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Theoretical Investigations of Molecular Wires

Permanent Link: http://ufdc.ufl.edu/UFE0024291/00001

Material Information

Title: Theoretical Investigations of Molecular Wires Electronic Spectra and Electron Transport
Physical Description: 1 online resource (132 p.)
Language: english
Creator: Palma, Julio
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: azobenzene, dendrimer, dft, electronic, electronics, molecular, nanostar, negf, quantum, spectrum
Chemistry -- Dissertations, Academic -- UF
Genre: Chemistry thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The results of theoretical and computational research are presented for two promising molecular wires, the Nanostar dendrimer, and a series of substituted azobenzene derivatives connected to aluminum electrodes. The electronic absorption spectra of the Nanostar (a phenylene-ethynylene dendrimer attached to an ethynylperylene chromophore) were calculated using a sequential Molecular Dynamics/Quantum Mechanics (MD/QM) method to perform an analysis of the temperature dependence of the electronic absorption process. We modeled the Nanostar as a series of connected units, and performed MD simulations for each chromophore at 10 K and 300 K to study how the temperature affected the structures and, consequently, the spectra. The absorption spectra of the Nanostar were computed using an ensemble of 8000 structures for each chromophore. Quantum Mechanical (QM) ZINDO/S calculations were performed for each conformation in the ensemble, including 16 excited states, for a total of 128,000 excitation energies. The spectral intensity was then scaled linearly with the number of conjugated units. Our calculations for both the individual chromophores and the Nanostar, are in good agreement with experiments. We explain in detail the effects of temperature and the consequences for the absorption process. The second part of this thesis presents a study of the effects of chemical substituents on the electron transport properties of the azobenzene molecule, which has been proposed recently as a component of a light-driven molecular switch. This molecule has two stable conformations cis and trans in its electronic ground state, with considerable differences in their conductance. The electron transport properties were calculated using first-principles methods combining non-equilibrium Green's function (NEGF) techniques with density functional theory (DFT). For the azobenzene studies, we included electron-donating groups and electron-withdrawing groups in meta- and ortho- positions with respect to the azo group. The results showed that the molecular structure is crucial in optimizing the electron transport properties of chemical structures, and that the transport properties in electronic devices at the molecular level can be manipulated, enhanced or suppressed by a careful consideration of the effects of chemical modification.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Julio Palma.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Krause, Jeffrey L.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024291:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024291/00001

Material Information

Title: Theoretical Investigations of Molecular Wires Electronic Spectra and Electron Transport
Physical Description: 1 online resource (132 p.)
Language: english
Creator: Palma, Julio
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: azobenzene, dendrimer, dft, electronic, electronics, molecular, nanostar, negf, quantum, spectrum
Chemistry -- Dissertations, Academic -- UF
Genre: Chemistry thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The results of theoretical and computational research are presented for two promising molecular wires, the Nanostar dendrimer, and a series of substituted azobenzene derivatives connected to aluminum electrodes. The electronic absorption spectra of the Nanostar (a phenylene-ethynylene dendrimer attached to an ethynylperylene chromophore) were calculated using a sequential Molecular Dynamics/Quantum Mechanics (MD/QM) method to perform an analysis of the temperature dependence of the electronic absorption process. We modeled the Nanostar as a series of connected units, and performed MD simulations for each chromophore at 10 K and 300 K to study how the temperature affected the structures and, consequently, the spectra. The absorption spectra of the Nanostar were computed using an ensemble of 8000 structures for each chromophore. Quantum Mechanical (QM) ZINDO/S calculations were performed for each conformation in the ensemble, including 16 excited states, for a total of 128,000 excitation energies. The spectral intensity was then scaled linearly with the number of conjugated units. Our calculations for both the individual chromophores and the Nanostar, are in good agreement with experiments. We explain in detail the effects of temperature and the consequences for the absorption process. The second part of this thesis presents a study of the effects of chemical substituents on the electron transport properties of the azobenzene molecule, which has been proposed recently as a component of a light-driven molecular switch. This molecule has two stable conformations cis and trans in its electronic ground state, with considerable differences in their conductance. The electron transport properties were calculated using first-principles methods combining non-equilibrium Green's function (NEGF) techniques with density functional theory (DFT). For the azobenzene studies, we included electron-donating groups and electron-withdrawing groups in meta- and ortho- positions with respect to the azo group. The results showed that the molecular structure is crucial in optimizing the electron transport properties of chemical structures, and that the transport properties in electronic devices at the molecular level can be manipulated, enhanced or suppressed by a careful consideration of the effects of chemical modification.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Julio Palma.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Krause, Jeffrey L.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024291:00001


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IgratefullythankandacknowledgemyadvisorDr.JereyL.Krauseforhiscontinualsupport,encouragement,guidanceandadviceduringmygraduateprogram.WithouthissupportIthinkIwouldnothavemadeit.IwouldalsoliketoexpressmymostsincereappreciationtoDr.Hai-PingChengforheradviceandinnitepatienceduringthetimethatIhavebeenhercollaborator,especiallyduringthelastthreeyearsthatDr.KrausehasbeeninWashingtonD.C.IwouldliketothankherforacceptingmeaspartofherresearchgroupandforinvitingmetoherpartieswhichIadmitarethebestpartiesever.Forhisscienticandpersonaladvice,patience,mentorshipbutmostofallhisunconditionalsupport,IwouldliketothankDr.AdrianE.Roitberg.Icannotndwordstoexpressmygratitudetohim.IthankDr.SamuelB.TrickeyandDr.FrankE.Harris;theyweretherstoneswhogavemetheopportunitytovisittheQuantumTheoryProject(QTP)duringthesummerof2002.IhonestlyconfessthatithasbeenagreatpleasuretodiscusssciencewithDr.Trickey,Ihavelearnedandbeenmotivatedbytheseconversations.IthankDr.JohnR.SabinandDr.ErikDeumensfortheirguidanceandsupport.Theyhavehelpedmetomakeimportantdecisionsformygraduateprogramandformyprofessionalfuture.ForhisadviceandforgivingmetheopportunitytobeinhislectureswhicharethebestclassesIhavetakeninmygraduateprogram,IwouldliketoexpressmyappreciationtoDr.N.YngveOhrn.IwouldalsoliketothankDr.ValeriaKleimanforthescienticfeedbackintheNanostarproject.SheandherresearchgrouphavealsoprovidedmewiththeexperimentaldataforthestudyoftheNanostar.IwouldalsoliketoexpressmygratitudetoDr.PredragS.KrsticandDr.Xiao-GuangZhangwhotaughtmetheprinciplesofelectrontransportduringmystayatOakRidge 4

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page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 8 LISTOFFIGURES .................................... 9 ABSTRACT ........................................ 11 CHAPTER 1INTRODUCTION .................................. 13 1.1Dendrimers ................................... 13 1.1.1GeneralAspects ............................. 13 1.1.2Phenylene-EthynyleneDendrimers ................... 14 1.2MolecularElectronics .............................. 15 2MOLECULARDYNAMICS ............................. 17 2.1HistoricalBackground ............................. 17 2.2TheoreticalPrinciples .............................. 17 3QUANTUMCHEMISTRY .............................. 20 3.1TheElectronicProblem ............................ 20 3.2Hartree-FockApproximation .......................... 21 4THENANOSTARDENDRIMER .......................... 25 5METHODSFORTHENANOSTARDENDRIMER ................ 32 5.1MolecularDynamicsAlgorithm ........................ 32 5.2ForceField ................................... 33 5.2.1Bondstretching ............................. 33 5.2.2Torsion .................................. 34 5.2.3Stretch-BendInteraction ........................ 34 5.2.4Torsion-StretchInteraction ....................... 35 5.2.5Bend-BendInteraction ......................... 35 5.2.6Inter-atomicvanderWaalsForces ................... 35 5.3ZINDO/S .................................... 36 5.3.1INDOHamiltonian ........................... 36 5.3.2CISParameterization .......................... 37 5.4ComputationalDetails ............................. 38 6

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...... 41 6.1MolecularDynamics .............................. 41 6.2ZINDO/SCalculations ............................. 42 7THEAZOBENZENE ................................. 60 8METHODSFORTHEAZOBENZENEDERIVATIVES ............. 64 8.1DensityFunctionalTheory ........................... 64 8.1.1Hohenberg-KohnTheorem ....................... 64 8.1.2Kohn-ShamMethodology ........................ 65 8.2ElectronTransportthroughMolecularJunctions ............... 67 8.2.1Landauer-ButtikerFormula ....................... 68 8.2.2CaroliFormula ............................. 69 8.2.3Non-EquilibriumFormalism ...................... 70 8.3ComputationalDetails ............................. 75 9ELECTRONTRANSPORTTHROUGHAZOBENZENEDERIVATIVES ... 81 9.1TransmissionatZero-Bias ........................... 81 9.2ElectronicStructureAnalysis ......................... 82 9.2.1HighestOccupiedMolecularOrbitalEnergies ............. 82 9.2.2LocalandProjectedDensityofStates ................. 83 9.3Finite-Bias .................................... 86 10CONCLUSIONS ................................... 117 REFERENCES ....................................... 122 BIOGRAPHICALSKETCH ................................ 132 7

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Table page 6-1Calculatedspectralfeaturesoftheindividualchromophores ........... 50 9-1Transmissioncoecientfortransmolecules ..................... 90 9-2Transmissioncoecientforcismolecules ...................... 91 9-3Dierencebetweentransandcistransmissioncoecients ............. 92 9-4HighestOccupiedMolecularOrbitalenergyoftransmolecules .......... 93 9-5HighestOccupiedMolecularOrbitalenergyofcismolecules ........... 94 8

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Figure page 4-1TheNanostardendrimer ............................... 30 4-2Nanostarexperimentalspectra ............................ 31 5-1TheNanostarasseparateunits ........................... 40 6-1Snapshotsofthetwo-,three-andfour-ringsystemsMDat300K ........ 51 6-2Distributionofthetorsionangleofthetwo-ringsystem .............. 52 6-3SnapshotsoftheNanostarMDat10K ....................... 53 6-4SnapshotsoftheNanostarMDat300K ...................... 53 6-5Calculatedabsorptionspectraoftheindividualchromophores .......... 54 6-6Experimentalandcalculatedspectraoftheindividualchromophores ....... 55 6-7Calculatedelectronictransitionsoftheindividualchromophores ......... 56 6-8ExperimentalandcalculatedspectraoftheNanostar ............... 57 6-9Oscillatorstrengthandwavelengthsscannedfrom0to90 58 6-10Energyleveldiagramforthetwo-,threeand2,3-ringsystems .......... 59 7-1Theazobenzenemolecule ............................... 62 7-2Isomerizationoftheazobenzenemolecule ...................... 63 8-1Schematicofthelead-molecule-leadsystem ..................... 77 8-2Tight-Bindingmodel ................................. 78 8-3Non-EquilibriumGreen'sFunctionself-consistentdiagram ............ 79 8-4Azobenzenederivatives ................................ 80 9-1LocalDensityOfStatesofrepresentativesystems ................. 95 9-2ProjectedDensityOfStatesintheazobenzeneregionofrepresentativesystems 96 9-3ProjectedDensityOfStatesinthesubstitutionregionofrepresentativesystems 97 9-4Current-Voltagecharacteristicsoftheazobenzenesystem ............. 98 9-5Current-Voltagecharacteristicsofthem-CH3system ............... 99 9-6Current-Voltagecharacteristicsoftheo-CH3system ................ 100 9

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.............. 101 9-8Current-Voltagecharacteristicsoftheo-OCH3system ............... 102 9-9Current-Voltagecharacteristicsofthem-Clsystem ................ 103 9-10Current-Voltagecharacteristicsoftheo-Clsystem ................. 104 9-11Current-Voltagecharacteristicsofthem-CF3system ............... 105 9-12Current-Voltagecharacteristicsoftheo-CF3system ................ 106 9-13Current-Voltagecharacteristicsofthem-Fsystem ................. 107 9-14Current-Voltagecharacteristicsoftheo-Fsystem ................. 108 9-15Current-Voltagecharacteristicsofthem-CNsystem ................ 109 9-16Current-Voltagecharacteristicsoftheo-CNsystem ................ 110 9-17Current-Voltagecharacteristicsofthem-NO2system ............... 111 9-18Current-Voltagecharacteristicsoftheo-NO2system ................ 112 9-19Current-Voltagecharacteristicsofthem-NH2system ............... 113 9-20Current-Voltagecharacteristicsoftheo-NH2system ................ 114 9-21Current-Voltagecharacteristicsofthem-NO2-NH2system ............ 115 9-22Current-Voltagecharacteristicsoftheo-NO2-NH2system ............. 116 10

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Theresultsoftheoreticalandcomputationalresearcharepresentedfortwopromisingmolecularwires,theNanostardendrimer,andaseriesofsubstitutedazobenzenederivativesconnectedtoaluminumelectrodes. TheelectronicabsorptionspectraoftheNanostar(aphenylene-ethynylenedendrimerattachedtoanethynylperylenechromophore)werecalculatedusingasequentialMolecularDynamics/QuantumMechanics(MD/QM)methodtoperformananalysisofthetemperaturedependenceoftheelectronicabsorptionprocess.WemodeledtheNanostarasaseriesofconnectedunits,andperformedMDsimulationsforeachchromophoreat10Kand300Ktostudyhowthetemperatureaectedthestructuresand,consequently,thespectra.TheabsorptionspectraoftheNanostarwerecomputedusinganensembleof8000structuresforeachchromophore.QuantumMechanical(QM)ZINDO/Scalculationswereperformedforeachconformationintheensemble,including16excitedstates,foratotalof128,000excitationenergies.Thespectralintensitywasthenscaledlinearlywiththenumberofconjugatedunits.OurcalculationsforboththeindividualchromophoresandtheNanostar,areingoodagreementwithexperiments.Weexplainindetailtheeectsoftemperatureandtheconsequencesfortheabsorptionprocess. Thesecondpartofthisthesispresentsastudyoftheeectsofchemicalsubstituentsontheelectrontransportpropertiesoftheazobenzenemolecule,whichhasbeenproposedrecentlyasacomponentofalight-drivenmolecularswitch.Thismoleculehastwo 11

