ucl discovery - ucl discovery · 3 abstract in this ph.d. project, i introduce a new computational...

Modellingthephotochemical

propertiesofconjugated

oligomers;understandingtheir

applicationasphotocatalysts

PierreGuiglion

PrimarySupervisor:Dr.MartijnZwijnenburg

Secondarysupervisor:Prof.FurioCorà

UniversityCollegeLondon

DepartmentofChemistry

ThesissubmittedforthedegreeofDoctorofPhilosophy

February2017

2

I,PierreGuiglion,confirmthattheworkpresentedinthisthesisismyown.Where

information has been derived from other sources, I confirm that this has been

indicatedinthethesis.

PierreGuiglion

February2017

3

Abstract

InthisPh.D.project,Iintroduceanewcomputationalmethodology,basedon(time-

dependent) Density Functional Theory ((TD-)DFT), in order to determine if a

molecule,hereaconjugatedoligomer,hastherequiredphotochemicalpropertiesto

drive thermodynamically one or both water splitting half-reactions. This new

approach takes electronic excitations into account rather than only relying on a

staticHOMO-LUMOdescriptionoftheelectronicstructure,andthereforeprovidesa

morerigorouspredictionofrelevantthermodynamicpotentialsthanground-state

DFT alone; it offers a relatively quick way of consistently screening for new

photocatalystsforsolar-drivenwatersplitting.

Usingthiscomputationalframework,Iinvestigatetheopticalpropertiesofoligo(p-

phenylene), one of the simplest conjugated oligomers imaginable, as well as its

thermodynamic potentials, relevant to the splitting of water into molecular

hydrogen and oxygen. I then validate the methodology by confronting it to

experimentaldata,beforeapplying it toawiderangeofconjugatedoligomers, to

determine whether or not they could be promising photocatalysts for water

splitting, be it for theproductionofmolecularhydrogen, oxygen gas, or both. In

particular,Iexposethereasonsfortheexperimentallackofoverallwatersplitting

usuallyobserved,andmoreparticularly,theinabilityofmanymaterialstooxidise

water.

Aside from purely photocatalytic considerations, I also discuss the optical

properties of those oligomers and polymers, as they are tightly linked to their

photocatalytic performance, with a particular emphasis on p-phenylene. I

consistently study its three main isomers in order to shed some light into the

relationship between their molecular structures and absorption/fluorescence

spectra,andfindtheoriginofthedramaticdifferenceinthefeaturesexhibitedby

the latter, using a single computational approach, which, to the best of my

knowledge,hasneverbeendonebefore.

TableofcontentsAbstract....................................................................................................................3

Tableofcontents.......................................................................................................4

Listofabbreviations..................................................................................................7

Listoffigures...........................................................................................................10

Listoftables............................................................................................................13

Listofpublications..................................................................................................14

CHAPTER1:Introduction.........................................................................................15

1.1.Photocatalyticwatersplitting...................................................................................16

1.2.Inorganicphotocatalysts...........................................................................................19

1.3.Conjugatedoligomersandpolymers.........................................................................211.3.1.Linearconjugatedpolymers....................................................................................221.3.2.Carbonnitridematerials..........................................................................................251.3.3.ConjugatedMicroporousPolymers.........................................................................27

1.4.ObjectivesofthisPh.D.project.................................................................................32

1.5.References................................................................................................................34

CHAPTER2:Theoreticalfoundations.......................................................................39

2.1.DensityFunctionalTheory(DFT)...............................................................................402.1.1.Thomas-Fermimodel...............................................................................................412.1.2.Hohenberg-Kohntheorems.....................................................................................422.1.3.Kohn-Shamapproach..............................................................................................432.1.4.Functionals...............................................................................................................462.1.5.Basissets..................................................................................................................47

2.2.Time-DependentDensityFunctionalTheory.............................................................502.2.1.Formalism................................................................................................................502.2.2.Adiabaticapproximation.........................................................................................522.2.3.Strengthsandlimitationsof(TD-)DFT.....................................................................52

2.3.Coupled-cluster........................................................................................................54

2.4.Conductor-likescreeningmodel...............................................................................56

2.5.Conformationalsearch.............................................................................................58

2.6.References................................................................................................................60

Tableofcontents

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CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater..........................62

3.1.MotivationandLiteraturereview.............................................................................63

3.2.Modellingthepolymerandsacrificialreagents.........................................................663.2.1.Modellingthepolymer............................................................................................663.2.2.Modellingthepotentialsofwaterandsacrificialelectrondonors..........................70

3.3.Computationalmethodology....................................................................................72

3.4.Resultsanddiscussion..............................................................................................743.4.1.PPPmodelanditsopticalproperties.......................................................................743.4.2.Probingtheinfluenceoftheenvironment..............................................................753.4.3.Excitondissociation.................................................................................................783.4.4.Understandingtheeffectofoligomerlength..........................................................803.4.5.AssessingthewatersplittingpotentialofPPP........................................................82

3.5.Conclusions..............................................................................................................85

3.6.References................................................................................................................86

CHAPTER4:Confrontingtheoreticalpredictionstoexperimentaldata....................90

4.1.MotivationandLiteraturereview.............................................................................91

4.2.Computationalmethodology....................................................................................94

4.3.Resultsanddiscussion..............................................................................................954.3.1.Ionisationpotentials................................................................................................954.3.2.Electronaffinities...................................................................................................1004.3.3.Excited-statepotentials.........................................................................................102

4.4.Perspectives............................................................................................................103

4.5.Conclusions.............................................................................................................104

4.6.References...............................................................................................................105

CHAPTER5:BeyondPPP;screeningforsuitablephotocatalysts.............................109

5.1.MotivationandLiteraturereview............................................................................111

5.2.Resultsanddiscussion.............................................................................................1145.2.1.Fluorene-basedoligomersandderivatives............................................................1145.2.2.Conjugatedmicroporouspolymers.......................................................................1185.2.3.Linearconjugatedoligomers.................................................................................1245.2.4.Carbonnitride........................................................................................................129

5.3.Conclusions.............................................................................................................135

5.4.References...............................................................................................................137

Tableofcontents

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CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP.....139

6.1.MotivationandLiteraturereview............................................................................140

6.2.Computationalmethodology...................................................................................142

6.3.Resultsanddiscussion.............................................................................................1446.3.1.Structuralmodels..................................................................................................1446.3.2.Predictingtheeffectofisomertypeandoligomerlengthonopticalgaps...........1466.3.3.Linkingstructure,topology,andopticalgap.........................................................1486.3.4.Investigatingtheeffectofexcitedstatelocalisationonfluorescenceenergies....1526.3.5.Instabilityofo-terphenyl.......................................................................................1596.3.6.Understandingthefundamentaldifferencebetweeno-andp-phenylene...........160

6.4.Conclusions.............................................................................................................163

6.5.References...............................................................................................................164

CHAPTER7:Summaryandperspectives.................................................................168

Acknowledgements...............................................................................................172

Listofabbreviations

2PPE:two-photonphotoelectronspectroscopy

B3LYP:hybridXCfunctional,whichincorporates20%ofHF-likeexchange

BHLYP:hybridXCfunctional,whichincorporates50%ofHF-likeexchange

CAM-B3LYP:longrangecorrectedB3LYPusingtheCoulomb-AttenuatingMethod

(19%HF-likeexchangeatshortrangeand65%atlongrange)

CB:conductionband

CC:coupled-cluster

CC2:approximatecoupled-clusterssingles-and-doublesmethod

CGF:contractedGaussianfunction

CMP:conjugatedmicroporouspolymer

CN:carbonnitride

COSMO:conductor-likescreeningmodel

CT:charge-transfer

CTF:covalenttriazineframework

CV:cyclicvoltammetry

Cz:carbazolemoiety

DBT:dibenzothiophene

DBTsulf:dibenzothiophenesulfone

DCM:dichloromethane

DEA:diethylamine

def2-SVP:split-valencepluspolarisation

def2-TZVP:triplezetasplit-valencepluspolarisation

DFT:densityfunctionaltheory

DFT-D3orDFT+D:DFTplusGrimme’sdispersioncorrection

DZP:doublezetapluspolarisation

EA:electronaffinity

EA*:excitedstateelectronaffinity

EBE:excitonbindingenergy

Listofabbreviations

8

ESSE:excitedstatestabilisationenergy

Fl:fluorenemoiety

GGA:generalisedgradientapproximation

GS:groundstate

GSDE:groundstatedestabilisationenergy

GTO:Gaussian-typeorbitals

H/C:hydrogen-to-carbonratio

HER:hydrogenevolutionrate

HF:Hartree-Fock

HOMO:highestoccupiedmolecularorbital

IP:ionisationpotential

IP*:excitedstateionisationpotential

KS:Kohn-Sham

LCAO:linearcombinationofatomicorbitals

LDA:localdensityapproximation

LUMO:lowestunoccupiedmolecularorbital

LVEE:lowestverticalexcitationenergy

OER:oxygenevolutionrate

P3HT:poly(3-hexylthiophene)

PBC:periodicboundaryconditions

PES:photoelectronspectroscopy

PF:polyfluorene

PFur:polyfuran

Ph:phenylenemoiety

PPP: poly(p-phenylene), or more generally any p-phenylene chain including

oligomers

PPV:poly(phenylenevinylene)

PPyra:polypyrazine

PPyri:polypyridine

PPyrim:polypyrimidine

PPyrr:polypyrrole

PT:polythiophene

S0:singletgroundstate

Listofabbreviations

9

S1:singletfirstexcitedstate

SCE:standardcalomelelectrode

SCF:self-consistentfield

SEA:sacrificialelectronacceptor

SED:sacrificialelectrondonor

SHE:standardhydrogenelectrode

SHEAP:SHEabsolutepotential

STO:Slater-typeorbitals

TD-DFT:time-dependentDFT

TDA:Tamm-Dancoffapproximation

TEA:triethylamine

UV:ultraviolet

UV-Vis:ultraviolet-visiblespectroscopy

VB:valenceband

WS:watersplitting

XC:exchange-correlation

ListoffiguresFigure1.1:Mainprocesses inphotocatalyticwatersplitting,andexcitationofanelectronfromamaterial’svalencebandtoitsconductionband.....................................17Figure 1.2: Scheme outlining the required properties that a photocatalystmusthavetodrivewatersplitting............................................................................................................18Figure1.3:Alignmentofthebandpositionsofvarioussemiconductorswithrespecttotheredoxpotentialsofwatersplitting...................................................................................20Figure1.4:MolecularstructureofPPP......................................................................................23Figure 1.5: Molecular structures of polypyridine, polypyrimidine, polypyrazine,polyfuran,polythiophene,andpolypyrrole..............................................................................23Figure1.6:Molecularstructureofpolyfluorene...................................................................24Figure 1.7: B3LYP optimised ground state structures of Fl-Ph-12 andDBTsulf-Ph-12........................................................................................................................................24Figure1.8:Structuresoftheplanarisedfluorene-typeoligomersstudied................24Figure1.9:Molecularstructuresofmelonandmelem.......................................................25Figure1.10:Molecularstructuresoftriazineandheptazine,ortri-s-triazine........26Figure1.11:DFToptimised3Dstructuresofselectedlinearheptazinechains......26Figure 1.12: DFT optimised 3D structures of selected graphitic carbon nitride“flakes”composedofheptazinemotifs.......................................................................................27Figure1.13:Molecularstructureofpyrene.............................................................................28Figure 1.14: Monomer structures of 1,4-benzenediboronic acid, 1,2,4,5-tetrabromobenzene,and1,3,6,8-tetrabromopyrene............................................................28Figure 1.15: DFT optimised 3D structures of the lowest-energy conformers forselectedringclusters..........................................................................................................................30Figure1.16:DFToptimised3D structures of selectedCTF clusters:TP3, PT2P4,TP3T3P6,andPT2P4T4P8...............................................................................................................31Figure3.1:Schemeshowinghowthe(standard)reductionpotentialsoftheidealphotocatalyststraddletheprotonreductionandwateroxidationpotentials...........64Figure3.2:Schemeillustratingtheconnectionbetweentheverticalpotentialsandthefundamentalgap,theopticalgap,andtheexcitonbindingenergy.........................67Figure3.3:Degradationof triethylamine intodiethylamineandacetaldehyde,viatwo1-electronoxidationsteps.......................................................................................................71Figure3.4:B3LYPoptimisedstructureofPPP-7...................................................................74Figure3.5:The(TD-)B3LYPpredictedIP,EA, IP*andEA*adiabaticpotentialsofPPP-7 at pH 0 as function of the dielectric permittivity of the embeddingmedium.....................................................................................................................................................76Figure3.6:Illustrationofexcitondissociationatthesurfaceofapolymerparticleforthecasewheretheholeoftheexcitongoesintosolution,whereitdriveswateroxidation,whiletheelectronremainsontheparticle..........................................................79

Listoffigures

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Figure 3.7: Comparison of the predicted IP, EA, IP* and EA* adiabatic potentialvaluesofPPP-2,PPP-7andPPP-11inwateratpH0............................................................81Figure3.8: TD-B3LYP/DZP predicted absorption onset values of PPP in eV as afunctionofthenumberofphenyleneunitsinthechain......................................................81Figure 3.9: Predicted potentials of PPP at pH 7 and 10, and potentials of the2-electronoxidationoftriethylamineandmethanol............................................................83

Figure4.1:Structuresofoligomermodelsstudiedcomputationally...........................96Figure4.2:Comparisonbetween thepotentialspredictedusing (TD-)B3LYPandεr=2,andmeasuredexperimentally,forarangeofconjugatedpolymers.................99Figure5.1:Comparisonbetweenthepredictedpotentialsforthep-phenyleneandtheFl-Pholigomers,calculatedatpH=0................................................................................114Figure 5.2: Predicted potentials for the Cz-Ph, the DBT-Ph, and the DBTsulf-Pholigomers,calculatedatpH=0....................................................................................................115Figure5.3:PredictedLVEEinchloroform.............................................................................115Figure 5.4: Experimentally measured photocatalytic performance of oligomersagainsttheiropticalgap..................................................................................................................117Figure 5.5: Comparison between the B3LYP predicted LVEE of phenylene andpyrene-phenyleneclustermodelsofringsizes3to6.......................................................119Figure 5.6: TD-B3LYP predicted IP, EA*, IP* and EA values of the different ringclusters for the phenylene and pyrene-phenylene structures, vs. the standardreduction potentials of proton reduction, water oxidation and diethylamineoxidation................................................................................................................................................120Figure5.7:B3LYPoptimisedgroundstatestructureofCTF-1,modelledasasingleringcluster............................................................................................................................................122Figure 5.8: TD-B3LYP predicted IP, EA*, IP* and EA values of selected CTFfragments..............................................................................................................................................123Figure5.9:Comparisonbetween(TD-)B3LYPpredictedadiabaticpotentialsofPPPandPPyri,foroligomerlengthsof7and12,atpH=0......................................................124Figure5.10:Comparisonbetweenthepredictedadiabaticpotentialsofarangeofconjugatedmolecules,foroligomerlengthsof7and12,atpH=0andpH=7......125Figure5.11:Diagramshowingthedifferenceinelectronicconfigurationofthelonepairsofpyridineandpyrrole........................................................................................................126Figure 5.12: Resonance structures or pyridine and pyrrole, showing electron-depletedandelectron-richaromaticrings,respectively..................................................127Figure5.13:ComparisonbetweenthepredictedadiabaticpotentialsofthePPyriandPPyrimoligomers, and their phenylene co-oligomer analogues PPyri-Ph andPPyrim-Ph,allhavingachainlengthof12equivalentphenyleneunits....................128Figure5.14:Comparisonbetweenthepredictedadiabaticpotentialsofmelemandheptazine-based linear chains of length 2 to 6, taking into account two possibleconformers...........................................................................................................................................129

Listoffigures

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Figure5.15:Comparisonbetweenthepredictedpotentialsofgraphiticheptazine-basedclustersofsizes3,6and10..............................................................................................130Figure5.16:DFT-optimisedgroundstatestructuresofthreedifferentisomersofaheptazinetrimer................................................................................................................................131Figure5.17:ComparisonofthepredictedIPandEApotentialsofagraphiticcarbonnitrideclusterandapolypyrroleoligomerinwateratpH7..........................................133Figure6.1:Structuresofthep-,m-,ando-terphenyloligomers..................................140Figure6.2:TopandsideviewsofB3LYPoptimisedgroundstategeometriesofthelowest energy conformers of p-quinquephenyl and o-quinquephenyl, as well asthreelowenergyconformersofm-quinquephenyl............................................................145Figure 6.3: Optical gap values as a function of oligomer length for the differentphenyleneisomerscalculatedwithTD-B3LYP,BHLYP,CAM-B3LYPandRI-CC2146Figure6.4:TD-B3LYPpredictedaveragegroundandexcitedstateinterphenylenetorsionanglesvs.oligomerlengthforthedifferentphenyleneisomers...................149Figure6.5:HOMOandLUMOforthep-quaterphenyloligomer..................................149Figure6.6: Direct pathways of alternating double and single bonds inp- ando-terphenylandabsenceofsuchapathwayinm-terphenyl..............................................151Figure6.7:TD-B3LYPground-excitedstatedensitydifferenceplotforanoligomerconsistingoftwop-phenyleneregionsseparatedbyam-phenylenesegmentinthecentreofthemolecule.....................................................................................................................151Figure6.8:Fluorescenceenergiesvs.oligomerlengthforthedifferentphenyleneisomerscalculatedwithTD-B3LYP,BHLYP,CAM-B3LYPandRI-CC2.......................152Figure6.9:VariationintheESSEandGSDEwitholigomerlengthforp-phenylene,m-phenylene,ando-phenylene....................................................................................................153Figure 6.10: Variation of the TD-B3LYP calculated excited state interphenylenetorsion angles and ground state-excited state interphenylene torsion angledifferencealongtheoligomer,forthedifferentp-phenyleneoligomers..................154Figure6.11:p-quinonebondlengthdistortionforthep-phenylenetetramer.....155Figure6.12:VariationoftheTD-B3LYP+Dcalculatedexcitedstateinterphenylenetorsionanglesalongtheoligomerforthedifferento-phenyleneoligomers...........156Figures6.13:VariationoftheTD-B3LYPandTD-B3LYP+Dcalculatedgroundstate-excited state interphenylene torsion angle difference along the oligomer for thedifferento-phenyleneoligomers.................................................................................................156Figure6.14:o-quinonebondlengthdistortionfortheo-phenylenetetramer.....157Figure6.15:Thetwouniquetorsionanglechoices1–2–3–4and1’-2-3-4’...........157Figure 6.16: Variation of the TD-B3LYP calculated excited state interphenylenetorsion angles and ground state-excited state interphenylene torsion angledifferencealongtheoligomer,forthedifferentp-phenyleneoligomers..................158Figure6.17:Bondlengthdistortionforthem-phenylenetetramer..........................159Figure6.18: Variation in average excited state interphenylenebond lengthwitholigomerlength,foro-andp-phenylene.................................................................................161

13

Listoftables

Table3.1:ComparisonbetweentheexperimentalandTD-B3LYPpredictedopticalpropertiesofPPP-7andPPP-11.....................................................................................................75Table3.2:Vertical,adiabatic,andfreeenergycorrectedpotentialsofPPP-7inwateratpH=0.................................................................................................................................................77Table3.3:TD-B3LYPpredictedexcitonbindingenergyvaluesforPPP-6andPPP-12inthreedifferentenvironments:vacuum,polymer,andwater........................................78Table3.4:EffectofthepHontheadiabaticandfreeenergycorrectedpotentialsofwater,hydrogenperoxideandsacrificialelectrondonors..................................................83Table 3.5: Basis-set effects on adiabatic and free energy corrected standardreductionpotentialsofwater,hydrogenperoxideandsacrificialelectrondonors.84Table 4.1: Experimentally measured and computationally predicted IPs ofp-phenyleneoligomersandpolymersindifferentenvironmentsvs.SHE...................95Table 4.2: Experimentally measured and computationally predicted IPs ofp-phenyleneandfluoreneoligomersandpolymersinaDCMsolutionvs.SHE........97Table 4.3: Comparison of the computationally predicted IPs of p-phenyleneoligomers and IP and EA values of a polyfluorene polymer calculated using thedouble-zetaDZPandtriple-zetadef2-TZVPbasis-sets........................................................98Table 4.4: Comparison between solid-state IP values for the different polymerspredictedbyB3YLPcalculations,andexperimentalvaluesfromtheliterature.......99Table 4.5: B3LYP solid-state IP and EA values for polypyridine, polypyrrole andpolythiophenecalculatedusingεr=10insteadof2...........................................................100Table4.6:Comparisonbetweensolid-stateEAsforthedifferentpolymerspredictedbyB3YLPcalculations,andexperimentalvaluesfromtheliterature.........................101Table4.7:Comparisonbetweensolid-stateexcited-state ionisationpotentials forthe different polymers predicted by B3YLP calculations and experimental valuesfromtheliterature.............................................................................................................................102Table6.1:ComparisonbetweenTD-B3LYPpredictedopticalgapsofp-phenyleneoligomers,inthegasphaseanddichloromethaneandexperimentaldata..............147

14

Listofpublications

ThefollowingpublicationsresultfromtheworkdoneduringmyPh.D.project:

1. Guiglion P.; Butchosa C.; Zwijnenburg M. A., “Polymeric watersplittingphotocatalysts; a computational perspective on the water oxidationconundrum”,J.Mat.Chem.A2014,2,11996-12004.

2. ButchosaC.;GuiglionP.;ZwijnenburgM.A.,“CarbonNitridePhotocatalystsfor

Water Splitting: A Computational Perspective”, J. Phys. Chem. C2014, 118,24833-2484.

3. Guiglion P.; Zwijnenburg M. A., “Contrasting the optical properties of the

differentisomersofoligophenylene”,Phys.Chem.Chem.Phys.2015,17,17854-17863.

4. Sprick R.S.; Jiang J.-X.; Bonillo B.; Ren S.; Ratvijitvech T.; Guiglion P.;

ZwijnenburgM.A.;AdamsD.J.;CooperA.I.,“TunableOrganicPhotocatalystsfor Visible Light-Driven Hydrogen Evolution”, J. Am. Chem. Soc.2015, 137,3265-3270.

5. SprickR.S.;BonilloB.;ClowesR.;GuiglionP.;BrownbillN.J.;SlaterB.J.;Blanc

F.;ZwijnenburgM.A.;AdamsD. J.;CooperA. I., “VisibleLight-DrivenWaterSplittingUsingPlanarizedConjugatedPolymerPhotocatalysts”,Angew.Chem.Int.Ed.2016,55,1792-1796.

6. Guiglion P.; Berardo E.; Butchosa C.; Wobbe M. C. C.; Zwijnenburg M. A.,

“Modelling materials for solar fuel synthesis by artificial photosynthesis;predicting the optical, electronic and redox properties of photocatalysts”, J.Phys.:Condens.Matter2016,28,074001.

7. GuiglionP.;ButchosaC.;ZwijnenburgM.A.,“PolymerPhotocatalystsforWater

Splitting: Insights from Computational Modeling”, Macromol. Chem. Phys.2016,217,344-353.

8. Guiglion P.; Monti A.; Zwijnenburg M. A., “Validating a Density Functional

TheoryApproachforPredictingtheRedoxPotentialsAssociatedwithChargeCarriersandExcitonsinPolymericPhotocatalysts”,J.Phys.Chem.C2017,121,1498-1506.

9. MeierC.B.;SprickR.S.;MontiA.;GuiglionP.;ZwijnenburgM.A.;CooperA.I.,

“Structure-propertyrelationshipsforcovalenttriazine-basedframeworks:theeffect of spacer length on photocatalytic hydrogen evolution from water”,submittedtoPolymer,2017,DOI:10.1016/j.polymer.2017.04.017

CHAPTER1:

Introduction

In thischapter, Iwill introducetheconceptofphotocatalyticwatersplitting,and

specify the constraints that this process imposes on a photocatalyst. I will then

describe the general properties of inorganic photocatalysts, as well as those of

conjugatedpolymers,andtheiradvantagesoverinorganicsemiconductors.Next,I

willintroduceandpresentthedifferentpolymericmaterialsstudiedthroughoutthis

project.Finally,Iwillsumupthemainchallengesandobjectivesofmyproject.

Someofthecontentofthischapterhasbeentakenfrompartofthefollowingpublished

work:

Guiglion P.; Butchosa C.; Zwijnenburg M. A., "Polymeric watersplitting

photocatalysts;acomputationalperspectiveonthewateroxidationconundrum",J.

Mat.Chem.A2014,2,11996-12004.

CHAPTER1:Introduction

16

1.1.Photocatalyticwatersplitting

Photocatalyticwatersplittingreferstothesplittingofwaterintomolecularoxygen

(O2)andhydrogen(H2)usingnaturalorartificiallight.Solar-drivenwatersplitting

holds particular interest since it uses clean, renewable, inexpensive and readily

availableresourcestoproducemolecularhydrogen,oneofthekeystartingmaterials

usedinthechemicalindustry,aswellasapotentialautomotivefuel(fuelcells).

