Dipole_exp_fit

内容需要下载文档才能查看 内容需要下载文档才能查看

JournalofQuantitativeSpectroscopy&RadiativeTransfer112(2011)1543–1550

ContentslistsavailableatScienceDirect

JournalofQuantitativeSpectroscopy&

RadiativeTransfer

journalhomepage:http://wendang.chazidian.com/locate/jqsrt

Direct?tofexperimentalro-vibrationalintensitiestothedipolemomentfunction:ApplicationtoHCl

G.Lia,1,I.E.Gordonb,n,P.F.Bernatha,L.SRothmanb

ab

UniversityofYork,DepartmentofChemistry,YorkYO105DD,UK

Harvard-SmithsonianCenterforAstrophysics,AtomicandMolecularPhysicsDivision,Cambridge,MA02138,USA

articleinfo

Articlehistory:

Received12January2011Receivedinrevisedform21March2011

Accepted22March2011

Availableonline29March2011Keywords:

Hydrogenchloride

DipolemomentfunctionIntensitymeasurementsIntensitycalculations

Herman–Walliscoef?cients

abstract

Adipolemomentfunction(DMF)forhydrogenchloride(HCl)hasbeenobtainedusingadirect?tapproachthat?http://wendang.chazidian.combiningwavefunctionsderivedfromtheRydberg–Klein–Rees(RKR)numericalmethodandasemi-empiricalDMF,lineintensitieswerecalculatednumericallyforbandswithDv¼0,1,2,3,4,5,6,7uptov0¼7.TheresultshavedemonstratedtheeffectivenessofinclusionofrotationaldipolemomentmatrixelementsandappropriateweightingoftheexperimentaldataintheDMF?tting.Thenewmethodisshowntobesuperiortothecommonmethodof?ttingonlytherotationlessdipolemomentelements,whileatthesametimebeingsimpletoimplement.

&2011ElsevierLtd.Allrightsreserved.

1.Introduction

Theknowledgeofaccuratespectroscopiclinepara-metersofhydrogenchloride(HCl)isimportantinmodel-ingandinterpretingspectraofstellar[1]andplanetary[2]atmospheres.ItisalsorequiredfortheremotesensingoftheEarthatmosphere[3,4],laserphysics[5,6]andprecisionmeasurements.Duetotheirimportance,spec-tralparametersofHClhavebeenincludedintheHITRANspectroscopicdatabase[7]forthreedecades[8].InthemostrecentHITRANcompilation[7](withtheexceptionofthepurerotationalband)thelinepositionswerecalculatedusingthepotential-energysurfaceofCoxonandHajigeorgiou[9],whiletheintensitieswerebasedonthedipolemomentfunction(DMF)ofOgilvieetal.[10],slightlymodi?edtoincorporatehigh-accuracymeasure-mentsofthefundamentalbandbyPineetal.[11].

WehaverecentlyembarkedonthetaskofupdatingandextendingtheexistingHITRANdataforallhydrogen

Correspondingauthor:Tel.:þ16174962259.

E-mailaddress:igordon@cfa.harvard.edu(I.E.Gordon).1

Pre-doctoratefellowattheHarvard-SmithsonianCenterforAstro-physics,Fall2010.

0022-4073/$-seefrontmatter&2011ElsevierLtd.Allrightsreserved.doi:10.1016/j.jqsrt.2011.03.014