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Developmentcanbedenedasadvancementandprogress.Fromasocial,economicalandpoliticalperspective,developmentistheprocessofgrowingbydegreesintoamoreadvanced,matureandstablestate.Suchdevelopmentiscloselyrelatedtotechnologyandenergysources.Themoststableandpowerfulcountriesarealsotheonesthatproduceandacquireenergyandnewertechnology. Molecularwiresarecriticalcomponentsforfuturetechnologiesandalternativeenergysourcesbasedonmolecularelectronics.Inthisdissertationweconsidermolecularwiresthatcantransferenergywithorwithoutchargetransfer.Atheoreticalinvestigationispresentedbasedontwopromisingcandidatesasmolecularwires;theNanostardendrimerandtheazobenzenemolecule. Thedissertationisorganizedasfollows.Ageneralintroductionofdendrimersandmolecularelectronicsispresentedinthischapter.Chapter 2 andChapter 3 presentthetheoreticalbackgroundnecessarytounderstandthemethodsusedtostudymolecularwires.Chapter 4 ,Chapter 5 andChapter 6 describethestudiesontheNanostar.Chapter 7 ,Chapter 8 andChapter 9 describethestudiesontheazobenzenemolecules.Finally,inChapter 10 generalconclusionsarepresented. 1.1.1GeneralAspects 1 { 6 ].Thestericlimitationsoftheresultingdendriticwedgelengthlimitdendrimerstorelativelysmallsizes,butthetheirglobularshapesproducefairlyhighdensities. ThesynthesisofDendrimersisarelativelyneweldinpolymerchemistry,sincesuccessfulsynthesisofthemwasrstdemonstratedinthelate1970's.Dendrimersaredenedbyregular,highlybranchedmonomersleadingtoamonodispersetree-like 13

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1 2 ]. Dendrimershavetwomajorchemicalenvironments,thesurface,whichisdominatedbytheterminalfunctionalgroups,andtheinterior,whichislargelyprotectedfromtheexteriorenvironment[ 1 2 ].Theexistenceofatleasttwodistinctchemicalenvironmentsinsuchamoleculeenablesmanyapplications,whichrangefromadhesivesandlubricants[ 7 8 ]todrug-deliverysystems[ 8 9 ],catalysts[ 10 { 12 ]andbiomolecularmimics[ 4 8 13 { 21 ].Duetothelargevarietyofpotentialandprovenapplications,dendrimersremainunderactivestudybyexperimentalandtheoreticalresearchers[ 10 22 { 25 ]. 16 26 { 28 ].Experimentalandtheoreticalanalysisindicatesthatthesedendrimershaveadualroleaslight-harvestingantennasaswellasenergycollectors,allowingnewformsofsupra-molecularphotochemistry[ 3 4 16 27 { 30 ].Whenradiationimpingesonadendrimericmolecule,electronicenergyistransferedamongthechromophoresandcollectedinatraponaveryrapidtime-scale,consequentlypreventingtheenergyfromleakingout.Thisprocessisenhancedbythegeometryofphenylene-ethynylenedendrimers,inwhichthedensityofatomsincreasesrapidlywithgenerationandtheatoms 14

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3 4 27 { 32 ]. InthisresearchwestudytheNanostardendrimerwhichisaphenylene-ethynylenedendrimer. Manyreasonscanbefoundtomotivateustoexploreinterestingeldsinthesearchfornewmaterialstouseinthefutureasthebasisofelectronicdevices.Thesedevicescanbecomesmaller,ultimatelythesizeofmolecules,andthusrequireanewphysicaltreatment,sincemoleculesarequantummechanicalobjects.Thisneweldofstudyisknownas\molecularelectronics." In1965,GordonMoore,co-founderofIntelCorporation,predictedthatthecomplexityofintegratedcircuitswoulddoubleeveryyear[ 33 ].Tenyearslaterheupdatedhisempiricalobservation,betterknownasMoore'slaw,tostatethatitwoulddoubleevery18or24months.Sincethen,Moore'sLawhasbeengeneralizedtorefertocomputingpower.Itisexpectedtoremainaccurateforatleastseveralmoreyears.Nonetheless,solid-statedevicesarereachingfundamentalandphysicallimitations. MorethanthreedecadeshaspassedsinceAviramandRatnerproposedthatamoleculecouldfunctionasarectier[ 34 ].Thiswastherstattempttoreduceanelectronicdevicetomolecularsize.Theoreticalandexperimentalresearchwasthenperformedtoprepareandcharacterizevariouselectrondonor-acceptorsystemsand,althoughsomeoftheinitialpredictionswerelaterretracted[ 35 36 ],thiswas,indeed,thebeginningofaneweldthathasattractedtheattentionofscientistsforfundamentaland 15

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37 38 ],andistheultimatecomponentofthephenomenathatsucceedMoore'slaw. Inrecentyears,importantbreakthroughsinsynthesiswithadvancedmicro-fabricationandself-assemblytechniques[ 38 { 41 ],aswellaselectronconductionmeasurementsperformedbyscanningprobemicroscopy[ 42 ],micro-machinedsiliconnanopores[ 43 ],andconnectiontoproximalprobes[ 44 45 ]haveshownsubstantialandsignicantprogress.Theseexperimentsenablethestudyofelectrontransportinmolecular-scalesystems.Asaconsequence,thedevelopmentandapplicationofnanomaterialsconsistingofmolecularelectronicdeviceshaveaccentuatedtheimportanceofatheoreticalunderstandingofthescatteringprocessesthatoccurinthesesystems[ 46 47 ].Ratnerhimselfandco-workershavebeenpioneersanddevelopersoftheoreticalmodelstotreatmolecularelectronics[ 48 { 51 ].However,agapexistsintheagreementbetweenexperimentalmeasurementsandtheoreticalpredictions[ 52 ].Aclearexampleisbenzendithiolate,forwhichtransportpropertiesareover-predictedbytheory[ 53 ]byseveralordersofmagnitudewithrespecttoexperimentaldata[ 44 ]. Asdescribedbelow,weperformedtheoreticalstudiesoftheazobenzenemoleculesanditsderivatives,asaprototypesystemthatcanfunctionasamolecularelectronicdevice. 16

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54 ].Intheinitialsimulations,thespheresmovedatconstantvelocityinstraightlinesbetweencollisions,whichwereassumedtobeperfectlyelastic.Thecollisionsoccurredwhentheseparationbetweenthecentersofthespheresequaledthesumoftheirradii. AmajoradvanceintheeldwasmadebyRahman,whoperformedsimulationsin1964ofliquidargonusingarealisticpotential[ 55 ],andinhislatersimulationsofwaterandotherliquids[ 56 ].Sincethen,MDsimulationtechniqueshaveexpandedgreatly,andspecializedtechniquestostudyparticularproblemshavebeendeveloped,forexample,tostudyenzymaticreactionsanddrugdesign. 57 ].ThetrajectoryofthesystemparticlesisobtainedbyconsideringtheclassicallawsofmotiondiscoveredbyIsaacNewton,whichstate, 1. Unlessaforceactsuponabody,itcontinuestomoveinastraightlineatconstantvelocity. 2. Theforceisequaltotherateofchangeofthemomentum. 3. Foreveryactionthereisareactionequalinmagnitudebutoppositeindirection. Fromknowledgeoftheforcesoneachatom,itispossibletodeterminetheiracceleration.Theintegrationoftheequationsofmotionyieldsatrajectorythatdescribesthepositions,velocities,andaccelerationsoftheparticlesastheyvarywithtime.The 17

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Theclassicalequationofmotionisgivenby, whereFistheforceexertedonparticleiwithmassmiandaccelerationai.Theforcecanalsobeexpressedasthegradientofthepotentialenergy, Combiningthesetwoequations,thederivativeofthepotentialenergyisrelatedtothechangeinpositionasafunctionoftime, dri=mid2ri whereVisthepotentialenergyofthesystem. Asanexample,wecananalyzeasystematconstantacceleration.Inthiscase,theaccelerationisgivenasthederivativeofthepotentialenergywithrespecttotheposition,r, dr: Therefore,tocalculateatrajectory,onerequirestheinitialpositionsoftheatoms,whichcanbeobtainedfromexperimentaldataand/ortheoreticalmodels,aninitialdistributionofvelocities,whicharefrequentlyselectedrandomlyfromaMaxwell-Boltzmann 18

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Asjustreminded,classicalmechanics,discoveredbyIsaacNewtonbytheendofthe17thcentury,describesthelawsofmotionofmacroscopicobjects.Bytheendofthenineteenthcenturyexperimentsrevealedthatclassicallawswerenotsucienttodescribeproperlythebehaviorofsmallparticles.Theseexperiments,andtheassociatedtheoreticalanalysis,ledtothediscoveryofQuantumMechanics,thefoundationsofwhichweredevelopedinthersthalfofthe20thcentury. ThecoreofquantumchemistryistheimplementationofmethodstosolvetheSchrodingerequation,whichdescribesthequantumstateofachemicalsystem,representedasawavefunction,anditsevolutionintime. 58 ], @t(r;t)=^H(r;t); where~isPlanck'sconstant,(r;t)isthewavefunctionofthequantumsystemand^HistheHamiltonian,whichisanoperatorthatcontainsakineticenergytermandapotentialenergyterm. Whenwerestrictthewavefunctiontobeaproductofafunctionoftimeandafunctionofspace,as,forexample,isthecasewhenthepotentialenergytermoftheHamiltonianisindependentoftime,thetime-independentScrhodingerequationcanbeexpressedas: ^H=E: 20

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^H=MXA=11 2MAr2ANXi=11 2r2iNXi=1MXA=1ZA whereAandB,etc.,labelnuclei,andi,j,etc.,labelelectrons,Zistheatomicnumber,andHartreeatomicunits(~=e=me=1)havebeenused. TheBorn-Oppenheimerapproximation,whichisausefulandcentralapproximationinquantumchemistry,separateselectronicandnuclearmotions.Assumingthatthenucleiarexed(sincenucleiaremuchheavierthantheelectrons),thenuclearkineticenergyterm,whichistherstterminequation( 3{3 ),canbeneglected,andtherepulsionbetweennuclei,thethirdtermofequation( 3{3 ),isaconstant.ThisapproximationleadstoanelectronicHamiltonian, ^Helec=NXi=11 2r2iNXi=1MXA=1ZA andtheSchrodingerequationbecomes: ^Helecelec=Eelecelec: 21

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ConsideratrialfunctionintheformofasingleN-electronSlater-determinant,whichobeysthePauliexclusionprinciple, Here^Oisthespinprojectoroperatorthatensuresthatthewavefunctionremainsaneigenfunctionofthespin-squaredoperator(^S2),^Aistheantisymmetrizer,isaone-electronwavefunctionthatrepresentsthemolecularorbital,andDiracnotationhasbeenadopted. Themolecularorbitalscanbeexpandedasalinearcombinationofatomicorbitals, whichconstitutethebasissetforthecalculation. isvariedwithrespecttoCfollowingthevariationalprincipletominimizetheexpectationvalueoftheelectronicHamiltonian,^H(wheretheelectronicsubscripthasbeendroppedforsimplicity)togivethefollowingexpressionfortheeectiveone-particleFockoperator,f, 22

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3{4 )andJandKarethecoulombandexchangeoperatorsrespectively.UsingaunitarybasistodiagonalizetheHermitianmatrix,,withmatrixelementsjiyieldsthecanonicalHartree-Fockequation, Fromthisequationthefollowinggeneralized-eigenvalueexpressioncanbeobtained, whereFistheFockmatrix,Cisasquarematrixcontainingthemolecularorbitalcoecients,SistheoverlapmatrixandEistheenergymatrixcontainingtheorbitalenergiesi. TheFockmatrixelementsare, wherenaistheoccupationnumber. Theoverlapmatrixelementsare, 23

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TheseabinitioexpressionsfortheFockmatrixwillbeusedbelowtoexplainadditionaldetailsofthemethodsusedinthisresearch. 24

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TheNanostar(Figure 4-1 ),oneofthemainsubjectsofthisstudy,isaphenylene-ethynylenedendrimersynthesizedbyMooreandco-workers[ 31 59 ].AtthecoreoftheNanostarisanethynylperylenegroup,whichisconnectedtofourgenerationsofphenylene-ethynyleneunitsthatdecreaseinlengthasthegenerationincreases(four-,three-andtwo-ringchromophores).Thedierentlengthsofthechromophoresleadtoanenergygradient.Whentheperipheralgroupsareexcitedwithultravioletradiation,theenergyistransfereddownthebranchestothecorewithnearly100%eciency[ 3 25 27 31 ].Intheabsenceofthisgradient,theenergywouldbedispersedrandomlythroughoutthemolecule,losttotheenvironment,andtheenergytransfereciencyfromtheterminalgroupstothecorewoulddecreaseconsiderably[ 27 32 ]. ExperimentsshowthattheabsorptionfeaturesintheNanostarforwavelengthslowerthan400nmcorrespondtothedendrimericportionandarenearlyunaectedbythepresenceoftheethynylperylenegroup.However,emissionfromtheNanostaroccursatwavelengthsassociatedwiththeisolatedethynylperyleneemission.Thisuorescenceisthreeordersofmagnitudemoreintensethantheemissionobtainedfromisolatedperyleneexcitedatthesamewavelength.TheseobservationsindicatethattheNanostaractsasahighlyecientenergyfunnelandtheperylenegroupasanenergytrapfromwhichtheenergyisemittedasvisibleradiation[ 25 27 31 ]. Themechanismandthekineticsoftheenergytransferprocesshavebeenthemainsubjectofseveralinvestigations.Usingtime-correlatedsinglephotoncounting,Swallenetal.[ 27 ]determinedanupperlimittotheensemble-averagedenergy-transfertimefromtheperipheralgroupstotheethynylperylenetrapas270ps,andabout10psfromthefour-ringsystemtotheperylenegroup.Kleimanetal.[ 60 ]measuredtherelaxationtimefromtheexcitedtwo-ringsystemwithintheNanostar.Theresultscanbemodeledasthesumoftwoexponentialcomponents,withthefastercomponentdecayingwitha 25