Currently, fossil fuels amount to about 90%of energyworldwide, leading to the

emission of greenhouse gases including carbon dioxide, which is a top-priority

globalissue.Thereareseveralalternativeenergysources,amongwhichhydrogen,

anadvantageousfuelduetoitsavailabilityfromvarioussustainablesources,high

energyyield,environmentalfriendliness,andhighstoragecapacity.1However,using

hydrogenasanalternativesourceofenergyhassomedrawbacks,e.g.theextracosts

associated with compressing it before storage, the dangers associated with the

concurrentproductionofhydrogenandoxygengasesand thecostsof separating

those two gases, and the limited infrastructure available for the widespread

distributionofhydrogenfuel.

Theoretically,onlywater,solarenergy(renewable,free,andvirtuallyunlimited)and

aphotocatalystareneeded,asdescribedbelow.Inpracticehowever,theuseofco-

catalystsand/orsacrificialreagentsisalmostalwaysrequiredexperimentally.

In a naive picture, when light irradiates a photocatalytic molecule or particle, a

photon of sufficient energy can promote an electron from the highest occupied

molecularorbital(HOMO,inthecaseofmolecules,ortopofthevalenceband(VB)

inthecaseofmaterials)tothelowestunoccupiedorbital(LUMOformolecules,or

bottomoftheconductionband(CB)formaterials).Itcreatesanelectron-holepair

that can either recombine or take part in thewater splitting half-reactions (see

Figure1.1).


17

Figure1.1:(a)Mainprocessesinphotocatalyticwatersplitting2:(i)photonabsorption,(ii)electron-holepaircreation,(iii)undesirablerecombination,(iv)migrationtoreactionsites,and(v)surfaceredoxreactions.(b)Excitationofanelectronfromamaterial’svalenceband(VB)toitsconductionband(CB).

Note:thisschemeshowsanaivepictureofthephotocatalyticprocessesinvolvedinwatersplitting;inreality,aswillbediscussedinChapter3,itismuchmore

complicated.

Theelectron(e-)andthehole(h+)respectivelytakepartintwohalf-reactions:the

reduction of protons into molecular hydrogen, and the oxidation of water into

molecularoxygen.

(A)

(B)

In practice however, aswill be discussed later, the use of co-catalysts (typically

platinum,palladiumorruthenium)isneededtoaidthereductionofprotonsinto

molecular hydrogen and the oxidation of water into molecular oxygen, at the

photocatalyticallyactivesites.Inaddition,sinceitisnotoriouslydifficulttoachieve

overallwatersplitting(i.e.driveboththehydrogenandoxygenproducingreactions

concurrently),oneusually focussesononlyoneofthesehalf-reactions;sacrificial

electrondonors(SED,i.e.holeacceptorsthatwillbeoxidisedinsteadofwater,such

asmethanolor triethylamine)are typicallyused to triggerhydrogenproduction,

andsacrificialelectronacceptors(SEA,i.e.holedonors,thatwillbereducedinstead

ofprotons,e.g.Ag+orCe4+salts)totriggertheoxygenproduction.

Theexperimentalpotentialsofprotonreductionandwateroxidationrelativetothe

standard hydrogen electrode are respectively 0 eV and -1.23 eV under standard

conditions.Forthesereactionstooccursuccessfully,thereareseveralconstraints


18

on thephotocatalyst.Theconjugatedpolymermusthave: (i) a fundamentalgap3

larger than 1.23 eV,which corresponds to the difference in energy between the

protonreductionandwateroxidationpotentials,(ii)anopticalgap3smallerthan

approximately3.5eV,sothatitcanabsorbvisiblephotons(atwavelengthslarger

thanapproximately350nm),and(iii)HOMO/LUMOlevels(inthemolecularcase,

orVB/CBpositionswhenconsideringmaterials) that “straddle” thepotentialsof

protonreductionandwateroxidation(seeFigure1.15).

Additionally, the photocatalyst should allow for facile exciton dissociation and

electron-holeseparation,havealowoverpotentialforthedesiredredoxreactions,

andbestableunderilluminationandredoxconditions.

Figure1.2:Schemeoutliningtherequiredpropertiesthataphotocatalystmusthave

todrivewatersplitting.

Inotherwords,theenergyoftheelectron-donatingexcitedstatemustbeabovethe

hydrogen-producing half-reaction potential, while the electron-accepting ground

state must be below the oxygen-producing half-reaction potential. More details

about the photocatalyst's optical gap, fundamental gap, and standard reduction

potentials(intuitivelysimilartotheHOMO/LUMOandVB/CBnotions)willbegiven

inthefollowingchapters,especiallyinChapter3.

Experimentally,theelectrolysisofpurewateralsorequiresexcessenergyintheform

ofoverpotentialtoovercomevariousactivationbarriers;withoutthis,thesplitting

wouldoccurveryslowlyornotatall.Thisisinpartduetothelimitedself-ionisation,


19

and the very low conductivity of purewater. The required overpotential for the

oxidationofwaterisexpectedtobeslightlylargerthantheoverpotentialforproton

reduction,duetothefactthattheformerreactioninvolvesthetransferof4electrons

through several steps, whereas the latter is a more straightforward, 2-electron

reaction.Inpractice,apromisingphotocatalystwillhaveaLUMO/CBlevelatleast

0.5-0.7Vabove(morenegative) than theprotonreduction level,andaHOMO/VB

levelatleast0.8-1.2Vbelow(morepositive)thanthewateroxidationlevel.

1.2.Inorganicphotocatalysts

Inorganic photocatalysts are semiconductor materials, i.e. which electrical

conductivityliesbetweenthatofaninsulatorandofaconductor.Theirconducting

properties can be altered via the controlled introduction of small amounts of

impurities or defects (doping), making them either electron-rich (n-type) or

electron-poor(p-type),orbyapplyinganelectricalfield,orlight.Theirintroduction

revolutionisedthefieldofelectronicsinthelate1940s(e.g.diodes,transistors),and

morerecently,theyfoundapplicationsanphotocatalysts.

Toachievewatersplitting,inorganicphotocatalystssuchasmetaloxides,sulphides,

andnitrideshavebeenemployed,inwhichhighcrystallinityandsmallparticlesize

aredesiredtominimizetherecombinationofphoto-generatedelectronsandholes.1

Indeed,followingthediscoverybyFujishima,Hondaandco-workers,in1969,that

a TiO2 photoanode (that uses a combination of light and electrical bias) could

catalyse the splitting of water,4 the search for water splitting catalysts focussed

primarilyuponinorganicsystems5-7(e.g.besidesTiO2;Zn1.44GeN2.08O0.38(ref.8)and

TaON9).Manyofthosesystemsshowpromisingalignmentoftheirconductionand

valencebandswithrespecttothetwowater-splittinghalf-reactions(seeFigure1.3).


20

Figure1.3:Alignmentofthebandpositionsofvarioussemiconductorswithrespectto

theredoxpotentialsofwatersplitting.FigureadaptedfromOngetal.work.10

Tominimizethebandgapinordertoabsorbvisiblelight,whilemaintainingsuitable

band positions, severalmethods have been attempted. Several possible dopants

have been studied by first principles computations. For instance, doping with

cationsofelementssuchasV,11Mn,12Fe,12andCo,13orwithanionsofC,14N15-16,P,17,

andS,17 aswell as co-doping strategieshavebeen studiedbyDensityFunctional

Theory(DFT)forTiO2.Similarinvestigationshavealsobeencarriedoutforother

photocatalysts,e.g.ZnO,18-19WO3,20andSrTiO3.21Aniondopingorco-dopinghave

beenshowntoreducethebandgap,sometimessignificantly(althoughaniondoping

intooxidesischallenginginpractice),whilecationdopingexhibitsverylimitedband

gapreduction.

Oneofthemainstrengthsofinorganicphotocatalystsistheirtypicallylowexciton

binding energies, and the possibility to achieve high charge carrier mobility,

allowingforfacilebulkchargeseparationandtransport.


21

1.3.Conjugatedoligomersandpolymers

Organic conjugated polymers and oligomers are mostly semiconductors, where

conductivityisachievedbythemovementofchargecarriers:πelectrons,andholes

(absenceofelectrons).Insuchpolymers,themolecularbackboneisconstitutedof

sp2hybridisedatoms,withalternatingsingleandmultiplebonds.Theelectronsare

assumedtobedelocalisedandtorelatively freely"circulate"via theoverlapofπ

orbitals.

Inmostorganicsemiconductors,theintermolecularforcesaretooweaktoform3D

crystal lattices, which is fundamentally different to crystalline inorganic

semiconductors, where the individual LUMOs and HOMOs form a CB and a VB

throughoutthematerial.Consequently,inconjugatedoligomersandpolymers,the

molecularLUMOsandHOMOsdonotinteractstronglyenoughtoformaCBandVB.

Thuschargetransportproceedsbyhoppingbetweenlocalisedstates,ratherthan

transportwithin a band. Thismeans that charge carriermobility in organic and

polymeric semiconductors are generally low compared to inorganic

semiconductors.Also,chargeseparationismoredifficultinorganicsemiconductors

due to the low dielectric constant. In many inorganic semiconductors, photon

absorptionproducesafreeelectronandafreehole,whereastheexcitedelectronis

boundtothehole(atroomtemperature)inorganicsemiconductors.

Conjugatedpolymersareafascinatingclassofmaterials.Theyarelightweightand

canabsorb light.Theirmainadvantagesover inorganicsemiconductorsare their

flexibilityandtransparency,sincetheyareusuallyamorphous(whichgivesthem

great potential for new display technologies22), ease of manufacture (e.g. roll

printing on large surfaces), disposability, environmental friendliness (based on

earth-abundant elements), and low cost. Moreover, conjugated polymers offer a

diverse synthetic modularity, which allows their electronic and structural

propertiestobetailoredwithoutdoping,althoughdopingcanbeaviablestrategy.

They can be produced over a continuous range ofmonomer compositions, thus

achievingsystematiccontroloverphysicalproperties.Organicconjugatedpolymers


22

thus offer the long-term vista of solution-processable photocatalysts that can be

optimisedthroughexploitingtheunrivalledsyntheticversatilityofferedbyorganic

chemistry.

Those materials are found in a wide variety of applications, ranging from

photocatalysis to organic light-emitting diodes, organic solar cells, and

supercapacitors. In this project, the focus will be on their application as

photocatalystsforsolarwatersplitting.

Organicsemiconductorshavereceivedmuchattentionsince1985,whenYanagida

and co-workers23 demonstrated that an organic conjugated polymer, poly(p-

phenylene), could successfully catalyse the proton reduction half-reaction (see

section 1.1, reaction (A)) under ultraviolet light, like many inorganic

semiconductors reported before, greatly widening the scope of possible

photocatalysts. However, until recently, the progress of research into polymeric

water splitting catalysts was very slow compared with that of their inorganic

analogues,possiblyduetoperceivedstabilityissues.Thisallchangedin2008with

thediscoverybyAntoniettiandco-workers24thatcarbonnitridepolymerscouldact

asaphotocatalystforboththeprotonreductionandwateroxidationhalf-reactions

(see next section), although, until very recently25-26, not concurrently. Since this

report, there has been a steady stream of publications on polymer systems for

photocatalytic water splitting, including (doped) carbon nitrides,27-34

poly(azomethine),35polyimides,36andpolymericdisulfides.37

1.3.1.Linearconjugatedpolymers

Thisprojectwillmainlyfocusonlinearconjugatedpolymers.Specifically,Iwillfirst

investigate the optical properties and the water splitting potential of poly(p-

phenylene)(PPP,seeFigure1.1)andotherrelatedpolymers.PPP,alsoknownas

poly(1,4-phenylene),isrecognisedasausefulhigh-performancepolymerduetoits

thermalandchemicalstabilityanditselectricalandoptoelectronicproperties;itis

usedinlight-emittingdevices38-39andwasoneofthefirstpolymerstobereported


23

tocatalysethereductionofprotonsintomolecularhydrogen,underultravioletlight

irradiation.23,40

Figure1.4:MolecularstructureofPPP.

Othersimplelinearconjugatedpolymerscanbecreatedbyreplacingcarbonatoms

byheteroatomsinthearomaticringofPPP.Iwillfocusonsomenitrogen,oxygen,

andsulphur-containingpolymers(seeFigure1.2)thatarewidelydescribedinthe

literature, for applications in photocatalysis, but also in organic photovoltaic or

displaytechnologies.

Figure1.5:Molecularstructuresofpolypyridine(PPyri),polypyrimidine(PPyrim),polypyrazine(PPyra),polyfuran(PFur),polythiophene(PT)andpolypyrrole(PPyrr).

Mostmolecularchainspresentedabovearenotplanar.Forexample,inthecaseof

PPP, two consecutive phenylene building blocks form a dihedral angle of

approximately30 to40degrees, in its electronic ground state, according toDFT

calculations.Someothers,however,areoverall flatter,sincetheycomprise fewer

hydrogenatomsontheiraromaticrings,hencedecreasingthesterichindranceand

favouringplanarity(e.g.somepyrimidineandpyrazinepolymers).

Inaddition, inChapter5, Iwill study theeffectofpurposefully41planarisingand

rigidifyingsomephenylene-containinglinearchains.InthecaseofPPP,rigidityand

planaritycanbeincreasedbyintroducingaphenylenelinkerbetweeneveryother

phenyleneunit,resultinginthecreationoffluorenemotifs(seeFigure1.3forthe

structureofpolyfluorene).Inthisproject,fluorene-co-phenylenechains(hereafter


24

referred to as Fl-Ph), as well as other fluorene-type copolymers (obtained by

planarisationviatheintroductionofotherlinkers,suchasheteroatoms,e.g.sulphur,

orfunctionalgroups,e.g.aminoorsulfone)willbeinvestigated(seeFigure1.4for

the3Dstructuresofselected“planarised”oligomers,andFigure1.5fordetailsabout

thechosennomenclature).

Figure1.6:Molecularstructureofpolyfluorene(PF).

Figure1.7:B3LYPoptimisedgroundstatestructuresofFl-Ph-12(leftside)andDBTsulf-Ph-12(rightside),bothcontaining12phenylenemoietyequivalents.

Figure1.8:Structuresoftheplanarisedfluorene-typeoligomersstudied.Forsimplicity,theoligomersorpolymerscorrespondingtoX=CH2,NH,SandSO2willbereferredtoasFl-Ph,Cz-Ph,DBT-PhandDBTsulf-Phrespectively.Thenumbersinbold

correspondtothenumberofphenylenemoietyequivalents.


25

1.3.2.Carbonnitridematerials

Aside from simple linear conjugated polymers, Iwill also introduce some larger

linear or 2D polymericmaterials based on carbon nitride. Carbon nitrides, with

generalformula(C3N3H)nwerefirstreportedbyBerzeliusin1830,andnamedmelon

(seeFigure1.6)afewyearslaterbyvonLiebig,in1834.42Sincethen,manyrelated

materials have been synthesised, including melem (see Figure 1.6) and high

molecularweightpolymers.

Figure1.9:Molecularstructuresofmelon(leftside)andmelem(rightside).

Thisclassofmaterialssparkedasurgeofinterestinthelate2000s,whenAntonietti

andco-workers24reportedthatcarbonnitridepolymerscouldactasphotocatalysts,

undercertainconditions, for thereductionofprotonsandtheoxidationofwater.

Sincethen,asteadystreamofpublicationshaveappeared,recentlyculminatingin

thereportoftwoextremelypromisingcarbonnitridematerials25-26thatcancatalyse

theoverallsplittingofwater.

However,theexactstructureofcarbonnitrideisstillpoorlyunderstood.Whilethe

structures of low-molecular-weight carbon nitride were elucidated (relatively

recently43),itisnotthecasefortheirpolymericcounterparts.Thosehigh-molecular

versionsofcarbonnitride,structurallyverycomplex,mightbebasedontriazineor

heptazinemotifs(seeFigure1.7),linkedtogetherinvariousproportionsthrough-

NH-bridgestoformlinearchains,throughsingle3-coordinatednitrogenatomsto

formflakeswithastructureresemblinggraphite(graphiticcarbonnitride,org-CN)

or amix of the two44 (see Figure 5.16 in Chapter 5). Moreover, high-molecular-

weightcarbonnitrideisnotoriouslydifficulttocharacterise;itisoftenamorphous


26

or poorly crystallised, and adsorbs water, making characterisation via X-ray

diffractionandelementalH/Ccontentanalysis,respectively,verychallenging.

Figure1.10:Molecularstructuresoftriazine(leftside)andheptazine,ortri-s-triazine(rightside).

Sincetheexactatomicstructureoftheamorphous/semi-crystallinecarbonnitridesamplesusedinwatersplittingarepoorlyknown,calculationsarehenceperformed

onclustermodelsrepresentativeofdifferentpossiblematerialstructures.Carbon

nitrideoligomersaremodelledassinglemolecularclusters(asopposedtoperiodic

materials),asarethePPPoligomerspresentedintheprevioussection.Suchclusters

aremadeoflineararrangementsofeithertriazineorheptazinemotifs(i.e.fragments

ofmeloninthelattercase,seeFigure1.8),orbuiltassingle,relativelysmallflakes

ofgraphiticcarbonnitride(seeFigure1.9).

Figure1.11:DFToptimised3Dstructuresofselectedlinearheptazinechains.44ForHrefertothe“flat”or“helical”shapeofthestructures.


27

Figure1.12:DFToptimised3Dstructuresofselectedgraphiticcarbonnitride“flakes“composedofheptazinemotifs.44

The validity of such models was jointly assessed in previous work from the

Zwijnenburg group by Butchosa and co-workers, 44 who used a TD-DFT-based

approach to predict the optical properties (absorption spectra and absorption

onsets) of carbon nitride oligomeric clusters, before comparing them to

experimentaldata.Ourgroup’seffort to investigateopticalproperties inorder to

shed some light on those materials’ molecular structure was motivated by the

observation24that,duringpolymersynthesis,changingthetemperature(andthus,

the final structure of the polymer) affects UV-Vis absorption spectra. Overall,

experimentalresultshavebeensuccessfullyreproduced,whichsuggeststhevalidity

of those models, except for graphitic triazine-based frameworks, whose result

discrepancy has been attributed to the presence of nitrogen vacancies in the

experimentalsamples.44

1.3.3.ConjugatedMicroporousPolymers

Conjugatedmicroporouspolymers(CMPs)areafascinatingclassofmaterials.They

combinethefeaturesandpropertiesofbothmicroporousmaterials(highporosity

andsurfacearea)andconjugatedpolymers(lightabsorption,photoluminescence,

photocatalysis). CMPs present very valuable features: their pore size and gas

sorptionpropertiescanbetuned,andtheirfluorescenceenergyandopticalgapcan

bevariedtoalargeextentbystatisticalcopolymerization45.SeveraltypesofCMPs,

including phenylene45-50, pyrene45, 51 (see Figure 1.10), and carbon nitride based


28

materials32,37,52,havebeensuccessfullysynthesised,andhavebeenshowntoexhibit

visiblelightabsorptionandfluorescenceproperties.

Figure1.13:Molecularstructureofpyrene.

Phenylene- and pyrene-based CMPs are mainly synthesised via metal-catalysed

couplingreactions(Yamamoto53,Sonogashira-Hagihara54,orSuzuki55),usingonly

one (the resulting material is a homopolymer) or several distinct monomers

(copolymer).Inthisproject,theCMPsofinterestwillbemodelledasringclusters,

comprisingseveral“corners”orvertices,consistingofphenyleneorpyrenemoieties,

attachedtogetherthroughphenylenebridgesor“linkers”.Themonomersusedfor

synthesis typically consist of 1,2,4,5-tetrabromobenzene and 1,3,6,8-

tetrabromopyrene for thetwopossiblevertextypes,andof1,4-benzenediboronic

acid for the linkers45, 51 (see Figure 1.11). They yield a wide range of CMPs

(phenylenehomopolymersorpyrene-phenylenecopolymers)withortho-orpara-

substituted phenylene units, and 1,3- or 1,8-substituted pyrene units. Those

materials are typically amorphous. Because they can comprise small rings,

dendrimers,orextendedthree-dimensionalnetworks,characterisingthemcanbe

challenging, hence theneed to take such structural features (strained rings) into

accountinthemodels.

Figure1.14:Monomerstructures:1,4-benzenediboronicacid(1),1,2,4,5-tetrabromobenzene(2)and1,3,6,8-tetrabromopyrene(3).


29

InlinewiththepyrenemodelsusedinM.A.Zwijnenburg’sstudy51,andinorderto

be consistentwith themonomers used during synthesis, phenylene and pyrene-

phenylene CMPs will be modelled as clusters of ring-sizes 4 to 6 (containing

respectively4to6phenyleneorpyrenevertices,and4to6phenylenelinkers).Two

differentisomerswillbetakenintoaccount(referredtoas“short”whenphenylene

andpyrenecornersarelinkedthroughthe1,2and1,3positions,respectively,and

“long” when phenylene and pyrene corners are linked through the 1,3 and 1,8

positions, respectively, see Figure 1.12). Additionally, across a range of possible

conformers,theoneswithlowestenergywillbeconsidered.Theclustermodelswill

thereforebeeitherentirelycomposedofphenyleneunits,orinthecaseofpyrene-

phenylene,comprise50%phenylene(alllinkers)and50%pyrene(allvertices).

Previous research by M. A. Zwijnenburg51 showed that pyrene oligomers and

polymersdisplayinpracticeamuchsmallerabsorptionandfluorescenceshiftwith

chain length than other conjugated polymers such as para- and ortho-

polyphenylenes.Inlaterinvestigations,Zwijnenburgandco-workers56rationalised

the difference in absorption and fluorescence spectra, between insoluble pyrene

CMPsandtheirlinearorbranchedsolublecounterparts,bythepresenceofstrained

closedringsinthenetwork.Thisallowsonetolinktheabsorptionandfluorescence

spectraofpolymerswith informationabout theirunderlyingmolecular topology,

andjustifiesourgroup’schoicetomodelthoseCMPsasringclusters.


30

Figure1.15:DFToptimised3Dstructuresofthelowest-energyconformersforselectedringclusters.AtomsrepresentedasbluespheresindicatewheretheringswouldconnecttotherestoftheamorphousCMPnetwork."B"standsforphenylenevertices,"P"forpyrenevertices.The"L"and"S"subscriptsrespectivelyindicatelong

andshortorientationofthevertices.

Anothertypeofrelatedmaterials,halfwaybetweenCMPsandcarbonnitrides,will

alsobestudied:covalenttriazineframeworks(CTFs).CTFsareparticularlyrelevant

towatersplittingthankstotheiruniqueproperties,astheycombinetypicallyhigh

surfaceareas,beingmicroporous,andpromisingphotochemicalproperties29,57-58,

beingfluorescent.Moreover,likemanyotherpolymers,theypossessahighsynthetic

versatility,astheirchainlength,molecularweight,poresizeandchemicalstructure

canbetunedtoachievetarget(photocatalytic)properties.Besidesring-containing

CTFs, alreadywell described in the literature (e.g. CTF-0, CTF-1, and CTF-2)59-60

otherplanarCTFclusterswillbemodelled(seeFigure1.13),builtwithalternating

triazineandphenylenemotifs,inadendrimericfashion.


31

Figure1.16:DFToptimised3DstructuresofselectedCTFclusters:TP3(1),PT2P4(2),TP3T3P6(3)andPT2P4T4P8(4).Thenomenclaturereflectsthedendrimericnatureofthemolecules:TandPstandfortriazineandphenylene,respectively.


32

1.4.ObjectivesofthisPh.D.project

This project focusses on the application of quantum chemicalmethods tomodel

excited state processes in conjugated oligomers and polymers. It aims at

understanding and optimising those properties of conjugated polymers that

underlietheiruseinsolarcellsandasphotocatalystsforrenewablehydrogenand

oxygenproduction,byphotocatalyticwatersplitting.

The main goal of this Ph.D. project is to develop a robust computational

methodology tocalculate targetpropertiesofpolymericphotocatalysts,and then

use thismethodology toscreen forpromisingcandidatephotocatalysts forwater

splitting, i.e. either find whichmaterials are theoretically themost adequate, or

eliminate theones that arepredicted tobe ineffective.Thosepredictionswill be

confrontedtoexperimentaldatafromtheliterature,andtotheexperimentalresults

ofourclosecollaboratorsat theUniversityofLiverpool (thegroupofProf.Andy

Cooper61).

Bycombining theoretical calculationsusing (time-dependent)DensityFunctional

Theory62-64 and other excited-state methods, with spectroscopic and catalytic

experiments carried out by our collaborators, one can explore the relationship

betweenthestructureandpropertiesofconjugatedpolymers.Theuseoftheoretical

methodstopredicttheopticalpropertiesofconjugatedpolymerswillenableusto

extractinformationunattainablebyexperimentalone,andtosuggestnewpolymers

forexperimentalscreening.Indeed,theuseofacomputationalapproachismainly

motivated by the fact the materials of interest are relatively straightforward to

synthesise, although the same does not necessarily hold for the precursors, but

notoriously challenging to characterise. Indeed, the properties of polymers

synthesised in different batches may vary, which, coupled to delicate

characterisation,canresultinalackofmeaningfulandrepeatableresults.

Inthenextchapter,Iwilllaythetheoreticalfoundationsbyintroducing(TD-)DFT

and all other methods or frameworks used. In Chapter 3, I will describe the


33

computational method used throughout this project, and apply it to poly(p-

phenylene).InChapter4,Iwillvalidatethismethodologybycomparingtheyielded

results to experimental data, before applying it, in Chapter 5, to awide range of

polymericsystems,andexaminingtheirrelativephotocatalyticperformances.Then,

inChapter6,Iwillcomebacktoouroriginalpolymer,PPP,anddiscusstheoriginof

the dramatic difference in optical properties by exploring the structure of its

different isomers.Finally,Chapter7will summarisemy results and findings, and

offer a perspective on the use of theoretical tools tomodel the use of polymeric

materialsforphotocatalyticwatersplitting.