n

halidesbyimprovingexistinglineparametersandinclud-ingmorelines,bandsandisotopologues[12].DuringtheevaluationoftheexistingintensitydataforHCl,wehavefoundsigni?cantdiscrepanciesbetweenmostcommonlyusedsemi-empiricaldipolemomentfunctions[10,13–17].ItisunfortunatethatalmostnoneoftheseDMFshasbeenusedforintensitycalculationsthatcanbecomparedwithexperimentalvalues.Intheevaluationprocess,itwasfoundthattheuseofthedipolemomentfunctionderivedbyKiriyamaetal.[17]leadstoseverediscrepanciesinlineintensities(upto40%evenforlowvibrationallevels)whencomparedwiththebestavailableexperimentaldata.Moreover,beingconsideredasthemostrecentandextensivesemi-empiricalwork,Ref.[17]wasusedtocon-structapiecewisedipolemomentfunctionatnear-equili-briuminternucleardistancesbyBuldakovandCherepanov[18].Itwasalsousedasan‘‘experimental’’functioninordertoevaluaterecenttheoreticalcalculationsbyHarrison[19]andinthecalculationoftheEinsteinA-coef?cientsforvibrationaltransitionsintheHCllaser[20].

In1955,HermanandWallisderivedamethodologytodescribethein?uenceofthevibration–rotationinteractiononlineintensitiesofro-vibrationalbandsofdiatomicmolecules[21].Subsequently,theirapproachwasmodi?ed

1544G.Lietal./JournalofQuantitativeSpectroscopy&RadiativeTransfer112(2011)1543–1550

andwidelyusedasastandardmethodofdeterminingtherotationlessdipolemomentmatrixelementforthero-vibra-tionalbandsby?ttingtheexistingexperimentaldata.Theserotationlessdipolemomentmatrixelementsareemployedin

´asecondsteptodeterminethepowerseries(orPade

approximants)coef?cientsoftheelectronicdipolemomentfunction[10,13,14].Howeverthismethodcannotbeappliedtoasingleline-intensitymeasurementsinceHerman–Wallis?ttingisbasicallyapolynomial?tofmeasurementsofmanylineswithinonero-vibrationalband.

Therehavebeenseveralnewline-intensitymeasure-mentsofHCl.Althoughthesemeasurementsarequiteprecise,theyoftenonlycontaininformationforoneortwolinesofanentirevibrationalband[22,23].Inordertoutilizetheindividualhigh-qualitymeasurementsforinten-sitycalculations,adirect?tapproachwasdevelopedinthiswork.Furthermore,becausetheintensitymeasurementsintheliteratureareofteninconsistent,carefulselectionandappropriateweightingofthedatawerecarriedout.Ulti-mately,anewDMFforHClwasderived,?ttedtothebestavailable(andappropriatelyweighted)experimentaldatausingthisdirect?tapproach.Thero-vibrationallineintensitiesderivedfromourfunctionwerecomparedwiththeonesbasedonpreviouslyreportedDMF’s,HITRAN,andexperimentaldata.

2.Methodologyandpreviousresults

TraditionallytheDMFofadiatomicmoleculeasafunctionoftheinternucleardistance,r,isgivenbythepowerseries

X

MðrÞ¼Mixi,ð1Þ

i

coef?cientsfromEq.(1),theseobtainedrotationlessmatrix

elementsRv0(0)arethen?tto

X

Mi/v9xi90S,ð3ÞRv0ð0Þ¼

i

wheretheexpectationvalues/v9xi90Scanbedetermined

fromthepotentialenergyfunction.InthecaseoftheHClmolecule,bandswithv00¼0andv0¼0–7areavailableintheliterature,andinEq.(3)iisusuallytakentorunfrom0to7.Thedoubleandsingleprimescorrespondtolowerandupperstate,respectively.

In2001,Kiriyamaetal.[17]hadsuggestedthatinclusionofrotationalcomponentsintothe?tcanallowforabetterdeterminationoftheMicoef?cientsthrough?ttingtoalargernumberofpoints/vJ09MðxÞ90J00S¼

nXi¼1

Mi/vJ09xi90J00S:

ð4Þ

TheyhadchosenexperimentalvaluesfromPineetal.

