Controlling the Spin − Orbit Branching Fraction in Molecular Collisions - Heid et al. - 2021 - Unknown

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pubs.acs.org/JPCLLetterControllingtheSpin−OrbitBranchingFractioninMolecularCollisionsCorneliaG.Heid,ImogenP.Bentham,VictoriaWalpole,PabloG.Jambrina,F.JavierAoiz,andMarkBrouard*CiteThis:J.Phys.Chem.Lett.2021,12,310−316ReadOnlineACCESSMetrics&MoreArticleRecommendations*sıSupportingInformationABSTRACT:Thecollisiongeometry,thatis,therelativeorientationofreactantsbeforeinteraction,canhavealargeeffectonhowacollisionorreactionproceeds.Certaingeometriesmaypreventaccesstoagivenproductchannel,whileothersmightenhanceit.InthisLetter,wedemonstratehowtheinitialorientationofNOmoleculesrelativetoapproachingAratomsdeterminesthebranchingbetweenthespin−orbitchangingandthespin−orbitconservingrotationalproductchannels.Weusearecentlydevelopedquantumtreatmenttocalculatedifferentialandintegralbranchingfractions,atanyarbitraryorientation,fromtheoreticalandexperimentaldatapoints.Ourresultsshowthatasubstantialdegreeofcontroloverthefinalspin−orbitstateofthescatteringproductscanbeachievedbytuningtheinitialcollisiongeometry.nmanyinelasticorreactivemolecularencounters,theHere,weinvestigatetheimplicationsofhavingfullcontrolIspatialarrangementinwhichthecollisionpartnersapproachovertherangeofpossiblecollisiongeometriesintermsoftheeachotherplaysavitalroleindeterminingtheoutcomeofthespin−orbitbranchingfractionsinthescatteringofNOinteraction.WhilearelativegeometrythatalignswiththemoleculeswithAratoms.Weshowhowourrecentlyreactioncoordinatewillfacilitateproductformation,1,2adevelopedquantummechanical(QM)treatmentofthe19,23geometryinwhichaccessofthereactioncoordinateisscatteringdynamicsforelectricfieldorientedmolecules3,4canbeemployedtopredictspin−orbitbranchingfractionsasahinderedwilllessefficientlyleadtoproducts.Thetrajectoryfunctionofinitialrelativeorientationofthecollisionpartners,amoleculeoratomapproachingfromaspecificdirectionwillfrombothcalculatedandexperimentallymeasuredquantities.DownloadedviaCLARKUNIVonMay16,2021at05:39:36(UTC).followisgovernedbytheattractiveandrepulsiveforcesthatWeusetheNO+Arcollisionsystemasanillustrativeexample,makeupthelocalenergylandscape.Controlovertheinitialbutthemethodcouldpotentiallybeextendedtolargerorientationthusalsoprovidescontroloverthereactionorsystems,forwhichtheidentificationoftheoptimumcollision5−8collisionpathway.Inaddition,theremightbecompetinggeometrythatmaximizestheyieldofacertainproductchannelSeehttps://pubs.acs.org/sharingguidelinesforoptionsonhowtolegitimatelysharepublishedarticles.pathwaysassociatedwithdifferentproductchannels,andmightbeveryvaluable.alteringtheinitialspatialconfigurationmayfavoronechannelOwingtoitsunpairedelectron,theNOmoleculepossessesa9overanother.spincomponentandanelectronicangularmomentumwith1,7,9−11MoleculescanbealignedwithpolarizedlaserlightorprojectionsΣ=±1/2andΛ=±1,respectively,ontothe6,12−1516−18orientedinanelectricormagneticfield;theseintermolecularaxis.Thisgivesrisetotwospin−orbittechniquesmakeitpossibletodefineparallelorperpendicularmanifolds,specifiedbythespin−orbitquantumnumberΩ=1,7,9,10Σ+Λ.Thelowerlyingstatecorrespondsto|Ω|=1/2andthe(alignment)and“end-on”or“side