34

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33. Chu,S.;Wang,Y.;Guo,Y.;Feng,J.;Wang,C.;Luo,W.;Fan,X.;Zou,Z.,"BandStructure Engineering of Carbon Nitride: In Search of a PolymerPhotocatalyst with High Photooxidation Property",ACS Catalysis2013, 3,912-919.

34. Kailasam,K.;Schmidt,J.;Bildirir,H.;Zhang,G.;Blechert,S.;Wang,X.;Thomas,A.,"RoomTemperatureSynthesisofHeptazine-BasedMicroporousPolymerNetworksasPhotocatalystsforHydrogenEvolution",MacromolecularRapidCommunications2013,34,1008-1013.

35. Schwab, M. G.; Hamburger, M.; Feng, X.; Shu, J.; Spiess, H. W.; Wang, X.;Antonietti,M.;Müllen,K.,"Photocatalytichydrogenevolutionthroughfullyconjugated poly(azomethine) networks", Chemical Communications 2010,46,8932-8934.

36. Chu,S.;Wang,Y.;Guo,Y.;Zhou,P.;Yu,H.;Luo,L.;Kong,F.;Zou,Z., "Facilegreen synthesis of crystalline polyimide photocatalyst for hydrogengeneration from water", Journal of Materials Chemistry 2012, 22, 15519-15521.

37. Zhang, Z.; Long, J.; Yang, L.; Chen, W.; Dai, W.; Fu, X.; Wang, X., "Organicsemiconductorforartificialphotosynthesis:watersplittingintohydrogenbya bioinspired C3N3S3 polymer under visible light irradiation", ChemicalScience2011,2,1826-1830.

38. Grem, G.; Leditzky, G.; Ullrich, B.; Leising, G., "Realization of a blue-light-emittingdeviceusingpoly(p-phenylene)",AdvancedMaterials1992,4,36-37.

39. Grem,G.;Leditzky,G.;Ullrich,B.;Leising,G.,"Blueelectroluminescentdevicebasedonaconjugatedpolymer",SyntheticMetals1992,51,383-389.

40. Shibata, T.; Kabumoto, A.; Shiragami, T.; Ishitani, O.; Pac, C.; Yanagida, S.,"Novel visible-light-driven photocatalyst. Poly(p-phenylene)-catalyzedphotoreductions of water, carbonyl compounds, and olefins", Journal ofPhysicalChemistry1990,94,2068-2076.

41. Sprick,R.S.;Bonillo,B.;Clowes,R.;Guiglion,P.;Brownbill,N.J.;Slater,B.J.;Blanc,F.;Zwijnenburg,M.A.;Adams,D.J.;Cooper,A.I.,"VisibleLight-DrivenWater Splitting Using Planarized Conjugated Polymer Photocatalysts",AngewandteChemieInternationalEdition2016,55,1792-1796.

42. Liebig, J., "Uber einige Stickstoff - Verbindungen",Annalen der Pharmacie1834,10,1-47.

43. Jürgens, B.; Irran, E.; Senker, J.; Kroll, P.; Müller, H.; Schnick, W., "Melem(2,5,8-Triamino-tri-s-triazine), an Important Intermediate duringCondensation of Melamine Rings to Graphitic Carbon Nitride: Synthesis,StructureDeterminationbyX-rayPowderDiffractometry,Solid-StateNMR,andTheoreticalStudies",JournaloftheAmericanChemicalSociety2003,125,10288-10300.


37

44. Butchosa,C.;Guiglion,P.;Zwijnenburg,M.A.,"CarbonNitridePhotocatalystsforWater Splitting: A Computational Perspective",The Journal of PhysicalChemistryC2014,118,24833-24842.

45. Sprick, R. S.; Jiang, J.-X.; Bonillo, B.; Ren, S.; Ratvijitvech, T.; Guiglion, P.;Zwijnenburg, M. A.; Adams, D. J.; Cooper, A. I., "Tunable OrganicPhotocatalystsforVisibleLight-DrivenHydrogenEvolution",JournaloftheAmericanChemicalSociety2015,137,3265-3270.

46. Lukeš, V.; Aquino, A. J. A.; Lischka, H.; Kauffmann, H.-F., "Dependence ofOpticalPropertiesofOligo-para-phenylenesonTorsionalModesandChainLength",TheJournalofPhysicalChemistryB2007,111,7954-7962.

47. Chen, L.; Honsho, Y.; Seki, S.; Jiang, D., "Light-Harvesting ConjugatedMicroporousPolymers:RapidandHighlyEfficientFlowofLightEnergywitha Porous Polyphenylene Framework asAntenna", Journal of the AmericanChemicalSociety2010,132,6742-6748.

48. He,J.;Crase,J.L.;Wadumethrige,S.H.;Thakur,K.;Dai,L.;Zou,S.;Rathore,R.;Hartley, C. S., "ortho-Phenylenes: Unusual Conjugated Oligomers with aSurprisingly Long Effective Conjugation Length", Journal of the AmericanChemicalSociety2010,132,13848-13857.

49. Hartley,C.S.,"Excited-statebehaviorofortho-phenylenes",JOrgChem2011,76,9188-91.

50. Xu,Y.;Jiang,D.,"StructuralInsightsintotheFunctionalOriginofConjugatedMicroporous Polymers: Geometr Management of Porosity and ElectronicProperties",ChemicalCommunications2014,

51. Zwijnenburg,M.A.,"ElucidatingtheMicroscopicOriginoftheUniqueOpticalProperties of Polypyrene",The Journal of Physical Chemistry C2012,116,20191-20198.

52. Wang,X.;Maeda,K.;Thomas,A.;Takanabe,K.;Xin,G.;Carlsson,J.M.;Domen,K.; Antonietti, M., "A metal-free polymeric photocatalyst for hydrogenproductionfromwaterundervisiblelight",NatMater2009,8,76-80.

53. Jiang, J.-X.;Trewin,A.;Adams,D. J.;Cooper,A. I., "Bandgapengineering influorescent conjugatedmicroporous polymers",Chemical Science2011,2,1777-1781.

54. Ren,S.;Dawson,R.;Laybourn,A.;Jiang,J.-x.;Khimyak,Y.;Adams,D.J.;Cooper,A. I.,"Functionalconjugatedmicroporouspolymers: from1,3,5-benzeneto1,3,5-triazine",PolymerChemistry2012,3,928-934.

55. Cheng,G.;Hasell,T.;Trewin,A.;Adams,D.J.;Cooper,A.I.,"SolubleConjugatedMicroporousPolymers",AngewandteChemieInternationalEdition2012,51,12727-12731.

56. Zwijnenburg,M.A.;Cheng,G.;McDonald,T.O.;Jelfs,K.E.;Jiang,J.X.;Ren,S.J.;Hasell,T.;Blanc,F.;Cooper,A.I.;Adams,D.J.,"SheddingLightonStructure-Property Relationships for Conjugated Microporous Polymers: TheImportanceofRingsandStrain",Macromolecules2013,46,7696-7704.

57. Lau,V.W.-h.;Mesch,M.B.;Duppel,V.;Blum,V.;Senker,J.;Lotsch,B.V.,"Low-Molecular-WeightCarbonNitridesforSolarHydrogenEvolution",JournaloftheAmericanChemicalSociety2015,137,1064-1072.

58. Schwinghammer,K.;Hug,S.;Mesch,M.B.;Senker,J.;Lotsch,B.V.,"Phenyl-triazine oligomers for light-driven hydrogen evolution", Energy &EnvironmentalScience2015,DOI:10.1039/C5EE02574E.


38

59. Butchosa,C.;McDonald,T.O.;Cooper,A.I.;Adams,D.J.;Zwijnenburg,M.A.,"Shining a Light on s-Triazine-Based Polymers", The Journal of PhysicalChemistryC2014,118,4314-4324.

60. Jiang,X.;Wang,P.;Zhao,J.,"2Dcovalenttriazineframework:anewclassoforganicphotocatalyst forwatersplitting", JournalofMaterialsChemistryA2015,3,7750-7758.

61. Cooper,A.http://www.liv.ac.uk/cooper-group/.62. Hohenberg, P.; Kohn, W., "Inhomogeneous Electron Gas", Physical Review

1964,136,864-871.63. Kohn, W.; Sham, L. J., "Self-Consistent Equations Including Exchange and

CorrelationEffects",PhysicalReview1965,140,1133-1138.64. Runge,E.;Gross,E.K.U., "Density-FunctionalTheory forTime-Dependent

Systems",PhysicalReviewLetters1984,52,997-1000.

CHAPTER2:

Theoreticalfoundations

Inthischapter,Iwilllaythefoundationsofthethesisbyintroducingthetheoretical

frameworks used throughout my project. I will first present Density Functional

Theory(DFT),themaincomputationalquantummechanicalmodellingmethodof

choicehere, that isparticularlyvaluable to investigate theelectronic structureof

atomsandmolecules.Iwillexplainhowthetheorywasconstructedovertime,and

howseveralkeyinsightsledittobecomeoneofthemostpowerfulandroutinely

used computational methods. I will then outline the functionals and basis-sets

neededwithinitsframework.Second,Iwilldescribetime-dependentDFT(TD-DFT),

a crucial extensionofDFT that enablesone, amongother things, to calculate the

electronicstructureofatomsandmoleculesintheirexcitedstate.Third,Iwillbriefly

outlineanadditionalcomputationalmethod,coupled-cluster,ormorepreciselythe

approximate coupled-clusters singles-and-doublesmethod (CC2), that involves a

completelydifferentapproach tomodelling theelectronicstructure,and ishence

verycomplementaryto(TD-)DFT.Fourth,Iwilldiscusstheconductor-likescreening

model(COSMO),asolvationmodelthatthatwillbeparticularlyusefultomodelthe

effectofthechemicalenvironment.Finally,Iwillexplainthemethodologyusedto

carryoutconformationalsearches,whichiscrucial inordertofindthemolecular

structuresofrelevantconformersbeforeDFToptimisation.

CHAPTER2:Theoreticalfoundations

40

2.1.DensityFunctionalTheory(DFT)

Theultimategoalofmostquantumchemicalapproachesistofindtheground-state

energyofnon-relativisticelectronsforarbitrarypositionsofnuclei,withintheBorn-

Oppenheimerapproximation1.Thedirectapproachtotreatthisproblemistosolve

thetime-independent,non-relativisticelectronicSchrödingerequation:

(1)

where:

• is themany-bodywavefunctiondescribing theelectronic stateof the

system, depending on 3N spatial coordinates andN spin coordinates

,whicharecollectivelytermed (with ),

• istheelectronicHamiltonian,containingthetotalenergy

of the electrons ( denotes the kinetic energy operator, and the

potentialenergyoperators,respectivelyforthenuclear-electronattraction,

andtheelectron-electronrepulsion).

Solving this equation is an exceedingly difficult task, whose computational cost

scalesexponentiallywith thenumberof electrons.For instance, just to store the

groundstateoftheoxygenatom, woulddependon24coordinates,threefor

eachoftheeightelectrons,disregardingspin.Consideringonlytengrid-pointsfor

each coordinate, onewould need 1024 numbers to represent thiswavefunction2.

Therefore,amethodsuchasDensityFunctionalTheorythatcanyieldinteresting

quantities, namely the ground state energy of a system, bypassing the need to

calculate ,isextremelyattractive.InDFT,onewritesthegroundstateenergyin

terms of the electron density (defined by the probability of finding any

electroninthevolume around )insteadofthewavefunction .


41

2.1.1.Thomas-Fermimodel

Thefirstattemptstoemploytheelectrondensityratherthanthewavefunctiondate

backto1927,withtheworkofThomas3andFermi4.Theirapproachwasbasedon

approximatingthekineticenergy usingaquantumstatistical(fictitious)model

of a uniform, non-interacting, spin-unpolarised N-electron gas of density ,

while treating the other two contributions to the total energy, and , in a

purelyclassicalway:

(2)

(3)

(4)

isthenminimisedundertheconstraintsthattheelectrondensitymustbe

positiveandintegratetoN:

and (5)

Thisextremelycrudeapproximationgivesroughlycorrectenergies (errorsabout

10% for many systems5) but is not nearly good enough for most properties of

interest(forinstance,moleculesdonotbindinthismodel6).However,itprovidesfor

thefirsttimeawayofmappingtheelectrondensitytotheenergy,withoutanyother

informationrequired.TheThomas-Fermienergyisthefirstexampleofagenuine

densityfunctional,as isafunctionalofthedensity .


42

2.1.2.Hohenberg-Kohntheorems

Itisonlyin1964,nearly40yearslater,thatHohenbergandKohn7gavearigorous

proofthatsuchamappingbetweentheelectrondensityandthegroundstateenergy

oftheelectronswasphysicallyjustified.Theyshowedthatthesolutionofthemany-

bodyproblemcouldbefound,inprinciple,fromadensityfunctional.

The firstHohenberg theoremstates that theground-statedensity uniquely

determinestheexternalpotential (whichincludes andhypothetical

externalelectromagneticfields)feltbytheelectrons,uptoanarbitraryconstant.It

follows that the density completely and uniquely determines the Hamiltonian,

whichinturndefinesthegroundstateenergy,andallotherpropertiesofthesystem.

Intheabsenceofadditionalexternalelectromagneticfield,theexternalpotentialis

fullydefinedbytheattractiontothenuclei.Sincethegroundstateenergy isa

functionalofthegroundstatedensity ,soareitsindividualconstituents,andit

followsthat:

(6)

where the first integral is the only system-dependent part, and the second part,

,alsocalled istheHohenberg-Kohnfunctional,auniversal

functional(i.e.uniqueandvalidforanypossiblesystem).

If this universal functional (also known as the “holy grail” of DFT) was known

formally,onewouldbeabletosolvetheSchrödingerequationexactly,foranysystem.

Unfortunately,itisnotthecase,asitcontainsthefunctionalforthekineticenergy

and for the electron-electron interaction, which are completely unknown due to

instantaneouselectroncorrelations(Coulombandexchange)thatcan’tbedescribed

inaclassicalway.


43

The secondHohenberg-Kohn theorem,using thevariationalprinciple, states that

deliversthegroundstate(lowest)energyofthesystemifandonlyifthe

inputdensityis ,thetruegroundstatedensityofthesystem.

2.1.3.Kohn-Shamapproach

It has to be noted at this point that for all practical purposes, there is no

wavefunctionindensityfunctionaltheory(thereisnowayinpracticetogobackto

the true wavefunction of a system, even with its exact ground state energy or

density). However, aswewill see in this section, it is possible to build fictitious

orbitals(andhenceafictitiouswavefunction)thatwillhelpusdescribethesystem

ofinterestandapproximateitsgroundstateenergy.

ShortlyaftertheHohenberg-Kohntheorems,in1965,KohnandSham8madeavery

clever observation: they found that a major flaw in most density functional

approaches (as the Thomas-Fermi one)was theway kinetic energywas treated.

Indeed, due to electron correlations, thepositions andvelocitiesof electrons are

unknown,andthe term can’tbewrittenexplicitly in theHamiltonian.

Kohn and Sham realised that another method performed much better in this

respect9:theHartree-Fockmethod.

TheHartree-Fockmethod,inordertosolvetheSchrödingerequation,approximates

thefullmany-bodywavefunctiontoaN-electronsingleSlaterdeterminant(i.e.an

antisymmetricproductofNone-electronorbitals).Thisapproachtreatsallelectrons

asnon-interactingparticles.Instead,eachsingleelectronevolvesindependentlyin

themeanfieldcreatedbytheN-1others(theCoulombrepulsionisonlydescribed

in an average, classical way, and the remaining instantaneous electron-electron

correlationiscompletelyneglected).However,byconstruction,suchawavefunction

mustsatisfytheconditionthattwoelectronsofanti-parallelspinscannotbefound


44

atthesamepositioninspace(Pauliexclusionprinciple).Theelectronsthereforefeel

anadditionalrepulsion,knownastheexchange,orFermicorrelation.

The game-changing idea of Kohn and Sham, in order to capture asmuch kinetic

energyaspossible,was to treat theelectronsasnon-interactingparticles, like in

Hartree-Fock. Considering such a non-interacting reference system, they built an

effectiveHamiltonianwith an effective, one-electron potential , containing

theaverageelectron-electronrepulsionandthenuclear-electronrepulsion:

(7)

(8)

Findingmuch inspiration in the Hartree-Fockmethod, they built a “Kohn-Sham”

wavefunction for thisreferencesystem,definedasaSlaterdeterminantofN

non-interacting one-electron “Kohn-Sham” orbitals . These orbitals are

determinedbysolvingNone-electronSchrödingerequations:

(9)

TheKohn-Shamelectrondensity is thenretrieved,bydefinition,bysumming the

squared moduli of these orbitals. Kohn and Sham then introduced a crucial

condition:theeffectivepotential mustbechosensuchthattheelectrondensity

ofthisfictitioussystem, ,exactlyequalsthegroundstatedensityofthereal

system,composedoffullyinteractingelectrons.

(10)

Havinganexpressionforthedensity,alltermsincludedinthetotalelectronicenergy

cannowbeexpressedasafunctionalof ,exceptthekineticenergythatstillneeds

tobewrittenintermsoforbitals,asintheHartree-Fockscheme.


45

(11)

(12)

(13)

(14)

Inthisapproach,allknownenergies(namelythenon-interactingkineticenergy,the

classical(average)Coulombelectron-electronrepulsion,andtheclassicalnuclear-

electronattraction)aredescribedexplicitlyviatheKohn-ShamHamiltonian,while

allremainingcorrectionsneededtoreachtheexactgroundstateenergyofthereal

interacting system (namely the missing part of the kinetic energy, the Coulomb

correlation,theexchangecorrelation,andtheelectronself-interactioncorrection)

are gathered in an additional term, the so-called exchange-correlation energy

.

As ,which is needed to build the orbitals and compute the electron density,

dependsitselfontheelectrondensity,thisisaself-consistentequationthatmustbe

solvediteratively,byloopingthrough:

• Guessinganinitialeffectivepotential ,

• Buildingtheeffectiveone-electronHamiltonians,

• Solving the one-electron Schrödinger equations to build the Kohn-

Shamorbitals,

• Computingtheelectrondensity,andthetotalelectronicenergy,

• Recalculating fromthedensity,andsoon…

One can also start by guessing initial orbitals, and then compute the density,

calculate , build and solve the Schrödinger equation, to finally find the

orbitals,andrepeattillconvergence.


46

2.1.4.Functionals

We just sawthat theexchange-correlation (XC) functional playsacrucial

roleinDFT.Itistheonlyremainingpartthatneedstobeapproximated,inorderto

getcloser tochemicalaccuracy.Manydifferent typesofXC functionalshavebeen

developedover the years, and fall in threemain categories: LDA,GGA, or hybrid

functionals.

ThesimplestapproximationtotheXCpotentialisthelocaldensityapproximation

(LDA),where the density is treated locally as a uniform electron gas. This

model israther far fromanyrealisticsituationforatomsormolecules,whichare

usually characterised by rapidly varying densities. However, it does give rather

accurate results in many cases, due to serendipitous error cancellation. The

generalisedgradientapproximation(GGA)wasthenintroducedtoaccountforthe

non-homogeneity of the real electron density, by adding information about the

gradientofthechargedensity, .

As ithasbeenknown from theHF theory that theexactexchangeenergycanbe

computedfromaslaterdeterminant,itthenseemedappropriatetointroducesome

“exact” Hartree-Fock exchange in the XC term, instead of relying on density

functionals.However,onlysomefractionofthis“HF-like”exchangeenergycanbe

usedtogoodaccuracy,sincethisisnowbuiltfromKohn-Shamorbitals,insteadof

thetrueorbitalsofthereal, interactingsystem.Thisistheconceptbehindhybrid

functionals.Forexample,theB3LYP10-13hybridfunctional,whichisoneofthemost

popularforchemicalapplications,contains20%ofHF-likeexchange.Inthisproject,

unlessstatedotherwise,IwillusetheB3LYPfunctional,oneofthemostsuccessful

andwidelyusedfunctionalsintheliterature,thatisoverallwell-balanced;itgives

accuratepredictions formanypropertiesoverawide rangeof chemical systems.

However,theB3LYPfunctionalhaswell-knownshortcomings:amongothers,itfails

atpredictingcharge-transfer(CT)excitations,Rydbergstates,andotherlong-range

interactionssuchasvanderWaalsforcesandhydrogenbonding.Toaddressthose

issues, the BHLYP (50% HF-like exchange) and the CAM-B3LYP14 (Coulomb-


47

attenuated, with a distance-dependent HF-like exchange percentage) functionals

will also be used. CAM-B3LYP is a range-separated exchange-correlation that

combinesthehybridqualitiesofB3LYPandthelong-rangecorrectionpresentedby

Tawada et al.15 The CAM-B3LYP functional comprises 19% HF-like exchange

interactionatshort-range,and65%HF-likeatlong-range,whichmakesitperforms

wellforCTexcitations,whichB3LYPunderestimatesenormously.

2.1.5.Basissets

In DFT, the complex system of coupled equations introduced by the Kohn-Sham

scheme needs to be solved in a computationally efficient way. Procedures that

expand theorbitalsonagrid canbeemployed,but are toomuchdemanding for

routine applications, and other techniques are required. For most applications,

linearcombinationsofatomicorbitals(LCAO)areusedtolinearlyexpandtheKohn-

Shamorbitalsinasetofbasisfunctions ,asintroducedbyRoothaanintheHF

framework:

(15)

If thebasiswascomplete ( ),everyorbital couldbeexpressedexactly.

However,thisisnotpossibleinrealapplications,andfinitesetsofLbasisfunctions

are used. The basis should be designed in away that allows for an orderly and

systematic extension towards completeness, rapid convergence to any atomic or

molecularelectronicstate(requiringjustafewtermsforanaccuratedescriptionof

theelectronicdistribution)andthefunctions shouldhaveananalyticalform

allowingforsimplemanipulation16.

Oneofthemostaccuratewaystodescribeatomicorbitals,fromaphysicalpointof

view, is touseSlater-typeOrbitals (STOs): indeed, theydecayexponentiallywith

distancefromthenuclei,andreachamaximumatzero,accuratelydescribingthe

long-rangeoverlapbetweenatomsandthechargeandspinatthenucleus.However,

STOsare computationallydemanding. Inmolecular calculations, themostwidely


48

used type of basis functions is Gaussian-type Orbitals (GTOs): they combine

reasonably short expansions with a fast integral evaluation, and relatively high

computational efficiency. Therefore, GTOs are used almost universally as basis

functionsinmolecularcalculationsandtheyarecentredatthenucleioftheatoms.

TheycanbeexpressedinCartesianform,as:

(16)

whereζistheorbitalexponentwhichtranslateshowcompact(largeζ)ordiffuse

(smallζ)theresultingfunctionis,and determinesthetypeoforbital(e.g.

or ,respectivelyforasoraporbital).

Nowadays,mostmolecular quantum chemistry codes relying on the Kohn-Sham

approach employ the so-called contracted Gaussian functions (CGFs), where the

basis functions are designed as linear combinations of primitive GTOs, with

coefficientschoseninsuchawaythattheyresembleasmuchaspossibleasingle

STOfunction.

Thenumberofprimitivefunctionsusedfortheexpansionof theelectrondensity

definesthequalityoftheCGFbasisset.Thesimplestexpansionutilisesonlyenough

functionstocontainalltheelectronsoftheneutralatomsanditiscalledtheminimal

basis set. The next level of accuracy is obtainedwith the double-zetabasis sets,

wherethetermζreferstotheexponentoftheprimitiveGTOsanddoublemeansthat

two contracted functions are employed for each atomic orbital. However, by

consideringthatchemicalreactivityisbetterdescribedbythevalencespace,onecan

limittheuseofCGFstothevalenceorbitals,anddescribetheinertcoreelectrons

with theminimal set. This defines the split-valence basis sets. The next level of

sophistication requires the use of polarisation functions, i.e. functions of higher

angular momentum than those occupied in the atom, such as p-functions for

hydrogen,whichensurethattheorbitalscandeformfromtheirinitialsymmetryto

betteradapttothemolecularenvironment9.


49

Inthisproject,unlessstatedotherwise,IwillmainlyusetheDZP(DoubleZetaplus

Polarisation) basis set, but the def-SVP (Split-Valence plus Polarisation), and the

def2-TZVP(P) (Triple Zeta Split-Valence plus Polarisation) basis setswill also be

employedinparticularcases.


50

2.2.Time-DependentDensityFunctionalTheory

Nowadays,DFTisawidelyusedmethodtopredictground-statequantities(ground

state energies and equilibrium geometries, binding energies, forces and electric

constants, dipolemoments, and static polarisabilities). However, to describe the

behaviourofmoleculesthatarenotintheirgroundstate,staticDFTisnotenough.

Indeed,theinabilityofthelattermethodtodescribeexcitationsseverelyrestrictsits

range of applications, since many crucial properties such as the band gap in

semiconductors, or the optical/fundamental gaps in molecules, as well as their

opticalabsorptionandemission,areassociatedwithexcitedstates.

Insuchcases,time-dependentDFTisthemethodofchoice.TD-DFTallowsoneto

followthedynamicresponseofsystemsoutofequilibrium(e.g.moleculesirradiated

byanexternalelectromagnetic field). Insuchaquantumsystem,whenelectronic

transitionsoccur,TD-DFTcanbeusedtocomputeexcitedstateproperties,suchas

excitationenergies,excited-stategeometriesandelectronicdensities17.

In this project, I will carry out linear-response TD-DFT calculations within the

context of the adiabatic approximation (see below), to predict absorption and

fluorescenceenergies,excited-stategeometries,forselectedconjugatedoligomers,

andcalculatethestandardreductionpotentialsassociatedwiththem,whentheyare

involvedinthephotocatalysisofwatersplittinghalf-reactions.

2.2.1.Formalism

The most direct approach to calculating the behaviour of electrons in a time-

dependent field would be to solve the time-dependent Schrödinger equation.

However, this taskcanrapidlybecomeextremelycomputationallyexpensive, and

henceprohibitive,mainlyduetotheCoulombrepulsionbetweenelectrons.Instead,

manyaspectsofTD-DFTbuilduponthegroundstateDFTframework.InDFT,the

Hohenberg-Kohn theorem provides a one-to-one mapping between any time-


51

independentexternalpotentialandtheresultingelectronicdensity,uptoaconstant.

InTD-DFT,itsanalogue,theRunge-Gross18theorem,providesaone-to-onemapping

between any time-dependent external potential and the resulting time-dependent

electronic density, up to a time-dependent constant. For a given initial state, the

electronicdensity,afunctionofjustthreespatialvariablesplustime,determinesall

otherpropertiesoftheinteractingmany-electronsystem2.

AnadaptationoftheKohn-Shamapproachcanthenbeused,asformallyprovenby

van Leeuwen19. It guarantees that the time-dependent density of an

interacting system, evolving from an initial state under the influence of a

potential can also be represented by a non-interacting system17, evolving

undertheeffectivepotential:

(17)

whichisafunctionalofthetime-dependentdensity,theinitialmany-bodystate,and

theinitialstate ofthenon-interactingsystem.However,ifthesystemisinitially

(at ) in itsgroundstate, theHohenberg-Kohn theoremsapply,and and

becomefunctionalsoftheground-statedensity,turning intoafunctionalofthe

densityonly, .Theinitialwavefunction ismadeupoftheKohn-Sham

orbitals ,followingaself-consistentsolutionofthestaticKohn-Shamequation.

Immediately after , the time-dependentpotential kicks in: the system starts to

evolveunderitsinfluence,andthetime-dependentdensityisgivenby:

(18)

wherethe followfromthetime-dependentKohn-Shamequation:

(19)


52

which translates the time-propagation of the N initially occupied single-electron

orbitalsfromatime (withtheconditionthat istime-independent)toa

timet.LikeinstaticDFT,aformallyunknownexchange-correlationpotentialisnow

definedasatime-dependentquantity,whichasalwaysneedstobeapproximated,in

aquantumchemistrycode,for“real”applications.

Currently,mostapplicationsofTD-DFTareintheso-calledlinearresponseregime

(i.e. for external perturbations that are small, in the sense that they do not

completelydestroythegroundstatestructureofthesystem),andarebasedupon

thelinearresponsetheory.Nevertheless,TD-DFTcanalsobeusedinthenon-linear

regime(e.g.whenusingstronglaserfields).

2.2.2.Adiabaticapproximation

Asthetime-dependentdensityevolves,theexchange-correlationpotentialexhibits

ahistorydependence,20meaningthatitisdefinednotsolelybythepresentdensity

butalsobyitshistory 0≤t′<t.Theadiabaticapproximation,which

is used in the vast majority of TD-DFT calculations in the literature, ignores all

dependenceonthepast,andallowsonlyadependenceontheinstantaneousdensity

ofthesystem21(i.e.itapproximatesthedensityasbeinglocalintime,whichisvalid

whenthetime-dependentpotentialchangesslowly).Inpractice,itmeansthatthe

(TD-)DFT functionals used throughout this project are in fact ground state

functionals.

2.2.3.Strengthsandlimitationsof(TD-)DFT

As seen previously, in DFT, the Kohn-Sham orbitals are a useful fictitious

representation for the real, interacting system. As a result, some properties are

poorlydescribedbythisapproach.Forexample,theKohn-ShamHOMO-LUMOgap

isnotthefundamentalgapofthesystem(asexplainedintheprevioussection,see


53

alsoChapter3).For theHeliumatom, thedifferencebetweentheKSgapandthe

fundamentalgaprangesupto3.5eV.

Time-dependent DFT generally yields accurate excited state properties, such as

bond lengths, vibrational frequencies, forces and dipolemoments, and it is well

establishedthatconventionalGGAandhybridfunctionalsareaccuratetowithin0.1-

0.5 eV in the description of local excitations22-23. In practice, adiabatic linear-

responseTD-DFTachievesremarkablebalancebetweenaccuracyandefficiency,to

calculatetheexcitedstatepropertiesofmolecularclusters.

However, it isknownthatTD-DFTusuallyfailstodescribenon-localexcitedstate

processes, such as charge-transfer and Rydberg excitations, or multiple

excitations24.Althoughitdoesn’tfundamentallysolvetheissue(intrinsictotheway

TD-DFTdescribesexcitations),therange-separatedCAM-B3LYPfunctionalwillbe

used,asmentionedearlier,inordertobetterapproximateexcitationsforsystemsin

whichcharge-transferislikelytobeproblematic.


54

2.3.Coupled-cluster

Coupled-cluster(CC)methods25-27,developedfromtheHartree-Fockframework,are

anotherwaytotacklethemany-bodyproblem.Insteadofrelyingontheelectronic

density, like(TD-)DFTdoes,theyreformulatetheelectronicSchrödingerequation

byexpressingthegroundstatewavefunction usinganexponentialexcitation

operator:

(20)

(21)

where isareferencewavefunction(typicallyaSlaterdeterminant),and isthe

clusteroperator,whichproducesacombinationofexciteddeterminants fromthe

referencewavefunction(where istheoperatorofallsingleexcitations, isthe

operatorofalldoubleexcitationsandsoforth).

CCmethodsallowforefficient,accurate,andsize-extensivedescriptionofsolutions

of the Schrödinger equation, for weakly correlated systems (i.e.where a single-

determinantHFsolutionalreadygivesagoodapproximationtothesoughtground-

statewavefunction,leavingonlyaverysmallcorrelationenergyunaccountedfor).

Dependingonthelevelofapproximationneeded,theclusteroperator caninclude

single excitations only (CCS, where , scaling as N4, N being the number of

orbitals), or also double excitations (CCSD, where , scaling as N6) and

triple excitations (CCSDT, where where scaling as N8), and so on.

Becauseofthehighcomputationalcostoffullytreatingmanyexcitations,someof

them can be estimated non-iteratively using Many-Body Perturbation Theory

arguments (e.g. CCSD(T) includes a full treatment of singles and doubles, while

approximatingthecontributionoftriplesusingperturbationtheory).


55

In this project, to complement (TD-)DFT calculations in specific cases, Iwill use

CC2:28itisanapproximationtoCCSDthatscalesasN5insteadofN6,whichmakesit

more computationally tractable. From the CC2 response functions, dynamic

propertiesaswellasexcitationenergiesandtransitionmomentscanbeobtained28.


56

2.4.Conductor-likescreeningmodel

When using computationmethods to studymaterials, especially when trying to

modelthepropertiesofmolecularclusters,takingintoconsiderationthechemical

environmentofsaidmolecularclusterisofutmostimportance.Indeed,molecules

arerarelyisolated,andthepresenceofasolventcanhaveastronginfluenceontheir

electronic,electrostaticandgeometricproperties.Thisisespeciallyrelevantinthe

caseofphotocatalysis,wherethephotoexcitationofelectronsleadstothecreation

ofexcitons,thatcansubsequentlydissociate,usuallyataninterface(e.g.betweena

solidparticle and the solution around it), andgenerate charge carriers thatmay

drivechemical(half-)reactions.Inordertocorrectlydescribethosephenomena,the

inclusionofsolventmodelsthereforebecomescrucial.

One strategy would be to model solvent molecules explicitly, by adding those

discrete molecules directly to the chemical system of interest. One would then

simulate their behaviour and interactions, not onlywith respect to the chemical

systemofinterest,butalsobetweenthesolventmoleculesthemselves.Forsuchan

approach to be relevant, it should take into account both short and long-range

solventeffects(e.g.hydrogenbonding,orthescreeningofchargesduetosolvent

polarisation),whichwouldrequiretheinclusionofhundredsofsolventmolecules,

andcanthereforerapidlybecomeprohibitivelyexpensivecomputationally.

Anotherstrategy(theoneusedthroughoutthisproject),fundamentallydifferent,is

todescribe the solventmolecules implicitly. The conductor-like screeningmodel

(COSMO)29-30 is a solvationmodel inwhich the solvent is treated as a dielectric

continuum,possessingarelativepermittivityεr.Itsurroundsthesolutemolecules

bythisdielectriccontinuumoutsideofacavity,constructedbyanaggregationof

atom-centredspheres,slightlylargerthantheirVanderWaalsradii.

In the context of a DFT calculation, for example, the COSMO model generates

screeningchargesonthecavitysurface,whosedistributionpolarisesthesolventas

a response. A three-dimensional cavity surface grid is constructed, and the


57

screening charges calculated. Then, the potential generated by those charges is

included in each self-consistent field (SCF) step of the DFT calculation, which

guaranteesthatbothscreeningchargesandmolecularorbitalsareconstantlybeing

updatedandoptimisedwhiletakingthesolventintoaccount.


58

2.5.Conformationalsearch

Somestructurallysimplemolecules,suchasmethanol,benzeneandethane,have

onlyoneuniqueconformer,atroomtemperatureintheirelectronicgroundstate.In

thatcase,theirmeasuredpropertiescanbeobtainedbyconsideringthestructureof

this single conformer. This is not necessarily the case for systems that possess

additionaldegreesoffreedom(e.g.chemicalgroupsthatcanrotatearoundsingle

bonds,suchasethanolandbutane),whereseverallow-energyconformersmayco-

exist,whichislikelytohappenwhenmodellinglarger,morestructurallycomplex

moleculeslikeoligomersandpolymers.Thepresenceofdifferentconformers,even

when structurally similar or close in relative energy, can dramatically alter the

overall properties of a chemical system, hence theneed toperforma conformer

analysis before choosing a particular molecular structure as a basis to run

simulations.

Inmyproject,Iwillusealow-modesamplingalgorithm31coupledwiththeOPLS-

2005forcefield32.Low-modesearchingexploresthelow-frequencyeigenvectorsof

thesystemtogeneratenewconformations.Startingfromagiveninputstructure,

thealgorithmgeneratesnormalmodes,thenselectsoneofthesemodes,amplifiesit

and distorts the molecule along it (within a predetermined distance limit) to

generateaverydifferentstructure.Thisdistortedstructure isthenoptimisedvia

theforcefield,andiftheresultinggeometryisunique,anditstotalenergyfallswithin

achosenenergywindow(typicallyafewhundredsofkJ/mol,i.e.afeweV)thenthe

newstructureissaved,andthewholeprocessrepeatedusingadifferentmode,until

themaximumnumberofsteps(typicallyseveralthousand)isreached.Insummary,

upon completion, the conformational search algorithm finds other molecular

structuresthatareenergyminimaonthepotentialenergysurfaceandranksthem

accordingtotheirenergies(theconformerswiththelowestenergybeingthemost

abundant).

In thecaseofconjugatedoligomers,modelledasmolecularclusters,several low-

energyconformersfoundviaconformationalsearcharesystematicallyconsidered,


59

andthenoptimisedusingDFT.Theiroptimisedstructuresandrelativeground-state

energiesarethencompared. Inthisproject, foreacholigomerstudied, I typically

selected the lowest-energy conformer found, as well as one higher-energy

conformer,andallotherconformersdescribedintheliterature,whenrelevant(e.g.

seeChapter6).


60

2.6.References

1. Born,M.;Oppenheimer,R.,"ZurQuantentheoriederMolekeln",AnnalenderPhysik1927,389,457-484.

2. Gross, E. K. U.; Maitra, N. T., Fundamentals of time-dependent densityfunctionaltheory.Springer:2012;Vol.837.

3. Thomas,L.H.,"Thecalculationofatomicfields",MathematicalProceedingsoftheCambridgePhilosophicalSociety1927,23,542-548.

4. Fermi,E.,"EinestatistischeMethodezurBestimmungeinigerEigenschaftendesAtomsundihreAnwendungaufdieTheoriedesperiodischenSystemsderElemente",ZeitschriftfürPhysik1928,48,73-79.

5. Burke,K.;Wagner,L.O.,"DFTinanutshell",InternationalJournalofQuantumChemistry2013,113,96-101.

6. Teller, E., "On the Stability of Molecules in the Thomas-Fermi Theory",ReviewsofModernPhysics1962,34,627-631.

7. Hohenberg, P.; Kohn, W., "Inhomogeneous Electron Gas", Physical Review1964,136,864-871.

8. Kohn, W.; Sham, L. J., "Self-Consistent Equations Including Exchange andCorrelationEffects",PhysicalReview1965,140,1133-1138.

9. Koch,W.; Holthausen,M. C., Bibliography. InA Chemist's Guide to DensityFunctionalTheory,Wiley-VCHVerlagGmbH:2001;pp265-293.

10. Vosko,S.H.;Wilk,L.;Nusair,M., "Accuratespin-dependentelectron liquidcorrelationenergies for local spindensitycalculations:a criticalanalysis",CanadianJournalofPhysics1980,58,1200-1211.

11. Lee,C.;Yang,W.;Parr,R.G.,"DevelopmentoftheColle-Salvetticorrelation-energyformulaintoafunctionaloftheelectrondensity",PhysicalReviewB1988,37,785-789.

12. Becke, A. D., "Density-functional thermochemistry. III. The role of exactexchange",JournalofChemicalPhysics1993,98,5648-5652.

13. Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J., "Ab InitioCalculationofVibrationalAbsorptionandCircularDichroismSpectraUsingDensityFunctionalForceFields",TheJournalofPhysicalChemistry1994,98,11623-11627.

14. Yanai, T.; Tew, D. P.; Handy, N. C., "A new hybrid exchange-correlationfunctionalusingtheCoulomb-attenuatingmethod(CAM-B3LYP)",ChemicalPhysicsLetters2004,393,51-57.

15. Tawada,Y.;Tsuneda,T.;Yanagisawa,S.;Yanai,T.;Hirao,K.,"Along-range-corrected time-dependent density functional theory", The Journal ofChemicalPhysics2004,120,8425-8433.

16. Helgaker, T.; Jørgensen, P.; Olsen, J.,Molecular electronic-structure theory.Wiley:2000.

17. Ullrich, C. A., Time-Dependent Density-Functional Theory: Concepts andApplications.OUPOxford:2012.

18. Runge,E.;Gross,E.K.U., "Density-FunctionalTheory forTime-DependentSystems",PhysicalReviewLetters1984,52,997-1000.

19. vanLeeuwen,R.,"MappingfromDensitiestoPotentialsinTime-DependentDensity-FunctionalTheory",PhysicalReviewLetters1999,82,3863-3866.


61

20. Maitra,N.T.;Burke,K.;Woodward,C.,"MemoryinTime-DependentDensityFunctionalTheory",PhysicalReviewLetters2002,89,023002.

21. Marques, M. A.; Maitra, N. T.; Nogueira, F. M.; Gross, E. K.; Rubio, A.,Fundamentals of time-dependent density functional theory. Springer: 2012;Vol.837.

22. Peach,M.J.G.;Benfield,P.;Helgaker,T.;Tozer,D.J.,"Excitationenergiesindensityfunctionaltheory:Anevaluationandadiagnostictest",TheJournalofChemicalPhysics2008,128,-.

23. Elliott,P.;Furche,F.;Burke,K.,ExcitedStatesfromTime-DependentDensityFunctional Theory. In Reviews in Computational Chemistry, John Wiley &Sons,Inc.:2009;pp91-165.

24. Burke,K.,"Perspectiveondensityfunctionaltheory",TheJournalofChemicalPhysics2012,136,-.

25. Čížek, J., "On the Correlation Problem in Atomic and Molecular Systems.Calculation ofWavefunction Components in Ursell-Type Expansion UsingQuantum-FieldTheoreticalMethods",TheJournalofChemicalPhysics1966,45,4256-4266.

26. Čižek,J.;Paldus,J.,"CorrelationproblemsinatomicandmolecularsystemsIII. Rederivation of the coupled-pair many-electron theory using thetraditionalquantumchemicalmethodst", International JournalofQuantumChemistry1971,5,359-379.

27. Čížek,J.,OntheUseoftheClusterExpansionandtheTechniqueofDiagramsinCalculationsofCorrelationEffectsinAtomsandMolecules.InAdvancesinChemicalPhysics,JohnWiley&Sons,Inc.:2007;pp35-89.

28. Christiansen, O.; Koch, H.; Jørgensen, P., "The second-order approximatecoupled cluster singles and doublesmodel CC2", Chemical Physics Letters1995,243,409-418.

29. Klamt,A.;Schüürmann,G.,"COSMO:anewapproachtodielectricscreeningin solvents with explicit expressions for the screening energy and itsgradient",JournaloftheChemicalSociety,PerkinTransactions21993,799-805.

30. Barone, V.; Cossi, M.; Tomasi, J., "Geometry optimization of molecularstructures in solution by the polarizable continuum model", Journal ofComputationalChemistry1998,19,404-417.

31. Kolossváry, I.; Guida, W. C., "Low Mode Search. An Efficient, AutomatedComputational Method for Conformational Analysis: Application to CyclicandAcyclicAlkanesandCyclicPeptides",JournaloftheAmericanChemicalSociety1996,118,5011-5019.

32. Jorgensen,W.L.;Tirado-Rives,J.,"TheOPLS[optimizedpotentialsforliquidsimulations] potential functions for proteins, energy minimizations forcrystalsof cyclicpeptidesandcrambin", Journalof theAmericanChemicalSociety1988,110,1657-1666.

CHAPTER3:

PredictingPPP’sthermodynamic

abilitytosplitwater

Inthischapter,Iwillpresentanewcomputationalmethodologythatwasdeveloped

inordertomodelthethermodynamicabilityofamolecule,inthiscaseaconjugated

polymer,poly(para-phenylene)(PPP),modelledasoligo(p-phenylene)clusters, to

splitwater intomolecularhydrogenandoxygen.Morespecifically, Iwilldescribe

andinvestigatekeyphotochemicalpropertiesofoligomers,suchastheiropticaland

fundamentalgaps,excitonbindingenergy,ionisationpotentialandelectronaffinity,

usingphenyleneasastartingpoint, thatwill thenbeused in thenextchapter to

consistently screen for new suitablewater splitting photocatalysts. The chemical

compositionandenvironmentofoligophenylenes,aswellastheirsizeandtopology,

willbetakenintoaccount.

Thecontentofthischapterhasbeentakenfrompartofthefollowingpublishedwork:

Guiglion P.; Butchosa C.; Zwijnenburg M. A., "Polymeric watersplitting

photocatalysts;acomputationalperspectiveonthewateroxidationconundrum",J.

Mat.Chem.A2014,2,11996-12004.

Guiglion P.; Butchosa C.; Zwijnenburg M. A., "Polymer Photocatalysts for

Water Splitting: Insights from Computational Modeling",Macromol. Chem. Phys.

2016,217,344-353.

CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater

63

3.1.MotivationandLiteraturereview

InthischapterIdiscussacomputationalmethodofanalysingthethermodynamic

abilityofmaterialstoactasphotocatalystsforwatersplitting,andapplyittoaclass

ofphotocatalysts thathaverecentlyattractedgreatattention;organicconjugated

polymers.

Chemically,theoverallphotocatalyticwatersplittingreactionisthecombinationof

twohalf-reactions:1-2

(A)

(B)

AsbrieflydescribedinChapter1,half-reaction(A)runsintheforwarddirection,the

reductionofprotonstohydrogengas,and(B)backwards,theoxidationofwaterto

oxygengasandprotons. Inorder forbothof thesehalf-reactions to takeplace,a

photocatalyst will have to provide electrons for half-reaction (A), and accept

electrons,orinotherwordsdonateholes,forhalf-reaction(B).Experimentally,half-

reaction (A) has a standard reduction potential of 0 V relative to the Standard

HydrogenElectrode(SHE)andhalfreaction(B)astandardreductionpotentialof

1.23V.Aphotocatalystneedsthereforetoprovideatleastthisamountofpotential

to split water. In practice, generally, a larger potential (e.g. 2 V) is required to

overcomekineticbarriersandenergeticlosses,thedifferencebetweentheeffective

andthermodynamicpotentialsbeingtheoverpotential.Anotherrequirementfora

successfulwatersplittingphotocatalystisthatthe(standard)reductionpotentialof

itscharge-carriers(electrons,holes)straddlethoseofhalf-reactions(A)and(B).In

otherwords, the (standard) reduction potential of its electrons should bemore

negativethanthatoftheprotonreductionhalf-reaction(A)andthepotentialofits

holesmorepositivethanthatofwateroxidationhalf-reaction(B)(seeFigure.3.1).


64

Figure3.1:Schemeshowinghowthe(standard)reductionpotentialsoftheidealphotocatalyststraddletheprotonreductionandwateroxidationpotentials.3

Experimental potential values are given relative to the Standard Hydrogen

Electrode(pH=0).Inthescheme,asexplainedin-depthinthenextsection,IPrefers

tothephotocatalyst'sground-stateadiabaticionisationpotential(theenergeticcost

ofextractinganelectronfromthetopofthephotocatalyst'svalenceband),EAtothe

ground-state adiabatic electron affinity (the energy released upon adding an

electrontothebottomofthephotocatalyst'sconductionband),IP*theexcited-state

ionisationpotential,andEA*theexcited-stateelectronaffinity.

Currently,mostpolymericphotocatalystsonlycatalysetheprotonreductionhalf-

reaction (A) in the presence of a sacrificial electron donor (e.g. methanol or

triethylamine)andthus,forthemoment,veryfewcansplitwaterassuch.Moreover,

oneofthefewpolymericsystemsinthe literaturethatarereportedtosplitpure

water, a carbon nitride polymer with polypyrrole nanoparticles on its surface4,

produceshydrogenandhydrogenperoxideinsteadofhydrogenandoxygen.Inthe

last twoyearshowever, twoadditionalpolymericsystemswerereportedthatdo

split pure water without using any sacrificial reagent; (i) a metal-free carbon

nanodot–carbon nitride nanocomposite5 that splits water via a two-step two-

electronpathway,oxidisingwaterintohydrogenperoxide,butthecarbonnanodots

subsequentlycatalysetheconversionofhydrogenperoxideintomolecularoxygen,

and(ii)acarbonnitridepolymer6decoratedwithin-situphotodepositedPtandPtOx


65

that act as co-catalysts for the proton reduction and water oxidation reactions,

respectively.

Thelackofexperimentalactivityforthewateroxidationhalf-reaction(B)couldin

principle be thermodynamic in nature, e.g. because the (standard) reduction

potentialofthepolymersholesisnotsufficientlypositive,oralternativelyakinetic

issue.Inthelattercase,aco-catalystthateitherlowersthekineticbarriersforwater

oxidation (i.e. reduces the required overpotential) or prevents electron–hole

recombination,mightturnapolymerthatonlycatalyseshalf-reaction(A)intoone

thatsplitspurewater. Incontrast, if the lackofactivity forreaction(B) isdue to

thermodynamics,apossibleroutetowardstruewatersplittingwouldbetousethe

polymer as a photocathode in combinationwith an electrical bias and a suitable

counterelectrode,oraspartofaZ-scheme.7-8

Inordertoresolveiftheissuewithwateroxidationforagivenpolymeriskineticor

thermodynamicinnature,intheZwijnenburggroup,wedevelopanapproachthat

notonlyconsidersthefreeelectronandholesbutalsotheboundexciton(excited

electron–holepair).Wealsoexplicitlyconsidertheeffectoftheenvironmentandthe

nuclear relaxation associatedwith localising an excited electron, hole, or exciton

(adiabaticpotentialsversusverticalpotentials).Iusethisapproachhereprimarily

torationalisethelackofwateroxidationactivityintheoriginalpoly(p-phenylene)

(PPP)photocatalyst9-10ofYanagidaandco-workers.Iwilldemonstratethattheholes

inPPPthermodynamicallycannotdrivetheoxidationofwater,butalsosuggestthat

forothersystemstheproblemmustbekineticinnatureandshouldberesolvable

withthechoiceofasuitableco-catalyst.


66

3.2.Modellingthepolymerandsacrificialreagents

3.2.1.Modellingthepolymer

In Kohn-Sham DFT, molecular orbitals are one-electron wavefunctions, each

associatedwithaspecificenergylevel.ThedifferenceinenergybetweentheHighest

OccupiedMolecularOrbital(HOMO)andtheLowestUnoccupiedMolecularOrbital

(LUMO)ofamoleculeisofparticularinterest,sinceitgivesanapproximationofits

optical gap, that is often sufficient.However, it is important tonote thatwhat is

measuredexperimentallyuponexcitationisthedifferenceinenergybetweentheN-

electron ground state and the N-electron excited state of themolecule (the real

opticalgap11).Inthatcase,thevalueoftheKohn-ShambandgapyieldedbyaDFT

calculationisoflittleinterest.Moreover,duringphotocatalysis,theeffectiveenergy

tobeprovidedbytheincidentphotonmustexciteoneelectron,andovercomethe

electron-holebindingenergy:inotherterms,itmustbeequalto,orhigherthanthe

molecule’sfundamentalgap11(seeFigure3.2).