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25 60 ]. AlthoughForstertheoryhasbeenusedsuccessfullywithmanysystems,itmustbeappliedcarefullyindendrimericstructuresduetothepresenceofmultipledonorsindierentconformationalenvironmentsandtherelativelyshortdistancesbetweendonorsandacceptors[ 61 62 ].Ortizetal.[ 62 ]comparedrateconstantsforenergytransferbetweenthetwo-ringandthethree-ringsystemsobtainedviatheidealdipoleapproximation,Forstertheory,andthetransitiondensitycubemethod(TDC)[ 63 ].TheTDCmethodgivesthemostaccurateapproximationoftheCoulombiccouplingandwasfoundtobethemostsensitivemethodtoaccountforthephenylenegrouprotation,whichmustbeconsideredforpredictionofthetemperaturedependence.Thisfeaturewasnotconsideredinmanypreviousinvestigations,althoughtheopticalpropertiesoftheNanostardo,infact,displaydistincttemperaturedependence. TheexperimentalabsorptionspectraoftheNanostarat10Kandatroomtemperaturearequitedierent.Figure 4-2 displaystheexperimentalexcitationspectrumoftheNanostarat10Kandtheabsorptionspectrumatroomtemperature.Kopelmanandco-workersshowedthattheexcitationandabsorptionspectraintheNanostararenearlyidentical[ 31 ]. At10K,threemajorpeaksareobservedat313,361and384nm,whereasatroomtemperature,onlytwobroadbandsat300and350nmareobservedwithbroadshoulders.Thepeakat313nmobservedatlowtemperaturehasasmalldisplacementatroomtemperaturetowardshorterwavelength.Thepeaksat361nmand384nmseenatlowtemperaturearenotdenedsharplyathightemperature,andonlyshouldersareobservedbetween330and370nm. 26

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25 27 31 ].Questionsremain,though,regardingtheNanostarabsorptionprocess.Whatcausesthetemperature-dependenceoftheNanostarabsorptionspectrum?Whichchromophorescontributetotheabsorptionprocess?Aretheexperimentalassignmentsofthepeaksandshoulderscorrect? Mukamelandco-workerscalculatedtheabsorptionspectrumandfrequency-gateduorescencespectrafortheNanostarusingacollectiveelectronicoscillatorapproach,anddevelopedaFrenkelexcitonHamiltoniantodescribetheenergytransferandopticalpropertiesoftheNanostar[ 32 64 { 66 ].Theirresultsareinagreementwithexperimentsatroomtemperature;however,theydidnotconsiderthetemperaturedependenceofthesystem.Ortizetal.[ 62 ]includedtheseeectsforenergytransferstudies.Theirresultsshowthattherotationofphenylenegroupsisthemostimportantaspectthatmustbeconsideredtounderstandthetemperaturedependenceobservedintheabsorptionspectrum. Garcia-Garibayandco-workersperformedsemi-empiricalcalculationsforaromaticchromophoreslinearlyconjugatedbyethynylenelinkagestodeterminetheeectsofthephenylenegrouprotation.TheyexaminedtheeectsoftheinterruptionoftheconjugationduetorotationonverticalexcitationusingZINDO/S[ 67 { 69 ],whichisasemi-empiricalmolecularorbitalmethodparameterizedattheCI-singles(CIS)leveltoreproduceelectronictransitions[ 70 ].Itisworthnotingthatsomeoftheexperimentalresultswerelaterretractedbutourpointhereisonlytogaugetherelevanceofthesemi-empiricalcalculations[ 68 71 ].Magyaretal.[ 72 ]performedatheoreticalandexperimentalstudyofphenylene-ethynylenemolecularwires.TheystudiedexcitationenergiesatdierentlevelsoftheoreticalaccuracyincludingZINDO/S.Theyalsoconsideredplanarmolecularstructuresandalternatinggeometriesatspecicanglesbetweenthephenylrings. 27

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73 ]studiedtheabsorptionspectraofphenyleneethynyleneoligomersandtheirunusualaspectsduetorotationofthephenylenerings.Theabsorptionspectrawereobtainedfromasetoftorsionalcongurationsinwhichthegroundstatewasmodeledwithamolecularmechanicsexpression,andtheelectronictransitionsweremodeledwithanexcitonmodelandINDO/SCIcalculations.Theyfoundthatinclusionofthetorsionaldisorderisessentialtounderstandthespectroscopyandphotophysicsofconjugatedpolymers. InthisresearchwecompareMolecularDynamics(MD)simulationsfollowedbyQuantumMechanical(QM)calculationswithsteady-statespectroscopymeasurementstodeterminethetemperature-dependenceoftheabsorptionprocessintheNanostarat10Kandroomtemperature.Sincemetasubstitutionsuppresses-electronconjugation,wemodeltheNanostarasastructurecomposedofindependentchromophores. TheoreticalcalculationsbyMukameletal.indicatethatmetabranchingdecouplestheresonantelectronicconjugationamongphenylene-ethynyleneunits[ 5 ].Asaresult,theopticalexcitationislocalizedoneachphenylene-ethynylenechainincompactandextendeddendrimers.Chernyakandco-workersalsoshowed,usinganexcitonmodel,thatmeta-connectionbreaksmolecularwiressuchasthenanostarintolinearsegmentsintheexcitedstate[ 74 ].Experimentalevidenceforthisexcitoniclocalizationisobservedbysteady-stateabsorptionspectroscopy[ 3 ],leadingtothepredictionthattheoverallabsorptionspectrumoftheNanostarcanbeinterpretedasthesumofthespectraoftheindividualchromophores[ 25 27 31 ].Inaddition,evidenceforstronglocalizationoftheorbitaldensityinthesegmentshasobtainedinmolecularorbitalcalculations[ 75 ]. Incontrast,Martnezandco-workershaveproposedthatalthoughmetasubstitutionblocksconjugationinthegroundstate,thisisnotnecessarilytrueintheexcitedstate.Infact,theirmodelsuggeststhattheexcitationsarenotlocalizedontheexcitedstatesofchromophoresseparatedbymeta-substitution.Theyfound,however,thattheelectroniccouplingissmallintheabsorbinggeometrywhileintheemittinggeometryitislarge[ 76 28

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]whichwouldhaveadirectimpactontheenergytransferprocessbutnotinstudiesoftheabsorptionprocessasourresultswillshow.Itisworthnoting,too,thattheworkofMartnezandco-workerswasperformedforisoenergeticdiphenylacetyleneoligomerslinkedatthemetaposition,whichcancouplestronglywhentheelectronicinteractionincreasedintheexcitedstate.EvenifsimilarphenomenaexistedintheNanostar,thedierencesinenergyandlengthofthesegmentswouldpreventsignicantdelocalization.Infact,thiseectwasnotfoundtobeanissueinpreviousenergytransfercalculationsbyMukamelandco-workers[ 65 66 ]andOrtizetal.[ 62 ]sincechromophoreswithlargeenergydierencesarenotlikelytoformdelocalizedexcitedstates,andtheenergytransferbetweenlocalizedstatesisthrough-space,orForster-like. Inthisresearch,weperformedMDsimulationsatdierenttemperaturestoconstructequilibriumcanonicalensemblesofeachindividualchromophore.TheseensemblesweresubsequentlyusedtoperformedZINDO/Scalculations,whichisamethodthatisknowntoprovideagooddescriptionofconjugatedsystems[ 78 ].AsimilartechniquehasbeenusedbyCanutoandco-workerstodeterminesolventeectsinsystemssuchasbenzene,N-methylacetamideandbenzophenone.TheycalculatedelectronictransitionsusingfullQMZINDO/ScalculationsinclustersgeneratedbyMonteCarlosimulations[ 79 { 81 ].Insimilarresearch,Kruegerandco-workersusedMDsimulationsfollowedbyaQMtime-dependentevaluationofelectronictransitionenergiesforthesystemofoxazine-4inmethanol[ 82 ]. Asshowninthefollowingchapters,basedonabsorptionspectraoftheindividualchromophores,wepredicttheabsorptionspectraoftheNanostarat10Kand300K,whichallowsustoidentifythecontributionfromeachchromophoretothetotalspectrum.WecomparetheresultsfromourMDsimulationsandelectronicspectracalculationswiththeexperimentalabsorptionspectraoftheindividualphenylene-ethylenechromophoresandtheNanostarcollectedatlowandroomtemperature.TheexperimentalspectrawereprovidedbythegroupofDr.ValeriaKleiman[ 83 ]. 29

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TheNanostardendrimer.Two-dimensionalsketch. 30

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Nanostarexperimentalspectra.ExcitationspectrumoftheNanostarat10K(solidline)andexperimentalabsorptionspectrumatroomtemperature(dashedline)[ 83 ]. 31

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2 )isbasedonclassicalmechanicswhichrelatestheforcetothepotentialenergyasseeninEquation( 2{2 ). Thepotentialenergyisafunctionofallatomicpositionsand,sincenoanalyticsolutionexistsfortheequationsofmotion(formorethantwoorthreeparticles),theequationsmustbesolvednumerically. SeveralnumericalalgorithmstoperformMolecularDynamicshavebeendeveloped.Allassumethatthepositions,velocitiesandaccelerationscanbeapproximatedbyaTaylorseriesexpansion.Inthisresearch,MolecularDynamicsisbasedontheVelocity-Verletalgorithm.Thisalgorithmgivespositions,velocitiesandaccelerationsatthesametime,butdoesnotcompromiseprecision. ToderivetheVelocity-Verletalgorithm[ 84 ],thefollowingexpressionsareused: 2a(t)t2; 2(a(t)+a(t+t))t: TheVelocity-Verletalgorithmisimplementedasathree-stepprocedureasitrequirestheaccelerationattandt+ttocalculatethenewvelocities.Intherststep,thepositionattandtarecalculatedusingtheexpressioninEquation( 5{1 ),withthevelocitiesandaccelerationsattimet.Thevelocitiesattimet+1 2tarethendeterminedby, 2t)=v(t)+1 2a(t)t: 32

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2t)+1 2a(t+t)t: Theadvantagesofthisalgorithmarethatitisstraightforwardtoimplement,storagerequirementsaremodest,theprecisionincreasesasthetimesteptdecreasesandthecancellationoftermsintheTaylorexpansionmakesthisalgorithmmoreaccuratewithalargertimestep. TheforceeldthatwasusedforthemoleculardynamicsinthisresearchisMM3[ 85 { 87 ],whichwasdevelopedforhydrocarbons.TheMM3forceeldhasbeenusedwidelytocalculateandpredictenergiesandstructures,includingheatsofformation,conformationalenergies,androtationalbarriers. ToconstructtheMM3forceeld,vibrationalfrequencieswereconsideredforasetofsimplehydrocarbons.Torsionalfrequenciescangenerallybecalculatedwithsmallerrors,whichallowscalculationsofentropiesnearroomtemperatureforavarietyofalkenesandcycloalkanes.MM3isaseven-termforceeld,asdescribedbelow. 33

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122:55(RRe)2; whereRandRearethebondlengthandthebondlengthatequilibriuminangstroms,ksistheforceconstantandthecoecientistheconversiontermtoobtaintheenergiesinkcalmol1. 2V1(1cos(!))+1 2V2(1cos(2!))+1 2V3(1cos(3!)); where!isthedierenceofthedihedralangleandtheequilibriumdihedralangle,andV1,V2andV3arethetorsionalforceconstant. whereKs!istheforceconstant,and0aretheangleandequilibriumangle,respectively,andR0andR0earetheadjustmentsinthebondlengthandequilibriumbondlength,respectively. 34

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whereK!sistheforceconstant,RandRearethebondlengthandequilibriumbondlengthrespectivelyand!isthetorsionalangle. whereK0istheforceconstantand!0and!00aretheadjustmentsintheangleandequilibriumanglerespectively. rv)]: 35

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ZINDO/Sisasemi-empiricalmolecularorbitalmethoddevelopedbyZernerandco-workers[ 70 ].Thismethodisparameterizedtoreproducespectroscopictransitionsaccurately.Themethodcanbeappliedtoawiderangeofmoleculesandsystemsincludingthosecontainingtransitionmetals[ 88 ],aswellaspolymers,organometalliccompounds,andmacromoleculessuchasdendrimers.Topredictelectronicspectra,ZINDO/SsolvesanINDOHamiltonianparameterizedataCongurationInteraction-Singles(CIS)level. 89 ],includesmonoatomicdierentialoverlap,andintegralsinvolvingspin-basisfunctionscenteredonthesameatom.Thisenablestheinteractionbetweentwoelectronsonthesameatomtobedierentdependingonwhethertheyareparallelorpaired. TheFockmatrixelementsforaclosed-shellmoleculecanbewrittenas, 36

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whereAandBrepresentatomiccenters,uandv,etc.,representindividualorbitals,thebarovertheindividualorbitalsindicatesthattheactualorbitalisreplacedbythe\s"symmetryorbitalofthesamespatialextentandtheintegralUisthecoreintegral.Thecoreintegralisdenedastheatomic-likeone-electronintegral, 2r2ZA whereVisaneectivecorepotential. Someoftheone-centertwo-electronintegralscanbedenedassemi-empiricalparametersobtainedbyttingtoatomicspectroscopicdata.ThecoreintegralsUareobtainedfromexperimentalionizationenergies,withaconsiderationoftheelectroniccongurationsoftheatomsandtheircationsandanions. 58 ],INDObecomesanextremelyusefulmethodtocalculatespectroscopicproperties.Thismethodbeginsbychoosingaxedmoleculargeometry.Thecalculationyieldsun-occupiedorbitals,whosenumberdepends 37

