and C D reaction H with OH An experimental theoretical and study on the kinetic isotope effect ofC Chemical Physics Letters

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Chemical Physics Letters

j o ur na l ho me p ag e :w w w . e l s e v i e r . c o m / l o c a t e / c p l e t t

An experimental and theoretical study on the kinetic isotope effect of C 2 H 6 and C 2 D 6 reaction with OH

Fethi Khaled

, Binod Raj Giri

, Milán Sz ˝ori

, Béla Viskolcz

, Aamir Farooq

aCleanCombustionResearchCenter,DivisionofPhysicalSciencesandEngineering,KingAbdullahUniversityofScienceandTechnology(KAUST), 23955-6900Thuwal,SaudiArabia

bDepartmentofChemicalInformatics,FacultyofEducation,UniversityofSzeged,Boldogasszonysgt.6,H-6725Szeged,Hungary

cInstituteofChemistry,FacultyofMaterialsScienceandEngineering,UniversityofMiskolc,Hungary

a r t i c l e i n f o

Articlehistory:

Received18September2015 Infinalform23October2015 Availableonline30October2015

a b s t r a c t

Wereportexperimentalandtheoreticalresultsforthedeuteratedkineticisotopeeffect(DKIE)ofthe reactionofOHwithethane(C2H6)anddeuteratedethane(C2D6).Thereactionswereinvestigatedbehind reflectedshockwavesover800–1350KbymonitoringOHradicalsnear306.69nmusinglaserabsorp- tion.Inaddition,highlevelCCSD(T)/cc-pV(T,Q)Z//MP2/cc-pVTZquantumchemicalandstatisticalrate theorycalculationswereperformedwhichagreedverywellwiththeexperimentalfindings.Theresults reportedhereinprovidethefirstexperimentalevidencethatDKIEasymptotestoavalueof1.4athigh temperatures.

©2015ElsevierB.V.Allrightsreserved.

1. Introduction

Smallalkanes(<C5)constitutealmostallofthecompositionof naturalandliquefiedpetroleumgas(LPG),whereaslargerstraight orbranchedalkanes(≥C5)aretheprimaryconstituentsofgaso- line,dieselandaviationfuels[1–4].Hydrogenabstractionreactions fromalkanesbyhydroxylradicals(OH+RH→R+H2O)arethepri- maryoxidationpathwaysofthesefuelsatcombustionconditions.

Accuratemodelingofcombustionkineticsrequirespreciseknowl- edgeoftotalandsite-specificratecoefficientsoverawiderangeof temperaturesandpressures.Aconventionalwaytoderiveoverall andsite-specificratecoefficientsistostartfromsmallmolecules and then usegroup additivity approximationsto estimaterate coefficientsforlongchainmolecules.Variousapproximationshave beenusedin theliterature, suchasthe Next-Nearest-Neighbor (NNN)[5,6]andStructureActivityRelationship(SAR)[7].Tullyetal.

[8–13]pioneeredtheuseofdeuteriumforthestudyofdeuterium kineticisotopeeffect(DKIE)toelucidaterulesforthecalculation ofsite-specificratesofH-abstractionfromavarietyofhydrocar- bonmolecules.Thismethodologyhas,forexample,beenusedto discernthebranchingratiosofthetwocompetingchannelsduring thereactionofpropane(C₃H₈)withOHatlowtemperatures[10]

andhightemperatures[14].Recently,Badraetal.[15]published

∗Correspondingauthors.

E-mailaddresses:binod.giri@kaust.edu.sa(B.R.Giri),aamir.farooq@kaust.edu.sa (A.Farooq).

experimentalresultsanddetailed kineticanalysisontheappli- cationofDKIEtoextractbranchingratiosofthethreecompeting channelsduringthereactionofpropene(C₃H₆)withOHradicalsat hightemperatures[15].TheimportanceofDKIEofsmallmolecules suchasethane,ethyleneand acetyleneinthedetermination of branchingratiosoflongerchainalkanes,alkenesandalkynesis demonstratedtherein[15].Theaimofthecurrentworkistoextend low-temperature(290–800K)DKIEdataofethane[9]tohightem- peratures(800–1350K)usingratecoefficientmeasurementsofthe reactionofethaneanddeuteratedethanewithOHradicals:

C₂H₆+OH →C₂H₅+H₂O (R1)

C₂D₆+OH→ C₂D₅+HDO (R2)

These resultswill be helpful in elucidating thecompetition ofdifferentH-abstractionchannelsduringthereactionoflarger alkaneswithOHradicals.Moreover,acloserlookintothedatabase fortheratecoefficientsofR1revealsthatthereareonlythreedirect high-temperature(T>950K)measurementsavailableintheliter- ature[16–18].Muchoftheearlierstudiesarelimitedtonearroom temperatures[9,16,17,19–23];andingeneraltheyshowexcellent agreementtoeachotherwithinoveralluncertaintiesof±20%at 298K[19].Surprisingly,therearenotmanyreportsoftheoretical rateconstantestimationsusingtheelectronicstructuremethods otherthantwostudiesfromKrasnoperovandMichael[18] and MelissasandTruhlar[24].ThelateremployedPMP2//MP2/adj2- cc-pVTZleveloftheorytocomputethepotentialenergysurface forthereactionofethanewithOHradicals.Theycomputedthe http://dx.doi.org/10.1016/j.cplett.2015.10.057

0009-2614/©2015ElsevierB.V.Allrightsreserved.

rateconstantsusingabinitioandcanonicalvariationaltransition statetheorycalculationswithsmallcurvaturetunnelingcorrec- tions.Theircalculatedvalueswerefoundtoagreewellwiththe experimentswithinafactorof2.3overawiderangeoftemper- atures.KrasnoperovandMichael[18]usedB3LYP/6-31G*levelof theorytomapoutthepotentialenergysurfaceforethane+OHreac- tion.Theyhadtoadjustthebarrierheightto10.2kJ/molandone ofthelowbendingmodewastakenas250cm⁻¹toachievegood matchwiththeavailableexperimentaldataover140≤T/K≤1600. Theyfurthersuggestedthata highleveltheoryshouldbeused tostudythereactionbetweenethane and OH.Asfor R2,there isonlyoneexperimentalstudyfromTullyetal.[9]atrelatively lowtemperaturesandnotheoreticalreportsarefoundinlitera- ture.ThecurrentworkthusaimstoreportthetheoreticalDKIEfor ethane/d-ethane+OHreactionusinghigh-levelquantumchemical andstatisticalratetheorycalculations.

2. Experimentalsetup

Thelow-pressureshocktubefacility (LPST)atKingAbdullah UniversityofScienceandTechnology(KAUST)wasusedtoconduct allexperimentspresentedhere.Asthedetailsofourexperimental facilitycouldbefoundelsewhere[25],onlyabriefdescriptionis providedhere.TheLPSThas9mlongdriveranddrivensections withaninnerdiameterof14.2cm.Thelengthofthedriversection ismodifiabledependingontherequiredtesttime.Opticalwin- dowswereinstalledatthesidewalllocation,20mmfromtheend walloftheshocktube.Shocktubewaspumpeddowntolessthan 10⁻⁵mbarusingturbo-molecularpumppriortoeachexperiment toensurehighpurityoftheshocktube.Theshocktubewasfound tohavealeakrateof<1×10⁻⁶mbar/min.Allexperimentsreported herewereconductedbehindreflectedshockwaves,andthecon- ditions(T5,P5)werecalculatedbymeasuringtheincidentshock speedandusingRankine–Hugoniotshock-jumprelations[26,27]

embeddedintheFroshcode[28].

Hydroxylradicalswereproducedbyrapidthermaldecompo- sitionoftert-butylhydroperoxide(TBHP),whichisknowntobe acleanthermolyticsourceofOHradicalsandhadbeenvalidated inmanyearlierstudies[25,29,30].Hydroxylradicalsweremea- suredbyusingthewell-characterizedR1(5)absorptionlineinthe (0,0)bandoftheA²⁺←X²OHtransitionnear306.7nm.Mea- suredabsorbancetime-historywasconvertedtoOHconcentration time-historyusingtheBeer–Lambertlaw.A70% TBHPin water solutionwasobtainedfromSigmaAldrich.Ethane(99.99%),argon (99.999%),andhelium(99.999%)werepurchasedfromAHGases.