Inotherwords,onemustconsiderboththegroundandexcitedstatesinorderto

assessaconjugatedpolymermolecule’scapabilitytosplitwater.Insteadofrelying

onapureHOMO-LUMOpicture, thepresentedcomputationalmethod introduces

severalquantities,eachassociatedtoaspecificelectronorholebehaviour:

• the ionisationpotentialof thegroundstate, IP,describinghowreadilyan

electron canbe extracted from theground-state system (or alternatively,

how readily a hole from the ground state can accept an electron from

somewhereelse),

• the ionisation potential of the exciton, IP*, describing how readily the

highest-energyelectronfromtheexcitedstatecanbegivenaway,

• the electron affinity of the ground state, EA, describing how readily an

additionalelectroncanbeaddedtotheground-statesystem,

• theelectronaffinityoftheexciton,EA*,describinghowreadilyanadditional

electroncanbeaddedtotheexcited-statesystem.


67

Figure3.2:Schemeillustratingtheconnectionbetweentheverticalpotentialsandthefundamental(orband)gapΔEfundtheopticalgapΔEoptandtheexcitonbinding

energyEEB.

Whenconsideringtheabilityofaphotocatalysttodrivethereductionofprotonsand

theoxidationofwateroralternativesacrificialelectrondonors,therearetherefore

four redox half-reactions to consider. These half-reactions, written in line with

conventionasreductionreactions,are:

(C)

(D)

(E)

(F)

wherePistheneutralphotocatalyst,P*theexcitedphotocatalyst(i.e.theexciton,a

boundexcitedelectron–holepair),andP-/P+thephotocatalystwithafreeelectron

intheconductionbandorfreeholeinthevalencebandrespectively.Freerefershere

tothefactthatthechargecarrierinP-/P+doesnotformpartofaneutralexciton.In

theremainderofthechapterIwillrefertothelatterthreesimplyasexciton,free

electronandfreehole.

Inhalf-reactions(C)and(E)theexcitonandfreeelectronactasareductant;they

donateanelectronandthehalf-reactionwillrunintheoppositedirectiontothat


68

shownabove.Intheothertwohalf-reactionstheexcitonandfreeholewillactasan

oxidant; acceptingelectrons. Finally, the freeelectronsandholes responsible for

half-reactions(E)and(F)couldeitherbeformedasaby-productofhalf-reactions

(C)and(D)ordirectlybythermalorfieldionisationoftheexciton:

(G)

Thefreeenergiesofhalf-reactions(C)–(F)andreaction(G)thenare:

(1)

(2)

(3)

(4)

(5)

∆G(E)and∆G(F)areequaltonegativeofthecommondefinitionofadiabaticelectron

affinityandionisationpotential.Similarly,∆G(C)and∆G(D)canbethoughtofasthe

negativeoftheexcitedstateionisationpotentialandelectronaffinity,IP*andEA*

respectively(seeFigure3.1).

Finally, the(standard)reductionpotentialsofthehalf-reactionscanbecalculated

via:

(6)

wherenisthenumberofelectronsinvolvedinthehalf-reactionandFtheFaraday

constant.Forthepolymer,therespectivepotentialswillbelabelledasIP,IP*,EA,and

EA*.

TheGibbsfreeenergiesofeachrelevantspeciescanbeconsideredasasumofthree

contributions:

(7)


69

whereUistheelectronicenergy,Gvib/rot/transthecontributiontothefreeenergyfrom

vibration, rotation and translation, andGsol the free energyof solvation.One can

considerapproximationstoequation(7)whereeitherorbothofthelattertermsare

ignored.Below,Iwillcommentontheeffectofsuchanapproximation.

Another approximation is to model the species in equations (1)–(5) using the

ground state geometry of the neutral photocatalyst for all species, i.e. ignoring

nuclear relaxation. This would be the so-called vertical approximation, yielding

verticalpotentials,whichcanbecomparedwith their fulladiabaticcounterparts.

Theverticalapproximationisnotonlyanumericalsimplificationbutalsophysically

meaningful.Contrastingverticalandadiabaticvaluesallowsonetodistinguishwhat

would happen if electron transfer was respectively fast or slow compared with

nuclearrelaxation.

Now, as alluded to in the previous section, for a photocatalyst to be able to

thermodynamicallydriveboththereductionofprotonsandtheoxidationofwater,

thepotentialsofhalf-reactions (D)and (F) (thepotentialsEA*and IP) shouldbe

more positive than the O2/H2O reduction potential and the potentials of half-

reactions (C) and (E) (the potentials IP* and EA)more negative than the H+/H2

reduction potential (see Figure 3.1). For either half-reaction to occur at an

appreciablerate,likewithanyelectrochemicalreaction,anexcessoverpotentialis

usually required; i.e. the potentials should be even more positive and negative

respectively.

Atthispoint,twoimportantobservationsneedtobemade.Firstly,ascanbeseenon

Figure3.2,thefundamentalandopticalgaps11-12aremirroredinthepositionofthe

potentials;theopticalgapcorrespondstothedistancebetweenIPandIP*(orEA

andEA*)whilethefundamentalgapisthedistancebetweenIPandEA.Secondly,my

calculations intrinsicallyyield results atpH0. It canbeargued that suchapH is

hardly representative of real water splitting conditions, although

(photo)electrocatalysisrarelyhappenatneutralpH,becauseofconductivityissues.

ThereasonwhyIchose,inmostcases,toshowtheresultsatpH0istwofold.First,

shifting results to pH 7 instead of pH 0 wouldn’t affect the main conclusions,

qualitatively,asitonlyshiftstheprotonreductionandwateroxidationpotentialsby


70

0.413Vtomorenegativevalues(aswillbeshownlater).Quantitatively, itmakes

proton reduction slightly more difficult to drive, while slightly favouring the

oxidationofwater. Second,usingpH0makeswatersplittingpotentialseasierto

locate,andresultseasiertovisualise,sinceprotonreductionisintuitivelypositioned

at0Vandwateroxidationat1.23V(or1.05V if takingthecomputationalvalue

insteadoftheexperimentalone).

3.2.2.Modellingthepotentialsofwaterandsacrificialelectrondonors

Standardreductionpotentialsforthereductionofprotons,the4-electronoxidation

ofwater,andthe2-electronoxidationofthesacrificialelectrondonorsmethanoland

triethylamine(TEA),13canbecalculatedfromtheirrespectivehalf-reactions(A),(B),

and:

(H)

(I)

Allthesehalf-reactionsinvolveoneormoreprotons.Calculatingthefreeenergyofa

proton,however,israthercomplicated.14-15Followingworkofothers,Ithususethe

experimentallydeterminedabsolutevalueofthestandardhydrogenelectrodefor

the potential of reaction (A) (4.44 V).16 The proton free-energy (G(H+)), for

calculatingthepotentialsoftheotherhalf-reactions((B),(H),(I))isdeterminedvia:

(8)

where∆G(SHE)isthefreeenergyofthestandardhydrogenelectrode(4.44eV).

Tertiary aliphatic amines, such as TEA, are probably the most used sacrificial

electron donors to fuel photochemical reduction reactions, thanks to their

degradation pathway, that features a carbon-centered radical with significant

reductivepower.17TEA’s2electronoxidationisasuccessionoftwomonoelectronic

oxidation steps: 13, 17 (i) the formation of an aminyl radical, which is then

deprotonatedandrearrangedintoacarbon-centredradical,and(ii)theformation


71

ofaniminiumspecies,whichinthepresenceofwater isthenhydrolysedtoform

diethylamine(DEA)andacetaldehyde(seeFigure3.3).

Figure3.3:Degradationoftriethylamineintodiethylamineandacetaldehyde,viatwo

1-electronoxidationsteps(TEAH+referstoprotonatedTEA).


72

3.3.Computationalmethodology

To calculate the photocatalyst potentials outlined in the previous section, in the

Zwijnenburggroup,weuseacombinationofDFT,18-19fortheground(free)energies

includingthoseofthecationandanion,andTD-DFT,20fortheexcitedstate(free)

energies. We use a molecular rather than a periodic approach21-23 as this

convenientlygivesusaccesstothevacuumreferencestateandallowustostudy

cationandanions(P+,P-)withouthavingtointroduceadditionalapproximations,

such as a neutralising background charge. The molecular approach is also the

naturaldescriptionoftheamorphouspolymericphotocatalystsstudiedbelow,with

excitedstatesdelocalisedoverafinitenumberofpolymerunits.

My calculations consist effectively of four major steps. First, I perform a

conformational search using an interatomic potential to find the lowest energy

conformers.Second,IoptimisethegeometriesoftheseconformersusingDFTforits

neutral(P),cationic(P+)andanionicstate(P-).Third,Ioptimisethegeometryofthe

conformer in its lowest singlet excited state (S1) using TD-DFT (P*). Fourth, I

calculatethevibrationalspectraforallfourminimumenergygeometries(P,P+,P-

andP*)todeterminethevibrational,rotationalandtranslationalcontributionsto

thefreeenergy;Gvib/rot/trans(x)inequation(7).Asimilarset-upisusedtocalculate

thestandardreductionpotentialsofwaterandthesacrificialelectrondonors,except

forthelackofaconformersearchandnoneedofTD-DFTcalculations.

The effect of the solvent, and the environment in general, is included in all

calculations, except where explicitly stated, by using the COSMO dielectric

continuumsolvationmodel,24-25allowingmetoestimatetheGsol(x)terminequation

(7). I consider both single point COSMO calculations on the gas phaseminimum

energystructuresandfullCOSMOgeometryoptimisations,exceptinthecaseofTD-

DFTcalculations,wherenoCOSMOgradientsareavailableinthecodeused,andfor

which hence only the former option is available. Within the COSMOmodel, the

properties of the environment are characterised by its relative dielectric

permittivity(εr).Calculationsforthepolymersareperformedforarangeof3values


73

(εr=1,5,30and80.1),while thestandardreductionpotentialsofwaterandthe

sacrificialelectrondonorsareonlycalculatedforthecaseofεr=80.1(solvationin

water).

Fortheinitialconformationalsearch,theOPLS-2005force-field26andthelow-mode

samplingalgorithm27as implemented inMacroModel9.9(ref. 28)areemployed. I

typicallyusedacombinationof10000searchstepsandminimumandmaximum

low-modemovedistancesof3and6Årespectively.Allthestructureslocatedwithin

anenergywindowof100kJ/molrelativetothelowestenergyconformeraresaved.

All the DFT and TD-DFT calculations employ the B3LYP29-32 hybrid Exchange–

Correlation(XC)functionalandtheTurbomole6.5code.33-35Thestandardbasis-set

usedisthedouble-ζDZP36basisset,butforselectedcalculationsalsothelargerdef2-

TZVP37basis-setisemployed.InallTD-DFTcalculations,IusetheTamm–Dancoff38

approximation.

Finally,forselectedsystems,Peach'sΛdiagnostic39iscalculated.TheΛdiagnostic

characterisestheoverlapbetweentheoccupiedandunoccupiedorbitalsinvolved

withanexcitation,andthelikelinessthatthisexcitationiswronglydescribedinTD-

DFTduetoithavingacharge-transfer(CT)nature.TheΛscalerangesfrom0(no

overlap,CT-excitation)to1(fulloverlap,fullylocalexcitation),andforexcitations

with Λ > 0.3, TD-B3LYP has been found to normally not suffer from any CT-

problems.39TheΛvaluesobtained,typically0.4–0.8,suggestthatCT-problemsare

unlikely to be an issue in the TD-B3LYP excited state description of any of the

systemsstudiedhere.


74

3.4.Resultsanddiscussion

3.4.1.PPPmodelanditsopticalproperties

Inthefollow-uptotheoriginalpaperofYanagidaandco-workers,9Shibataetal.10

estimatethatthephotocatalyticallyactivePPPmaterialconsistsapproximatelyofp-

phenylenechainsof7and11phenyleneunits(seebelow).Henceinmycalculations,

Iprimarily focuson thesemolecules,hereafter referred toasPPP-7andPPP-11.

Figure 3.3 shows a picture of the DFT optimised structure of the lowest energy

conformer of PPP- 7. To probe the effect of chain length Iwill also contrast the

propertiesoftheselongerchainswiththoseofthep-phenylenedimer,PPP-2.

Figure3.4:B3LYPoptimisedstructureofPPP-7.

Before discussing my prediction for the (standard) reduction potentials of the

excitonandthefreechargecarriers,Ifirstcomparethepredictedabsorptiononset

and luminescence signal of PPP-7 and PPP-11 with experimental data for PPP

powdersamplesfromtheliterature.Differentauthors10,40reportslightlydifferent

powderabsorption spectra forPPP.Thesedifferencesprobably arise fromslight

variationsinthePPPchain-lengthdistributionsobtainedduringsynthesis,andfrom

theexperimentaldifficultyincharacterisingthischain-lengthdistributionduetothe

poorsolubilityofPPPoligomersandpolymersincommonsolvents.Inthecaseof

thePPPsamplesofShibataandco-workers,10thefactthatboththePPP-7andPPP-

11sampleshaveasimilarabsorptiononset(seeFig.2Bintheirpaper)andthefact

thatthefluorescencespectrumtheyobtainforPPP-11isbimodal(seetheirFig.3)

suggestthatbothsamplesmostlikelycontainadistributionofPPPchainlengths.

The experimental labels PPP-7 and PPP-11, while probably representative, are

hencelikelytobeaslightsimplificationofthetruecomplexityoftheexperimental

samples.


75

WhencomparingexperimentalspectrawithTD-DFTpredictedexcitationenergies,

I make, following previous work in the Zwijnenburg group,41-43 the implicit

assumptionthat the topof the firstpeakorshoulder in theabsorptionspectrum

equals theexperimentalverticalabsorptiononset, and thatall absorptionbefore

thispeakarises fromvibrationalbroadening. For the small oligomers, one could

assume that the lowest vertical singlet-singlet excitation energy (LVEE) would

coincidewiththemaximumofthefirstabsorptionpeakandthatallexperimental

absorption intensity at lower energy (in otherwords between the experimental

onsetoflightabsorption,i.e.theopticalgap,andthefirstpeakmaximum)wouldbe

due tovibrationalbroadening.For longeroligomers,and thepolymer, thematch

mightbemorecomplicatedduetoinhomogeneousbroadeningandscattering.

Ascanbeseen fromTable3.1,uponmaking thisassumption,TD-B3LYPyieldsa

goodmatchtotheexperimentaldata.Inlinewiththeliterature,addingadielectric

embeddingtomodelthepolymermatrixaroundthechains(assumedtohaveεr=5)

changestheresultsonlymarginally.

Table3.1:ComparisonbetweentheexperimentalandTD-B3LYPpredictedopticalpropertiesofPPP-7andPPP-11.Allvaluesgiveninnm,andεr=5TD-DFTCOSMO

resultsshowninparentheses.

3.4.2.Probingtheinfluenceoftheenvironment

Whiletheeffectofdielectricembeddingissmallinthecaseofthepredictedoptical

spectra,thisisnotthecaseforthecalculatedreductionpotentialsoftheexcitonand

thefreechargecarriers.Focusingfirstonthestandardreductionpotentialsofthe

freeelectrons(EA),Figure3.4showsthatinPPP-7theEApotentialbecomesmore


76

positivebyapproximately1Vwhengoingfromthegasphase(εr=1)toaPPPchain

surroundedbywater(εr=80.1).Thechangeisfarfromlinearwithrespecttothe

relative dielectric permittivity. The predicted standard reduction potential in a

methanolenvironment(εr=30), thesolventusedbyShibataandco-workers10, is

verysimilartothatpredictedforwater,whiletheεr=5resultliesnumericallymuch

closertothatobtainedforwaterthanthatpredictedforthegasphase.Thestandard

reductionpotentialofthefreeholes(IP)becomesmorenegativeuponembedding

PPP, but again the shift is in the order of 1 V. As a result of these shifts, the

thermodynamicabilityofthepolymer,orphotocatalystingeneral,willchangewith

theenvironmentitisembeddedin.

Figure3.5:The(TD-)B3LYPpredictedIP,EA,IP*andEA*adiabaticpotentialvaluesofPPP-7atpH0asfunctionofthedielectricpermittivityoftheembeddingmedium

(wateroxidationandprotonreductionpotentialscalculatedwithεr=80.1).

Thestandardreductionpotentialsinvolvingtheexciton(EA*andIP*)showsimilar

behaviour.Uponincreasingtherelativedielectricpermittivityoftheenvironment,

the standard reduction potential of the reaction where the exciton donates an

electron(IP*),becomesmorenegativeandthestandardreductionpotentialofthe

reactionwheretheexcitonacceptsanelectron(EA*)becomesmorepositive.The


77

difference in potential between EA and IP* and between IP and EA* becomes

progressivelysmaller,approachingzeroforwater(0.2eV).ForPPP-7embeddedin

water, less than 10 kT of additional energy (at room temperature) needs to be

providedtoionisetheexcitonintofreechargecarriers(comparedwithmorethan

100kTforthegasphase).Splittingtheexciton,requiredforchemistryinvolvingthe

free charge carriers, is thus predicted to be much easier in a high dielectric

permittivityenvironment,evenifstillunlikely(seenextsectionandTable3.3).

The large shifts in predicted potentials with changes in the relative dielectric

permittivity of the environment in which the PPP polymer is embedded make

physicalsense.Allpotentialsinvolvechargedspecies,thefreechargecarriers,and

thosechargedspeciesare toamuch largerdegreestabilisedenergeticallyby the

dielectric embedding than their neutral counterparts. The predicted adiabatic

potentialsinFigure3.4neglectthecontributionofGvib/rot/transinequation(7).Data

includingGvib/rot/trans (see Table 3.2) shows that neglecting it generally results in

changesoftheorderof0.1Vinthepredictedpotentials.Ignoringnuclearrelaxation,

usingverticalratherthanadiabaticpotentials,wouldintroducealargererror(0.2–

0.3 V, see Table 3.2). In the remainder of this chapter, all polymer potentials

discussedwillbeadiabaticpotentialscalculatedforanaqueousenvironment(εr=

80.1),whereGvib/rot/transisneglected.

Table3.2:Vertical,adiabatic,andfreeenergy(Gvib/rot/trans)correctedpotentialsofPPP-7inwateratpH=0,calculatedwith(TD-)B3LYP/DZPandtheCOSMOsolvation

model(εr=80.1).AllvaluesinVolt.


78

3.4.3.Excitondissociation

Commonly,whenstudyingphotocatalysis,peopleonlyfocusonprocessesinvolving

free charge carriers (i.e. half reactions (E) and (F) as introduced in section 3.2),

implicitly assuming that excitons spontaneously dissociate and that the exciton

binding energy is negligible.While this is a fair assumption formany inorganic

semiconductors,forwhichexperimentallymeasuredexcitonbindingenergiesare

onlyintheorderoftensofmeV,thisisnotnecessarilythecaseforpolymers.For

example,forPPP,theverticalexcitonbindingenergy(ignoringnuclearrelaxationas

aresultoflocalisingahole,electronorexcitononthepolymer)ispredictedtobe≈

1200meVinthemiddleofapolymermatrixand≈170meVonorneartheinterface

withwater(seeTable3.3).Thedifferencebetweentheexcitonbindingenergiesin

the twoscenariosarises from the fact thatdielectric screeningof free charges is

larger inwater (εr=80.1) than inpolymer (εr≈2). Suchexcitonbindingenergy

values aremuch larger than kT at room temperature (26meV) suggesting that

excitonsdonotspontaneouslydissociateinthesepolymers.Goingfromthevertical

to theadiabaticpicture,wherenuclearrelaxation is taken intoaccount,doesnot

changethispicture,exceptneartheinterfacewithwater,formaterialsmadeofvery

short oligomers, where calculations suggest that exciton dissociation might be

spontaneous.

Table3.3:TD-B3LYPpredictedexcitonbindingenergyvaluesforPPP-6andPPP-12inthreedifferentenvironments:vacuum(εr=1),polymer(εr=2)andwater(εr=80.1).

Asidefromthecaseof“bulk”excitondissociationdiscussedabove,whereboththe

freeelectronandfreeholeremaininthesamephaseafterdissociation,althoughfar

apart,excitonscanalsodissociateontheinterfacebetweentwophases.Thiscould

be on the interface between different solid phases, which together form the

photocatalyst,asexploited inphotocatalyticheterostructures,oron the interface

betweenthephotocatalystandtheaqueoussolution.44Inbothcases,oneofthefree


79

chargecarriersremains inthephasewheretheexcitonwasoriginallygenerated,

while the other gets transferred to the other phase, and in the case of exciton

dissociationonthephotocatalyst–solutioninterface,issubsequentlyconsumedby

asolutionredoxreaction(seeFigure3.5).

Figure3.6:Illustrationofexcitondissociationatthesurfaceofapolymerparticlefor

thecasewheretheholeoftheexcitongoesintosolution,whereitdriveswateroxidation,whiletheelectronremainsontheparticle.

Forexample,thefreeholecanbetransferredtothesolutionandtakepart inthe

oxidationofwater(halfreaction(B))orthatofasacrificialelectrondonor,whilethe

freeelectroncanremainonthephotocatalyst,andsubsequentlyreduceaproton

(halfreaction(A)).Formanypolymers/oligomers,forexamplePPP,thisisthecase

foreitherpurewateror thecombinationofwaterandaSED.Thephotocatalytic

activityofsuchpolymerscanthenbeunderstoodfromathermodynamicpointof

view as resulting from excitons dissociating at the polymer–solution interface,

drivingoneofthesolutionhalfreactions,andgeneratingfreechargecarriersinthe

process,todrivetheothersolutionhalf-reaction.

Thisobservation,thatexcitonsinconjugatedpolymersshouldbesostronglybound

that they are unlikely to spontaneously fall apart in the bulk, is confirmed

experimentally (see section4.3ofChapter4 for an estimateof the experimental

adiabatic exciton-binding energy in P3HT and PPV). From the difference in the

measuredelectronaffinity45-47andtwo-photonphotoelectronspectroscopy(2PPE)


80

intermediate state energy45-46, their excitonbindingenergy is estimated tobe as

highas∼0.7(e)V.

Theimportanceofthepolymer–waterinterfaceinexcitondissociationsuggeststhat

ahighsurfaceareaisadesirablepropertyforapolymerphotocatalysttohave,and

should result in better quantum efficiencies. As such, photocatalysts based on

conjugated microporous polymers48 and covalent organic frameworks,49-50 with

largeinternalsurfaceareasbecauseoftheirporosity,aswillbediscussedinChapter

5,mightbeanattractiveproposition.

3.4.4.Understandingtheeffectofoligomerlength

Figure3.6comparesthestandardreductionpotentialspredictedforPPP-7,PPP-11

andthePPP-2dimer,inwater.ClearlythedifferencesbetweenPPP-7andPPP-11

are relatively small, while, in contrast, the potentials of PPP-2 are significantly

different.Overall,thepotentialsinwhichthepolymeracceptselectrons(IPandEA*)

becomemore negativewith chain length,while potentials inwhich the polymer

donateselectrons(EAandIP*)becomemorepositive.

ThesetrendsarelinkedtothefactthatPPPisaconjugatedpolymer,withafinite

conjugationlength,calculatedbelow.Theabsorptiononsetvalues(modelledasthe

LVEE)oftheinfinitechainweredeterminedbyperformingaleastsquaresfitofthe

TD-B3LYPpredictedabsorptiononsetvaluestotheequationsdevelopedbyMeier

etal.:51

(i)

(ii)

whereE(∞)andλ(∞)aretheabsorptiononsetoftheinfinitechain(ineVandnm

respectively),E(1)andλ(1)theabsorptiononsetofthemonomer(benzene),anda

andbnumericalconstants.


81

Figure3.7:ComparisonofthepredictedIP,EA,IP*andEA*adiabaticpotentialvalues

ofPPP-2,PPP-7andPPP-11inwater(εr=80.1)atpH0.

FollowingMeier,theconjugationlengthisheredefinedasthevalueofnforwhich

λ(n)differsfromλ(∞)bylessthan1nm,yieldingaconjugationlengthvalueof22

for PPP, which is rather long. The 1 nm value is, however, to a certain degree

arbitrary,anditshouldbenotedthat,ascanbeseenfromFigure3.7,thedifference

oftheabsorptiononsetofPPP-11andtheinfinitechainisoftheorderofonly0.05

eV. Additionally, while conjugation length may be a useful concept for linear

conjugated polymers, it might not be as well defined or meaningful for real

polymericmaterials,duetomolecularchainbending,entanglement,orcrosslinking.

Figure3.8:TD-B3LYP/DZPpredictedabsorptiononsetvaluesofPPPineVasa

functionofthenumberofphenyleneunitsinthechain.ThedashedlineindicatesthefittedabsorptiononsetofaninfinitePPPchain.


82

3.4.5.AssessingthewatersplittingpotentialofPPP

UsingthepotentialsshownonFigure3.6,Icannowshedlightontheabilityofthe

differentPPPoligomerstosplitwater.Thesepotentialsarestrictlyspeakingfora

solutionofpH0,becauseG(H+)iscalculatedfromtheexperimentalSHEpotential.

The Nernst equation can be used to correct these results, where the polymer

potentials relative tovacuumstay fixed,butall thewaterandsacrificialelectron

donorpotentialsthatinvolveH+shiftby0.059VperpHunit,tomoreexperimentally

relevantpHvalues.Figure3.8showsthesituationforpHvaluesof7(neutralwater)

and10(the likelypHof themethanol–triethylamine–watersolutionsused in the

work of Shibata and co-workers, see Table 3.4 for the numerical values of the

predictedpotentialsatthedifferentpHvalues).Itisclearfromthefiguresthatfor

the pH range studied, there is a strong thermodynamic driving force for proton

reductionbyboththefreeelectronandtheexciton.Theseresultssuggestthatthe

excitondoesnotneed tobesplit inorder forphotocatalysis to takeplace,as the

exciton itself can thermodynamically reduce protons. This is an important

observation,sinceinpolymersthereislesslikelytobeaspacechargelayertosplit

excitonsthroughfieldionisation.Thesituationforwateroxidationissubstantially

different. At pH 0, water oxidation by both the free hole and the exciton is

endothermic,whileatpH7and10 there isonlyamarginaldriving force for the

oxidationreactiontoproceed.Basedontheseresults,purewatersplittingisthus

unlikelytohappenintheabsenceofsomeexternalelectricalbias.Alternatively,PPP

mightfinduseaspartofaZ-scheme.7-8

Figure 3.8 also includes the predicted potentials for the 2-electron oxidation of

methanol and triethylamine (reactions (H) and (I)). Clearly there is a

thermodynamicdrivingforcefortheoxidationofbothbyPPP-7andPPP-11.The

drivingforceislargestfortriethylamine,inlinewiththeresultsofShibataandco-

workers,whereitsusegavethehighesthydrogenyield.Thetwoexpectedproducts

of the 2-electron oxidation of triethylamine (ethanol, produced through

photoreductionofacetaldehyde,seeequation(I)insection3.2,anddiethylamine)

areindeedobservedbyShibataandco-workerstobeproducedinconjunctionwith


83

hydrogen.10Thesuccessoftriethylamineasasacrificialelectrondonorisprobably

due to itsmore negative potential than that ofwater, combinedwith the fact it

involvesa2-ratherthana4-electronreaction.

Figure3.9:PredictedpotentialsofPPPatpH7(leftside)and10(rightside).Thepotentialsofthe2-electronoxidationoftriethylamine(TEA)andmethanolarealso

shown(blueandbrownlinesrespectively).

Table3.4:EffectofthepHontheadiabaticandfreeenergy(Gvib/rot/trans)correctedpotentialsofwater,hydrogenperoxideandsacrificialelectrondonors(triethylamineandmethanol).PotentialscalculatedusingB3LYP/DZPandtheCOSMOsolvation

model(εr=80.1).AllpotentialvaluesinVolt.

All results discussed here were obtained using the DZP basis-set. Some of the

potentialsforthepolymerandallofthesolutionreactionpotentials(reactions(A),

(B),(H)and(I),seeTable3.5)wererecalculatedwiththelargerdef2-TZVPbasis;

the effect of increasing the basis-setwas found to be generally small. Themost

noticeable change was an even better agreement of the calculated standard

reductionpotentialofwateroxidation(1.05VforDZPand1.21Vfordef2-TZVP)

withitsexperimentalvalue.Finally,whileGvib/rot/transisneglectedforthepolymer,it

is always includedwhen calculating the solution reaction potentials. Due to the

structural differences between reactants and products, the effect of neglecting

Gvib/rot/transwouldbesubstantiallybiggerhere.


84

Table3.5:Basis-seteffectsonadiabaticandfreeenergy(Gvib/rot/trans)correctedstandardreductionpotentialsofwater,hydrogenperoxideandsacrificialelectron

donors.CalculatedusingB3LYP(allvaluesinV,pH=0)


85

3.5.Conclusions

Using a newly developed computational approach, I probed the thermodynamic

abilityofapolymericwatersplittingphotocatalysts,PPP,todriveboththereduction

of protons and the oxidation of water. Some optical properties of PPP were

calculatedandcomparedtoexperimentaldata.Itookintoconsiderationtheeffect

ofthechemicalenvironmentaroundPPP,anddiscussedtheeffectofincreasingits

oligomerlengthonthepredictedIP,EA,IP*andEA*potentials.

Calculationsstronglysuggest(anditisconfirmedexperimentally)that,whilethis

materialcandrivetheoxidationofprotonsintohydrogengas,inthepresenceofa

sacrificial electron donor, it remains thermodynamically unable to oxidisewater

andhencesplitpurewater.ItisimportanttonotethatinPPP(andmoregenerally

for similar types of conjugated oligomers/polymers) according to calculations,

excitonsdonotspontaneouslydissociate,andareabletodriveoneelectronichalf-

reaction on their own, as they dissociate at an interface, similar to exciton

dissociation in organic photovoltaics on the donor−acceptor interface,52 and

generatefreechargecarriers.

Thepresentedcomputationalmethodproves itsvalueasa tool to systematically

study polymeric systems of interest, in the quest for an overall water splitting

photocatalyst,inarathercomputationallyinexpensiveway.Aftervalidatingitinthe

next chapter, itwill be used in Chapter 5 to carry out a broad screening among

varioustypesofchemicalsystems,anditspredictiveperformancewillbeassessed.


86

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51. Meier,H.;Stalmach,U.;Kolshorn,H.,ActaPolymerica1997,48,379-384.52. Few,S.;Frost,J.M.;Nelson,J.,"Modelsofchargepairgenerationinorganic

solarcells",PhysicalChemistryChemicalPhysics2015,17,2311-2325.

CHAPTER4:

Confrontingtheoretical

predictionstoexperimentaldata

In this chapter, I will compare the (TD-)DFT predicted reduction potentials

associatedwithchargecarriersandexcitonstothosemeasuredexperimentally,for

a variety of conjugated oligomers relevant towater splitting. Iwill confront the

resultsproducedbythetotal-energyΔDFTapproachtoexperimentalresultsfound

in the literature, obtained via two different methods, ultraviolet photoemission

spectroscopy(UV-PES)andcyclicvoltammetry(CV),formaterialsinthegasorsolid

phase, and in solution, respectively. Iwill thengaugehowwell predictions fit to

experimentaldata,andevaluatethequalityofmyresultsandoftheapproximations

used.Finally,Iwilldiscusswhatsuchacomparisoncanteachusabouttheuseof

conjugated polymers as photocatalysts, focussing on their large exciton binding

energy,andthemechanismthroughwhichfreechargecarriersaregenerated.

Thecontentofthischapterhasbeentakenfrompartofthefollowingwork:

Guiglion,P.;Monti,A.;Zwijnenburg,M.A., “ValidatingaDensityFunctional

Theory Approach for Predicting the Redox Potentials Associated with Charge

CarriersandExcitonsinPolymericPhotocatalysts”,J.Phys.Chem.C2017,121,1498-

1506.

CHAPTER4:Confrontingtheoreticalpredictionstoexperimentaldata

91


Oneofthecrucialrequirementsforapotentialphotocatalyst,polymericornot,to

meetisthethermodynamicabilitytodrivebothofthewatersplitting,asseeninthe

previouschapter,orCO2photoreductionsolutionhalf-reactions.Knowledgeofthe

IP,EA,IP*andEA*potentialsishencecrucialwhentryingtounderstandtheactivity

ofknownphotocatalystsordevelopnewones.Reliablymeasuringsuchpotentials,

especiallyunderoperatingconditions,however,isfarfromeasy.Forexample,cyclic

voltammetry on solid polymer films, placed on an electrode in contact with an

aprotic polar solvent system, is generally hard to interpret because the

voltammogramstendtobebroad,showsignsof irreversibility1-3and involve the

incorporationofcounterionsandsolventmoleculesintothefilm,4whichwouldnot

be expected under photocatalysis conditions. A related problemwith CV is that

measuringtheelectronaffinityvaluesofpolymersiscomplicatedbythefactthat

theseoftenlieoutsidethestabilitywindowofcommonsolvents,andthatonethus

hastobecautiousnottoconfuseasignalduetosolventoxidationwiththesignature

ofelectronaffinity.Theabilitytocalculatetheredoxpotentialsofchargecarriers

andexcitonsthereforeisveryuseful,especiallyasitmoreoverallowsonetopredict

thoseofhypotheticalmaterialsthathavenotbeensynthesisedasyet,andthusto

screencomputationallyforpromisingphotocatalysts(seeChapter5).Thelatteris

anespeciallyattractivepropositionforpolymericmaterials,forwhichthesynthesis,

purificationandcharacterisationofboththepolymerandconstitutingmonomers

canbeverytimeconsuming.

The main difference between our group’s computational approach and that

developed by others5-11 is that it revolves around molecular calculations in

combinationwithacontinuumdielectricscreeningmodel12todescribethematerial

and itsenvironment rather thancalculationsusingperiodicboundaryconditions

(PBC).

Thefocus, inthecaseofpolymericmaterials,onasinglepolymerstrandandthe

assumptionthatallintermolecularinteraction,beitwithotherpolymerstrandsor


92

water,canbedescribedintermsofadielectricresponse,isrelatedtothefactthat

suchmaterialsareoftenamorphousoronlypoorlycrystallised.Therefore,wedo

not have good experimental structural models for polymers to use in PBC

calculations,andevenifwedidconstructperiodicmodelsartificially, theywould

not necessarily be representative of the solid. Another difference between our

approachandthatofmanyothersisthatwecalculatethepotentialsusingatotal-

energyΔDFTapproach,ratherthanequateIPandEAwithgeneralisedKohn-Sham

(GKS)orbitalenergies(seeChapter2),whichisproblematic,atleastconceptually,

especiallyforEA.13-14Finally,wealsotakeintoaccountthe(self-)trappingofcharge

carriers and excitons, i.e. the formation of polarons and polaronic excitons, into

accountbyconsideringadiabaticratherthanverticalpotentials.

In this chapter, I compare predicted polymer and oligomer potentials to those

measured from three distinctly different datasets; gas phase photoemission

spectroscopy(PES)foroligomersofpoly(p-phenylene),15solutionelectrochemistry

data for oligomers of poly(p-phenylene)16 and poly(fluorene)17 derivatised with

solubilisingalkylchains,andsolid-state(inverse)PESdata10,15,18-27forarangeof

conjugatedpolymers.Thedifferencesbetween thisandpreviousworkvalidating

the use of hybrid DFT for predicting redox potentials in the literature28-40 is a

combinationof(i)ourfocusonoligomers/polymersratherthansmallmoleculesor

metalcomplexes,(ii)ouremphasisonpotentialsincondensedphases,includingthe

solid-state,(iii)thefactthatwecalculateadiabaticratherthanverticalpotentials

and/or(iv)becausewealsoconsiderexcitedstatepotentials.

I will show that (TD-)DFT calculations using the standard B3LYP41-42 density

functional yield reasonable gas and solution phase potentials and rather

consistentlygoodsolid-statepotentials,thelatterinlinewithpreviousworkforthe

IPandEAofsmallmolecules.32-34Iwillfurtherdemonstratethatthesegoodsolid-

statepotentialsappear tobe theresultof ratherbenignerrorcancellation. Iwill

discussthatthegoodfitforsolid-statepotentialsinvacuumsuggeststhatasimilar

accuracycanbeexpectedforcalculationsonsolid-statepolymersinterfacedwith

water. Iwillalsooutlinetherequirementsonadensity functionaltoconsistently

calculatethepotentialsassociatedwithchargecarriersandexcitonsinpolymeric


93

materials. Finally, I will examine what a comparison of experimental and

computationally predicted potentials teaches us about conjugated polymers as

watersplittingphotocatalysts.


94


Potentials, be they computationally predicted or experimentally measured, are

always expressed with respect to a reference (typically vacuum in the case of

photoelectronspectroscopy)andareferenceelectrode,forexample,thestandard

hydrogen electrode (SHE), for liquid electrochemistry. A key parameter in the

conversionfromonepotentialreferencetoanotheristhevalueoftheSHEabsolute

potential (SHEAP), for which a range of experimental values are proposed,

something that is partly related to different possible choices for thermodynamic

standard states and partly due to extra-thermodynamic assumptions.43 In this

chapter, I consider two values of the SHEAP: 4.44 V, the original IUPAC-

recommendedvalue44asused in thepreviouschapterwhenstudyingPPP,anda

morerecentlyproposedvalueof4.28V.43Wherepossible,Iwillpresentresultsfor

bothSHEAPchoices.However,ifinthetextonlyonevalueismentionedforagiven

systemthiswillbebasedontheuseof4.44VforSHEAP,whichisthedefaultvalue

usedthroughoutthisthesis.


95


4.3.1.Ionisationpotentials

Whenanoligomerorpolymer,ormoregenerallyamolecule,istakenfromthegas

phaseintoasolution,thesolidstateorasolidincontactwithasolution,theIPofthe

molecule gets reduced and becomes shallower, through two different

mechanisms.45-46 Firstly, prior to ionisation, in solids, where the molecules are

densely packed, hybridisation raises the energy of the highest-energy occupied

orbital, fromwhichanelectronwillget removedupon ionisation.Secondly,after

ionisation,thedielectricnatureoftheenvironmentwillscreenthegeneratedcharge

by polarisation and stabilise energetically the charged species formed. The

differencebetweenthegasandcondensedIPvaluesiscommonlyreferredtoasthe

polarisation energy, even if only part of this difference is the result of dielectric

polarisation and, in contrast to what the names suggest, it also contains a

contributionduetohybridisation.

Table4.1:ExperimentallymeasuredandcomputationallypredictedIPvaluesofp-phenyleneoligomersandpolymersindifferentenvironmentsvs.SHE(allvaluesin

volts).

aAbsoluteIPvs.vacuumconvertedtoSHEscalebyashiftof4.44and4.28(insideparentheses),respectively.bOligomerswithbranchediso-alkylchainsattheterminalp-

carbonatoms.cMeasuredinDCMinthepresenceof0.2Mn-Bu4NPF6supportingelectrolyteagainstSCE,valuesconvertedtoSHEscalebyapplicationofashiftof+0.244.

dObtainedthroughlinearextrapolationvs.1/n.eValueobtainedbytwodifferentextrapolationmethodsintheoriginalexperimentalpaper.fModelledusinganoligomerof

12units.

ExperimentalCVdatatakenfromreference16,andUV-PESdatafromreference15.


96

Table4.1showsexperimentalandDFTpredictedvaluesoftheIPofoligomersand

polymersofp-phenyleneinthegasphase,inadichloromethane(DCM)solution,and

as a solid. I will first concentrate on the experimental values taken from the

literature.15-16 While one has to be slightly careful with comparing these

experimental potentials as they aremeasuredusing two fundamentallydifferent

methods, ultraviolet PES (UV-PES) and CV, and because of the need to convert

between different potential references, vacuum for UV-PES and the standard

calomelelectrode (SCE)/SHEand the ferrocene/ferroceniumredoxcouple in the

caseofCV,suchacomparisonisveryinsightful.

Asexpectedbasedontheliterature,thegasphaseIPvaluesarethedeepest,with

thesolidstateandDCMsolutionvaluesbeing1-2Vsmallerthanthecorresponding

gas phase values. More interestingly, the polarisation energies for the different

oligomersinthesolidstateandDCM,whichcanbeextractedfromtheIPvaluesin

Table 4.1, are very similar. As the dielectric permittivity of the solid-state

oligomer/polymerphaseislikelytobesmallerthanthatofDCM,especiallygiven

thefactthatthesupportingelectrolyteislikelytoincreasetheeffectivedielectric

permittivityoftheDCMsolutionthroughion-pairformation,47thissuggeststhatthe

smallerdielectriccontributiontothepermittivityandthusscreeningoftheformed

chargeinthesolidstaterelativetothesolutionismorethancompensatedbythe

largercontributionduetohybridisationintheformer.Onthebasisofthenumbers,

itishardtoextractanexactvaluefortheeffectofhybridisation,butitislikelytobe

atleastafewtenthsofvolts.Theexperimentalpolarisationenergyvaluesmeasured

fortheoligomers, finally,aresimilar inmagnitudetothosemeasuredfororganic

crystals45-46andappeartodecreasewitholigomerlength.

Figure4.1:Structuresofoligomermodelsstudiedcomputationally.


97

Moving on to the computational predictions, where the alkyl side chain is

approximatedbyanisopropylgroup(seeFigure4.1),inspectionofTable4.1shows

that,forthegasandsolutionphases,ΔDFTcalculationsusingtheB3LYPfunctional

yieldIPvaluesthatare0.5−0.6Vshallower,i.e.lesspositive,thanthosemeasured

experimentally.AsimilarshiftwasreportedbyBaikandFriesnerwhencalculating

EAvaluesofsmallmoleculesinsolutionusingB3LYP.28Calculationsusingaslightly

higherdielectricpermittivityfortheDCMsolutionthanthatofpureDCMinorderto

take intoaccount that thesupportingelectrolytewill likely increase theeffective

dielectricpermittivity(seeTable4.2),aswellascalculationswithlargerbasis-sets

(Table4.3),donotsufficientlychangethisobservation.

Table4.2:ExperimentallymeasuredandcomputationallypredictedIPvaluesofp-phenyleneandfluoreneoligomersandpolymersinaDCMsolutionvs.SHE(allvalues

involts).

aAbsoluteIPvs.vacuumconvertedtoSHEscalebyashiftof4.44and4.28(insideparentheses),respectively.cMeasuredinDCMinthepresenceof0.2Mn-Bu4NPF6

supportingelectrolyteagainstSCE,valuesconvertedtoSHEscalebyapplicationofashiftof+0.244.

PhenyleneexperimentalCVdatatakenfromreference16,andfluoreneCVdatafromreference17.

Moreover, a comparison between similar ΔB3LYP calculations and experimental

data forthe ionisationpotentialsofoligo(fluorene) insolution(Table4.2) findsa

similar0.5−0.6Vshift,suggestingthistobeaquitegeneralfeature.Incontrastto

thegasandsolutionphases,incalculationsforthesolidstate,inwhichhybridisation

isneglected,thepredictedIPvaluesare0.2−0.4Vmoreshallow,lesspositive,than

thosemeasuredexperimentally.


98

Table4.3:ComparisonofthecomputationallypredictedIPsofp-phenyleneoligomers(vs.SHE,leftside)andIPandEAvaluesofapolyfluorenepolymer(vs.Vacuum,rightside)calculatedusingthedouble-zetaDZPandtriple-zetadef2-TZVPbasis-sets.

cMeasuredinDCMinthepresenceof0.2Mn-Bu4NPF6supportingelectrolyteagainstSCE,valuesconvertedtoSHEscalebyapplicationofashiftof+0.244.

PhenyleneexperimentalCVdatatakenfromreference16

Forthedissolvedoligomers,thecalculationsreproducetheexperimentallyobtained

polarisationenergyvaluesratherwell,butthesolid-statepolarisationenergiesare

underestimated by ∼1 V. If the isotropic dielectric screeningmodel used in the

calculation correctly reproduces the dielectric component of the polarisation

energy, this would suggest that the effect of hybridisation is ∼65% of the

polarisationenergyandfarfromnegligible(calculatedfromvaluesinTable4.1for

the trimer and hexamer: comparison between the difference between (i)

experimentaldata ingasphaseandsolidstate,and(ii)B3LYPpredictions ingas

phase and solid state). However, the absolute values of the solid-state IPs,most

relevantinthiswork,are,asdiscussedabove,reasonablywellreproduced.Asthe

inherent density functional related error and the error introduced by neglecting

hybridisationhavesimilarmagnitudesandoppositesigns,thesolid-statevalueslie

closetotheirexperimentalcounterpartsbyerrorcancelation.

This success in reproducing experimental values of solid-state IP values for

polymersappearstobenotlimitedtooligomersandthepolymerofp-phenylene.

Figure4.2andTable4.4showacomparisonofIPsofarangeofconjugatedpolymers

measuredexperimentallybyUV-PES15,18-21,23,27andB3LYPcalculations,againusing

εr = 2, for oligomers of 12 units (see Chapter 1 for the structures of different

polymers studied). Concentrating on the polymers without side chains, for all

materials,exceptperhapspolypyrrole,thematchisquitegood(maximumdeviation

of−0.44V,forpolypyrrole,andameanabsolutedeviationof0.20V)andtheDFT

predictions correctly recover the relative ordering of the IPs of the different


99

polymers.Sincepolypyrrole iseasilyoxidisable,21 thedeviationobserved for this

materialcaninpartfinditsorigininexperiment.

Figure4.2:Comparisonbetweenthepotentialspredictedusing(TD-)B3LYPandεr=2(thicklines),andmeasuredexperimentally(thinlines),forarangeofconjugated

polymers.

Table4.4:Comparisonbetweensolid-stateIPvaluesforthedifferentpolymerspredictedbyB3YLPcalculations,andexperimentalvaluesfromtheliterature.All

valuesinVoltvs.vacuum.PPVreferstopoly(p-phenylene-vinylene).

avaluesincludingoutlyingchargecorrectioninbetweenparentheses.bvalueobtainedbytwodifferentextrapolationmethodsintheoriginalexperimental

paper.cresultforcalculationsincludingshortalkylchains.

drangeofvaluesreporteddependingontheregiochemistryandmolecularweight.


100

Useofaslightlyhigherdielectricpermittivitythan2fortheheteroatomcontaining

polymers, to account for the fact that such polymers probably have a higher

dielectricpermittivitythanpurehydrocarbonpolymers(seeTable4.5),ifanything

worsensthefit.Inthiscontext,itisimportanttorememberthatphotoemissionis

likelytomostlyinvolvemoleculesnearthepolymer−vacuuminterfaceduetothe

surface sensitivity of UV-PES and that such molecules as a result will be less

screenedthaninthebulk.48

Table4.5:B3LYPsolid-stateIPandEAvaluesforpolypyridine,polypyrroleandpolythiophenecalculatedusingεr=10insteadof2.AllvaluesinVoltvs.vacuum.

These results also suggest that the single oligomer embedded in a dielectric

continuumapproximation,whichignoresdetailsofmolecularpacking,worksvery

well for these amorphous/quasi-crystallinepolymers, even if for fully crystalline

materialstherearecasesknownwherenon-isotropicpackingeffectsarelargeand

onehastogobeyondthecontinuumapproach.49Overall,theseresultsandthefact

thatthe(dielectric)effectofgoingfromaninterfacewithvacuumtowaterismost

likelyadditivesuggestthatthecomputationalsetupusedwillalsoprovidedecent

predictionsfortheIPofapolymerinterfacedwithwater.Protonationofapolymer

mightinduceanadditionalshiftinthepotentials,butthisis,evenforthenitrogen

containingpolymers,unlikelytobeanissueat(near)neutralpH.

4.3.2.Electronaffinities

Incontrast totherelativemultitudeofreferencedataontheIPofoligomersand

polymers,thereisverylittleexperimentaldataontheEAofoligomersandpolymers,

especiallyinthesolidstate.Mostreportedelectronaffinitiesareobtainedbyadding

theopticalgap,i.e.theonsetoflightabsorption,tothevalueoftheIP,butthisisa

questionable approach.More theoretically justified values can be obtained from


101

either inverse PES or the high kinetic energy edge of two-photon PES (2PPE)

spectra.Suchdataonlyseemtobeavailable,currently, for threeof thepolymers

discussedintheprevioussection,whicharethealkyl-chainderivatisedversions:of

PT, poly(3-hexylthiophene) (P3HT),26-27 of PF, poly(9,9-dioctylfluorene)24 (PF8),

and of PPV, poly(2-methoxy-5-(2-ethyl-hexyloxy)-p-phenylene vinylene)25 (MEH-

PPV).

Table4.6:Comparisonbetweensolid-stateEAvaluesforthedifferentpolymerspredictedbyB3YLPcalculations,andexperimentalvaluesfromtheliterature.All

valuesinVoltvs.vacuum.PPVreferstopoly(p-phenylene-vinylene).

avaluesincludingoutlyingchargecorrectioninbetweenparentheses.bresultforcalculationsincludingshortalkylchains.

crangeofvaluesreporteddependingontheregiochemistryandmolecularweight.

AscanbeseenfromFigure4.2intheprevioussectionandTable4.6above,thefitis

good for P3HT and PPV, and slightly less good for PF8. This is for calculations

neglectingthealkylsidechains.However,calculationsthattakethesesidechains

intoaccount,includedinTable4.6,showthatthesesidechainsarepredictedtoonly

haveasmalleffecton theelectronaffinity.While these threedatapointsarenot

sufficient to properly test it in terms of its ability to correctly predict electron

affinitiesofpolymers in thesolidstate, theyat leastgivesomeconfidence inour

approach.Similarly,asfortheIP,thedifferenceintheEAforapolymerincontact

with vacuum andwater is expected to be adequately described by changing the

dielectricpermittivityfrom2tothatofwater.


