Automatic Reaction Mechanism Generation with Group ... · Figure1:Part of a pair of trees for...
Transcript of Automatic Reaction Mechanism Generation with Group ... · Figure1:Part of a pair of trees for...
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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