[11]forthefundamentalband,Tothetal.[13]forthe?rstovertone,OgilvieandLee[16]forthesecondovertone,andZughul[25]forbands4-0through7-0.Theseexperi-mentalvalueswere?tted(inHerman–Wallis-typeman-ner)toEq.(5)(reproducedexactlyfromEq.(3.6)inthePh.D.thesis[26])withtheorderofthepolynomialbeingdeterminedusingtheGausscriterion[17,26]/vJ09MðxÞ90J00S¼

nXi¼1

cimi:

ð5Þ

wherex¼(rÀre)/re,reistheequilibriumseparationandi¼0,

1,2y.Someofthepreviousworks(Refs.[10,16]forinstance)employedtheacceptedapproachdevelopedbyTippingandHerman[24]ofusingonlypurevibrationalmatrixelementstodeterminetheDMF.Inordertoobtainpurevibrationalmatrixelements,onecantakeavailablemeasurementsand?tthemseparatelyforeveryband(inthecaseofHClthemeasuredbandsusedinthisworkhaven¼0asalowerstate)totheHerman–Wallisexpression9/vJ09MðxÞ90J00S9¼9Rv0ð0Þ9ð1þCvmþDvm2þ...Þ,

2

2

ð2Þ

whereRv0(0)isarotationlesspart,CvandDvaretheHerman–Walliscoef?cients,withm¼ÀJfortheP-branchandJþ1fortheR-branch.InordertoderivetheMi

NotethatEq.(5)isdifferentfromEq.(2),wheresquaresoftransitiondipolemomentsare?ttedratherthantheactualvalues.Althoughthisprobablydoesnothaveadramaticimpact,itismorephysicallycorrecttofollowthetraditionalapproachof?ttingthesquares,i.e.,itismorecorrecttouseEq.(2).

Thepolynomialswerethenusedtocalculatero-vibra-tionalmatrixelements,fromwhichtheMicoef?cientsweredeterminedusingEq.(4).TheMicoef?cientsdeter-minedinRef.[17]aregiveninTable1.Unfortunately,ifoneusesthesecoef?cientstocalculatero-vibrationaltransitiondipolemoments,theresultsdrasticallydifferfromexperimentalvaluesincludingthosethatwereusedasinputinRef.[17].Moreover,ifonecomparestherotationlessmatrixelementsfromRef.[17]withthosedeterminedintheoriginalexperimentalworks[11,13,16,27]onecannoticesigni?cantdifferencesevenintheseparameters,especiallyinthefundamentaland

Table1

Dipolemomentfunctioncoef?cientsofHClinunitsofDebye.Thenumberlistedinparenthesesisthestandarddeviationinthelastdigitsofagivenvalue.

Presentstudy

M0M1M2M3M4M5M6M7

1.093164(86)1.23679(135)0.01518(375)À1.5377(96)À0.8729(342)À0.4066(639)À0.7531(3011)1.9268(8062)

OgilvieandLee[16]1.093004(75)1.23614(44)0.02063(530)À1.5318(131)À0.9188(264)À0.3519(425)À0.4367(725)0.3513(2068)

Kiriyamaetal.[17]1.095056(1)1.076259(152)À0.001429(155)À1.252768(94)À0.383620(52)0.104152(100)À0.223482(1828)2.024332(4263)

G.Lietal./JournalofQuantitativeSpectroscopy&RadiativeTransfer112(2011)1543–15501545

?rstovertonebands.ThesourceofthediscrepancybecomesobviousifonetakestheratiosofthesquaresoftheKiriyamaetal.[17]rotationlessmatrixelementstotheonesdeterminedintheoriginalworkofPineetal.[11]andTothetal.[13].Bothratiosareverycloseto0.76,avaluematchingtheisotopicabundanceofH35Cl(0.757587),whichmistakenlywasnotaccountedforintheKiriyamaetal.[17]analysisoftheintensitiesdirectlymeasuredinRefs.[11,13].InRefs.[16,27]thereportedexperimentalintensitiesareat100%abundance(i.e.theactualexperimentalintensitieswerealreadydividedbynaturalabundance),andthereforeforthesecondthroughsixthovertonesthereisnoerrormadebyKiriyamaetal.[17].