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k=occXiunoccXaCiakai; wheretheoccupiedspinorbitaliinthegroundstatehasbeenreplacedbytheunoccupiedspinorbitala.TheconstantsCiakarevariationalcoecients. Aself-consistentprocedureisusedtondthelowestseveralrootsofthesecularequationandtondthecoecientsassociatedwitheachroot.Eachoftheserootsisanapproximationtotheenergyofanexcitedelectronicstateatthexedgeometrychosenforthecalculationandtheoscillatorstrengthsarecalculatedusingthedipolelengthoperator. Open-shellsystemscanbetreatedbasedonmethodssuchasunrestrictedHartree-Fock[ 88 ]orgeneralizedrestrictedopen-shellHartree-Fock[ 90 ],whicharebeyondthescopeofthediscussioninthisdissertation. 5-1 )Finally,amodeloftheentireNanostarwasconstructedandanalyzed. WeperformedMolecularDynamicssimulationsforeachsystemdescribedaboveusingTINKER(version3.9)[ 91 ].Fortheinteratomicinteractions,theMM3forceeldwasused,which,asdiscussedabove,hasbeenparameterizedtotreatorganiccompounds[ 85 { 87 ]. 38

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92 { 94 ].Theforceeldwasmodiedbychangingthetorsionpotentialtoobtaintheexperimentalenergybarriervalueof0.6kcalmol1,andaperiodicityoftwo. TheNanostaranditsseparatechromophoreswerebuiltasfullyextendedmolecules,andthenminimizedlocallytoarootmeansquaregradientofenergylessthan0.01kcalmol1A1. Stochasticdynamicssimulations,whichincludeafrictionparametertosimulatesolventeects,wereperformedattwotemperatures,10Kand300K.Thecollisionfrequencyfrictioncoecientwassetto1.0ps1,lowenoughtosimulatevacuumconditions.Forthechromophoresstudied,thecore,two-,three-,four-ringsystems,50nsofdynamicswereperformed,whereasfortheentireNanostar20nsofdynamicswasobtained.ThesimulationswerepropagatedusingavelocityVerlet-basedstochasticdynamicsalgorithmassummarizedalready[ 84 ]. ZINDO/ScalculationswereperformedforeachseparateunitusingtheGaussian03package[ 95 ].Twoensemblesconsistingof8,000conformationsobtainedfromtheMolecularDynamicssimulationswereconstructedforeachsystem,onefromthesimulationat10Kandonefromthesimulationat300K.TheZINDO/Scalculationsconsideredonlysingletexcitedstatesandincluded16excitedstates,resultinginatotalof128,000computedelectronictransitionsforeachsystemateachtemperature.Fromthesetransitions,electronicspectraforthesystemsweresynthesized. 39

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TheNanostarasseparateunits.Two-dimensionalsketchoftheNanostarandthechromophoresstudiedasseparateunitsarenoted. 40

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During50nsofMolecularDynamicsat10K,thetwo-,three-,andfour-ringsystemsmaintainedastructureclosetoplanar.At300K,thestructuresarenolongerplanarandtheringsrotate,indicatingthatatthistemperatureconformationsbeyondtherotationalbarrierareaccessible.Inaddition,themoleculeslosetheirlinearconformationsandbendalongthelongaxis,atrendwhichismorepronouncedasthesystemsgetlarger;seeFigure 6-1 InFigure 6-2 ,thetorsionangledistributionsofthephenylringsofthetwo-ringsystemat10Kand300Kareshown.At10Kthetwo-ringsystemisessentiallyplanar;themeantorsionangleis0.0,withadistributionwidthof16.4.Mostoftheconformationsareneartheplanarstructure,butthereissucientenergytoallowforsmalldeviationsfromplanarity.Theseresultsdemonstratethatatlowtemperaturefreerotationoftheringsisnotpermitted. Incontrasttothenarrowdistributionat10K,amuchbroaderdistributionofanglesisobservedat300K.Atthistemperature,therotationalbarrieriseasilysurmountedandtherotationoftheringsisnearlyfree,asseeninFigure 6-2 .Thereisnospecicmaximumorminimuminthedistribution,becauseoncetheenergyofthesystemishigherthantherotationalbarrier,theprobabilitytondaconformationatanyangleisnearlyuniform. Inthecaseofthethree-andfour-ringsystems,wefoundsimilarresultsasinthetwo-ringsystem.At10K,mostoftheconformationsareneartheoptimizedstructurewithlowvaluesofthetorsionangle,whereasat300Ktherotationalbarrierissurpassedandfreerotationoftheringsoccurs,allowingamuchlargerdistributionofconformations. 41

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ForthecompleteNanostar,theoptimizedstructureisnearlyplanar.At10Ktherearesmallmotionsandthestructureisnolongerplanarduetostericeectsbetweenbranchesthatlieindierentplanes.However,thereisinsucientenergytosurmounttherotationalbarrieroftheringsandfreerotationoftheringsisnotobserved(Figure 6-3 ). At300K,thebranchesofthedendrimerrotate.Allofthebranchesareindierentplanes,whichindicatesthatathighertemperaturethemotionofthesystemismuchlessconstrained,andthattheentanglementamongdierentbranchesishigher.Theenergyissucienttorotateeveryringofthesystem,includingtheonethatisbondedtothecore.Thisbehaviorwasnotunexpected,basedontheresultsfortheseparatechromophores.Asshownabove,everyringofthetwo-,three-,andfour-ringsystemsrotatesat300K.Theringswithineachgenerationrotate,whiletheringsatthebranchingpointsdonot.Inthethree-ringsystem(secondgeneration),thereisoneringthatrotatesfreely,i.e.,thecentralring,whileinthefour-ringsystem,therearetworingsthatrotatefreely.Thedistancebetweenthetwocentralbranchesgoesfrom35.9Aatlowtemperatureto16.0Aathightemperature,andtheentanglementobservedisduetothebendingofthelinearchromophoresasmentionedpreviously(Figure 6-4 ). 6-1 42

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6-5 showsthecalculatedabsorptionspectraoftheindividualphenylene-ethylenecomponents.At10Kandat300K,theabsorptionspectraofthetwo-ringsystemsarecenteredat353nmand352nm,respectively.Athightemperaturethespectrumisbroaderthanatlowtemperature;at300Kthefullwidthathalfmaximum(FWHM)is30nmwhileat10Kitis7nm(Figure 6-5 A ).ThisbroadeningreectstheconformationalvariabilityseeninFigure 6-2 Inthethree-ringsystem,theabsorptionpeakat10Koccursat391nmwhileat300Kitisblue-shiftedby11nmto380nm(Figure 6-5 B ).Inthefour-ringsystem,theabsorptionpeakisat420nmand399nmat10Kand300K,respectively(Figure 6-5 C ).Forbothsystemsthespectrumathightemperatureisbroaderthanatlowtemperature.Itisclearthatasthelengthofthechromophoreincreases,thehighertemperatureinducesalargershiftandincreasedbroadening. Inthecaseoftheethynylperylenecore,at10K,theabsorptionpeakiscenteredat481nmandtheFWHMis12nm,whileat300K,thepeakiscenteredat479nmandtheFWHMis48nm(Figure 6-5 D ). Figure 6-6 showstheexperimental(toppanel)andcalculated(bottompanel)absorptionspectraoftheindividualchromophoresatlowandhightemperature.AllexperimentalspectrawereprovidedbyKleiman'sresearchgroup[?].Atthispointweshouldnotethatthelow-temperatureexperimentalspectraforthechromophoresweremeasuredat77K.Itisnotexpectedthesetoberemarkabledierentfrommeasurementsat10K,whichexperimentaldataisnotavailableatthispoint.Therefore,wecomparethemdirectlywithour10Kcalculatedspectra.Thelow-temperaturespectrumoftheNanostaritselfwasmeasuredat10K. Goodagreementisobservedbetweentheexperimentalandcalculatedspectraatlowtemperature(Figures 6-6 A and 6-6 C )andhightemperature(Figures 6-6 B and 6-6 D )forthetwo-,three-andfour-ringsystems.Theexperimentalspectrumat77Kdisplaysasharpbandattheredendofthespectrum,followedbyhighenergystructuredueto 43

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Similarfeaturesareobservedinthecalculatedspectra.Thethreebandsatlowtemperaturecorrespondtothereddestabsorptionbandsseenintheexperimentalspectra.Atroomtemperature,thesesharpbandsbecomeverybroadandblueshifted. Itisclearthatasthenumberofphenylene-ethynyleneringsincrease,theprimaryeectofincreasingthetemperatureistoinducealargershiftandtobroadenthebands.Asaresult,thepeaksarewellseparatedatlowtemperature,butnotathightemperature.Thevibronicstructureobservedintheexperimentalspectraisnotincludedinthecalculations. InFigures 6-7 A and 6-7 B thelowesttwotransitionenergiesforthe8,000congurationsofthetwo-ringsystemat10Kandat300Kareshown,respectively.At10K,themaintransitionislocalizedat353nm.Animportantresulttonoteisthatthemaintransitionistothesecondsingletexcitedstate(S2)andnottothelowest(S1),whichisinagreementwithexperimentalresults.Theexcitationofthetwo-ringsystemnear300nmwasexploredpreviouslybyHirata[ 96 ]andbyKleiman[ 60 ].Measurementsshowthatexcitationat297nminitiallypopulatestheS2(1B1u)manifold,whichcaneitherreturntothegroundstatethrough(mainly)non-radiativerelaxation,orundergointernalconversiontotheS1state.Ultrafasttime-resolvedexperimentsyieldedanS2lifetimeof6.3psinCH2Cl2[ 60 ]andalifetimelessthan8psinhexane[ 96 ].At300K,theS1andtheS2transitionscontributetotheabsorptionspectrumsinceconformationalchangesbreakthesymmetry.Thedistributionoftransitionsisbroader,rangingfrom310nmto450nm,becausethenumberofpopulatedconformationsincreasesasafunctionoftemperature,asthedistributionsofFig. 6-2 indicate. Forthethree-andfour-ringsystemsat10K,thetransitionsarelocalized(seeFigure 6-7 C ),whileat300Kthedistributionisconsiderablybroader(seeFigure 6-7 D ). 44

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Theincreaseinthewidthofthedistributionofthetransitionsaectsthecharacterofthespectrumdirectly.Inthespectrumofthetwo-ringsystemat10K,theFWHMofthepeakincreases,butthepeakremainslocalizedat353nm.Forthefour-ringsystemat300K,theFWHMofpeakisaected,aswellasthepositionofthepeak,whichisshiftedtohigherenergy. TheMDsimulationsat10Kshowthattheringsinthetwo-ringsystemdonotundergosignicantrotation,whileat300K,ringrotationisobservedandthemoleculebends.At300K,manymoreaccessibleconformationsarepresent,asshowninFigures 6-1 and 6-2 ,resultinginmoreaccessibleexcitedstatesandaconsequentincreaseinthewidthoftheabsorptionband. Forthefour-ringsystem,similarbehaviorisobservedtothatfoundinthethree-ringsystem.At10K,noringrotationoccursandthemoleculeisplanar,whileat300K,theringsrotateandthemoleculebends.Thepresenceoffourringsincreasesthenumberofconformationsandstates,causingthedistributionandvariancetoincrease.Thus,thewidthofcontributingtransitionsis70nmbroaderthanthewidthofthetwo-ringsystem. Thedisplacementoftheabsorptionmaximumofthefour-ringsystemat300Kcanberationalizedbyconsideringtheconjugationlengthofthemolecule,astheenergyoftheelectronictransitionisinverselyproportionaltotheconjugationlength.At300K,theringsofthefour-ringsystemrotatefreelyandlossofconjugationresultingfromlackofco-planarityoftheringscauses,ineect,adivisionofthesystemintosmallersubsystems.Eachofthesesubsystemshashigherexcitationenergiesthantheco-planarfour-ringsystem,arealitywhichresultsinadisplacementofthepeaktowardshorterwavelengths. 45

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ToinvestigatethepredictionthattheabsorptionspectrumoftheNanostarcanbeconstructedfromtheabsorptionspectraofeachofitschromophoresweassembledthespectrumbyconsideringthefactthatthereare24two-ringsystems,4three-ringsystems,2four-ringsystemsandonecoremoiety. Experimentally,thespectraoftheNanostar(Figure 6-8 toppanel)at300Kand10Karewell-reproducedbytheweightedsumofthespectraoftheindividualchromophores(Figure 6-8 middlepanel).Aweakcouplingamongchromophores,asaconsequenceofachangeinthechemicalenvironmentandresonancecoupling,isobservedasasmallfrequencyshift(10nm)towardlowerwavelengthbetweentheNanostarabsorptionspectrumandthespectrumobtainedasthesumofthephenylene-ethylenecomponents. Thecalculatedspectrawereshiftedby40nmalongthewavelengthaxistotthemainpeakoftheexperimentalspectraoftheNanostar.Thecalculatedspectrumat10Kdisplaysfourmainpeaksat313nm,351nm,380nmand447nm.However,at300Konlytwopeaksarevisibleclearly,at309nmandat438nm;between328nmand390nmthereisaprominentshoulder. At10K,eachofthemainpeakscorrespondstotheabsorptionofonespecicunit,astheelectronictransitionsarelocalizedinenergyandhomogeneousinintensity.Thepeaksat313,351,380and447nmcorrespondtotheabsorptionsofthetwo-,three-,andfour-ringsystems,andtothecore,respectively.TheexperimentalspectrumoftheNanostarat10Kalsoshowsfourmainpeaksat313,361,384and484nm. At300K,whilemostofthecontributiontothepeakat309nmisfromthetwo-ringsystem,thethreeandfour-ringsystemsalsocontributetoalesserextent.Thecorecontributestothepeakat438nm,andthethreeandfour-ringsystemscontributetothe 46

