NO分子的基态（X^2П）和激发态（a^4П and B^2П）光谱常量和振动能级的计算

NO分子的基态（X^2П）和激发态（a^4П and B^2П）光谱常量和振动能级的计算 NO分子的基态(X^2П)和激发态(a^4 П and B^2П)光谱常量和振动能级的计算 第39卷第7期 2O1O年7月 光子 ACTAPH0TONICASINICA Vo1.39No.7 July2010 ArticleID:1004—4213(2010)07-13l2—7 CalculationofSpectroscopicConstantsandVibrationalLevelsinthe X1I,a11,andBIIStatesofNitricOxide WANGJian (a.SchoolofScience:b — kun,YANGZhi—yong,WUZhen—Sen SchoolofTechnicalPhysicsXidianUniversity,Xian710071,China) Abstract:Theequilibriumstructureandsingle—pointenergyscanningofthegroundstateX兀and theexcitedstatesa1-IandB.IIofNOmoleculearecalculatedusingtheCASSCF/MRCImeth od andthecc—pVDZbasisset.Thepotentialenergycurvesareobtainedbyaleastsquarefittingto themodifiedMurrell—Sorbicfunction.EmployingtheRydberg—Klein— Reesmethod,theharmonic frequencyandotherspectroscopicdata(a,to,to,)ofthegroundstateX兀andtheexcited statesaIIandB兀ofNOmoleculearecalculatedandthecalculationresultsareinbetter agreementwiththeexperimentalonesthanothertheoreticaIdata.Inaddition,theeigenvalues of vibrational】evelsarecalculatedbysolvingtheradialone— dimensionaJSchr6dingerequationbased ontheanalyticalpotentialenergyfunction. Keywords:Potentialenergyfunction;Multireferenceconfigurationinteraction;Harmonic frequency;Vibrationallevels CLCN:0561DocumentCode:Adoi:10.3788/gzxb20103907.13l2 0Introduction Nitricoxide(NO)playsasignificantroleina widerangeofchemicalandphysicalprocesses whichincludeitscontributiontophotochemical smog,anditswellknownroleinatmospheric phenomenaincludingdayglowandauroral processes.Theaccurateknowledgeforthealtitude dependenceofNOconcentrationisessentia1forthe understandingofatmosphericchemistry[?.NOis anopenshellmolecule,andthevalenCeelectronic configurationisgivenby(16)(26).(36)(46) (56)(1?)(1J1)l2.Studiesoftheelectronic structureandspectroscopicdataoftheNO moleculehavebeenincreasingintereststothe chemiealorphysicalscientists.Thisisduetothe progressoftheinstrumentsusedinsatellitesand rockets,whichhasmadeitpossibletodetermine thecompositionoftheouteratmosphereE.The groundstateofnitricoxide,NO(XH),isan importantemitterintheatmosphere.Radiation fromitsfundamental(5.4um)andfirstovertone( 207um)rotation—vibrationtransitionshavebeen observedinatmosphericemissionspectraunder bothdisturbed(aurora1)andambient conditions~. TheN0(aII)stateistheIowest SupportedbytheNationalNaturalScienceFoundationof China(60771038) Tel:029—88202635Email:jkwang@mail.xidian.edu.cn Receiveddate:2009一l1—2lReviseddate:2010,01—25 electronicallyexcitedstateoftheNOmolecule, andiSmetastablewithrespecttoopticaltransitions tothegroundstateE.TheB?ofN0isavalence— typestateandtheCIIRydberg—typestate.An obviouscharacteroftheRydbergstatesiSthe strongphotoelectronspectrafromthe?u=0 transition【.F.GreinandA.Kapurreportedthat theCIIRvdbergstateioinswiththeB.IIvalence stateatapproximately0.116nm[. Theanalysis oftheabsorptionspectrumofNOhaverevealeda wealthofdetailedinformationconcerningthe mutuaIperturbationbetweenthebandsofthe (B兀一X兀)and(Cn—X兀)systems.R. GallusserandK.Dresslerhavepresented informationonthehigherelectronicstatesofthe np7[Rydbergseries3pC兀,4pK兀,5pQ.兀,6p W.nandonthesecondexcitedIIstateofvalence characterI兀.Highquantumstatesbelonging totheA—X(0—1)bandofNOhavebeenfoundtobe themostvaluableandhaveledtoaNOmole fractiondeterminationwithanaccuracyof?13. NOabsorptionintheflamewascompletelymasked usingtheA,X(O—O)bandL.Electronicquenching ofN0(A?