Ethane-d₆ (98%) was obtained from CDN Isotopes Inc. Several reflected-shockexperimentswereconductedforeachfuel(C2H6

andC₂D₆)andtheconcentrationsofreactants(fuel,TBHP)were chosenbasedonsensitivityanalysestoachievepseudo-first-order kinetics.

3. Quantumchemicalcalculations

Molecularand transitionstategeometrieswereoptimizedat theMP2/cc-pVTZleveloftheory[31–33]applyingthe‘tight’con- vergencecriterionoftheGaussian09programpackage[34].The MP2/cc-pVTZharmonicvibrationalwavenumbersofthemolecules and transition states were scaled by a factor of 0.95 adopted fromCCCBDBdatabase[35].Similartopreviousworks[36–38], theaccuratedescriptionoftheelectronicstructureswasapprox- imatedbyextrapolationschemes.WhileFellerextrapolation[39]

was utilized for HF energies (using cc-pVXZ basis sets, where X=D,TandQ[31]),Helgakerextrapolation[40]forCCSD(T)cor- relation energies [41] was applied with cc-pVTZ and cc-pVQZ basis sets. Sum of these extrapolated energies manifested in

100 50

0 -5 -4 -3 -2 -1 0

C₂H₆ + OH => C₂H₅ + H₂O

TBHP => TBUTOXY + OH

CH₃COCH₃ + OH => H₂O + CH₂CO + CH₃ CH₃ + OH => CH₂* + H₂O

C₂H₆ (+M) => 2CH₃ (+M) CH₃ + OH (+M) => CH₃OH (+M)

OH sensitivit y

t (µµs)

Figure1.HydroxylsensitivityforC2H6+OHreactionat1106Kand1.38atm.OH sensitivityisdefinedasSOH=(∂^XOH/∂^ki)×(k_i/XOH),whereXOHisthelocalOH-mole fractionandk_iistherateconstantfortheithreaction.Initialmixturecomposition:

342ppmethane,22.4ppmTBHP(70ppmwater)dilutedinargon.

CCSD(T)/cc-pV(T,Q)Z//MP2/cc-pVTZleveloftheorywhichischo- sentoestablishhigh-levelabinitiodescriptionofthezero-point correctedrelativeenergies(E₀)forbothisotopologues(C₂H₆and C₂D₆).

The rateconstantsfor ethane+OH and ethane-d6+OH were calculatedusingcanonicaltransitionstatetheory(CTST)withthe molecularparametersfromourabinitiocalculations.IntheseCTST calculations,allspecieswereassumedtobeintheelectronicground stateexceptOH,forwhichtheelectronicpartitionfunctionwascal- culatedwithaspinorbitsplittingof139.7cm⁻¹[42].Onelowlying bendingmodecorrespondingtoC-Crotationinthereactantsand twoofthelowfrequencytorsionalmodesofthetransitionstates correspondingtoC CandOHrotationsweretreatedashindered rotorswithinPitzer–Gwinn[43]approximations.Ratecalculations werecarriedoutusingChemRatecode[44].

4. Resultsanddiscussion

The JetSurf 1.0 mechanism [45] is used asthe basemecha- nismand tert-butylhydroperoxide(TBHP)chemistryfromPang et.al[46]isaddedtothebasemechanismtosimulateOH-time histories.Sensitivityanalysiswasperformedtoexploretherole ofsecondaryreactionsthatmightaffectOHconcentrationtime- profileinourexperimentalconditions.AscanbeseeninFigure1, thesecondarychemistryhasnegligiblecontributiontoOH-decay profile.Measurements forR1 werecarried outin thetempera- turerangeof847–1285Kusingamixtureof342ppmofethane with22.4ppmTBHPdilutedinargon,whereasthemeasurements ofR2rangedfrom805to1345Kusingamixtureof310ppmof ethane-d₆with22.2ppmTBHPdilutedinargon.Toensurepseudo- firstorderkinetics,theconcentrationofTBHPwasalwayskeptat least10timessmallerthanthatofethaneorethane-d6.Therate coefficientsofreactionsR1andR2areobtainedbyfittingthesimu- latedOHtimeprofilestotheexperimentalOHtime-profileswhile varyingtherateconstantofthetargetreactioninthekineticmech- anism.RepresentativeexperimentalandmodeledOHprofilesin additiontotheeffectof20%deviationfromthebestfitforethane andethane-d6areshowninFigures2and3,respectively.Measured valuesoftheratecoefficientsalongwithexperimentalconditions arecompiledinTables1and2.OurdataareplottedinFigure4 along withthepreviouslow-temperaturedatafromTullyetal.