-on”collisiongeo-metries(orientation).6,12−15,19PreviousworkonorientedNOhigherlyingstateto|Ω|=3/2.Withinbothmanifolds,each+raregascollisionshasfocusedonend-oncollisions,inwhichrotationalstateisfurthersplitintotwoΛ-doubletlevelswiththeraregasatomapproachestheNOfromeithertheN-endorsymmetryindices1(e)and−1(f).Inourexperiments,we15,20−22theO-end.Morerecently,wehaveinvestigatedside-oncollisions,inwhichwedistinguishedbetween(predominantly)Received:September25,2020repulsivecollisionstowardtheN-sideortowardtheO-sideofAccepted:December14,2020theNOmolecule.19,23,24However,inprinciple,ourexper-Published:December22,2020imentalsetupallowsfororientationoftheNOmolecules(as15definedbyabroadcosinedistribution)atanyarbitraryanglerelativetothecollisionpartner.©2020AmericanChemicalSocietyhttps://dx.doi.org/10.1021/acs.jpclett.0c02941310J.Phys.Chem.Lett.2021,12,310−316

1TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterFigure1.Definitionoftheelectricfielddirectioninthescatteringframe(a),side-onorientation(b),andend-onorientation(c).Thez-axisinthescatteringframeisdefinedparalleltotherelativevelocityvector,k=vAr−vNO,andthe+xz-planeisthatcontainingkandk′,wherek′=v′Ar−v′NOistherelativevelocityvectorafterthecollision.θisthescatteringangle,andθEandϕEarethepolarandazimuthalanglesoftheelectricfieldvector,E.TheorientationsoftheNOmoleculein(b)and(c)arelabeledaccordingtotheaxisalongwhichEispointing.Notethattheelectricfield15createsacosinedistributionofpossibleNOorientations;thedipolemomentpointingantiparalleltotheEvectoristhemostprobableone.19,26employahexapoletoselecttheinitial|j=1/2,m,|Ω|=1/2,f⟩crosssections,andαandβarethefield-dependentmixingquantumstateoftheNOmolecules(wherej=1/2istheparametersmentionedabove.13,25TheR(k)(θ)quantifytheqrotationalgroundstate,whichcanonlybeoriented,andmitsdependenceofthecollisionoutcomeonthepolarizationoftheprojectionontotherelativevelocityvector,k),beforebondaxis(asafunctionofscatteringangle),withtheisotropicsubjectingthemtoastaticelectricfield.Intheelectricfield,R(0)(θ)momentequaltothenormalizedDCSintheabsence0theinitiallypurefstatewavefunctionevolvesintoaofreagentpolarization,butinthepresenceofanorientation19superpositionoftheeandfstatewavefunctions,andtheirfield.relativecontributions,whicharedependentonthestrengthofForagivenθEangle,andϕE=0°orϕE=180°,wecanwritetheelectricfield,arequantifiedbythemixingparametersαandβ(seeSupportingInformation).13,25SincethefΛ-doubletϕE=°0/180°σiso(0)(1)[]d()σθθ=[−RR0()θα|βθθ|(cosE0()stateislow-fieldseeking,thedipolemoment(N→O)oftheE2πstateselectedmoleculeswillorientantiparalleltotheelectric±]2sinθθR(1)())E1(2)fieldvector,E,duetotheStarkeffect.Byswitchingthepolarizationoftheelectricfield,wecanchangetheorientationComputationally,theR(k)(θ)momentscanbecalculatedqofthemoleculesinagivenconfigurationby180°.readilyfromthescatteringamplitudes(seetheSupportingWedefinetheorientationoftheelectricfieldwithintheInformation).Experimentally,theR(0)(θ)momentcanbe0scatteringframe,asillustratedinFigure1.Fortheanalysisextractedfromthesumofthevelocity-mapionimagesforthepresentedbelow,wefocusonin-plane(andnear-side)twoside-on,orthetwoend-on,orientations.Similarly,thescattering,withElyingwithintheplaneoftheinitialandR(1)(θ)andR(1)(θ)momentscanbedeterminedfromthe01finalrelativevelocityvectors,kandk′,respectively.Wecandifferenceimageforthetwoend-onandthetwoside-onthuscoverthefullrangeofpossibleorientationsbysamplingorientations,respectively.19,23KnowledgeofallthreeR(k)(θ)qthepolarangleθEbetween0°and180°atfixedazimuthalmoments,andsubstitutionintoeq1,wouldthenallowanglesofϕE=0°andϕE=180°.PanelsbandcofFigure1calculationoftheDCSatanyarbitraryorientation.Notethatalsoshowtheelectricfieldvectorandthemostprobableforend-onorientation,θE=0°or180°andthethirdterminorientationoftheNOmoleculeforthetwoside-on(b)andeq1goestozero,whileforside-onorientation,θE=90°,andthetwoend-on(c)configurations.Thelabels“+x”and“−x”thesecondterm,containingtheR(1)(θ)moment,goestozero.0correspondtorepulsivecollisionsoftheAratomofftheN-sideToillustratetheabovediscussion,theR(0)(θ)andR(1)(θ)01andO-side,while“+z”and“−z”correspondtorepulsivemomentsextractedfromtheionimagesintheside-oncollisionstowardtheO-endandN-end,respectively(thelabelsorientationarecomparedtotheQMcalculatedmomentsinindicatethedirectionofEineachcase).19,23Figure2forthej′=5.5e−10.5efinalstates.TransitionswithinAsshowninourpreviouswork,foranarbitrarythegroundspin−orbitmanifold(ΔΩ=0)areshownontheorientation,definedbytheelectricfieldvectorinthescatteringleft-handside,andtransitionsintothespin−orbitchangingframe,thedifferentialcrosssection(DCS),forinitialj=1/2,manifold(ΔΩ=1)areshownontheright-handside.Thecanbeexpressedintermsofthebond-axis-polarization-19,26agreementbetweentheexperimentandcalculationsisgooddependentdifferentialcrosssections(r-PDDCSs):overall.ThemostsignificantdeviationsareobservedintheR(0)(θ)momentforj′=7.5eand9.5e(inbothspin−orbitϕEσiso(0)(1)0[]d()σθθ=[−RR0()θα|βθθ|(cosE0()manifolds),wheretheexperimentalmomentisnotquiteableE2πtoreproducethedouble-peakedfeaturesintheQM(1)−]2sinθϕθEcosER1())(1)calculation.Thisisbecausethemainscatteringintensityoverlapswiththepositionofzerolaboratoryvelocity,whereHere,σisoisthe“isotropic”integralcrosssection(ICS)intheevensmallinaccuraciesintheinstrumentfunctionbecomepresenceofafield,theR(k)(θ)arether-polarization-dependentmagnified.23q311https://dx.doi.org/10.1021/acs.jpclett.0c02941J.Phys.Chem.Lett.2021,12,310−316

2TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterϕ=°0/180°[]dσEfracθEϕ=°0/180°[]dσEΔΩ=1θE=ϕ=°0/180°ϕ=°0/180°[]ddσσE+[]EΔΩ=1θEΔΩ=0θE(3)Theabilitytodeterminethedifferentialbranchingfractionatanyarbitraryorientationenablesustoquantifytheextentofcontroloverthecollisionoutcomeachievablebyvaryingthecollisiongeometry.Figure3showstheQMcalculatedbranchingfractionsasafunctionofthescatteringangle,θ(y-axis),andtheinitialrelativeorientationoftheNOandArcollisionpartners,asdefinedbytheanglesoftheelectricfield,θEandϕE(x-axisinthefigure).Thebranchingfractionsareshownforj′=5.5e−10.5e;therightpanelforeachstatecorrespondstoϕE=0°andtheleftpaneltoϕE=180°.NotethatθE=0°correspondstothe+z(O-end)orientationandθE=180°tothe−z(N-end)orientation,irrespectiveofϕE.The±zand±xorientationsareindicatedatthetopofthefigure.Redindicatesdominanceofthespin−orbitchangingtransition(dσfrac>0.5),whileyellowindicatesdominanceofthespin−orbitconservingtransition(dσfrac<0.5).Themaximainthespin−orbitfractionsareduetosomecombinationoflocalmaximum,orsignificantscatteringintensity,inthespin−orbitchangingmanifold,andlocalminimum,orlowscatteringintensity,inthespin−orbitconservingmanifold.Itisremarkablehowthespin−orbitbranchingfractioncanbechangedbyvaryingtheorientationoftheelectricfield.Figure3demonstratesthat,iftheinitialgeometryofthecollisionsystemcanbedefined,therelativeyieldsofspecificproductchannelsatagivenscatteringanglecanbecontrolled.Forexample,inthecaseofj′=8.5ethecontributionofΩ′=3/2canbemaximizedtodσfrac≈1inthebackwardscatteredregionbysettingtheorientationfieldnearlyperpendiculartotherelativevelocityvector(−zorientation).Conversely,itscontributionatthesamescatteringanglescanbereducedtolessthan0.1bysettingθE=45°andϕE=180°.Analogously,ifwewantedtooptimizetherelativeyieldofspin−orbitchangingproductsinthebackwardscatteredregionofthej′=6.5estate,wewouldorienttheelectricfieldinourexperimentattheanglesofθE∼135°andϕE=0°.Asimilardependenceofthebranchingfractionontheinitialorientationisobservedfortheotherj′statesshowninFigure3.ThisdependencecanbeinterpretedinageneralpictureinwhichreactantsfollowacertainpathwaytoproductsdependingonFigure2.ComparisonoftheexperimentalandQMcalculatedtheirinitialpositiononthepotentialenergysurface(PES)andpolarizationmomentsforj′=5.5e−10.5e(toptobottom)inthetheinternalandtranslationalenergytheypossessatthatpoint.spin−orbitconserving(ΔΩ=0,left,takenfromref23)andchanging(ΔΩ=1,right)manifolds.TheexperimentalR(0)(θ)andR(1)(θ)Bycarefullychoosingtheinitialgeometry,ascatteringprocess01momentsareshowninredandblue,andtheirQMcounterpartsareorreactioncanthusbetunedinfavorofaparticularoutcome.representedbythepurpleandgreendashedlines,respectively.TheByintegrationofthedifferentialcrosssectionsforgivenθEerrorbarsintheexperimentaldatacorrespondtoonestandardandϕEangles,wecantestwhetherthedependenceonthedeviation.TheQMdatawereaveragedovertheexperimentalcollisioninitialrelativeorientationsurvivesintheintegralspin−orbitenergydistributionwithameanof651cm−1.branchingfractions.TheintegralcrosssectionsareobtainedbyintegratingtheDCSsineq2:ϕE=°0/180°σiso(0)(1)(1)σθE=[−rrr0||αβ(cosθE0±2sinθE1)]2πThespin−orbitbranchingfraction,thatis,thefractionofthe(4)wherether(k)momentsaretheintegratedR(k)(θ)moments,26spin−orbitchangingtransitiontothesumofthetransitionsqqintobothmanifolds,canthenbeevaluatedatanygiven+1()k()krq=∫Rq()d(cos)θθorientation:−1(5)312https://dx.doi.org/10.1021/acs.jpclett.0c02941J.Phys.Chem.Lett.2021,12,310−316

3TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterFigure3.ContourplotsshowingthedifferentialQMspin−orbitbranchingfractionsasafunctionofthescatteringangle,θ(y-axis),andthepolarangleoftheelectricfield,θE(x-axis),forj′=5.5e−10.5e.TheθEanglescorrespondingtothe±zandthe±xconfigurationsareindicatedatthetop.Notethattheright-handsideforeachstatecorrespondstoϕE=0°andtheleft-handsidetoϕE=180°(seeSupportingInformation).Theblacklineindicatesabranchingfractionof0.5.Thecalculationswererunattheexperimentalfieldstrengthusingacollisionenergyof651cm−1.SinceR(0)isthenormalizedisotropicDCS,r(0)isequaltobecalculatedanalogouslytothedifferentialbranching00one.Ther(1)andr(1)moments,fortheirpart,aredirectlyfractions:10relatedtotheintegralstericasymmetry(ISA)forthex-andz-23[]σϕE=°0/180°axisorientations,respectively,ϕ=°0/180°ΔΩ=1θ[σ]=EEfracθEϕ=°0/180°ϕ=°0/180°(1)Sx[]σσE+[]Er1=ΔΩ=1θEΔΩ=0θE2||αβ(6)(9)(1)SzThetoppanelinFigure4showstheexperimentalintegralr0=branchingfractionsobtainedusingtheSxandSzvaluesfrom||αβ(7)15,21,23,24previousmeasurements.ThesearecomparedwiththewhereSxandSzaretheISAsforthex-axis(side-on)andz-axisQMcalculatedbranchingfractionsinthebottompanel.Since(end-on)configurations,respectively,asdefinedintheintheseexperimentswehavenotmeasuredtherelativecrossSupportingInformation.TheISAisameasureoftheintegralsectionsforthetwospin−orbitmanifolds,proportionaltoσiso,preferenceofoneorientationovertheotherforagiventheexperimentalICSratioswerescaledtotheQMICSratiosproductrotationalstate.Usingtherelationshipsineq6and7,toallowadirectcomparisonbetweenexperimentandtheory.theintegralcrosssectionscanberewrittenintermsofSxandThetheoreticalisotropicspin−orbitbranchingfractionsandSz:theirdependenceonthestaticfieldstrengthareshownintheσSupportingInformation.Notethat,inprinciple,therequiredϕ=°0/180°isoσE=−±(1cosθθSSsin)θEEEzx(8)crosssectionratiosforspin−orbitconservingandchanging2πcollisionscouldbedeterminedrelativelystraightforwardlyfromTheintegralcrosssectionscanthusbecalculatedsolelyfromtheresonantlyenhancedmultiphotonionization(REMPI)theexperimental(orQM)ISAsintheside-onandtheend-onspectrumorlaser-inducedfluorescencemeasurementsoftheorientations.Usingtheintegralcrosssectionsforbothspin−scatteredNO(X),ashasbeenundertakeninprevious27,28orbitmanifolds,theintegralspin−orbitbranchingfractionscanwork.313https://dx.doi.org/10.1021/acs.jpclett.0c02941J.Phys.Chem.Lett.2021,12,310−316

4TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterpreferenceforN-side/N-endcollisionswasobserved,inthe21,2429spin−orbitexcitedstate.AlexanderhasshownthatforpureHund’scase(a)molecules,ΔΩ=0andΔΩ=1transitionscanbeassumedtooccuronthehalf-sum(Vsum)andhalf-difference(Vdiff)potentials,respectively.ThesepotentialsreflectthepreferentiallocationoftheunpairedelectronlyingclosertotheNatomoftheNOmolecule,eitherinoroutoftheplanedefinedbythethreeatoms29−31(correspondingtotheA′andA″PESs,respectively).Theconfigurationinwhichtheelectronisintheplaneofthethreeatoms(i.e.,ontheA′PES)facilitatestheinteractionbetweentheincomingAratomandtheloneelectronnecessary24forspin−orbitchangingtransitionstooccur.ThemaximafortheevenΔjtransitionsaroundθE=135°/ϕE=0°inFigure4,whichcorrespondtocollisionsneartheNatom,areamanifestationoftheoverallshifttowardanN-side/N-endpreference.Theoppositeorientation,correspondingtoθE∼45°/ϕE=180°,isintheregionoftheminimaofthebranchingfractions.Thus,placingtheelectricfieldatapproximatelyθE=135°fromtherelativevelocityvectorwillmaximizethespin−orbitchangingintegralfractionfortheevenΔjtransitions,whentheAratomapproachestowardtheNatom,whileconcomitantlyminimizingthefractionfortrajectoriestowardtheOatom.Ouranalysisofthespin−orbitbranchingfractionsshowsthattheabilitytoselecttheinitialorientationoftheNOmoleculespriortocollisionprovidesalargedegreeofcontroloverthespin−orbitbranchingfraction.TheimplicationsofourresultsmaybegeneralizedtoothersystemswithanasymmetricPESandatleasttwocompetingproductchannels.Figure4.Fractionofthespin−orbitchangingintegralcrosssectiontoWeexpectthatthemoreasymmetricthepotentialenergythesumoftheICSsforthetwospin−orbitmanifolds,asafunctionoflandscape,themoreimportanttheinitialorientationwillbeinθE,forj′=5.5e−10.5e.Thetoppanelshowsthefractionsobtaineddefiningtherelativepopulationsoftheaccessibleproductfromtheexperimentalstericasymmetries(witherrorbarsstates.Inthecurrentwork,themaximaofthespin−orbitrepresentingonestandarddeviation);thebottompanelshowsthechangingfractionsfortheevenΔjtransitionsneartheNatomcalculatedQMfractions,whichhavebeenaveragedovertheofthemoleculereflectthepositionoftheunpairedelectron,24experimentalcollisionenergydistribution.EvenΔjtransitionsareanditmightbeexpectedthatothercollisionprocessesorrepresentedinpurple,andoddΔjtransitionsinorange.TheθEanglesreactions,inwhichunpairedorweaklyboundelectronsarecorrespondingtothe±zandthe±xconfigurationsareindicatedatinvolved,willshowasimilarsensitivitytothelocationofthethetopofthefigure.Theright-handsidecorrespondstoϕE=0°andtheleft-handsidetoϕE=180°.relevantelectronicorbitals.ThecurrentQMtreatmentcanbeappliedtootherlinearopen-shellmolecules,suchasOH,TheexperimentalandQM-field-dependentintegralspin−whichisslightlymorecomplexthanNOduetoits|Ω|=3/2orbitbranchingfractionsshowninFigure4areingoodgroundspin−orbitstate.Althoughthedegreeofcomplexityagreement,whichisnotunexpectedgiventhegenerallywillincreasefurther,webelievethatitisalsopossibletoextendexcellentagreementbetweenexperimentalandQMintegralthetheorytosymmetricandasymmetrictops.Thecapabilitiesstericasymmetriesfoundinthepreviousstudies.15,21,23,24Asoftheexperimentalmethodsusedinourstudycouldbealreadyobservedinthedifferentialbranchingfractions(Figureexpandedaswell.Inparticular,itmightbepossibletoperform323),theintegralbranchingfractionsvaryasafunctionofelectriclaseralignmentwithinanelectricfieldsothat“heads”andfieldorientation,roughlyaveragingbetween0.2and0.3.The“tails”maybedistinguished.ThiswouldprovideameansforvariationsaremorepronouncedfortheevenΔjtransitionsstateselectionwithouttheneedofahexapoleandthe(purplelines),wherethefractionsspanarangefromabout0.1limitationtoenergeticallylow-lyingquantumstates.Moreover,to0.45,andaremoresubtlefortheoddΔjtransitions(orangeitwillbeinterestingtoseeiffullcontrolovertheinitiallines).ComparisonwithFigure3revealsthatthemaximaforgeometrycanbeimplementedincollisionprocessesandtheevenΔjtransitionsaroundθE=135°/ϕE=0°aremainlyreactionsinsolution,onsurfaces,orongas−liquidinterfaces.duetoastrongspin−orbitexcitedcontributioninthebackwardscatteredregion(θ≥60°).■ASSOCIATEDCONTENTTheintegralstericasymmetriesmeasuredintheside-onand*sıSupportingInformationtheend-onorientationsexhibitedanN-side/N-endpreferenceTheSupportingInformationisavailablefreeofchargeatforoddΔj,andanO-side/O-endpreferenceforevenΔjinhttps://pubs.acs.org/doi/10.1021/acs.jpclett.0c02941.15,21,23,24bothspin−orbitmanifolds.However,whilethemagnitudeoftheN-side/N-endpreferencewasrelativelyComputationalandexperimentalmethods,branchingsimilarinthetwomanifolds,themagnitudeforO-side/O-endfractionsforanisotropicdistributioninthepresenceandcollisionswassignificantlydiminished,andanoverallabsenceofanelectricfield(PDF)314https://dx.doi.org/10.1021/acs.jpclett.0c02941J.Phys.Chem.Lett.2021,12,310−316

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