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ThetoppanelofFigure 6-8 showstheexperimentalspectraoftheNanostarat10K(Figure 6-8 A )andatroomtemperature(Figure 6-8 B ).Themiddlepanelshowsthesumoftheexperimentalspectraofthetwo-,three-andfour-ringsystemsat77K(Figure 6-8 C )androomtemperature(Figure 6-8 D ).Thebottompanelshowsthesumofthecalculatedspectraofthetwo-,three-,four-ringsystemandtheethynylperylenecore.Forthemiddle(experimental)andbottom(calculated)panels,thespectraofthesubsystemsareincludedtoidentifytheircontributiontothetotalabsorptionspectra.ThecalculatedspectraareingoodagreementwithexperimentsandthefeaturesintheNanostarspectrumareobservedtoscalelinearlywiththenumberofchromophoresinthemolecule.Smalldierencesareduetotheabsenceofsolventeectsinthedynamicsandquantummechanicalcalculations,andthepresenceofaweakcouplingamongchromophores,whichleadstoslightlyshiftedexcitontransitions. Itisimportanttonotethattheensembleforthetransitionsoftheindividualcomponentsrepresentsonlythedynamicsoftheindividualsegments.However,conformationsexistinwhich,forexample,theterminalringinthethree-andfour-ringsystemrotatefreelyat300K.TheseconformationsarenotpresentinthetruedynamicsoftheNanostar,becausetheseterminalringsareconnectedtootherchromophores. Todeterminetheeectthattheseadditionalconformationsmighthaveonthetotalspectrum,wescannedtheZINDO/Sexcitationenergiesandoscillatorstrengthswithrespecttotherotationoftheterminalringandthemiddlering.Werotatedtheringsfromzeroto90.Figures 6-9 A and 6-9 B showthevaluesoftheoscillatorstrengthandwavelengthsatdierentvaluesoftheanglesfortheouterandinnerring,respectively,ofthethree-ringsystem.Itisclearthatastheangleofrotationincreasesboththeoscillator 47

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Forthefour-ringsystems,theresultsaresimilartothoseofthethree-ringsystem.Figures 6-9 C and 6-9 D showthevaluesoftheoscillatorstrengthsandwavelengthsasafunctionofanglefortheouterandinnerring,respectively.Adecreaseintheoscillatorstrengthandexcitationenergyisobservedastherotationangleincreases.Whentheouterringisrotatedby90,asmalldecreaseintheoscillatorstrengthandashiftof15nmtowardsmallerwavelengthisobserved.Thesevaluesaresimilartothoseoftheplanarthree-ringsystem.Incontrast,adramaticblueshiftisobserveduponrotationoftheinnerring.Theminimumvalueisalsoat90,butthisvaluedoesnotfalltozeroastherotationofoneofthetwoinnerringsdoesnotbreaktheconjugationcompletelysincetwoconsecutiveringsremaininthesameplaneandso,asinthetwo-ringsystem,theabsorptionintensityisnon-zero. Theseresultsindicatethatthedisplacementofthespectratoshorterwavelengthandthechangeinintensityaremainlyduetotherotationoftheinnerrings,whichoccursbothinthedynamicsoftheNanostarandtheindividualchromophores.Weconcludefromthisanalysisthattheadditionalconformationspresentinthesimulationdonotcontributesignicantlytotheresults. 48

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6-10 ,wepresentanenergyleveldiagramillustratingtheHOMOsandLUMOsobtainedfromHartree-Fock[ 58 ]calculationswitha6-31G**basissetforthetwo-andthree-ringsystemsandasegmentoftheNanostarconsistingofatwo-ringsystemlinkedtoathree-ringsystem(2,3-ringsystem)atametaposition.Tadaetal.[ 75 ]performedasimilarstudyofthemolecularorbitalinteractionsintheNanostarusingtheHuckelmethod.Wendsimilarresults;themolecularorbitalsarelocalizedinspaceandenergy.Inparticular,weobservethattheHOMO-1ofthe2,3-ringsystemcorrespondstotheHOMOofthetwo-ringsystem,theHOMOandLUMOofthe2,3-ringsystemcorrespondtotheHOMOandLUMOofthethree-ringsystem,respectively,andtheLUMO+1ofthe2,3-ringsystemcorrespondstotheLUMOofthetwo-ringsystem.Althoughthispicturedoesnotdescribethecharacteroftheexcitedstatescompletely,itindicatesthattheallowedtransitionsinthe2,3-ringsystemareHOMO!LUMOandHOMO-1!LUMO+1. ThismodelisinagreementwithZINDO/Scalculationsperformedforthesamesystems.Themaintransitionsinthe2,3-ringsystemaretoS1andtoS4states,whichcorrespondtotheHOMO!LUMOandHOMO-1!LUMO+1respectively.ThetransitiontoS1hasanoscillatorstrengthoff=1:7at315nm,whichcorrespondscloselytothetransitiontoS1ofthethree-ringsystem.ThetransitiontoS4hasanoscillatorstrengthoff=0:64at289nm,whichmatchesthetransitiontoS2ofthetwo-ringsystem.Asexpected,transitionsinthe2,3systemtoS2andtoS3havenegligibleoscillatorstrengthsandthereforedonotcontributetothespectrum. WendaslightincreaseinthegapbetweentheLUMO+1andHOMO-1ofthe2,3-ringsystemwithrespecttheHOMO-LUMOgapofthetwo-ringsystem,aswellasaslightdecreaseintheHOMO-LUMOgapofthe2,3-ringsystemwithrespecttothatofthethree-ringsystem.Thisisclassicbehaviorforaweaklycoupledfour-levelsystemand,inaccordwiththeexcitonmodel,providesadditionalevidencethatstudiesofthesystemasseparateunitsisavalidapproach. 49

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Calculatedspectralfeaturesoftheindividualchromophores.Comparisonoftheindividualchromophoresat10Kand300K.Allvaluesareinnanometers. SpectrumPeakCenterFWHM 10K300KDispl.10K300K 2-ringsystem35335217303-ringsystem391380118474-ringsystem42039921960core48147921248 50

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Snapshotsofthetwo-,three-andfour-ringsystemsMDat300Kduring50nsofsimulation.Rotationofthearomaticringsandbendingofthemoleculesareobserved. 51

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Distributionofthetorsionangleofthetwo-ringsystemat10K(openbars)and300K(lledbars).At10K,thetorsionanglemeanis0.0withadistributionwidthof16.4.At300K,therotationalbarrieriseasilysurmountedandtherotationoftheringsisessentiallyfree. 52

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SnapshotsoftheNanostarMDat10Kduring20nsofsimulation Figure6-4. SnapshotsoftheNanostarMDat300Kduring20nsofsimulation 53

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Calculatedabsorptionspectraoftheindividualchromophores.Forthetwo-ringchromophore(A)thethree-ringchromophore(B)thefour-ringchromophore(C)andthecoreunit(D)at10K(solidlines)and300K(dashedlines). 54

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Experimentalandcalculatedspectraoftheindividualchromophores.Experimental(A)andcalculated(C)spectraat77Kand10K,respectively,forthetwo-(solidline),three-(dashedline)andfour-ringsystem(dottedline)andexperimental(B)andcalculated(D)spectraatroomtemperatureand300Kforthetwo-(solidline),three-(dashedline)andfour-ringsystem(dottedline). 55

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Calculatedelectronictransitionsoftheindividualchromophores.Forthetwo-ringsystemat10K(A)andat300K(B).Blacktransitionsrepresentrstsingletexcitedstatesandredtransitionsrepresentsecondsingletexcitedstates.Calculatedelectronictransitionsforthetwo-(black),three-(red),four-ring(green)andcoresystems(blue)at10K(C)andat300K(D).Eachdotcorrespondstooneofthe8000structuresoftheensemble. 56

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ExperimentalandcalculatedspectraoftheNanosta.Toppanel:experimentalabsorptionspectrumoftheNanostarat10K(A)and300K(B).Middlepanel:sumofexperimentalabsorptionspectraoftheindividualcomponentsat10K(C)and300K(D).Bottompanel:CalculatedabsorptionspectrafortheNanostarat10K(E)and300K(D). 57

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Oscillatorstrengthandwavelengthsscannedfrom0to90fortheouterandinnerringsofthethree-andfour-ringsystems. 58

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Energyleveldiagramforthetwo-,threeand2,3-ringsystems.HOMOandLUMOforthetwo-ringsystem(left),three-ringsystem(right)andatwo-ringsystemlinkedtothree-ringsystematthemetaposition(center). 59

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Azobenzenemolecules(Figure 7-1 )havebeenproposedascomponentsofalight-drivenmolecularswitch[ 97 ].Thefeaturethatmakesazobenzeneapromisingmoleculardeviceisthatithastwostableconformationsinitsgroundstate:cisandtrans[ 98 { 100 ]Azobenzenecanbeconvertedfromoneconformationtotheotherbyphoto-excitation.Abeamoflightwithawavelengthof365nmisomerizesthetransconformationtothecisconformationandasecondbeamoflightwithawavelengthof420nmreversestheisomerization(Figure 7-2 )[ 100 ].Thestructuralchangeoccursonanelectronicexcitedstate.Previouscalculationsshowedthatthetransconformationhasaconsiderablyhigherconductancethanthecisconformationatequilibrium(zerobias)[ 97 ]enablingtheuseoftheazobenzeneandpossiblyitsderivativesasasingle-moleculelight-drivenmolecularswitchwithONandOFFstatesrepresentedbythecisandtransconformations,respectively. Thetransconformationismorestableby0.6eV[ 101 ]andtheenergybarrierbetweentheconformationisabout1.6eV[ 102 ]Therefore,inthegroundstate,thermalrelaxationleadstoisomerizationfromcistotrans. Recentapplicationsoftheazobenzenemoleculeincludesitsuseasphoto-switchablemolecularglueforDNAtocontrolbiologicalfunctions[ 103 ],andasaionotropicreceptoringlutamatetocontrolionchannelsincells[ 104 ]. Inthiswork,westudytheeectsofchemicalsubstituentsontheconductanceofazobenzene.Experimentshaveshownthatsmalldierenceinmolecularstructurecanleadtogreatvariationsinconductanceandcurrent-voltagecharacteristics.Forexample,acomparisonofBenzenedithiolandBenzenedimethanethiolshowsthattheformerhasaconductanceof0.011G0whilethelatterhasaconductanceof0.0006G0(whereG0=2e2/h)[ 105 ]. 60

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106 ],andasubsequentimpactontheisomerizationmechanism. ExperimentsonarelatedseriesofmoleculeswereperformedbyVenkataramaetal.[ 107 ],inwhichconductancewasmeasuredinsubstitutedbenzenediaminemoleculeswithelectrondonatingandelectronwithdrawinggroups.Theexperimentaldatashowthatforthebenzenediaminemoleculeconnectedtogoldelectrodes,theelectrondonatinggroupsincreasetheconductance,whileelectronwithdrawinggroupsdecreaseit.TheresultswereexplainedbycomparingtheionizationpotentialandthealignmentoftheHOMOwithrespecttotheFermilevelofthegoldelectrodes. Huangetal.[ 108 ]presentedoneoftherstattemptsatatheoreticalinvestigationofchemicalsubstituentsinapotentialmolecularswitch.Theystudieddiarylethenederivativesusinganon-equilibriumGreen'sfunctionformalism(NEGF)withDensityFunctionalTheory(DFT).TheyfoundthatsubstitutingForSbyHorOledtoaremarkablechangeintheswitchingbehaviorunderabias. Tofunctionasaswitch,weconnecttheazobenzeneviatwolinkerCH2Sgroupstosemi-innitealuminumleads.Electron-donatinggroupsandelectron-withdrawinggroupsareincludedinmeta-andortho-positionswithrespecttotheazogroup.Para-substitutionsarenotconsideredasthecontactS-CH2groupsareinthatposition. 61

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Theazobenzenemolecule 62

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Isomerizationoftheazobenzenemolecule 63

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AsintroducedinChapter 3 ,theHartree-Fockmany-electron(N)wavefunctionisexpressedasanN-electronSlater-determinantcomposedofN-electronwavefunctionsthatenforcetheantisymmetryrequirement.Incontrast,althoughitalsoconsiderssingleelectronfunctions,DFTdoesnotattempttocalculatethefullN-electronwavefunction.Instead,DFTcalculatesanapproximationtothetotalelectronicenergyandtheelectronicdensitydistribution. 109 ].Thistheoremstatesthatitispossible,inprinciple,tocalculatethegroundstatewavefunctionandthereforethegroundstateenergy,ifthegroundstatedensityisobtained.Inotherwords,thereisaone-to-onemappingbetweenthegroundstateelectrondensityandthegroundstatewavefunction.Thisimpliesthattheenergyisauniquefunctionaloftheelectrondensity. InDFTtheenergyfunctionalisexpressedas, wherethersttermisthesumofthekineticenergyoftheelectronandtheinter-electronicinteractionsandthesecondtermistheinteractionoftheelectronswithanexternalpotential(Vext(r)).Usually,theexternalpotentialischosenastheCoulombicinteractionoftheelectronswiththenuclei.Aconstraintisplacedonthedensitytomaintainaxed 64