+)isalsoimportantforunderstanding theintermolecularpropertiesrelatedtothe collisioncomplexformationLJ.Ref.rl1]has calculatedthePESforseveralconfigurationsofthe NO—Nedimer,usinghighlyaccurateabinitio quantumchemistrytechniquesandfittedthemtoa simpleanalyticalformconvenientforfurther dynamicalstudies.Theaccuratepotentialenergy 7期WANGJian— kun,etal:CalculationofSpectroscopicConstantsandVibrationalLevelsinthe XII,a1I,andBIXStatesofNitricOxide1313 surfaceavailableforNO+Arsystemswere calculatedbyusingCCSD(T)method[.The C?,A?,B1I,andb?statesareallformed, directlyorindirectly,fromthea.11state[.The NOysystem(A.?.r—X?)hasbeenusedto measureNOcolumndensitiesinthemesosphere andfortheinterpretationofemissionsin aurora.Ref.[15]reportedthemagnetic hyperfineparametersofN0(X1I).Predictionsof thespectroscopicconstantsofdiatomicmolecules, e.g?,叫,,andaareoftenusedto benchmarknewtheoreticalmethodsorstudy electroncorrelationorbasisseteffects.Basedon thetheoryofatomicandmolecularstatics,the reasonabledissociationlimitforthegroundstate (X?)andtheexciteda兀andB?ofNO moleculearederived.UsingtheCASSCF/MRCI approach,theequilibriumgeometryoftheground state(X?)andtheexcitedstatesa.nandBIIof NOmoleculearecalculated.Atthesametime,the singlepointenergyscanningcalculationisalso madeatcc—pVDZbasissetneartheequilibrium inter—nuclearseparationobtainedbythegeometry optimizationsoastoattainthemoreaccurate result.AleastsquarefittingtotheMurrell—Sorbic functionismadeandotherspectroscopicdata(a, fo,?,)arefurthercomputed,whichareingood agreementwiththeexperimenta1results.In addition,withtheanalyticpotentialenergy functionobtainedontheCASSCF/MRCI1eve1. wehavealsocalculatedthevibrational1evelsby solvingtheradialSehr6dingerequationofnuclear motion. Computationaldetails 1.1Determinationofappropriatedissociationlimit Theinteractionofatomswithinamoleculeis governedbytheelectronicpotentialenergysurface ofthesystem.Itdescribesthemolecularstructure andmolecularspectrumandfoundsthebaseof researchingthetime—dependantprocess,which matchesadefiniteelectronicstateofamoleculeor radical[.Potentialscanbecalculatedusingab initiocalculation,bychoosingasetofinternuclear separations,solvingthe. resultingSchr6dinger equationfortheelectronicmotionandrepeating theprocedureuntilagridofpointshasbeen generated.Inordertodescribethesystematic potentialfunctionaccurately,theproper dissociationlimitofNOradicalandconceivable electronicconfigurationmustbedetermined. Nitricoxideisanopenshellmoleculeandthe electronicconfigurationofthegroundstateofNO (X?)is12盯34.5a17【;1了c2丁【1whichhasA symmetry.Theoutermostelectronoccupiesan antibondingorbital,namely2zrl~..Thea?stateof NOistheIowestexcitedstatesandhavethree referenceconfigurationswhichare17c—2丁【,17c — '37【,17【1丁c27r27【.Thdominant configurationis1兀2.Thedominant configurationscorrespondingtotheB11statesare 17c2丁【and17c27c. Accordingtotheatomicandmolecular reactionstaticsE.一.thepossibleelectronicstates canbedetermined.Thegroundelectronicstateof Oatomis.Pg,andthatofNatomisS,which belongstotheSU(n)group.NOradicalisinC— group.WhentheN(S)atomreactswithO(.Pg) atomandproducesNOmolecule,thesystematic symmetrydecreased.Theirreducible representationofSU(")groupcanbedecomposed intothedirectsumoftheirreduciblerepresentation ofCgroup.Usingdirectproductandreduction, theirreduciblerepresentationofC一groupcanbe obtained,namelythepossibleelectronicstatescan bedetermined.Thedirectsumofirredueible representationofC(.Pg)andO(.Pg)resolution intoC..groupare 3P一.?.?(1) S..一?一(2) ThegroundstateelectronicconfigurationofN atomisSTheirreduciblerepresentationof N(S)decompositionintoC..groupis?.On thedirectsumandreductiontothecombinationof NO(.P+S),itshoulebedeterminedthatthe combinationof(.?o不)?(?一)includesthe groundstate(X?)ofNOmolecule.Sothe combinationofthegroundstate0andNatomcan producethethegroundstate(X.11)ofNO molecule.Accordingtotheinvertibleprincipleof micro—processE.thedissociation1imitofthe groundstate(X?)andexcitedstates(aH,and B兀)ofNOmoleculerespectivelyare NO(X?)