102

4.3.3.Excited-statepotentials

Experimentalbenchmarkdatafortheexcitedstatepotentialsofrelevantpolymers

areasrareasdataforEA,ifnotrarer.Thereexistsome2PPEdata,wheretheprocess

ofionisationoftheintermediatestatebythesecondphotoncanbehypothesisedto

correspondtotheionisationofa(self-trapped)excitonandthusIP*,foronlytwo

polymers: P3HT,26 and MEH-PPV.25 As can be seen from Figure 4.2 in previous

section4.3.1,andinTable4.7below,theexperimentallymeasuredvaluesappearin

linewith the values predicted by our computational approach for the polymers

withoutsidechains.Moreover,forbothP3HTandMEH-PPV,EAandIP*aresplitby

∼0.7(e)V,i.e.theadiabaticexciton-bindingenergy,inexperiment,andby∼1(e)Vin

my calculations. Similarly, as forEA,while these twodatapoints for IP* arenot

sufficienttoproperlytestthecomputationalmethodologyintermsofitsabilityto

correctly predict electron affinities of polymers in the solid state, it does give

confidenceinourapproach.

Table4.7:Comparisonbetweensolid-stateexcited-stateionisationpotentialsforthedifferentpolymerspredictedbyB3YLPcalculationsandexperimentalvaluesfromthe

literature.AllvaluesinVoltvs.vacuum.

Experimental data that could directly validate EA* predictions, not found in the

literature,wouldrequirea2PPEequivalent inversephotoemissionspectroscopy.

However,asbydefinition,thesplittingbetweenIPandEA*isthesameasbetween

EAandIP*,thefitbetweenpredictedIP*and2PPEvaluesincombinationwiththe

fitbetweenexperimentalandcomputationalIPvaluessuggeststhatEA*mightbeas

welldescribedasIP*.Again,justasforIPandEA,theeffectofwaterislikelytobe

additiveforIP*andEA*.


103

4.4.Perspectives

Consistentlycalculatingthesetofpotentialsassociatedwiththechargecarriersand

excitonisaratherdemandingapplication.OtherdensityfunctionalsthanB3LYP,for

exampleoptimally tuned range-separateddensity functionals, 36, 39, 50might very

likelyyieldmoreaccuratevaluesfortheionisationpotentialorelectronaffinityof

oligomersinthegasphaseorinsolution.However,tobeusefulinthiscontext,use

ofsucha functionalshouldsimultaneouslyallowforthecalculationsof theother

potentials,includingtheexcitedstatepotentials(andhencetheopticalproperties

ofasystem)andthepotentialsofsolutionreactions,andalltoasimilarconsistent

standard.Additionally,whilethedependenceonerrorcancelationtopredictdecent

solid-statevaluesisunsatisfyingfromatheoreticalpointofview,itsavesonefrom

havingtodocalculationsonextendedmodelsofthesolid.

Ifourestimateof thecontributionofhybridisationto thepolarisationenergy for

PPPiscorrectandageneralfeatureofconjugatedpolymers,thencalculationswith

functionalsthatgivebettergasphasevaluesmightrequirecalculationsonexplicit

stacks to obtain solid-state values or ad hoc shifts. The latter is probably as

conceptually unsatisfying as relying on error cancelation,while the former is, at

leastforpolymersthatareamorphousorpoorlycrystallised,difficulttoachievedue

to,asdiscussedinthefirstsectionofthischapter,thelackofmeaningfulstructural

models.Anadditionalcomplicationwithcalculationsonexplicitstacks is the fact

thatthepercentageofHartree−Fockexchangeincludedthedensityfunctionalfixes

theintermoleculardielectricscreeninginsidethestack.51Asaresult,theeffective

dielectric constant inside the stackmightbedifferent from itsdesiredvalueand

differentfromthatusedintheexternalcontinuumdielectricscreeningmodel.


104

4.5.Conclusions

For a range of polymers relevant to photocatalysis, the predictions of density

functional theory for the redox potentials associated with charge carriers and

excitonswerecomparedtothosemeasuredexperimentally.Agoodfitwasfound

betweenthevaluespredictedusingΔB3LYPandthosemeasuredexperimentally,for

theionisationpotentialsofsolid-statepolymersincontactwithvacuum.Amongthe

differentclassesofpotentialsavailableexperimentallyforconjugatedpolymers,the

onesconsideredwerethosemeasuredundertheconditionsmostsimilartothose

occurringduringwatersplitting.

Although experimental datameasured under similar conditions for the electron

affinity and excited state ionisation potential are much more limited, the fit to

ΔB3LYP is decent in both cases.Overall, the comparisonwith experimental data

givesgoodconfidenceintheuseofΔB3LYPtopredictpolymerpotentialsforsolids

andsuggeststhat,iftheeffectofreplacingtheinterfacewithvacuumbyaninterface

withwaterislargelydielectricinnature,thehereusedapproachshouldalsogive

accuratepredictionsunderwatersplittingconditions.

In contrast to the case of solid-state polymers, the ΔB3LYP predicted ionisation

potentials for oligomers of p-phenylene in the gas phase and solutions and

oligomersoffluoreneareoffby0.5−0.6Vwithrespecttoexperiment.Acombination

ofthisobservationandcomparisonofexperimentalandtheoreticalestimatesofthe

polarisationenergysuggeststhattheconsistentlygoodfitforsolidpolymersmay

betheresultoferrorcancellation.Despitethelackofsimilardatafortheelectron

affinity and excited state potentials, but it stands to reason that the decent

descriptionofthesepotentialsissimilarlytheresultoferrorcancelation.


105

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CHAPTER5:

BeyondPPP;screeningfor

suitablephotocatalysts

Inthischapter,IwillapplythecomputationalmethodologypresentedinChapter3

and validated in Chapter 4, to systematically calculate the redox potentials

associatedwithfreechargecarriersandexcitons(IP,EA*,IP*,EA),foravarietyof

oligomericsystems.Thoseincludeoligofluorenederivatives,phenyleneandpyrene-

based conjugated microporous polymers (CMPs), linear oligomers of common

conjugated “building blocks” (pyridine, pyrimidine, pyrazine, pyrrole, furan, and

thiophene),andcarbonnitrideflakesoroligomers(basedontriazineandheptazine

motifs).Iwillcommentonkeyfactorsthatcanenhancephotocatalyticproperties,

anddescribethestrengthsandlimitationsofourcomputationalapproach.

Someofthecontentofthischapterhasbeentakenfromthefollowingpublishedwork:

Guiglion P.; Butchosa C.; Zwijnenburg M. A., “Polymeric watersplitting

photocatalysts;acomputationalperspectiveonthewateroxidationconundrum”,J.

Mat.Chem.A2014,2,11996-12004.

ButchosaC.;GuiglionP.;ZwijnenburgM.A.,“CarbonNitridePhotocatalysts

forWaterSplitting:AComputationalPerspective“,J.Phys.Chem.C2014,118,24833-

24842.

Sprick R.S.; Jiang J.-X.; Bonillo B.; Ren S.; Ratvijitvech T.; Guiglion P.;

ZwijnenburgM.A.;AdamsD. J.; CooperA. I., “TunableOrganicPhotocatalysts for

VisibleLight-DrivenHydrogenEvolution”,J.Am.Chem.Soc.2015,137,3265-3270.

SprickR.S.;BonilloB.;ClowesR.;GuiglionP.;BrownbillN.J.;SlaterB.J.;Blanc

F.;ZwijnenburgM.A.;AdamsD.J.;CooperA.I.,“VisibleLight-DrivenWaterSplitting

CHAPTER5:BeyondPPP;screeningforsuitablephotocatalysts

110

UsingPlanarizedConjugatedPolymerPhotocatalysts”,Angew.Chem.Int.Ed.2016,

55,1792-1796.

GuiglionP.;ButchosaC.;ZwijnenburgM.A.,“PolymerPhotocatalystsforWater

Splitting:InsightsfromComputationalModeling”,Macromol.Chem.Phys.2016,217,

344-353.


111


The computational method introduced in Chapter 3 and validated in Chapter 4

offersatoolforscreeningmoleculesthatisrobustandcomputationallytractable.

The idea of using computational screening in order to find promising candidate

photocatalystsisnotanewone.However,studiesthatcomparetheeffectivenessof

chemicalsystemstosplitwatertraditionallyemployarathercrudeapproximation.

Such studies generally assess the relevance of photocatalysts by predicting and

comparing the positions of their Kohn-Sham HOMO and LUMO. As explained in

Chapter3,thepresentedmethodologygoesbeyondthoselimitationsbyconsidering

both the ground state and excited state of chemical systems, using a TD-DFT

approach.

Thescreeningforrelevantphotocatalystswillbecarriedoutbygraduallymoving

awayfrompurePPP.Iwillfirstinvestigatecopolymersofphenyleneandfluorene

(and of other fluorene-type derivatives), then focus on ConjugatedMicroporous

Polymers(CMPs)basedonphenyleneandpyrene,beforeshiftingmyattentiontoa

varietyofheteroatom-containinglinearoligomers.Finally,Iwilldiscussoneofthe

mostpromisingcandidatephotocatalystsforoverallwatersplitting,CarbonNitride

(CN).

Copolymersbasedonfluoreneanditsderivativesareaclassofmaterialsthatshow

greatpotential. Starting froma rather flexiblePPPchain, it ispossible to further

planariseandrigidifythemolecularbackbone,by introducingamethylene linker

betweeneveryotherphenyleneunit(effectivelyreplacingsomephenylenemoieties

byfluorenemotifs).Indeed,extendedplanarisationinpolymershasbeenshownto

decrease the electron-hole binding energy, and to increase exciton dissociation

yields1-2 and charge carrier mobility.3-4, which should result in overall better

photocatalyticactivity.Additionally,Sprickandco-workers5recentlydemonstrated

experimentallythatplanarisationleadstoincreasedhydrogenevolutionrates.Iwill

thereforediscussseveralplanarisedcopolymersofphenyleneandfluorene,andof

fluorene-typederivatives(introducedinChapter1)tohopefullyfindtheoriginof


112

such enhanced photocatalytic performance for the reduction of protons to

molecularhydrogen.

ConjugatedMicroporousPolymers(CMPs)havealsogeneratedalotofinterestin

the last few years6-9. Phenylene and pyrene-based CMPmaterials (introduced in

Chapter1)areratherchallengingtocharacteriseexperimentally,hencetheneedfor

acomputationalapproachtohelpelucidatetheirstructure-propertyrelationships.

In particular, the origin of the relatively good performance of pyrene-phenylene

CMPscomparedtotheirpurephenylenecounterparts,notedbySpricketal.,10needs

tobeexplained.

Apartfromfluorenederivativesandpyreneandphenylene-basedCMPs,othertypes

of oligomers, built from linear arrangements of common conjugated molecules

(introduced,alongwithPPP,inChapter1),widelydescribedinfieldssuchasorganic

photovoltaicsandorganiclight-emittingdiodes,willbeinvestigated.Thoseinclude

linear homopolymers of pyrrole, pyridine, diazine, pyrimidine, thiophene,

phenylene-vinylene,andfuran,aswellastheirphenylenecopolymers.

Linearpolymerand2Dcarbonnitridematerialsareanotherverypromisingtypeof

materials, that have received much attention in the last few years, due to the

experimentalreport,in2009,byAntoniettiandco-workers,oftheirexperimental

activityforthereductionofprotons,inthepresenceofasacrificialelectrondonor,

and for the oxidation ofwater, in the presence of a sacrificial electron acceptor,

undervisiblelight.11Morerecently,othercarbonnitridesystemscontainingcarbon

nanodots12ordecoratedwithPt-basedco-catalysts13werereported tosplitpure

waterintheabsenceofanysacrificialreagent.

Inthenextsection,thestandardreductionpotentialsofCNclustermodelswillbe

calculated, first, inorder toevaluate theestablishedcomputationalmethodology,

and second, to hopefully determine the reason why in most cases12-13,

experimentally,carbonnitride,untilrecently12-13,wasonlyknowntocatalyseeither

theprotonreductionhalf-reactioninthepresenceofaSED,ortheoxidationofwater

intomolecularoxygeninthepresenceofaSEA,butnotbothconcurrently.11


113

Amongthosedifferenttypesofmaterials,Iwillaimatfindingthemostpromising

candidatesforsolar-drivenwatersplitting,i.e.photocatalyststhathavedeep(very

positive)IPandEA*,andshallow(verynegative)EAandIP*,alwaysbearinginmind

theadditionalconstraintthattheabsorptiononsetoftheidealmaterialshouldbe

smallenoughforittoabsorbvisiblelight,andlargeenoughforittodrive,atleast

thermodynamically,ideallyboththeprotonreductionandthewateroxidationhalf-

reactions.


114


5.2.1.Fluorene-basedoligomersandderivatives

The standard reduction potentials of four fluorene-type oligomers (Fl-Ph, Cz-Ph,

DBT-Ph andDBTsulf-Ph, as introduced in Chapter 1, see p. 24)were calculated,

usingthesamemethodologyasforPPPinChapter3,i.e.using(TD-)B3LYP/DZPand

theCOSMOsolvationmodel,withεr=80.1totakeintoaccounttheinfluenceofan

aqueous environment. The standard reduction potentials of the

diethylamine/triethylamine(DEA/TEA)redoxcouplewasalsocalculated.Asshown

in our previous work on PPP14, using the dielectric permittivity of methanol or

triethylamine(experimentallyusedasamixtureofsacrificialreagentsbySpricket.

al5) instead of water only makes a small difference. The magnitude of the

contributionofvibrational/rotational/translationalfree-energytothepotentialsof

thehalf-reactionsassociatedwith thereductionof theoligomers(IP,EA, IP*and

EA*)issmall,asfoundinourpreviouswork14-15,becauseofthestructuralsimilarity

betweenproducts and reagents,but it is large for theoxidationhalf-reactionsof

waterandtriethylamine.

Figure5.1:Comparisonbetweenthepredictedpotentialsforthep-phenylene(left)andtheFl-Ph(right)oligomers,calculatedatpH=0.Thenumbersalongthex-axis

correspondtothenumberofequivalentphenylenemoieties.


115

Figure5.2:PredictedpotentialsfortheCz-Ph(left),theDBT-Ph(centre),andtheDBTsulf-Ph(right)oligomers,calculatedatpH=0.

Theabsorptiononsetsofthoseoligomerswerealsopredictedbycalculatingtheir

lowestverticalsinglet-singletexcitationenergy(LVEE)usingTD-B3LYP,eitherin

thegasphase,orinchloroform,thesolventusedexperimentallywhenmeasuring

theUV-Visspectrumofthesolubleoligomers,byusingtheCOSMOmodelwithεr=

4.81.

Figure5.3:PredictedLVEEinchloroform.

Foragiventypeofoligomer,ourcalculationspredictadecreaseinabsorptiononsets

andashiftofEA/IP*potentialstowardsmorepositivevalues,whentheoligomer

lengthincreases(seeFigures5.1,5.2and5.3),inlinewithpreviousobservationsfor


116

PPP.However,inallcases,thosepotentialsremainconsiderablymorenegativethan

thepotentialforprotonreductiontohydrogen,meaningthattherewillstillbe,in

principle,amplethermodynamicdrivingforceforhydrogengeneration(Figures5.1

and 5.2) in the long chain limit. It is therefore predicted that all fluorene-type

oligomersconsideredshouldbeabletorunthereductionofprotonstohydrogen,

althoughitisdifficulttoknowwithcertaintywhichmaterialwillperformbestbased

oncalculationsonly,duetothesimilarityoftheirEA/IP*potentials.

Sprickandco-workers,ourcollaboratorsfromtheUniversityofLiverpool,carried

outaseriesofexperiments5wheretheymeasuredthehydrogenevolutionratesof

small molecules including p-phenylene and Fl-Ph oligomers, and of polymers

including PPP and Fl-Ph (and other fluorene-type, such as Cz-Ph, DBT-Ph and

BDTsulf-Ph) copolymers. They also observed (unpublished work) that the

photocatalyticperformanceofsomefluorene-typehomopolymers,i.e.withoutany

phenylenemoiety,wasworse,ingeneral,comparedtotheirphenylenecopolymer

analogues.For thisreason,althoughsomepure fluorene-likehomopolymers(e.g.

polyfluorene, not shown here) are predicted to have slightly more favourable

potentials forprotonreductionandsmalleropticalgapthanFl-Phpolymers, this

sectionwillfocusoncopolymersinsteadoffluorene-likehomopolymers.Forallthe

oligomers considered, Sprick et al. measured a steady, almost linear increase in

hydrogenevolutionrateswithincreasingchainlength(seeFigure5.4),relatedtoa

redshiftofabsorptiononsets,enablinglongeroligomerstoabsorbalargerpartof

thevisiblespectrum,andthustogeneratemorechargecarriers,leadingtoenhanced

ratesofhydrogenformation.5

Withina rangechemical compositions, foragivenoligomer length,my(TD-)DFT

calculationspredictnosignificantchangeinabsorptiononset(Figures5.1and5.2

foroptical/fundamentalgaps,andFigure5.3forLVEE).Forshortoligomerlengths,

oligo(p-phenylene)s are expected to have consistently higher LVEE values than

fluorene-co-phenylenes.Incontrast,inthelongoligomerlimit,allthematerialswe

modelledhaveverysimilarLVEEvalues.This isconfirmedexperimentallybythe

fact that the measured absorption onsets lie between 2.7 and 2.9 eV for all

copolymers (where theconjugation limit ispresumably reached),whereas forall


117

smalloligomers,theyrangefrom4.4to3.5eV,decreasingasexpectedwitholigomer

length.

Figure5.4:Experimentallymeasured5photocatalyticperformanceofoligomersagainsttheiropticalgap.SM1-5refertoPPPofoligomerlengths3-7,FSM1-3refertoFl-Phcontaining2-4phenyleneequivalents,andDBT,DBT-SO2andCzrefertoour

DBT-Ph,DBTsulf-PhandCz-Phrespectively.

Itcanbeobservedthat,inlinewiththesuccessfuluseoftriethylamineasasacrificial

electrondonor,triethylamineoxidationisoverallpredictedtobeexothermic;the

calculatedIP/EA*potentialsareconsiderablymorepositivethanthetriethylamine

oxidationpotential.Thesamealsoholdsformethanoloxidation,notshownhere,

althoughthere,theoverpotentialissmaller,asthemethanoloxidationreactionis

predicted to have a potential of +0.29 V instead of +0.03 V in the case of

triethylamine(seeChapter3).

Interestingly, it is the DBTsulf-Ph copolymer that achieves the highest hydrogen

evolution rate experimentally,5 both under UV and visible light irradiation

(~145µmol/h,i.e.upto15timesbetterthanpurePPP,whichevolvesfrom~10to

~15µmol/hofhydrogendependingonthetypeofpolymerisation)followedbythe

DBT-Phcopolymer(~102µmol/h).BylookingattheEAandIP*potentialsalone,it

seems that the computational approach doesn't predict those dramatic

improvementsinHER,whichcan’tberationalisedbyadecreaseinopticalgap,nor

byan increasedthermodynamicdrivingforceforprotonreduction.However, it is

importanttokeepinmindthathydrogengenerationisenabledbytheoxidationofa


118

SED,heretriethylamine,whosereactionrateisregulatedbythepositionsofIPand

EA* potentials. The overall water splitting reaction rate (and HER), therefore, is

limited by the slowest reaction between proton reduction and triethylamine

oxidation.TheIPandEA*values,fortheDBTsulf-Pholigomers,areslightlydeeper

thatforallotherfluorene-typecopolymers(seeFigure5.2),whiletheirEAandIP*

levels(responsibleforhydrogengeneration)donotvarysignificantly,meaningthat

triethylamineoxidationwouldbeslightlyfavoured,whichcouldpartlyexplainthe

better performance of DBTsulf-Ph compared to the other fluorene-types, if

triethylamineoxidationisindeedtherate-limitingstep.ThisincreaseinHERisalso

likelytobeascribedtoacombinationofotherfactors,suchasachangeincharge

carrierlifetime,chargecarriermobility,orspecificsurfacewettability.

5.2.2.Conjugatedmicroporouspolymers

Phenyleneandpyrene-phenyleneCMPs

Inafirststep,theLVEEofthephenyleneandpyrene-phenyleneCMPclustermodels

(presentedinChapter1)werecalculatedusingTD-DFTwithacombinationofthe

B3LYPandCAM-B3LYPfunctionals(theCAM-B3LYPresultsarenotshownhereas

theyyieldsimilarresultsandleadtothesimilarconclusions).

As discussed previously in the case of fluorene, for small molecules, one could

assumethattheLVEEcoincideswiththemaximumofthefirstabsorptionpeak.For

themorecomplicatedextendedCMPs,however,thesituationismoreconvoluted.

TheabsorptionspectrumofaCMPcanbeunderstoodastheweightedaverageof

theabsorptionspectraofthedifferentlocalenvironmentspresent,thosesampled

inourcalculationsbythedifferentclustermodels.Asaresult,ifthemorered-shifted

environmentsformonlyarelativelysmallpartoftheCMPstructure,thetruevertical

absorptiononsetoftheCMPandotherverticalexcitationswill lieinbetweenthe

experimentalabsorptiononsetandthemaximumofthefirstabsorptionpeak.


119

Figure5.5:ComparisonbetweentheB3LYPpredictedLVEEofphenylene(BLandBS)

andpyrene-phenylene(PSandPL)clustermodelsofringsizes3to6(seenomenclaturep.30,Fig.1.15).

Weobservethat,independentlyofringsizeandringtype(i.e.shortorlongvertices),

phenylene ringsarealwayspredicted tohave themostblue-shiftedLVEEvalues

(seeFigure5.5).TheLVEEofthepyrene-phenyleneringsarefoundtobemorered-

shiftedrelative to thepurephenylenerings(whilepurepyrenerings,notshown

here,arepredictedtohavethemostred-shiftedverticalabsorptiononsetvalues,

unsurprisingly16).Itislikelythattheabove-mentionedtrendinLVEEforringcluster

modelsisvirtuallyindependentofringsizeandringtype,andthatthisshiftisalso

theoriginoftheexperimentallyobservedredshiftinabsorptiononsetsoftheseries

ofCMPsconsideredbySpricketal.,10frompurephenylene,topyrene-phenylene,

andpurepyrene.Forrealmaterials,thering-sizedistributionislikelytobedifferent

fordifferentCMPsintheseries,andsomeoftheintermediatecompositionsmight

havephenylene-richorphenylene-poordomains,butwebelievethatthiswillonly

resultinsecond-ordershiftsrelativetothesimpleeffectofcomposition.

Computationally,theoriginoftheeffectofcompositionappearstobeachangein

the character of the orbitals contributing to the excitations responsible for the

absorptiononset.Thehighestoccupiedmolecularorbital(HOMO)ofapyrenering

alwayslieshigherinenergythanthatofitsphenyleneequivalentandequallythe


120

lowestunoccupiedmolecularorbital(LUMO)ofapyreneringalwayslieslowerin

energythanthatofitsphenyleneequivalent.

Inasecondstep,toassessthesematerials’relevanceforwatersplitting,theirIP/EA*

and EA/IP* potentials were calculated for the different cluster models (see

nomenclaturep.29andp.30Fig.1.15).

Figure5.6:TD-B3LYPpredictedIP,EA*,IP*andEAvaluesofthedifferentringclustermodelsforthephenyleneandpyrene-phenylenestructures,versusthestandardreductionpotentialsofprotonreduction,wateroxidationanddiethylamine

oxidation.PotentialscalculatedforpH=0,inwater(usingCOSMOwithεr=80.1).

Allisomersconsideredshowsignificantdrivingforceforthereductionofprotonsto

hydrogen, regardlessofclustersizeseeFigure5.6).Thereare,however, twokey

differencesbetweenphenyleneandpyrene-phenylenematerials.Weobservethat

phenyleneclusters(BSandBL)overall,havemorenegativeEA/IP*potentials(by

~0.5 to 0.7 V), but that their optical gaps are on average 1 eV larger than their

pyrene-phenylene counterparts (as can be seen on both the potential and LVEE

figuresabove).Wecanthereforepredictthat,althoughphenyleneclustershavea

larger thermodynamic driving force for proton reduction, pyrene-phenylene

clusters will absorb visible photons more readily, creating more excitons, thus

generating more charge carriers, potentially resulting in improved hydrogen


121

evolutionrates.Unfortunately, thoseobservationsarenotsufficienttodetermine

accurately which of those two competing effects will predominate. However, in

contrast to theprevioussection,where thesurprisinglygoodHERofDBTsulf-Ph

wasinpartrationalisedbyalargerdrivingforceforSEDoxidation,weknowthat

hereitcannotbethecase,sinceforpyrene-phenyleneclusterscomparedtopure

phenyleneclusters,boththeIP/EA*andtheEA/IP*couplesaremoreunfavourable

(respectivelyforSEDoxidation,andforprotonreduction).

Incontrasttotheirgoodpredictedperformanceforprotonreduction,allphenylene

and pyrene-phenylene clusters show no or negligible driving force for water

oxidation to oxygen. Therefore, sacrificial electron donors such as di- or

triethylamine,whoseoxidationispredictedtobeveryexothermic,willneedtobe

usedaselectrondonors.