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wherethesubscriptVextindicatesthatthenucleiarexed.ItisimportanttonotethattheLagrangianmultipliercorrespondstothechemicalpotentialoftheelectrondensity. TheKohn-Shammethodology[ 110 ]proposesanapproachtosolveforF[(r)]as, wherethersttermistheKohn-Shamkineticenergy,thesecondtermistheelectron-electronCoulombicenergy,andthethirdtermcombinestheexchangeandcorrelationcontributions. TheKohn-Shamkineticenergyisthatofasystemwithnon-interactingelectronsandelectrondensityequaltothatinthephysicalsystem, 2r2(i(r)dr: 65

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2ZZ(r1)(r2) CombiningthepreviousequationsgivesthesolutionforanN-electronsystemas, 2r2i(r)dr+1 2ZZ(r1)(r2) Ascanbeseeninthisequation,theexchange-correlationenergyfunctionalEXC[(r)]containsnotonlytheexchangeandcorrelationcontributionsbutalsothedierencebetweenthetruekineticenergyandtheenergygivenbyEKE[(r)],sincethislatterquantityonlyconsidersnon-interactingelectrons. ThedensityisrepresentedaccordingtoKohnandShamas, Applyingthevariationalprincipleandincorporatingthepreviousdenitionofdensitygivestheone-electronKohn-Shamequation, 2r21MXA=1ZA wheretheexplicitexpressionfortheexternalpotentialhasbeenused,iaretheorbitalenergiesandVXCistheexchange-correlationpotentialenergyfunctional,whichisdenedas, 66

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ThesolutionoftheKohn-Shammethodisdeterminedviaaself-consistentprocedureinwhichaninitialdensityisguessed,andtheKohn-Shamequationsaresolvediterativelyuntilconvergenceisachieved.ChemicallyusefulresultsdependuponhavingasuitablyaccurateapproximationforEKE[(r)]. 111 { 113 ].Inamolecular-scaledevice,alloftheseassumptionsandapproximationsareinvalid,andtheelectronicstructureofthedevicemustbeconsideredexplicitly,sincetheelectronsarescatteredbyafewatomswhosespecicarrangementiscrucial. Inamolecularelectronicdevice,amolecule(orcluster)isconnectedtoacircuitwithatleasttwoterminals,orelectrodesatwhichtheboundaryconditionsaredened.Allsuchdevicesareopenquantumsystemswithrespecttoelectrontransport.Therefore, 67

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Althoughinprinciplemoleculescanbeconnectedtomorethantwoelectrodes,doingsocausestheproblemquicklytobecomecumbersome.Welimitourworktoasimplecircuitinwhichamoleculeisconnectedtotwoperfectsemi-inniteleads.Suchsystemsareusuallyconsideredbyasingle-particleballistictransportapproachwithinthelinear-responseregime.Thisisoneofthesimplestmodelsforelectrontransport.Itassumesthattheelectronstravelperfectlycoherentlythroughoutthedevice.Theelectronisscatteredbyastationary,spatiallyvaryingpotential,situatedbetweentwoelectronreservoirsrepresentedbythetwoelectrodes,whichactaswaveguidesfortheelectronwaves.Thereservoirssupplyelectronswithanequilibriumdistributionandatdierentchemicalpotentials;thedierenceisproportionaltotheappliedvoltagebias.Thetotaluxofelectronsistheelectroncurrentconductedbythedevice.Inthelinear-responseregime,nearthermodynamicequilibriumisassumed,withaverysmallvoltagedropacrossthedevice[ 112 113 ].Thisapproachallowstheuseofself-consistentelectronicstructurecalculations,usuallywithaDensityFunctionalmethod,forthegroundstateofthesystem.Linear-responsetheoryhasprovidedqualitativelycorrectdescriptionsofcurrent-voltagepropertiesuptoafewvolts[ 114 ].Movingbeyondthelinear-responseregimerequiresaself-consistentnon-equilibriumGreen'sfunctionformalism.Thishasbeenwidelyconsideredbyotherresearchers[ 53 115 ],andisthemethodusedinthisresearch. 114 116 { 118 ].Forthisregime,particularlyforsystemsthatconsistoftwoterminals,thesimplebutveryeectiveformulationbyLandauer[ 119 ]hasbeenthestartingpointandthebasisforprogressintheeld. TheLandauerformula;alsocalledthetwoterminalformula, 68

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expressestheconductance()intermsofthetotalelectrontransmissionprobability(T).ThetransmissioncanbeobtainedbysolvingthescatteringproblemviaaquantummechanicaltreatmentoftheSchrodingerequation.Thefactoroftwoisduetotheelectronspindegeneracyinthechannels. Thisequationassumesthatallinelasticprocessesoccurintheelectronreservoirsthatareconnectedtothedevice.Italsoassumesthatthetemperatureisequaltozeroandthatthereisaninnitesimalvoltagebias.Thisapproachhasbecomethestandardtheoreticalmodelforsingle-particleballistictransportwithinthelinear-responseregime. Incasesofmorethanonedimension,thetransmissionprobability,asButtikersuggested[ 120 ],canbeobtainedasthesumoftheindividualtransmissionprobabilitiesbetweentheentranceandexitBlochchannelsoftheelectronwaveguides.Inotherwords,thetransmissionprobabilityisthetraceofthetransmissionmatrix,whichcanberepresentedinthefollowingform, wherenandn'aretheBlochchannelsintheleads. 121 ],whichincludestheGreen'sfunctionsofthemolecule,whichisthelectronpropagatorinthedeviceregion,andtheself-energiesoftheleads,whichcontaintheeectsofthesemi-innitenano-wiresonthedeviceregion.TheCaroliformulacanbewrittenas, 69

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whereGistheGreen'sfunctionofthemoleculefortheHamiltonianoperator.Thesignsrepresenttheretarded(+)andadvanced()solutionsoftheGreen'sfunctionandindicatethataninnitesimalimaginaryparthasbeenaddedorsubtractedtotheenergyterm(Ei)respectively.ThefL;Rgisthebroadeningmatrixwhichisexpressedinthefollowingform: fL;Rg=i[+(L;R)(L;R)]: Inthisexpression,(L;R)representstheself-energytermsoftheleft(L)andright(R)semi-inniteleads. TheCaroliformularepresentsthetransmissionprobabilityintermsofthepropagationofanelectronthroughamolecule.TheGreen'sfunctionswillcontainalloftheinformationaboutthepropagationfromaninitialstate(anincomingwave)toanalstate(anoutgoingwave)afterpassingthroughthescatteringregion.Aconsiderationoftheself-energiesisnecessarybecausetheycontaininformationabouttheeectsofthesemi-inniteleadscoupledtothemolecule. 114 116 { 118 ].Thetheoryofmacroscopicsemiconductorsmustbemodiedtoincludetheelectronicstructureofthedeviceandtheeectsoftheinterfaceontheexternalcontact.Astricttreatmentofmolecularelectronicsdevicesmustincludethese 70

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112 113 122 ].TheimportantfeatureintheNEGFformalismistheconsiderationofinteractionsratherthanaballistictransportapproach.Itcombinesastatisticaldescriptionofthedissipativeinteractionsandquantumdynamics[ 112 113 122 123 ].PreviousworkwiththeNEGFformalismwasbasedonacombinationofquantummechanicaltransportwithmodelHamiltoniansandsemi-empiricalHamiltonians.Forexample,oneapproachusedasemi-empiricaltight-bindingformulation[ 124 ].Morerecently,mostpublishedworkisbasedontheNEGFcombinedwithdensityfunctionaltheory[ 123 125 126 ].Themostrecentattempttotreatsystemsoutofequilibriumusesabinitioelectronpropagatortheory.Propagatorshaveprovensuccessfulpreviouslyincalculatingspectraofclosedsystems[ 127 ],anditispossiblethatthisapproachcanspannon-equilibriumelectronicproperties,aswell[ 128 129 ]. Thesystemconsideredhereisconstructedintheusualthree-subsystemfashionfortwoterminalmoleculardevicesconsistingofaleftlead(orelectrode),rightlead(orelectrode)andacentralregionbetweenelectrodesasseeninFigure 8-1 .Thecentralregionisthedeviceregioninwhichthemoleculeislocatedandthescatteringprocessoccurs.Consideringonlynearest-neighborcoupling(thetight-bindingmodel)asseeninFigure 8-2 ,wecandeneatridiagonalmatrixinwhichtheonlynon-zeroelementsare, 71

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whereH0istheHamiltonianmatrixrepresentingtheinteractionswithinalayerintheelectrodes,andH1andH1representtheinteractionsbetweenneighboringlayersintheelectrodes.ThemoleculeisrepresentedbythesubscriptMandisassumedtointeractwiththenearestlayeroftheelectrodes.TheLandRsubscriptsrepresenttheleftandrightleadsrespectively. TheGreen'sfunctionoftheentiresystemis, [+SH]G+(E)=I; wherethe+signindicatesthataninnitesimalpositiveimaginaryfunctionhasbeenaddedtotheenergyterm(E+i),therefore,thepreviousequationdenesonlytheretardedGreen'sfunction.TheadvancedGreen'sfunctioniscalculatedastheadjointcomplexconjugateoftheretardedGreen'sfunction. TheexplicitformoftherstfactorontheleftsideofEquation( 8{15 )is, 72

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Therefore, andtheblockstructureoftheGreen'sfunctionis, SolvingfortheGreen'sfunctionofthemoleculesleadsto, wheretheself-energytermsaredeterminedasfollows, +L=M+MLG0+LM+LM; fortheself-energyoftheleftelectrodeand, 73

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fortheselfenergyoftherightelectrode.G0+LandG0+RaretheGreen'sfunctionsofthesemi-innitenano-wires(theleads)withoutthepresenceofthemolecule,usuallycalledthesurfaceGreen'sfunctions. Undernon-equilibriumconditionsitisassumedthattheeectofanexternalbiasisonlytoproducearigidshiftinthechemicalpotentialoftheelectrodes.Infact,though,thereisalsoachangeinthechargedistributioninthemolecule.TheHamiltonianofthemoleculeoutofequilibriumisnotknown,ingeneral.However,inthistreatmentitsdependenceonthedensityis,HM=HM[],sinceDFThasbeeninvoked. TheHamiltonianoftheentiresystembecomes, whereIistheidentitymatrixwithsamedimensionsofHLandHRandVistheappliedvoltage.NotethatthedimensionsofHLandHRarenotnecessarythesame,forexampleinthecaseofleadsmadewithdierentmaterial. Themostimportantphysicaltermistheelectrondensity,whichiscalculatedaccordingtothefollowingexpression, 2iZdEG
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Thenon-equilibriumformalismgivesthecorrectexpressionforthisfunctionundernon-equilibrium(biased)conditions.Thisfunctioncanbewrittenas, whereL=R=i[+L=RL=R],fistheFermidistributionfunctionandL=R=EfV=2,andVisanitebiasvoltage.Thedensitymatrixcanbesolveiterativelyinaself-consistentprocedure(seeFigure 8-3 )untilnumericalconvergenceisobtained.ThenthetransmissioncoecientTcanbecalculatedas andthecurrentcanbeobtainedfromtheintegralofthetransmissioncoecient, hZdETr[LGCRG+C][f(EL)f(ER)]: 130 131 ]code,whichincorporatesanon-equilibriumGreen'sfunction(NEGF)[ 112 113 122 ]formalismforquantumtransport.TheelectronicstructurecalculationswereperformedattheDensityFunctionalTheory(DFT)[ 110 ]level,basedontheSIESTApackage[ 132 ]. Figure 8-4 presentsthesystemsthatwereconsideredinthisresearch.Thegurepresentsallofthemolecules,alongwithashort-handcodethatwillbeusedinthisthesis 75

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8-4 Weoptimizedtheelectronicstructureoftheisolatedmolecules,usingdouble-zetasplit-valancenumericalbasicsetsuntiltheforceoneachatomwassmallerthan0.01eV/A.Wechoseanaluminum(111)crystallatticeasthestructureoftheleads.ThemoleculeisconnectedtotheleadsusingSCH2linkers.Aminimalsingle-zetabasisset[ 133 ]wasusedforthetransportcalculations.ThisbasisissucienttodescribethechannelsneartheFermienergyoftheleads,whicharethedominantchannelsforelectrontransport.Adouble-zetabasissetleadstosingularitiesinthematricesrequiredtoobtaintheGreen'sfunctions,andhencewasnotconsidered.Thelocaldensityapproximation(LDA)parameterizedinthePerdew-Zungerform[ 134 ]wasusedastheexchange-correlationfunctionalinallcalculations.TosampletheBrillouinzone,weuseda1132Monkhorsttypek-grid[ 135 136 ]fortheleadsandonlythegammapointforthedeviceregion.Finally,200Rywasusedastheenergycutofortherealspacegrid. 76

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Schematicofthelead-molecule-leadsystem.Thecentralregionisformedbyincludingatleastoneunitcellofeachlead. 77

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Tight-Bindingmodelforalead-molecule-leadsystem 78

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Non-EquilibriumGreen'sFunctionself-consistentdiagram 79

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Azobenzenederivatives.Labelsandstructuresoftheazobenzenederivativesconsideredinthiswork. 80

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9-1 Note,inTable 9-1 ,thatinthecaseoftheelectrondonatinggroups,theortho-substitutionsinduceahighertransmissionthanthemeta-substitutions.Inthecaseoftheelectron-withdrawinggroupsthispatternisnotobserved,andthemeta-substitutionsalwayshavehighertransmissioncoecientsthantheortho. Inthecaseofo-NO2-NH2andm-NO2-NH2,whichcontainbothanelectron-donatingandanelectron-withdrawinggroupthetransmissionislowerthanintheunsubstitutedazobenzenesystem.Thisresultindicatesthatthedominanteectderivesfromtheelectron-withdrawinggroupandtheorthosubstitution. Inthecaseofmoleculesinthecisconformationthepatternisdierent.Allelectron-donatinggroupsinducehighertransmissioncoecientsthantheunsubstitutedazobenzene.However,incontrasttothetranscase,someelectron-withdrawinggroupsalsoinducehigherconductancethantheunsubstitutedazobenzenesystem.Alloftheelectron-withdrawinggroupswithenhancedconductanceareinmeta-positions,andnoelectron-donatinggroupsdisplaylowerconductancethantheunsubstitutedazobenzene.TheseresultsarepresentedinTable 9-2 .Inthecaseofthemixedsystems,theo-NO2-NH2andm-NO2-NH2,theformerhasalowertransmissioncoecientthanthelatter. 81