一O(.P)+N(S)(3) No(a兀)一O(.P)+N(S)(4) N0(B?)一0(D)+N(S..)(5) 1.2Computationalmethods Themultireferenceconfigurationinteraction (MRCI)isemployedinthecalculations,which offeredanefficientanduniformwayoftreating multi—configurationseffectsinthewholeregionof interatomicseparationsforthegroundandexcited electronicstates.Aful1CIexactlysolvesthe 1314光子39卷 SchrOdingerequationwithinsomebasissets,butis usuallytoocomplexacalculationtocompute moleculescontainingmoreelectrons.Thesingle referencemethodscanalmostalwaysbedone,and usuallyarenotverychallenging(tothecomputer ortheuser),however,theiraccuracyis1imited. MRCIisawaytosystematicallyincludethose CSFsthatcontributemostsignificantlytothe correlationenergy.TheorbitalsfortheCI calculationsofNOmoleculearederivedfroma multi—configurationse1f-consistentfield(MC—SCF) solution,obtainedincompleteactivespaceself— consistentfield(CASSCF)method.ThefulI valenceactivespaceconsistsofeightvalence orbitals36—66,1,27r,whichdenotedby(422)in C2pointgroupsymmetry.Withineachspin symmetry.acommonsetofaveragednatural orbitalstobeusedforallstateswascomputed usingtheCASSCF(11,8)wavefunctions,where allpossibleelectronicexcitationsresultingfromthe distrutionof11electronsinto8activeorbitals (4,2,2,0)三(4×"l,2×b1,2×b2,0×a2)were allowed.Theincorporationofasmuchdynamic correlationaspossibleinthefinalwavefunction wasmadewithamu1tireferenceconfiguration interactionwavefunction(MRCI),withthe inclusionofal1singleanddoubleexcitationsfrom thereferencesetsgeneratedbyal1CASSCF configurations.Inallcalculationscoreorbitals werekeptfrozen. Althoughtherearemanybasissetsthatwe canchoose,onlyfewonesworkwel1.Theatomic basisfunctionsusedinthepresentinvestigationis thecorrelation—consistentpolarizedvalence quadruple—zeta(cc—pVDZ)typedevelopedby Dunningandcoworkersasobtainedfromthe theinter—nucleardistanceRbetweentwoatomsN andOarekeptconsistentwiththatusedinthe calculationofoptimizationofmolecularstructure. ThecalculationsatCASSCF/MRCIlevelare startedwiththeinternucleardistanceof0.36nm, andtheinternalis0.004nm.Totally,69,65and 69pointswerecalculatedrespectivelyforthe groundstateX兀andtheexcitedstatesa兀and B.兀ofNOmolecule.Partsofthesinglepoint energiesfordifferentstatesarelistedinthe Table1whichisthebaseofourfurther ca1cu1ations. Table1ThepotentialenergiesE(R)atdifferentinter-nuclear distanceoftheX11,a4IIandB11statesofNOmolecule 2Resultsanddiscussion 2.1Analyticalpotentialenergyfunctionand spectroscopicparameters Amongthefunctionsthatproposedtofit analyticalpotentialenergyfunctions(APEFs)of diatomicmolecules,Murrel—Sorbic(MS) potentialenergyfunctionseemstobethebest.It canaccuratelyreproduceinteractionmolecules, andhasbeenusedtodeduceAPEFsformany molecules.Sotheseriesofsinglepointenergyare fittedasthefollowingMurrel—Sorbicfunctions(6) usingthenormaIequations. (P)一一De(1+alp+a2p.+a3p.)exp(m171fD)(6) Wherepequalsr—r,ristheinter—nuclear distanceandreiSEquilibriuminter—nucleardistance ofNandOatom.Deisthedissociationenergyand al,d2anda3arefittingcoefficient.Theparameters a1,0g2anda3andDearedeterminedbyfitting.Itis significanttopointoutthatKCisalsotreatedasa fittingparameterduringthefittingprocess.In 7期 WANGJiankun,etal:CalculationofSpectroscopicConstantsandVibrationalLevelsinthe X?,aII,andB2nStatesofNitricOxide1315 manycasessatisfactoryresultscanbeobtained whennequals3[..soweusetheMSfunctionas formula(6). Thepotentialenergycurvesoftheground stateXIIandtheexcitedstatesagIandB.iIof NOmoleculeshowedintheFig.1withthe minimumenergypointsdemonstratethatthe groundstateX兀andtheexcitedstatesaI-iand BnofNOmoleculecanexiststably.Byiterating asystemofnormalequationsbasedonaleast— squarefit,theparametersd1,d2anda3ofEq.