H2/Cs)&Averageof: (O/H/NonDeC C-rad/H/NonDeC) &Averageof: (Averageof: (O/H/NonDeCC-rad/Cs3))&Averageof: (Averageof: (H2O2C4H9O/c12345&H2O2C4H9O/c134(2)5&H2O2C4H9O/c134(2)5&H2O2C4H9O/c14(2,3)5)&Averageof: (H2O2C3H5/c132))&Averageof: (Averageof: (H2O2C4H9O/c12345&H2O2C4H9O/c12345&H2O2C4H9O/c134(2)5)&Averageof: (Averageof: (H2O2C4H9O/c12345)))&Average

resultsofusingthisschemeforthecaseswhenthecombinationX andY isnotknown, areshowninFigure 3a.

Usingthenew, groupadditivemethodtoestimatethekineticsforunknowncombinationsofX andY issimplertoexplainthantheaveragingscheme. Thereaction HC−−−C · + H2O −→ HC−−−CH +HO · (point893inFigure 3)matchesthepairofgroups(O-pri, Ct-rad), eachofwhichistrainedindependently. O-priwastrainedfrom11rules(incombinationwithY groupsotherthatCt-rad)andcontributes −2.35 to log(k@1000 K). Ct-radwastrainedfrom7rules(incombinationwithX groupsotherthanO-pri)andcontributes +2.53 to log(k@1000 K). Figure 3b showstheresultsofusingthisschemetoestimatethecaseswhentherulesarenotavailableforthematchedcombinationofXandY.The95%confidenceintervals(dashedlines)arenarrower, thereislessstratification, andthepredictedratesspanalargerrangethanwiththeaveragingmethodusedinFigure 3a.

893

430

877

PrIMe database rate coefficient (cm³/mol/s)

Pre

dic

ted r

ate

coeffic

ient

(cm

³/m

ol/s)

877

893

994

444

PrIMe database rate coefficient (cm³/mol/s)

Pre

dic

ted r

ate

coeffic

ient

(cm

³/m

ol/s)

Figure 3: Parityplotscomparingpredicted k(1000 K) withdatafromPrIMedatabase, forhydrogenabstractionreactionsthatdonotmatchaknownXHY rule. Left(a): oldmethodofav-eraging“similar”XHY rules. Right(b): newmethodofestimatingfromindependentXHand Y · contributions.

Conclusions

ThereactionmechanismgenerationsoftwareRMG estimatesreactionrateexpressionsusingrulesbasedonthefunctionalgroupssurroundingthereactingcenter. A reactiontypicallyinvolvesmorethanonefunctionalgroup(e.g.anatomwithahydrogenligandXH andaradical Y · ), whichcom-binetoforma“supergoup”XY.Whenarulefor thesupergroupXY isknown, itcanbeusedtopredictthereactionkineticswithreasonableaccuracy. However, whendataaresparseandarule

of: (Averageof: (Averageof: (H2O2C4H9O/c134(2)5)))&O/H/OneDeC-methyl)&Averageof: (O-priCd-pri-rad)&Averageof: (O/H/NonDeC Cd-pri-rad&Averageof: (H2O2C4H7/c1342)&Averageof: (H2O2Cd-rad/NonDeC))&Averageof: (O/H/NonDeC Ct-rad)&Averageof: (O-priCO-pri-rad)&Averageof: (O-priO-pri-rad&Averageof:(O-priO-rad/NonDeC)) &Averageof: (O/H/NonDeC O-pri-rad&Averageof: (H2O2O-rad/NonDeO &H2O2O-rad/OneDe)))))

forXY isnotknown, RMG currentlyaverages‘similar’XY supergroups. Forthesescenarioswearehavetestedagroupadditivemethod, addingseparatecontributionsfromX andY whicharederivedfromknownXY supergroups. Thegroupvaluescanbetrainedusingexistingsupergrouprulesorexplicitreactions. Thegroupvaluescanbere-trainedwhennewkineticdataareavailableorthedefinitionsandhierarchyofthegroupsareupdated. Byrecordingthegoodnessoffitwhenthegroupvaluesaretrained, confidenceintervalscanbecalculatedoneachreactionrateestimatedusingthismethod. Forthehydrogenabstractionfamilyofreactions, estimatescalculatedinthismannerarebetterthanthoseestimatedusingtheaveragingschemepreviouslyusedinRMG software, andtheiroriginissimplertotrace. Thisapproachisnowbeingextendedtofamiliesofreactionsotherthanhydrogenabstraction.

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