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9-3 presentsthedierenceinthetransmissioncoecientatzerobiasbetweenthetransandcisconformationsforeachmolecule.Thiscomparisonprovidesareferenceforhowtheconductanceofapotentialmolecularswitchmightbemanipulated.Thedierencesthatarelargerthanthedierencebetweentheunsubstitutedazobenzenearethosewithelectron-donatinggroups:m-NH2,o-OCH3,o-NH2,o-CH3.Theremainingelectron-donatinggroupsandalloftheelectron-withdrawinggroupsdisplaydierencessmallerthanthedierenceintheunsubstitutedazobenzene. Theswitchingcharacteristicobservedfortheunsubstitutedazobenzeneprevailsforallsystemsstudied.Thatis,amajordierenceinconductanceisobservedbetweenthecisandthetransconformations.Thisoutcomewasexpectedsincethebreakintheconjugationfromthetranstothecisconformationistheprimaryfeatureresponsibleforthiselectronicfeature.Inthecaseofthetransconformations,sinceallofthestructuresareplanar,aclearpatternofelectron-donatingandelectron-withdrawingwasobserved,aswellasacleartrendbasedonthestrengthofthesubstituents.Inthecaseofthecisconformationsweobserveddeviationsinthepatternssincethepresenceofthesubstituentscanalsochangethegeometryofthehostazobenzenemolecule,particularlythetorsionalanglearoundtheazogroup(-N=N-).Smalldierencesinthecouplingandalignmentoftheleadsandmoleculecaneasilycausechangesofthemagnitudeobservedamongthevarioussubstituents. 9.2.1HighestOccupiedMolecularOrbitalEnergies 134 ]astheexchange-correlationfunctionaltype.Periodicboundary 82

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InTable 9-4 wepresenttheresultsofthecalculationsforthetransconformation.Asexpected,theelectron-donatinggroupsincreasetheenergyoftheHOMOwhiletheelectron-withdrawinggroupsdecreaseit.InregardtothedierencebetweentheHOMOandtheFermienergy,weobservethatthegroupswithahighertransmissioncoecientaretheoneswhoseHOMOenergiesareclosertotheFermienergy. InTable 9-5 wepresenttheresultsforthecisconformations.Wedonotobservethesamepatternaswedidwiththetransconformations.Nonetheless,weobserveapatternsimilartothatobtainedinthetransmissioncalculations. OurconclusionfromtheelectronicstructurecalculationsisthatthechangesintheHOMOenergiescausedbysubstituentsprovidesomeinformation,butarenotsucienttorepresentthechangesintheelectronicstructurecausedbyconnectiontosemi-inniteleads. TheLDOSwerecalculatedbyintegratingtheGreen'sfunctioninrealspaceinthedeviceregion: wherewechoose=0.04eV. TheLDOSresultsarepresentedinFigure 9-1 .Theleftpanelsdisplaytheresultsforthetransconformationsandtherightpanelspresenttheresultsforthecisconformations. 83

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9-1 A and 9-1 B ,showresultsfortheunsubstitutedazobenzenemolecule.Themiddlepanels,Figures 9-1 C and 9-1 D ,showresultsfortheo-OCH3system.Thebottompanels,Figures 9-1 E and 9-1 F ,presentresultsfortheo-NO2system. TheresultsinFigure 9-1 showthatinthetransazobenzenetheLDOSspreadsalongtheentiredeviceregion,whileinthecisconformationtheLDOSislocalizedatthealuminumleadsandthecontactregionbutnotinthebenzeneringsontheazobenzeneregion.Somedensityofstatescanalsobeobservedinthe-NN-region. Thecomparisonsbetweenthetransconformationsandthecisconformationsofthesubstitutedmoleculesaresimilartothoseobservedfortheunsubstitutedcase.Inthetransconformationthedensityofstatesspreadsalongthemainaxiswhileinthecisconformationsalesslocalizeddensityofstatesisobserved.Theseresultswereexpectedsinceconjugationisbrokeninthecisconformations,leadingtoalowerdensityofstatesintheseregions. Themostilluminatingresultsareobtainedbycomparingtheeectsofthesubstituents.Forthetransconformation,inthecaseoftheelectron-donatinggroup,thedensityofstatesisnotaslargeinthesubstituentregionasintheazobenzeneregion,andislocatedprimarilyonthe-NN-group.Inthecaseoftheelectron-withdrawinggroup,asignicantdensityofstatesisobservedinthesubstituentregions.Thedensityofstatesisslightlydiminishedinthe-NN-region. Forthecisconformations,theelectron-donating-substitutedmoleculedisplaysasimilardensityofstatesastheazobenzenesystem,butaremarkabledierenceisobservedinthecaseoftheelectron-withdrawinggroupsubstitutedmolecule.Ahigherdensityofstatesispresentintheregionofthebenzenerings,but,thedensityisnotdelocalized,asitisinthecaseofthetransconformation. WealsoperformedananalysisoftheProjectedDensityofStates(PDOS)forthesystemsdiscussedabove.ThetoppanelofFigure 9-2 presentsthePDOSintheazobenzeneregionforthecisandtransconformations.Asthegureshows,thePDOS 84

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ThemiddlepanelofFigure 9-2 comparesthedensityofstatesprojectedintheazobenzeneregionforthetransconformationsoftheunsubstitutedazobenzene,andtheo-OCH3ando-NO2substitutedmolecules.ThegureshowsthatintheunsubstitutedazobenzenethePDOSishigherthanthatintheothertwosystems,andthePDOSfortheo-NO2inthisregionisthelowest.AtenergieshigherthantheFermienergyoftheelectrodes,itisclearthatthePDOSoftheo-NO2systemissignicantlylower,whichdecreasesthetransmissionaccordingly,sincefewerenergystatesforconductionareavailable.Theelectron-donatinggroupalsopresentsalowerPDOSthantheunsubstitutedazobenzenesystem,butdisplaysabroaderdistributionofstates. TheresultsforthePDOSfortheazobenzenemoleculeregionforthecisconformationsoftheazobenzenesystem,o-OCH3ando-NO2areshowninthebottompanelofFigure 9-2 .ThePDOSoftheo-NO2moleculeattheFermilevelishigherthanthatoftheothertwosystems,whileo-OCH3hasalowerPDOSattheFermilevel.IfwecomparetheseresultswiththetransmissionvaluesattheFermilevelshowninTable 9-2 ,inwhichtheorderisinverted,wecanconcludethatahigherPDOSdoesnotnecessaryimplyhighertransmission.AnotherpossiblereasonforthedierencesinthePDOSisrelatedtosmallchangesinthegeometry.Inthetransconformationcasesthemoleculesremainplanar,whileinthecisconformationcasesthemoleculesarenotplanarandthepresenceofasubstituentcausessmallchangesinthetorsionanglebetweenthebenzenerings,andhencesmallchangesinthePDOS. 85

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9-3 showtheelectronicdensityofstatesprojectedinthesubstituentregionofthetrans(toppanel)andcis(bottompanel)conformations.Intheseplotswecompareonlytheo-NO2ando-OCH3molecules,sincetheazobenzenesystemdoesnotcontainasubstituentregion.Theresultsaresimilartothosepresentedaboveforbothcases,withthesubstituentregionscontainingahigherdensityofstatesfortheo-NO2molecule,inaccordwithitsfunctionasanelectron-withdrawinggroup. AnimportantpointtonoteaboutthePDOSresultsisthatthemostrelevantdierencesintheelectronicstructureareinthecentralregioncontainingthemolecules,andnotinthealuminumleadsorthecontactregion.ThePDOSoftheelectrodesandcontactsatequilibriumarealmostidentical.Therefore,anydierencesinthetransportpropertiesarerelateddirectlytothechemistryofthemolecularregions,andadirectreectionoftheeectsofsubstituents. Figure 9-4 presentstheresultsfortheunsubstitutedazobenzenesystem.Acleardierencebetweentransandcisconformationsisobserved.Thetransconformationhasaconsiderablyhighercurrentatallbiasvoltages.AninterestingregionoftheI-Vcurvesforthetransconformationisobservedbetween0.42and0.48V.Therethecurrentremainsalmostconstant.Forthecisconformation,thecurrentdecreaseswhenthevoltageisincreasedbetween0.21and0.24V.Thisfeature,referredtoasnegativedierential 86

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Figures 9-5 and 9-6 presentresultsforthem-CH3ando-CH3systems,respectively,andacomparisonwiththeazobenzenesystem.Thiselectron-donatinggroup,whenpresentinthemetapositiondisplaysI-Vcharacteristicssimilartothatoftheunsubstitutedazobenzenesystem,especiallyatbiasvoltageslowerthan0.4V.Thecism-CH3systemdoesnotdisplayNDC.At0.4Vthetransm-CH3systembeginstoshowalowercurrentincrementthantheunsubstitutedsystem.Fortheo-CH3systems,bothconformationsdisplayahighercurrentthantheunsubstitutedsystem,andtheciso-CH3doesexhibitNDCnearthesamerangeofbiasvoltagesasthecisunsubstitutedazobenzene.Thisresultindicatesthatbothsystemshavesimilarchangesinelectronicstructurechangesasthebiasisincreased. Figures 9-7 and 9-8 presentresultsforthem-OCH3ando-OCH3systems,respectively,andacomparisonwiththeazobenzenesystem.Ingeneral,inbothconformationsthecurrentofthesubstitutedsystemsishigherthantheunsubstitutedsystems,exceptforthecism-OCH3system,whichdisplaysanalmostidenticalI-Vcurveasthecisunsubstitutedsystem.Theorthosubstitutionresultsinalargerenhancementofthecurrent. Figures 9-9 and 9-10 presentresultsform-Clando-Cl,respectively,andacomparisonwiththeunsubstitutedazobenzenesystem.Fortheseelectron-withdrawingsubstituentsbothtransandcisconformationdisplayalowercurrentthantheazobenzenesystem.Thecurrentforbothconformationsisalsolowerinthecaseoforthosubstitution.Theswitchingcharacteristicisalmostnonexistent,especiallyfortheorthosubstitution. Figures 9-11 and 9-12 presentresultsforthem-CF3ando-CF3systems,respectively,andacomparisonwiththeunsubstitutedazobenzenesystem.Themetasubstitutionenhancesthecurrentforthetransconformationwhileitsuppressesitforthecisconformation.Theorthosubstitutionsuppressesthecurrentforbothconformations.BothsubstitutedsystemsinthecisconformationdisplayNDCinsimilarbiasranges, 87

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Figures 9-13 and 9-14 presentresultsforthem-Fando-Fsystems,respectively,andacomparisonwiththeunsubstitutedazobenzenesystem.Thetransconformationofthesubstitutedsystemsdisplayslowercurrentthantheunsubstitutedsystem.Forbothsubstitutionsites,thecurrentofthecisconformationsisalmostcompletelysuppressed. Acomparisonbetweentheunsubstitutedazobenzenesystemandthe-CNsubstitutedsystemsispresentedinFigures 9-15 and 9-16 forthemetaandorthositessubstitutions,respectively.Thiselectron-withdrawinggrouplowersthecurrentforbothconformationswithrespecttheunsubstitutedsystem.Thesiteofthesubstitutiondoesnotcausearemarkabledierence, Acomparisonbetweentheunsubstitutedazobenzenesystemandthe-NO2substitutionispresentedinFigures 9-17 and 9-18 forthemetaandorthosubstitutions,respectively.Fortheseelectron-withdrawingsubstituents,bothtransandcisconformationsdisplaylowercurrentsthantheazobenzenesystem.Thesuppressionofthecurrentishigherinthetransmolecules.BothsubstitutedsystemsinthecisconformationsdisplayNDCnearthesameregionastheazobenzenesystem,overaslightlybroaderrange.Averysmalleectisobservedinthelocationofthesubstituent. Figures 9-19 and 9-20 presentresultsforthem-NH2ando-NH2systems,respectively,andacomparisonwiththeunsubstitutedazobenzenesystem.Ingeneral,thetransconformationsdisplayahighercurrentthantheunsubstitutedazobenzenesystem.Thehighestcurrent,amongallthesystems,isobservedfortheNH2substitutionintheorthoposition.Forthemetasubstitutedmoleculeinthecisconformationalowercurrentcomparedtothecisunsubstitutedazobenzenesystemisobserved,whichindicatesthatthissystemdisplaysanincreaseddierenceinthecurrentbetweenthecisandtransconformations.NDCfortheciso-NH2systemisobservedinasimilarbiasrangeasthe 88

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Figures 9-21 and 9-22 presentresultsforo-NO2-NH2andm-NO2-NH2,respectively,andacomparisonwiththeunsubstitutedazobenzenesystem.Inbothcases,asobservedinthecaseofzerobias,theeectoftheelectron-withdrawinggroupprevails,withaslightlylargereectatthemetasubstitution. 89

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Transmissioncoecientfortransmolecules MoleculeT o-NH20.883m-NH20.858o-OCH30.840m-OCH30.839o-CH30.834m-CH30.828azobenzene0.825m-CF30.808o-CF30.808o-NO2-NH20.801m-F0.776m-NO2-NH20.772o-F0.768m-Cl0.753m-NO20.753m-CN0.748o-Cl0.742o-CN0.738o-NO20.732 90

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Transmissioncoecientforcismolecules MoleculeT/102 91

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Dierencebetweentransandcistransmissioncoecients MoleculeTtranscis 92