[9] andthree-parameter Arrheniusexpression (k₁=2.68×10⁻¹⁸ (T/K)^2.224 exp(−373K/T)cm⁻³molecule⁻¹s⁻¹±13%)obtainedby Krasnoperov and Michael [18] from fitting the entire database

60 40

20 0

0 5 10 15

20 experimental data

k_{best fit}=1.4× 10^-11cm³ molecule^-1 s^-1 0.8 × k_{best fit}

1.2 × k_{best fit}

OH Mole Fraction (ppm)

t (µµs)

Figure2.Hydroxylmolefractionprofileforethane+OHreactionatT=1106K, P=1.38atm.Themixturecompositionwas342ppmethane,22.4ppmTBHP(70ppm water)inargon.Thebest-fittotheexperimentalprofilealongwith±20%perturba- tionsarealsoshown.

80 60

40 20

0 0 5 10 15 20

experimental data

k_{best fit}= 1.0 × 10^-12cm³ molecule^-1 s^-1 0.8 × k_{best fit}

1.2 × k_{best fit}

OH Mole Fraction (ppm)

t (µµs)

Figure3.Hydroxylmolefractionprofileforethane-d6+OHreactionatexperi- mentalconditionsofT=1133K,P=1.44atm,310ppmethane-d6,22.2ppmTBHP (80ppmwater)dilutedinargon.Alsopresentedarethebest-fitsimulatedprofile andperturbationsof±20%.

Table1

MeasuredratecoefficientsofreactionR1(ethane+OH).

Temperature Pressure k1

(K) (atm) (cm³molecule⁻¹s⁻¹)

847 1.68 6.81×10⁻¹²

925 1.6 8.93×10⁻¹²

970 1.46 1.06×10⁻¹¹

1034 1.4 1.23×10⁻¹¹

1106 1.38 1.39×10⁻¹¹

1142 1.31 1.54×10⁻¹¹

1275 1.31 1.94×10⁻¹¹

1277 1.08 2.08×10⁻¹¹

1285 1.21 1.96×10⁻¹¹

for ethane+OH reaction over 138–1367K. As can be seen, the three-parameterexpression[18]underpredictsourmeasuredrate coefficientsforR1bya meandeviationof20%.AsforR2,there arenoliteraturedataavailabletocomparewithinthetempera- turerangeofourstudy.Thebestfitofourexperimentaldataalong withlowtemperatureliteraturedataforR1andR2resultedinto

Table2

MeasuredratecoefficientofreactionR2(d-ethane+OH).

Temperature Pressure k2

(K) (atm) (cm³molecule⁻¹s⁻¹)

805 1.68 3.09×10⁻¹²

875 1.63 4.47×10⁻¹²

943 1.56 5.73×10⁻¹²

997 1.34 7.40×10⁻¹²

1030 1.62 8.25×10⁻¹²

1133 1.44 1.00×10⁻¹¹

1190 1.44 1.14×10⁻¹¹

1240 1.28 1.30×10⁻¹¹

1254 1.42 1.32×10⁻¹¹

1345 1.37 1.60×10⁻¹¹

0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 1E-13

1E-12 1E-11 1E-10

k (cm3 molecule-1 s-1 )

1000 K / T

Figure4. Comparisonofthecalculatedratecoefficientswiththeexperimentaldata.

( )thisworkforC2H6+OHreaction;( )Tullyetal.[9]forC2H6+OHreaction;( ) thisworkforC2D6+OH;( )Tullyetal.[9]forC2D6+OHreaction.Blueandredlines representtheresultsofourabinitio/CTSTcalculationsforC2H6andC2D6reactions withOHradicals,respectively.Solidlinesrepresentthecalculatedratecoefficients withouttunnelingcorrections,whereasthebrokenlinesincorporateWignertun- nelingcorrection.Dottedlinesaretheresultsfromfittingtheentiredatabasefor C2H6+OHreactionovertheT-rangesof138–1367KobtainedbyKrasnoperovand Michael[18].