(6) havebeencalculatedforthegroundstateX1-Iand theexcitedstatesa1-IandB0IIofNOmoleculeand tabulatedinTable2togetherwiththedissociation energiesandequilibriuminter—nuclearseparations forconvenientcomparison.Wehavemadesimple comparisonbetweentheexperimentalandother theoreticalvaluesE'.'. InFig.1,threethe potentialenergycurvesstandforthedifferent statesX.兀,aFIandB兀ofNOmolecule respectively.Consideringtheequilibriumpositions (re),thedissociationlimitanddissociationenergy (De)ofthesystem,wecanconcludethatthree curveswouldprovideuswithrelativelyreasonable results,andareworthyoffurtherinvestigation. Eithertheequilibriumpositionsorthedissociation energiesofthecurvesofdifferentstatesofNOare satisfactoryandareingoodagreementwiththe experimentalones.Thesethreecurvesareusedto fittotheMurrel—Sorbicpotentialfunctionsand becausetheyalsoprovideuswithgoodresults. Theleastsquarefittingisawidelyusedmethodin fittingwork,andinourfittingprocess,itis carriedoutwithLevenberg—Marquardtmethod employingMatlabprogram.Thefittingparameters ofanalyticalpotentialenergyfunctionsare tabulatedinTable2whileothertheoreticaland experimentalcounterpartsarealsocollected. R(N—O)/nm Fig.1Thepotentialenergycurvesofthegroundstate Xin/andtheexcitedstatesa不andB.12ofNO FromtheTable2,wecaneasilyseethatthe computeddissociationenergyisinagreementwith theexperimentalvalue[]within一0.096eV deviationfortheXnstate,andtherei8 0.11502nmwith0.0006nmdeviation. Deviations0.00122ofrefromRef.[19]arelager thanours.TheDeoftheexcitedstatea?and ?arealsoinaccordancewiththeexperimenta1 counterpartsLwithin0.007eVand0.004eV respectively,andthecomputedequilibriuminter— nucleardistanceofa兀andB1-Istatesarein accordwiththeexperimenta1datac]within 0.0002nmerroror0.14forthea兀state,and 0.0007nmerroror0.48%oofortheB.17Istateat thepresentatCASSCF/MRCIcalculationlevelof theoryinfullactivespace,respectively. Comparisonofthetheoreticaldeterminationsofthe dissociationenergiesandtheequilibriuminter— nucleardistanceswiththepreviousother theoreticaIresultsc''19,...clearlyshowsthatthe presentworkrepresentsanimprovementin agreementwithexperiments. Table2TheconstantsforthegroundstateX11and theexcitedstatesa4HandBnstatesofNomolecule Itisknowntousal1thatthepropertiesround theequilibriumpositionarewhatwereallycare,so wejustemployed69,65and69energypoints respectivelyforthegroundstateXIIandthe excitedstatesaIIandB.1-Iatdifferentinter— nucleardistanceofNandOatoms.There obtainedusingmoleculestructureoptimization methodisaccordancewiththeoneobtainedwith thesinglepointscanningmethod.Sowecan concludethatthepresentcalculationapproachis reliable. 2.2CalculationofharmonicfrequencyofNo radical Forceconstantofsecondordercanbederived fromanalyticalpotentialenergyequation(6). _厂2一De(a一2a)(7) Ontheotherhand,diatomicmoleculeforce 0?_I葛= 1316光子39卷 constantofsecondorderisrelatedwiththe harmonicfrequencyasfollowingequationaccording t0theRKRmethodE. 一47r?f(8) Eq.(9)canbederivedfromequation(7)and(8). 一『D~(at--2a2)(9)一l——J Whereisthediatomicmoleculereducedmass, andcisthespeedoflightinvacuum.Theother spectroscopicconstantscanbecalculatedfrom followingequations. 6DIa3一a11.] ".一百I . 一D(3a一12aa2+24a1a3)(11) Wheref?{3and{arequadraticcubicand quarticforceconstantsrespectively,after calculationofforceconstantsandharmonic frequency,otherspectroscopicconstantscanbe computedusingfollowingequations. Be=(12) 一 警[+豢]一一l十J 一 Bel_警+15(十g面A)eae)]… Thecalculationresultsofspectroscopicconstants aretabulatedintheTable3and4. Table3The,forceconstantsforthegroundstatex2IIandthe excitedstatesaaIIandB21I