InordertoderivethenewDMF,weidenti?edthebestavailableexperimentalresultsforeachbandand?ttedthemwithproperweights.IngeneralweusedthePineetal.[11]resultsforthefundamentalband,Tothetal.[13]forthe2-0band,OgilvieandLee[16]forthesecondovertone,andGelfandetal.[27]forbands4-0through7-0.Wealsoaddedseveralindividualro-vibrationaltransitiondipolemomentsthatweremeasuredwithloweruncertainty(forinstancetheR(3)lineinthe?rstovertonemeasuredbyOrtweinetal.[23]).Therotation-lessvalueinthepurerotationalbandwastakenas1.10857accordingtotherecommendationofOgilvieandTipping[28].Wethenusedanoverdeterminedsystemoflinearequations(Eq.(4)),thatweresolvedusingaweightedleastsquaresmethod[29].

3.Detailsofthecalculationsandtheresults

Tobeginwith,apotentialenergyfunctionforH35ClwasconstructedusingthepurelynumericalRKRmethod[30]withtheDunhamcoef?cientsfromParekunneletal.[31].ThisRKRpotentialwasthenemployedtocalculatethetransitionwavenumbers,lower-stateenergiesandtheexpec-tationvalues/uJ09xi90J00SusingLeRoy’sLEVELprogram[32].Thenthedipolemomentmatrixelementswereevaluatedfromthemeasuredlineintensities.Asequenceofsignsofthedipolemomentmatrixelements(þÀþÀÀþÀ)wasadoptedasinthepreviousstudies[14,16].Table2liststhedipolemomentmatrixelementsderivedinthisstudyfromtheexperimentalintensitiesandtheirexperimentaluncer-tainties.Agrand?tofalllisteddipolemomentmatrixelementstothesystemoflinearequations(Eq.(4),eighthorder)wascarriedoutusingaweightedleastsquares?tprogram[29]thatwasmodi?edforthepresentstudy.Eightcoef?cientsofdipolemomentfunction,M0,M1,M2,y,M7,weresubsequentlydeterminedandtheirvaluesarelistedinTable1.Forcomparison,thecoef?cientsofthedipolemomentfunctioncoef?cientsdeterminedbyOgilvieandLee[16]andKiriyamaetal.[17]areincludedinTable1.Finally,thethreedipolemomentfunctionslistedinTable1areplottedagainstinternucleardistanceinFig.1.WhilethedipolemomentfunctionderivedinthisworkdoesnotdifferdrasticallyfromtheonederivedinRef.[16],itclearlydiffersfromtheonederivedinRef.[17].Although,thecoef?cientsofMiinTable1werederivedusingslightlydifferentpotentials

Table2

MatrixelementsMv0(m)ofelectricdipolemomentofHClinunitsofdebye.Thesubscriptsvand0ofMv0(m)representthevthuppervibrationallevelandthegroundvibrationallevel,respectively.Pineetal.[11]resultswereusedforthefundamentalband,Tothetal.[13]forthe2-0band,OgilvieandLee[16]forthesecondovertone,andZughul[25]forbands4-0through7-0.Estimateduncertainties(inpercents)aregivenaftereachvalue.mÀ10À9À8À7À6À5À4À4À3À3À2À112344567891011

abc

M10(m)Â1028.256728.163478.053627.968567.883467.778397.679127.583567.482447.385627.194267.104037.022726.940086.842096.764186.664496.569306.457396.390336.29444

2%2%2%2%2%2%2%2%2%2%2%2%2%2%2%2%2%2%2%2%2%

M20(m)Â103M30(m)Â104M40(m)Â105M50(m)Â106M60(m)Â106M70(m)Â106

À8.46115À8.32351À8.25410À8.03939À8.07161b

15%15%15%15%4%

5.757235.745595.625285.627375.52761c5.551715.691025.531295.671575.895905.683416.242406.370956.132556.40364