thefollowingthreeparameterArrheniusexpressions (inunitof cm³molecule⁻¹s⁻¹):

k1(T)=1.02×10⁻¹⁷T^2.083exp

T

(290−1290K) (1) k2(T)=5.48×10⁻¹⁷T^1.866exp

T

(290−1350K) (2) Ourcalculatedenergyprofileofthereactionofethaneisotopo- logueswithOHisshowninFigure5.Theabinitioreactionenergy forethane(−75.9kJmol⁻¹)agreeswithintheuncertainty(1.70kJ mol⁻¹)oftheexperimentalvalue(−76.01kJmol⁻¹)calculatedfrom thedataavailableintheCCBDBdatabase.Ourabinitiobarrierheight forR1isfoundtobe9.3kJmol⁻¹whichisconsistentwiththeearlier reportof9.75kJmol⁻¹fromMelissasandTruhlar[24].Thesecom- parisonssuggestthattheenergiescalculatedinthecurrentworkfor thedeuteratedspeciesarealsohighlyaccurate.Thebarrierheight forR2iscalculatedtobe13.3kJmol⁻¹.Basedontheenergyprofile displayedinFigure5andmolecularparameterslistedinTable3, weperformedCTSTcalculationsthatarefoundtoreproduceour experimentaldataverywell(seeFigures4and6).However,the calculationsunderpredictexperimentalratecoefficientsforboth R1andR2inthelow-temperatureregion.Thissubtlediscrepancy maybeattributedtothetunnelingeffect.AscanbeseeninFigure4, thequantumtunnelingeffectislesspronouncedforR1asopposed toR2.Thisisexpectedasthereactionswithsmallbarrierscon- tributelesstothequantummechanicaltunneling().Tunneling

Figure5. Potentialenergy surface (includingzero-point energies) for the H- abstractionreactionofethaneandethane-d6withOHradicals;energiesarerelative tothereactantenergies.

()wascomputedusingWignerformulathatrequiresimaginary frequency(^=/)correspondingtothereactioncoordinateandthe thresholdenergy(E0)asgivenby:

=1− 1 24

1+RT E0

(3) AfterincorporatingWignertunnelingcorrection,thetheoretical ratecoefficients(dashedlines,Figure4)forR2showedexcellent agreementwithexperimentaldataover theentiretemperature range.ButforR1,thetunnelingcorrectionappearstobequantita- tivelylessreliableatlowtemperatures.Thecalculatedrateswere overestimatedbyroughlyafactoroftwointhelow-temperature region.AsimilarbehaviorwasreportedbyMelissasandTruhlar [24]whereWignertunnelingcorrectionresultedinanoverestima- tionoftheratecoefficientsbyafactorof2.3at300K.Thetunneling correction,however,isnearlynegligibleinourexperimentalcon- ditions.Moreover,thecontributionoftunnelingisexpectedtobe cancelledouttothelargepartwhencalculating theratioofthe ratecoefficients(k1/k2).Fromtheresultsofabinitioandtransition statetheorycalculations, theratioof thetunneling-uncorrected ratecoefficientsofreactionsR1andR2,i.e.,DKIE,canbeexpressed overthetemperaturerangeof290–1400K:

k1

k2

(T)=(0.38±0.10)exp

−(3046±70)K T

+(1.02±0.05) exp

T

(4)

Thebestfit of experimentaldata(this workandTully etal.

[9])yieldsthefollowingexpressionforDKIEovertheTrangeof

1400 1200 1000 800 600 0 400

2 4 6 8

k1/k2

T (K) 1.4

Figure 6.Comparison of the experimental and theoretical DKIE of ethane (H/D)+OH.(—)experimentalresultsfromthisworkandTullyetal.[9];( )cal- culatedvaluesfromourabinitio/CTSTmethods.(......)ahorizontallineshowing DKIE=1.4.

293–1350K:

k1

k2

(T)=(0.5±0.10)exp

−(2607±356)K T

+(0.9±0.1) exp

T

(5)

BoththeexperimentalandcalculatedvaluesforDKIEaredis- playedinFigure6.Ascanbeseen,thecalculatedandexperimental DKIEvaluesexhibitgoodagreementovertheentiretemperature range.OurcalculatedvalueforDKIEat290Kis6.4whichiscloseto thatreported(4.61±0.56)byTullyetal.[9].At850K,wemeasured aDKIEvalueof1.67whichagreesverywellwiththeextrapolated valueof1.72fromtheworkofTullyetal.[9].Ourexperimentally determinedDKIEasymptotestoavalueof1.4athightemperatures (T>1200K).