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HighestOccupiedMolecularOrbitalenergyoftransmoleculesineV MoleculeEHOMO 93

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HighestOccupiedMolecularOrbitalenergyofcismoleculesineV MoleculeEHOMO 94

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LocalDensityOfStatesofrepresentativesystems.LDOSinthedeviceregionsforthetrans(leftgures)andcis(rightgures)conformationsoftheazobenzenesystem(toppanel),o-OCH3system(middlepanel)ando-NO2system(bottompanel).ThecontouristakeatLDOSof1:0x104. 95

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ProjectedDensityOfStatesintheazobenzeneregionofrepresentativesystem.ComparisonoftheProjectedDensityOfStatesintheazobenzeneregionbetween,toppanel:thetransandcisconformationsoftheunsubstitutedazobenzenesystem,middlepanel:thetransconformationsoftheunsubstitutedazobenzene,o-OCH3ando-NO2systems,andbottompanel:thecisconformationsoftheunsubstitutedazobenzene,o-OCH3ando-NO2systems. 96

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ProjectedDensityOfStatesinthesubstitutionregionofrepresentativesystems.Forthetrans(toppanel)andcis(bottompanel)conformations 97

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Current-Voltagecharacteristicsoftheazobenzenesystemfortransandcisconformations. 98

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Current-Voltagecharacteristicsofthem-CH3system.ComparisonbetweentheI-Vcharacteristicsoftheazobenzenesystemandthem-CH3system 99

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Current-Voltagecharacteristicsoftheo-CH3system.ComparisonbetweentheI-Vcharacteristicsoftheazobenzenesystemandtheo-CH3system 100

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Current-Voltagecharacteristicsofthem-OCH3system.ComparisonbetweentheI-Vcharacteristicsoftheazobenzenesystemandthem-OCH3system 101

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Current-Voltagecharacteristicsoftheo-OCH3system.ComparisonbetweentheI-Vcharacteristicsoftheazobenzenesystemandtheo-OCH3system 102

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Current-Voltagecharacteristicsofthem-Clsystem.ComparisonbetweentheI-Vcharacteristicsoftheazobenzenesystemandthem-Clsystem 103

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Current-Voltagecharacteristicsoftheo-Clsystem.ComparisonbetweentheI-Vcharacteristicsoftheazobenzenesystemandtheo-Clsystem 104

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Current-Voltagecharacteristicsofthem-CF3system.ComparisonbetweentheI-Vcharacteristicsoftheazobenzenesystemandthem-CF3system 105

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Current-Voltagecharacteristicsoftheo-CF3system.ComparisonbetweentheI-Vcharacteristicsoftheazobenzenesystemandtheo-CF3system 106

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Current-Voltagecharacteristicsofthem-Fsystem.ComparisonbetweentheI-Vcharacteristicsoftheazobenzenesystemandthem-Fsystem 107

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Current-Voltagecharacteristicsoftheo-Fsystem.ComparisonbetweentheI-Vcharacteristicsoftheazobenzenesystemandtheo-Fsystem 108

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Current-Voltagecharacteristicsofthem-CNsystem.ComparisonbetweentheI-Vcharacteristicsoftheazobenzenesystemandthem-CNsystem 109

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Current-Voltagecharacteristicsoftheo-CNsystem.ComparisonbetweentheI-Vcharacteristicsoftheazobenzenesystemandtheo-CNsystem 110

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Current-Voltagecharacteristicsofthem-NO2system.ComparisonbetweentheI-Vcharacteristicsoftheazobenzenesystemandthem-NO2system 111

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Current-Voltagecharacteristicsoftheo-NO2system.ComparisonbetweentheI-Vcharacteristicsoftheazobenzenesystemandtheo-NO2system 112

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Current-Voltagecharacteristicsofthem-NH2system.ComparisonbetweentheI-Vcharacteristicsoftheazobenzenesystemandthem-NH2system 113

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Current-Voltagecharacteristicsoftheo-NH2system.ComparisonbetweentheI-Vcharacteristicsoftheazobenzenesystemandtheo-NH2system 114

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Current-Voltagecharacteristicsofthem-NO2-NH2system.ComparisonbetweentheI-Vcharacteristicsoftheazobenzenesystemandthem-NO2-NH2system 115

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Current-Voltagecharacteristicsoftheo-NO2-NH2system.ComparisonbetweentheI-Vcharacteristicsoftheazobenzenesystemandtheo-NO2-NH2system 116

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Wehaveperformedtheoreticalinvestigationsoftwopromisingmolecularwires,theNanostardendrimerandazobenzenederivativesconnectedtoaluminumelectrodes. TheNanostardendrimer,therstsubjectinthisresearch,hasbeenshowtotransferelectronicenergyfromtheperipherytothecorewithhigheciency.Thissystemmaynduseinthefutureasthebasisforanalternativeenergysource,iftheenergycollectedcanbeusedtoproduceelectricityortoperformotherchemicalfunctions.Todesignsuchapplications,itiscrucialtounderstandthedetailedmechanismbywhichthissystemabsorbslight,andhowthisprocessisaectedbytemperature. ThetheoreticalelectronicspectraoftheNanostarwereobtainedusingasequentialMolecularDynamics/QuantumMechanicsZINDO/Smethod.ThetemperaturedependenceoftheelectronicspectraoftheNanostarwasobservedandanalyzed.Thetheoreticalresultsobtainedbythismethodcorrespondwellwithexperimentaldata.Weaddressedtheissueofconformationalmobilityanditsspectroscopicsignature. Wendthatintheabsorptionprocesstheexcitationsarelocalizedonchromophoresseparatedbymetasubstitutions.Asaresult,theNanostarcanbeconsideredasthesumofseparatephenylene-ethynyleneunits,whichinclude24two-ringsystems,4three-ringsystemand2four-ringsystems.ThecoreoftheNanostarisanindependentethynylperyleneunitbondedtoanaromaticring. At10K,theNanostarexhibitslittledynamicalmotion.Freerotationoftheringsleadingtoanon-planarstructureisnotobserved,andthebranchestendtoseparatefromoneanotherduetostericeects.At300Kthebranchesseparatefromeachotherandfreerotationofthephenylringsisobserved. At10K,eachofthethreemainabsorptionpeakscorrespondsdirectlytooneofthechromophores.Thepeakattheshortestwavelengthcorrespondstothetwo-ringsystem,followedbypeaksforthethree-andfour-ringsystemsatlongerwavelengths.Aweakpeak 117

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At300K,thespectraoftheindividualchromophoresarebroader,andthethree-andfour-ringsystemsareblue-shifted(11and21nm,respectively),resultinginaspectrumwithonemajorpeakandashouldercontainingcontributionsfromallthreesystems.Additionalconformationsareaccessibleasthenumberofringsandthelengthofthemoleculeincreases.Thetwo-ringsystemhasfewerconformations,andtheyarenotdierentenoughtocauseconsiderabledisplacementofwavelengthmaximum.Inthecaseofthethreeandfour-ringsystemstherotationsoftheringscausethemoleculetobehaveasaunionofsmallersystemsthatabsorbathigherenergy.Thedisplacementsaresucientlylargetocausetheformationofashoulderinthespectrum.Duetothepresenceofmanydierentconformationswithdierentabsorptionwavelengthsandtransitionintensitiesat300K,theelectronictransitionsarenotlocalized.Instead,theyaredispersedoverawideenergyrange,whichcausesbroadeningaswellasdisplacementoftheabsorptionbands. Wealsopresentedtheresultsofastudyontheeectsofchemicalsubstituentsonthetransportpropertiesoftheazobenzenemolecule,inaneorttopredictstructuresthatmayhaveoptimizedpropertieswithslightlydierentchemicalstructures.Azobenzenehasbeenproposedasapotentialmolecularelectronicdevice,inparticularaphoto-inducedmolecularswitch.Thefeaturethatmakesazobenzeneapromisingmoleculardeviceisthatithastwostableconformationsinitsgroundstate:cisandtrans[ 98 { 100 ]andcanbeconvertedfromoneconformationtotheotheronebyphoto-excitation.Previouscalculationsshowedthatthetransconformationhasaconsiderablyhigherconductancethanthecisconformationatequilibrium(zerobias)[ 97 ]enablingtheuseoftheazobenzeneandpossiblyitsderivativesasamolecularswitchwithONandOFFstatesrepresentedbythecisandtransconformations,respectively. 118

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Forthetransconformations,themagnitudeoftheconductancefollowstheorderthatisknownasactivating(relatedtoelectron-donating)anddeactivating(relatedtoeectsofelectron-withdrawing)groupsinorganicchemistrywhere-NH2isastrongactivatorfollowedby-OCH3.Thegroup-CH3isaweakactivator,halogensareweakdeactivatorsandthedeactivatorsincreaseinstrengthinthefollowingorder:-CF3,-CNand-NO2.Thepatternobservedismoreregularinthe-orthosubstitutionthaninthe-meta.Thepatternisnotobservedclearlyforthecisconformations. OurresultsareinagreementwiththeexperimentsperformedbyVenkataramaetal.,[ 107 ],whichshowedthatforthebenzenediaminemoleculeconnectedtogoldelectrodes,theelectrondonatinggroupsincreasetheconductance,whileelectronwithdrawinggroupsdecreasetheconductance. Anelectronicstructureanalysisatzerobiasrevealedthattheelectron-donatinggroupsincreasetheavailablechannelswithinthedeviceregion,whiletheelectron-withdrawinggroupshavetheoppositeeect.Wealsoobservedthatthecontactandleadregionsareingeneralnotaectedbythepresenceofthesubstituents,whichallowedustoconcludethatallobserveddierencesinthetransportpropertiesareadirectresultofthepresenceofthesubstituents. Atnite-bias,theelectron-donatinggroupsingeneralenhancethecurrentwhiletheelectron-withdrawinggroupssuppressit.Thispatternisclearatverylowbias(lowerthan 119

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Theresultsindicatethatthetransportpropertiesinelectronicdevicesatthemolecularlevelcanbemanipulated,enhancedorsuppressedbyacarefulconsiderationoftheeectsofchemicalmodication.Theresultsalsoshowthatcalculationsperformedonlyatzero-biasarenotsucienttoobservetherichchemistrypresentinsuchdevices.Thepromiseofmolecularelectronicsistousemoleculestoperformelectronicfunctionsinnon-equilibriumconditions.Asthisworkindicates,thebehavioratzerobiasisnotnecessarythesameasitisoutofequilibrium,undertruedeviceconditions. Inthisdissertationwehavepresentedtheresultsofresearchperformedintwomolecularwires,theNanostardendrimerandmolecularelectronicsbasedonazobenzenederivatives.TheNanostardendrimerisacandidatesystemforthefutureofalternateenergysourcesanditiscrucialtounderstanditsabsorptionprocesssinceenergy,thatcanbeusedtoproduceelectricityforinstance,canbecollectedwithit.Wehavepresentedatheoreticalinvestigationandanalysisofsuchabsorptionprocessandwehaveworkedcloselywithexperimentaliststoconrmouranalysisandresults. Forthefutureofnewtechnologiesitisimportanttobeabletomanipulateelectrontransportpropertiesofmolecularscaledeviceandwehavepresentedawaytodosowithsimplechemicalalterationsinmolecularstructures.Wehaveshownthatresearchperformingonlyelectronicstructurecalculationsorelectrontransportcalculationsinequilibriumconditionsisnotsucientsinceinrealityanyfutureuseofmolecularelectronicswillbeinnon-equilibriumconditions.Thereforefutureresearchisnecessary 120

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Withthistwosystemswehavealsogoneonestepfurtherintheintegrationofarealisticopto-electronicdevice,asystemthatisphoto-sensitiveandbasedonafastlight-drivenprocess.Forinstance,anelectroniccircuitintegratedwithanantennabasedonadendrimerandamoleculewithmultiplestablestatesanddierenttransportproperties,inourcasetheNanostardendrimerandtheazobenzenemoleculesrespectively. Withthesestudieswenotonlyexpecttocontributewithfundamentalresearchinthefutureofnewtechnologiesandalternativeenergysourcesbutalsotomotivatefutureexperimentalworkbasedonthesystemsinvestigatedonthiswork. Iwouldliketonishaddressingagaintheproblemsthatwefaceintherstdecadeofthe21stcentury:energy,environmentalandnancialcrisis.Iampositivethatthenextsurgeofeconomicaldevelopmentwillcomefrominnovationswhichwillbeaccomplishedthroughfundamentalresearch,liketheresearchpresentedhere. 121

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JulioLeopoldoPalmaAndawasborninOctober25,1981inMexicoCity.Atage14hebeganhishighschoolstudiesattheMonterreyInstituteofTechnologyandHigherEducation(commonlyknownbyitsCastillianacronym,ITESM)CampusMexicoCity.Duringhishighschoolyearsherealizedhewantedtopursueadegreeinchemistry.Atage17hemovedtoMonterrey,NuevoLeon,MexicotostudyChemicalSciencesatITESMCampusMonterrey.DuringhisjunioryearhehadtheopportunityofaresearchexperienceattheQuantumTheoryProject(QTP)oftheUniversityofFlorida(UF)whereheperformedresearchonporphyrin-dendrimersunderthesupervisionofDr.AdrianE.Roitberg.DuringthosemonthshedecidedtoapplytothegraduateprograminchemistryatUFwherehemovedafterobtaininghisB.S.inChemicalSciencesinDecemberof2003.DuringhisgraduateprogramheworkedunderthesupervisionofDr.JereyL.Krause,Dr.Hai-PingChengandDr.AdrianE.Roitbergontheoreticalstudiesofrelevantsystemsforthefutureofnanotechnologyandalternativeenergysources.HereceivedhisPh.D.fromtheUniversityofFloridainthespringof2009.Julioisalsoamarathonrunnerandhisgoalsaretobecomeabetterrunneraswellasagoodscientist. 132