25%25%25%25%8%25%25%25%25%25%25%25%25%25%25%

À2.88234À2.86567À2.85896À2.87052À2.90552À2.96318À3.05364À3.15801À3.16065À3.19973À3.23565À3.28203À3.34624À3.41058À3.47490À3.53754À3.60597

10%10%10%10%10%10%10%10%10%10%10%10%10%10%10%10%10%

À8.08881À7.99619À7.95635À7.97178À8.05581À8.20179À8.42494À8.64716À8.62136À8.62304À8.68729À8.74468À8.82735À8.91616À8.99751À9.10332À9.21302

20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%

5.905935.965476.032076.112746.232526.390736.605766.849376.865046.920397.005337.110357.232597.365297.509397.657567.78105

25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%25%

À2.80935À2.89648À3.01341À3.24595À3.07238À3.15826À3.28765À3.39395À3.49778

30%30%30%30%30%30%30%30%30%

À8.19298À8.09780À7.8835415%15%15%

À7.99267aÀ8.01496bÀ7.75373À7.98751À7.73836À7.92135À7.72395À7.95144

1%4%15%15%15%15%15%15%

À3.62641À3.76753À3.80380À3.8074130%30%30%30%

ValuecalculatedfromlineintensityreportedbyOrtweinetal.[23].ValuecalculatedfromlineintensityreportedbyDeRosaetal.[22].ValuecalculatedfromlineintensityreportedbyStantonetal.[33].

1546G.Lietal./JournalofQuantitativeSpectroscopy&RadiativeTransfer112(2011)1543–1550

35000

1.4

30000250002000015000

Energy / cm-1

1.2µ / debye

1.0

0.8

100005000

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Internuclear distance / angstrom

Fig.1.DipolemomentfunctionsofHClusingtheMicoef?cientsfromTable1.

0.6

02.0

0.4

Percentagedifferencesofl

ineintensities/%

andvalueofre,thiscannotaccountforsuchalargedifference.Inthemeantimewearecon?dentinthequalityoftheRKRpotentialwhichisdiscussedinthelastsectionofourpaper.ThereasonforthediscrepancyisanincorrecttreatmentofexperimentalintensitiesbyKiriyamaetal.[17].

Itwasfoundthatadoptionoftheexperimentaluncer-taintiesreportedintheoriginalpublications(whenavail-able)didnotofferthebest?ttoallthedata.Thusadjustmentsweremade(generallybyincreasingreporteduncertainties)withtheaimofreducingtheoveralldevia-tionofthe?tting.Theuncertaintiesadoptedforeachlineinour?nal?tarelistedinTable2.

TheinnerandouterclassicalturningpointsontheRKRpotentialforv¼7werefoundtobeapproximately0.986

?whichsuggeststhatthepresentDMFisvalidand1.925A,

withinthisrange.

Bycombiningthewavefunctionsandthedipolemomentfunction,theEinsteinA-coef?cientswerecalculatedforDv¼0,1,2,3,4,5,6,7uptov0¼7,andwerethenconvertedtolineintensitiesinHITRANunits.Thecorresponding?leisgivenintheSupplementarymaterial.The?lecontainsonlytheH35Cllines,buttheintensitiesforH37Cl,D35ClandD37Clisotopologueswillbeincludedinthegloballinelist[12].Withthepurposeofevaluatingthein?uenceoftheDMFonreproducinglineintensities,thelineintensitiescalculatedusingLEVELwiththesamewavefunctionsbutdifferentDMFswerecomparedwithexperimentallineintensitiesforthefundamentalbandandovertonebandsuptov0¼7.HITRANintensitieswerealsoincludedinthecomparisons.TheresultsofthecomparisonsareplottedinFigs.2–7.

Percentagedifferencesoflineintensities/%

2.52.01.51.00.50.0-0.5-1.0-1.5-2.0

m

http://wendang.chazidian.comparisonoftheempiricallineintensitieswithPineetal.experimentalvalues[11]oftheH35Clfundamentalband.