The high-temperature asympoting behavior of DKIE can be exploredusingtheoreticalmethods.FromArrheniustheory,DKIE canbewrittenas:

k1

k2

(T)= A1

A2

exp

a

RT

(6) whereAisthepre-exponentialfactorandthesubscriptsidentify thecorrespondingreactions;Ea=Ea(D)−Ea(H)isthedifference intheactivationenergiesoftheisotopes.AsTapproachesinfin- ity,k1/k2≈A1/A2.TheratioofA1andA2 canbeapproximatedby takingtheratioofimaginaryfrequenciesofthetransitionstates (1=//2=/)[47].Using 1=/ =1303cm⁻¹ and 2=/ =1003cm⁻¹ (seeTable3),DKIE(k1/k2)comesouttobe1.3.Ontheotherhand,ab Table3

Rotationalconstants(A,B,andC)andharmonicfrequencies(i)ofthestationarypointscalculatedattheMP2/cc-pVTZleveloftheory.Frequenciesarescaledby0.95.

Frequenciescorrespondingtothetorsionalmodesareshowninbold.

Species A,B,C

(GHz)

i

(cm⁻¹)

C2H6 79.26966

19.81782(2)

3045(2),3025.5(2),2951.7,2950.3,1437.7(2),1437.3(2),1358.9,1331.0, 1166.8(2),990.3,785(2),308.5

C2D6 39.66530

13.70550(2)

2254.5(2),2242(2),2127.4,2116.6,1135.5,1041.8(2),1026(2),1017.4,929.1 (2),822.8,567.4(2),218.4

TS 26.33548

4.80059 4.28371

1303i,3621.5,3073.8,3047.0,3032.1,2992.8,2949.2,1432.6,1427.5,1412.7, 1342.1,1311.6,1266.5,1196.0,1154.4,1019.5,974.6,809.9,786.1,630.4, 160.1,114.6,373.3,51.2

TS-d6 17.78627

4.22738 3.74362

1003i,3621.4,2280.3,2258.9,2244.1,2174.0,2120.2,1138.6,1035.8,1026.2, 1017.8,991.5,959.7,937.9,900.4,888.9,846.0,673.2,567.7,537.5,120.8, 101.5,267.5,49.5

initio/CTSTcalculationspredictthatDKIEasymptotesto1.5athigh temperatures.Thesevaluesarequiteclosetotheexperimentally determinedDKIEof1.4.

5. Conclusions

The deuterated kinetic isotope effect (DKIE) for the reac- tionofethaneand ethane-d6 withOHradicalswasdetermined experimentallybetween800and1350K.Additionally,highlevel CCSD(T)/cc-pV(T,Q)Z//MP2/cc-pVTZquantumchemicalandstatis- ticalratetheorycalculationswereperformedtocalculatetheDKIE over290–1400K.Thetheoreticaland experimentalDKIEvalues are found to agree well over the entire temperature range of 290–1350K.Our ab initio/CTSTcalculations predictedthatDKIE asymptotesto1.5athightemperatureswhichisonly7%largerthan theDKIEvaluedeterminedexperimentallyinthecurrentwork.This workreports,toourknowledge,thefirstexperimentalevidence thatDKIEasymptotesto1.4athightemperatures.

Acknowledgments

WewouldliketoacknowledgethefundingsupportfromSaudi AramcoundertheFUELCOMprogramandbyKingAbdullahUni- versityofScienceandTechnology(KAUST).Dr.Sz ˝oriisaMagyary Zoltánfellow supportedbyStateof Hungary andtheEuropean Union,financedbytheEuropeanSocialFundintheframeworkof TÁMOP4.2.4.A/2-11-1-2012-0001“NationalExcellenceProgram”

under the respective grant number of A2-MZPD-12-0139. This workwassupportedbytheJánosBolyaiResearchScholarshipof theHungarianAcademyofSciences(BO/00113/15/7).

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