3.1.Lineintensityofthefundamentalband

InFig.2,allthecalculatedlineintensitiesforthefunda-mentalbandofH35Cl,includingHITRAN,arecomparedwithmeasurementsofPineetal.[11]andthepercentagediffer-enceswereplottedagainstm-values.Theresultsclearlyshowthatthelineintensitiescalculatedinpresentstudy,Ref.[16],andHITRAN,areallwithinthe1%experimental

m

http://wendang.chazidian.comparisonoftheline-intensitiesoftheH35Cl2-0bandcompar-isonwithpresentstudyasareference.

G.Lietal./JournalofQuantitativeSpectroscopy&RadiativeTransfer112(2011)1543–15501547

%

30/se25

itis20netn15ien10ilfo5se0cne-5reff-10ide-15gatn-20ecr-25eP-30

-8

-6

-4

-2

2

4

6

8

10

12

m

http://wendang.chazidian.comparisonoftheline-intensitiesoftheH35Cl3-0bandwithexperimentalvalues[16]asareference.

%

20/seiti15snetn10ienilf5osec0nereff-5idega-10tnecr-15eP-20

-8

-6-4-20

246810

m

http://wendang.chazidian.comparisonoftheline-intensitiesoftheH35Cl4-0bandwithexperimentalvalues[27]asareference.

%

50/seit40isnetn30ienilf20osec10nereff0idega-10tnecre-20P-8

-6

-4

-2

2

4

6

8

10

12

m

http://wendang.chazidian.comparisonoftheline-intensitiesoftheH35Cl5-0bandwithexperimentalvalues[27]asareference.

%

50/s45eiti40sne35tni30en25ilfo20se15cne10ref5fid0ega-5tne-10cre-15P-20m

http://wendang.chazidian.comparisonoftheline-intensitiesoftheH35Cl6-0bandwithexperimentalvalues[27]asareference.

errorlimitclaimedbyPineetal.[11].Furthermore,allthreecalculationsagreewellwitheachotherinauniquepattern.3.2.Lineintensityofthe?rstovertoneband

InFig.3,measurementsbyTothetal.[13],intensitiesderivedfromtheDMFofOgilvieandLee[16],andHITRANintensitiesforthe2-0bandofH35Clwerecomparedwiththepresentstudy.Additionally,thelatesthigh-precisionmeasurementsbyOrtweinetal.[23]andDeRosaetal.[22]werealsocomparedwithpresentstudy.FromFig.3,itisapparentthatbothourDMFandtheDMFbyOgilvieandLee[16]reproducedthelineintensitiesofthe2-0bandverywell.However,HITRANlineintensitiesappeartobeunderestimatedbyabout7%.TheintensityoftheR(3)linecalculatedfromourDMFhasshownslightlybetteragree-menttothemeasurementbyOrtweinetal.[23]($0.2%)thantheintensityderivedfromtheDMFbyOgilvieandLee($1%).Howeverthedifferencesareinsigni?cantandbotharewithinexperimentaluncertainties.3.3.Lineintensityofthesecondovertoneband

Asimilarcomparisonwascarriedoutforthe3-0band(seeFig.4).TheHITRANlineintensitiesseemtobesystematicallyunderestimatedby17.5%.Thereasonforthisisthatinthesemi-empiricalDMFusedforcalculatingHITRANintensities,outdatedlow-resolutionmeasure-mentsbyBenedictetal.[33]wereusedasaninput.ThevaluesfromRef.[33]haveshownlargedifferencesfrommorerecentmeasurementsbyOgilvieandLee[16]andStantonetal.[34]thatwereusedasinputparametersinthiswork.Interestingly,forthe3-0bandofH35Cl,ourcalculationhasshownbetteragreementwithmeasure-mentsbyOgilvieandLeethantheintensitiesderivedfromthesemi-empiricalDMFderivedinthesamework[16].3.4.Lineintensityofthe4-0,5-0,6-0and7-0bandsThreepapershavebeenpublishedbyZughuletal.onthelineintensitymeasurementsofthe4-0to7-0overtone