Experimentally10, all CMPs across a range of chemical composition, from pure

phenylene to 50:50 pyrene-phenylene, show steady hydrogen production under

visible-light illumination,with a gradual increase from the pure phenylene CMP

(~1µmol/h), to the 50:50 pyrene-phenylene CMP, which performs best

(~17µmol/h).Theconsistentdecreaseinopticalgapbetweenthosetwotypesof

CMPs, which is also confirmed experimentally, seems to be the origin of the

enhanced performance for the hydrogen evolution. Measurements subsequently

performed on CMPswith even increased pyrene content (obtained by gradually

replacingphenylenelinkersbypyrenelinkers,effectivelyincreasingpyrenecontent

graduallyfrom50%to100%)showeddramaticallyworsehydrogenevolutionrates,

correspondingtomuchsmalleropticalgaps(decreasingfrom2.33to1.94eV, i.e.

absorbingUVinsteadofvisiblelight).Allhydrogenevolutionratesweremeasured

inthepresenceofdiethylamineasasacrificialelectrondonor,sinceexperimentally

thewateroxidationhalf-reactioncannotbedrivenbytheseCMPs.

Itappears,despitethefactthatthepositionofEA/IP*potentialsiswhatdictatesifa

materialcantheoreticallydrivethereductionofprotonstohydrogen,thatthewidth

of the optical gap plays a crucial role in their overall experimental hydrogen

evolutionperformance.AmongtwoCMPsthathavewell-positionedEAlevels,the


122

bestcandidatewillthereforebetheonewhichhasanopticalgapbetween2.3and

2.5eV,i.e.smallenoughtoabsorbmanyvisiblephotons,butafundamentalgaplarge

enoughtostraddlethepotentialsofthetwowatersplittinghalf-reactionsanddrive

thosereactions.

Covalenttriazineframeworks

The standard reduction potentials of some CTF fragment clusters were also

calculated. TheCTFmaterials of interest (presented in Chapter 1) are similar to

CMPs,totheextentthattheyincludep-phenylene“linker”buildingblocksintheir

molecularbackbone,andcanformringstructures(suchasCTF-1,seeFigure5.7,

andother related ring clusters)17-18, but also veryunique since theyhave a high

nitrogencontent,aretypically2-dimensional(althoughinpractice,stackingusually

makes them 3-dimensional), and possess an inherently different connectivity

(trivalenttriazinevs.tetravalentphenylenevertices).

Figure5.7:B3LYPoptimisedgroundstatestructureofCTF-1,modelledasasingle

ringcluster.

Figure5.8belowshowsacomparisonbetweenthepredictedpotentialsofthoseCTF

clusters,andthatofCTF-1(seenomenclaturep.31Fig1.16).First,weobservethat

all CTF fragments havemuch deeper IP/EA* values than the phenylene/pyrene

CMPs,andthattheseareideallypositioned(morepositivethanthewateroxidation

potential),meaningthattheyshouldtheoreticallybeabletodriveoxygenevolution.

TheirEA/IP*values,althoughdeeperthanthoseoftheCMPsduetotheiroverall

smalleropticalandfundamentalgaps,arestillpredictedtobesufficientlynegative

to drive hydrogen evolution. Second, we notice that the potentials of cyano-


123

terminated CTF clusters are shifted to more positive values, which can be

rationalisedbytheveryelectron-withdrawingnatureofthecyanogroup.

Figure5.8:TD-B3LYPpredictedIP,EA*,IP*andEAvaluesofselectedCTFfragments(seenomenclaturep.31Fig1.16).The“–CN”suffixesindicateacyanoterminationoneachoftheterminatingphenyleneparaposition.Potentialscalculatedinwater.

Third,wenote that theexcitonbindingenergy(EBE)ofCTF-1, i.e. thedifference

betweenitsfundamentalandopticalgaps,ispredictedtobemuchsmallerthanthat

oftheotherCTFclusters.Moreprecisely,whiletheirfundamentalgapsstaysimilar,

theopticalgapofCTF-1islargerthanthoseoftheotherCTFs.Inotherwords,while

theringandnon-ringclustershaveasimilarability todrivewatersplittinghalf-

reactionsthroughchargecarriers,calculationspredictthatinthenon-ringclusters,

excitonsthemselvescandrivethosereactionsdirectly,anddonotneedtodissociate

(which is very unlikely to happen spontaneously, given the magnitude of the

predicted EBE values). However, for this last point, as the EBE values of most

materialsaretypicallyintheorderoftensofmeV,thecalculatedEBEvalues(upto

~1.5eV,i.e.largerbytwoordersofmagnitude)andtheassociatedinterpretations

shouldbetakenwithcaution.ThosehighEBEvaluesarelikelytobeartefactsdueto

thehighlysymmetricalstructureoftheCTFclusters,whichintroducesanadditional

excited state minimum where the excited state is delocalised over the whole

structure,notencounteredforreal,lesssymmetricalstructures.19


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5.2.3.Linearconjugatedoligomers

Although for PPP, in line with our predictions14, and similarly for fluorene-

phenyleneoligomers5and(pyrene-)phenyleneCMPs,10wateroxidationhasnever

beenobserved,otherphotocatalystsdooxidisewaterexperimentallywhenusinga

sacrificialelectronacceptor(orasacrificialholedonor)otherthanwater.Mostof

thesephotocatalystsarenotsimplehydrocarbons,butcontainheteroatoms.Aside

fromcarbonnitride(oneofthemostpromisingcandidates,whichwillbediscussed

in the next section) I will now discuss simple linear, heteroatom-substituted

variationsofPPP.Specifically,aspresentedinChapter1,Iwillfocusonoligomers

basedonpyridine,pyrimidine,pyrazine,pyrrole,thiopheneandfuran,someofthe

mostpopulararomaticbuildingblocksusedinthefieldsoforganicphotovoltaics

andorganiclightemittingdiodes.20-21

InouroriginalPPPstudy14,calculationsonaheptamerofpoly(pyridine-2,5-diyl)22-

23(PPyri),thepyridineequivalentofPPP-7,suggestedthatthepresenceofnitrogen

inthebackboneofthepolymerleadstoapositiveshiftoftheIPandEA*potentials,

andthustoalargerthermodynamicdrivingforceforwateroxidation(seeFigure

5.9).

Figure5.9:Comparisonbetween(TD-)B3LYPpredictedadiabaticpotentialsofPPPandPPyri,foroligomerlengthsof7and12,atpH=0.


125

PPyri has only been observed to catalyse the proton reduction reaction

experimentally22-23 in the presence of triethylamine as sacrificial electron donor

(although those studies, datingback to the years1990s, didn't aimat achieving

overall water splitting). Our calculations, however, predicted a significant

overpotential(0.6VatpH7),implyingthatthelackofwateroxidationactivitycould

alsoberesolved forPPyri throughtheadditionofasuitableco-catalyst.Wethus

observed that nitrogen substitution is a promisingmethod of shifting thewater

oxidationpotential inthedesireddirection.Moreover, inthelastsection,wealso

observedthatCTFs,whichwerereportedtooxidisewaterinthepresenceofaSEA24,

hadrelevantIP/EA*potentialsforwateroxidation.

Figure5.10:Comparisonbetweenthepredictedadiabaticpotentialsofarangeofconjugatedmolecules,foroligomerlengthsof7and12,atpH=0andpH=7.See

nomenclaturep.23Fig.1.5.

Nowconsideringthewholerangeofheteroatom-containinglinearoligomers(see

Figure5.10),weseethat inallcases, increasingtheoligomerlength,asobserved

previously, red-shifts the optical (and fundamental) gaps. The most promising

candidates forprotonreduction(thathave the largestdriving force, i.e. themost

negativeEA/IP*potentials)arethepyrroleoligomers(PPyrr).Thephenylene(PPP)

andfuran(PFur)oligomers, followedbythepyridine(PPyri)andthiophene(PT)


126

oligomers,alsohavesuitableEA/IP*levels,whereasthepyrimidine(PPyrim)and

pyrazine (PPyra) oligomers seem unpromising. All of these molecules can

theoretically drive the proton reduction half-reaction. The most promising

candidates forwater oxidation (that have the largest driving force, i.e. themost

positive IP/EA* potentials), on the contrary, are the pyrimidine and pyrazine

oligomers, and the pyridine oligomers only show a very small overpotential for

water oxidation. The remaining ones, namely PPP, PT, PFur and PPyrr, can be

eliminated because of very shallow IP/EA* potentials, regardless of the pH

considered.

ThepyrroleandfuranoligomershavemorenegativeIP/EAandEA*/IP*potentials

thantheotheroligomersconsidered.Thiscanbeexplainedbythefactthat,although

boththepyrroleandfuranmoleculesarearomatic,theycontainheteroatoms(an

oxygenandanitrogenatom,respectively)thateachhavetwolone-pairπ-electrons

thatparticipateinthemolecule'saromaticity,effectivelymakingthearomaticrings

electron-rich,whichshiftsreductionpotentialstomoreshallow(negative)values.

Conversely,thepyridineoligomerscontainnitrogenatomsthathavetwolone-pair

π-electronsthatdonotcontributetothemolecule'saromaticity,astheyresideina

sp2hybridorbital(asopposedtoa2patomicorbitalinthecaseofpyrroleandfuran,

see Figure 5.11), thusmaking the aromatic rings electron-deficient,which shifts

reductionpotentialstomorepositivevalues(seeFigure5.12thatshowselectron-

richandelectron-pooraromaticringsintheresonancestructuresofpyridineand

pyrrole)

Figure5.11:Diagram25showingthedifferenceinelectronicconfigurationofthelone

pairsofpyridine(leftside)andpyrrole(rightside).


127

Figure5.12:Resonancestructuresorpyridine(top)andpyrrole(bottom),showing

electron-depletedandelectron-richaromaticrings,respectively.

Forthesamereasons,as theycontaintwonitrogenatomsperaromaticringthat

make themevenmoreelectron-deficient, thepyrimidineandpyrazineoligomers

have even deeper IP/EA* potentials than pyridine oligomers. The potentials of

thiophene oligomers are in the same range as those of the pyrrole oligomers,

becausethiopheneandfuranhavethesimilarelectronicconfiguration,butthemore

electronegativesulphuratomofthiophenemakeshisaromaticringmoreelectron-

depletedthanfuran,thereforeshiftingpotentialstoslightlymorenegativevalues.

Aside from these homopolymers, their PPP copolymer homologues are also

investigated. For example, the pyridine-co-phenylene oligomers (PPyri-Ph) are

formedbyasuccessionofalternatingpyridineandphenyleneunits.Ourinterestin

phenylene copolymers rather than pyridine/pyrimidine homopolymers, for

example, finds its origin in experimental observations. This class of

(homo)polymers,aswellasCMPs,canbesynthesisedmainlythroughYamamotoor

Suzuki couplings; the former isnickel-catalysedand involvesa reactionbetween

twobromides,whilethelatterispalladium-catalysedandinvolvesacondensation

betweenabromideandaboronicacid.Firstly,polymersobtainedviaYamamoto

couplingexperimentallygiveworsehydrogenevolutionratesanddifferentoptical

spectra(comparedtothoseobtainedviaSuzukicoupling),andhencearelikelytobe

have different microstructures andmolecular weights. The possibility that such

differencesarisefromthepresenceofresidualtracesofnickelorpalladiuminthe

final product was ruled out by subsequent carbon monoxide poisoning

experiments10. Secondly, the preferred method of synthesis, Suzuki coupling,

requires the presence of a boronic acid. However, boronic acids of the small


128

nitrogen-containing aromatic monomers prove to be challenging to synthesise,

whichmakestheirhomopolymerisationviaSuzukicouplingunpractical.

Figure5.13:ComparisonbetweenthepredictedadiabaticpotentialsofthePPyri(pyridine)andPPyrim(pyrimidine)oligomers,andtheirphenyleneco-oligomeranaloguesPPyri-PhandPPyrim-Ph,allhavingachainlengthof12equivalent

phenyleneunits.

Unsurprisingly,thepotentialsofthephenyleneco-oligomers(Figure5.13),which

containanequalnumberofphenylenesandotheraromaticmotifs(e.g.PPyri-Ph-12

contains 6 phenylene and 6 pyridine aromatic rings) lie halfway between the

potentialsoftheirtwohomo-oligomercounterparts.Forexample,PPyri-Ph-12has

anIPof1.52eVvs.SHE,whilethepyridineandphenylenehomo-dodecamershave

IPvaluesof1.41and1.71eV,respectively.


129

5.2.4.Carbonnitride

In previousworkwithin our group, byButchosaet al.,15, the IP/EA* andEA/IP*

potentials of carbon nitride cluster models were calculated. Although the

calculationsonheptazineandtriazineoligomerswereoriginallyperformedbyC.

Butchosa,IrepeatedthecalculationsontheheptazinemodelsintroducedinChapter

1, starting from their ground state B3LYP optimised molecular structures, and

extended those calculations by taking into consideration different solvents (e.g.

acetonitrile)inordertocomparecalculatedvaluestoexperimentaldata.

Let’s first consider heptazine-based linear chains and graphitic clusters (see

nomenclaturepp.26-27).

Figure5.14:Comparisonbetweenthepredictedadiabaticpotentialsofmelem(heptazinemonomer),andheptazine-basedlinearchainsoflength2to6,takingintoaccounttwopossibleconformers(FstandsforflatandHstandsforhelical).See

nomenclaturep.26.

Aswediscussedintheoriginalpaper,15all linearclustermodelsarepredictedto

havesignificantthermodynamicdrivingforceforboththereductionofprotonsand

theoxidationofwater(seeFigure5.14).Smallerclustershavehigherabsorption


130

onsets than longer chains (increasing cluster size shifts absorptiononsets to the

red).Therefore,ifonemakesthereasonableapproximationthattheexcitonbinding

energy (i.e. thedifferencebetween the fundamental and theoptical gap)doesn't

varymuch,smallerclustermodelsarepredictedtohavea largerthermodynamic

drivingforceforprotonreduction(theEAandIP*oftheformerbeingmorenegative

thanthoseofthelatter),sinceIPandEA*donotvarysignificantly.However,smaller

clustersmightnotabsorb light in thedesiredrange (visible)becauseof thehigh

absorptiononset.

Figure5.15:Comparisonbetweenthepredictedpotentialsofgraphiticheptazine-

basedclustersofsizes3,6and10.Seenomenclaturep.27.

Allgraphiticclustersarepredictedtohavesignificantthermodynamicdrivingforce

for both the reduction of protons and the oxidation of water (see Figure 5.15).

Increasing thesizeof thecluster shiftsabsorptiononsets slightly to the red,and

brings both IP/EA* and EA/IP* to more positive values, which only slightly

decreases the driving force for proton reduction, but is beneficial for water

oxidation.

Additionalcalculationsongraphitictriazine-basedclustersofsizes3,6,10and15

byButchosaetal.15 (notshownhere) leadtosimilarconclusions;allclustersare


131

predicted to have sufficient driving force for the reduction of protons. Smaller

clustershavelargerdrivingforcethanthelargerones;clustersofsizes3and6are

predictedtohaveaverylowdrivingforceforwateroxidation,whileclustersofsize

10and15,however,arepredictedtoperformbetterforwateroxidationthattheir

smaller counterparts, but are slightly worse for proton reduction. In line with

graphiticheptazine-basedclusters,increasingtheclustersizeshiftsallabsorption

onsetstothered,whichisdesiredinordertousethosematerialsasphotocatalysts

undervisiblelightirradiation.

A comparison of three different isomers of heptazine trimers was subsequently

performed.Threeheptazineunitsare(A)linkedtoformalinearchain,(B)joined

throughacentral3-coordinatednitrogenatom,and(C)eachlinkedtothetwoothers

via-NH-bridgestoformagraphite-likeshape,relativelyflatbutslightlybuckled(see

Figure5.16).Thepotentials(notshownhere)ofallthreeisomersareinthesame

range,theoreticallymakingthemallsuitableforbothprotonreductionandwater

oxidation.Wealsoobserved slightly shallower IP/EA*anddeeperEA/IP* for the

graphiticcluster(C),i.e.slightlyworsepredictedperformanceforbothreactions,but

slightlybettervisiblelightabsorptionduetoitslowerabsorptiononset,inlinewith

previousobservations.15

Figure5.16:DFT-optimisedgroundstatestructuresofthreedifferentisomersofaheptazinetrimer.14Theblackspheresshowthepositionswheretheisomerswould

extend,inthecaseoflarger,morerealisticclusters.

Generally, the predicted potentials for all the carbon nitride cluster models

consideredaresignificantlydifferentfromthoseforPPP.Now,thereisnotonlya

cleardrivingforceforprotonreduction,butalsoforwateroxidation.Theseresults


132

stronglysuggest thatwithasuitableco-catalystsuchmaterialsshouldbeable to

photocatalysebothreactionsandsplitpurewaterintohydrogenandoxygen.

The reason why, until year 201512-13, no carbon nitride photocatalyst had been

observedexperimentallytosplitpurewaterintohydrogenandoxygenismostlikely

relatedtothefactthatwateroxidationtooxygenisa4-electronreaction;therefore

it is likely to be outcompeted by electron–hole recombination that prevents the

build-up of sufficient amount of holes for the oxidation, in the absence of some

mechanism of keeping electron and holes apart. In contrast, the oxidation of

sacrificialelectrondonors,typicallymethanol(asshownonFigures5.14and5.15)

or triethylamine, ismuchmore favourable both thermodynamically, because the

associated potentials are shifted by approximately 1 V, making them more

exothermic than water oxidation, and kinetically, since it involves only two

electrons(forbothmethanolandtriethylamine)insteadoffourforwater.

BeforethediscoveryoftwonewCN-basedoverallwatersplittingphotocatalystsby

Liuetal.andZhangetal.,theonlyexperimentintheliteraturewherecarbonnitride

splitpurewater,bySuietal.26,usedapolypyrroleco-catalystandformedhydrogen

peroxideratherthanoxygen.Below,Idiscussthereasonforsuchobservations.The

oxidation of water to hydrogen peroxide, while thermodynamically much less

favourablethantheoxidationofwatertooxygen(itinvolvesalargerpotentialof

1.64V,withanoverpotentialof0.4–0.6V),onlyrequires2insteadof4electrons.Liu

andco-workersthenshowedthatincorporatingcarbonnanodotswithinthecarbon

nitridematrix could subsequently catalyse thedecompositionof photogenerated

hydrogenperoxideintomolecularoxygen,12effectivelymakingCDot-CNanoverall,

metal-freewatersplittingphotocatalyst,althoughstillviaatwo-electronpathway.

CalculatingIPandEApotentialsforagraphiticheptazine-basedclustermodelanda

pyrroleisusefultounderstandtheobservationsofSuietal.(seeFigure5.17).We

have seen that most graphitic heptazine-based materials don’t catalyse the

oxidation of water, for kinetic reasons. The reduction of protons by PPyrr is

predictedtobestronglyexothermic,duetoitsverynegativeEApotential.However,

polypyrroleshouldn’tbeable,onitsown,todriveanyoxidation(watertooxygenor


133

to hydrogen peroxide), on purely thermodynamic grounds, due to its extremely

shallowIP.

Figure5.17:ComparisonofthepredictedIPandEApotentialsofagraphiticcarbonnitridecluster(H10G)andapolypyrroleoligomer(PPyrr-12)inwater(εr=80.1)at

pH7.EFdenotestheFermilevelsofcorrespondingmaterials.

However, taking the semiconductor nature of bothmaterials into account,when

carbonnitrideandpolypyrrolecomeintocontact,aheterojunctionisformed,and

theFermilevelsofthetwopreviouslyisolatedsemiconductors,whicharelikelyto

be very different, should equilibrate. This results in a shift between the vacuum

levels on both side of the junction, which generates a difference of electrical

potential,andhenceanelectricfield.Althoughtheexactcharacterofthejunction

formedisunknown,webelieve,basedonthealignmentofthepotentialsinFigure

5.17,thatthisbuilt-inpotentialwillcreate,afterequilibrationoftheFermilevels,a

net negative charge on the carbon nitride, and a net positive charge on the

polypyrrole.Thispreventsphoto-generatedelectronsfromtricklingdownfromthe

conductionbandofpolypyrroletotheconductionbandofcarbonnitride,andphoto-

generatedholesfromrisinguptothevalencebandofpolypyrrole.Notonlydoesit

keepelectrons andholeswhere theyare thermodynamically able todrivewater


134

oxidation to hydrogen peroxide and proton reduction to hydrogen, i.e. in the

polypyrroleconductionband,andinthecarbonnitridevalenceband,respectively,

but it also increases the lifetime of charge carriers, by preventing electron-hole

recombination to some extent. A similar mechanism probably explains why the

CDot-CN material reported by Liu and co-workers exhibits those high oxygen

evolutionrates.12

Moving away from fully polymeric photocatalytic systems, Zhang et al.’s latest

breakthrough13usessimilaramechanismtosplitwaterdirectly,forthefirsttime,

via a four-electron pathway, using selectively photodeposited Pt, PtOx and CoOx

speciesasredoxco-catalysts(e.g.PtforhydrogenevolutionandCo(OH)2foroxygen

evolution). Those catalysts greatly improve reduction and oxidation rates at the

activesites,leavingfewelectronsandholesavailableforrecombination.Whilethis

chemical system is not metal-free, it does overcome the kinetic barriers to the

oxidation of water, and doesn’t need any sacrificial reagent, which shows that

indeed, carbonnitride can inherently drivewater oxidation, as predicted by our

computationalmethod.


135

5.3.Conclusions

Applying the computational methodology described in Chapter 3 to a range of

conjugatedmolecularclustermodelsrevealssomeofthestrengthsandlimitations

ofthisapproach.

Firstly, the study of fluorene-type oligomeric materials shows that the

computationalapproachissuccessfulinpredictingwhichmaterialswillbeableto

catalysethereductionofprotonstomolecularhydrogen.However,therearesome

factors,relatedtoexperimentalconditionsduringsynthesisorphotocatalysis,such

askineticaspects,or thematerial’smicrostructure, thatcan’tbeeasilypredicted.

Therefore, although qualitative predictions seem robust, the main goal of those

calculations is not to yield an accurate and quantitative comparison of the

performanceofseveralmaterials.Thevalueofthismethodology,ratherthanfinding

theperfectcandidateforwatersplitting,liesinitsabilitytoeasilyandconsistently

rule out certain materials that would be poor choices, and hence not be worth

studyingforthatparticularapplication.

Secondly,comparingphenylenetopyrene-phenyleneCMPsshowsthatabsorption

onsetsrelatedtothewidthoftheoptical/fundamentalgap)playacrucialroleina

material’sphotocatalyticperformance; twomaterials thatarepredictedtohavea

similarabilitytodrivetheprotonreductionhalf-reaction,duetoverysimilarEAand

IP*values,mightinfactdifferradicallybecauseonecanabsorbalargerpartofthe

visiblespectrumthantheother.Ithenceappearscrucialtotakeintoconsideration

bothpotentialsandabsorptiononsetswhenscreeningforsuitablephotocatalysts.

Thirdly,applyingthecomputationalmethodologytolinearoligomersconfirmsthat,

byintroducingheteroatomsinalinearconjugatedchain, it ispossibletotunethe

positionoftheirstandardreductionpotentials,effectivelymakingthempotentially

suitable,intheory,foroverallwatersplitting.TheirIPandEApotentialscaneither

beshiftedtomorenegativevalues,whenmakingthearomaticringunitselectron-

rich(hencefavouringthermodynamicallythereductionofprotons,orofsacrificial


136

holedonors),or tomorepositivevalues,whenrendering thearomatic ringunits

more electron-deficient (hence favouring the oxidation of water, or of sacrificial

electrondonors).Thispredictionthatheteroatomdopingcontrols IP/EAlevels is

observedexperimentallyforpolymericmaterialsinvacuum(seeFigure4.2inthe

previouschapter).

Isisalsopossibletotunetheopticalgapsoftheselinearoligomersorpolymers,by

controllingtheirchainlength;forthematerialsstudied,increasingthechainlength

leads to smaller absorption onsets, and conversely, very short oligomers often

absorblightintheUVrange.

Finally,forcarbonnitride,incontrasttoPPP,wepredictthatoverallwatersplitting

isfeasibleintheory,whichwasrecentlyconfirmed12-13,althoughexperimentally,it

has been notoriously challenging to drive both water splitting half-reactions

concurrently. Typically, one would focus on hydrogen generation by using a

sacrificialelectrondonorthatwasoxidisedinsteadofwater,oralternativelywould

favouroxygengenerationbyusingasacrificialelectronscavengerthatwasreduced

insteadofprotons.Anypreviousissuewithwateroxidation,asdemonstratedbyour

approach, appears kinetic in nature, since the IP/EA* and EA/IP* are ideally

positionedforoverallwatersplitting.Indeedforthesematerials,thedevelopment

of suitable co-catalysts that minimises electron–hole recombination by keeping

them apart and maximises water oxidation kinetics (e.g. through the targeted

deposition of selective co-catalysts on the photocatalyst’s active sites)13 has the

potentialtotransformthemintotruewatersplittingphotocatalysts.


137

5.4.References

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2. Schwarz, C.; Tscheuschner, S.; Frisch, J.;Winkler, S.; Koch, N.; Bässler, H.;Köhler, A., "Role of the effective mass and interfacial dipoles on excitondissociationinorganicdonor-acceptorsolarcells",PhysicalReviewB2013,87,155205.

3. Zhang, W.; Smith, J.; Hamilton, R.; Heeney, M.; Kirkpatrick, J.; Song, K.;Watkins, S.E.;Anthopoulos,T.;McCulloch, I., "Systematic Improvement inChargeCarrierMobilityofAirStableTriarylamineCopolymers", JournaloftheAmericanChemicalSociety2009,131,10814-10815.

4. Sprick,R.S.;Hoyos,M.;Wrackmeyer,M.S.;SheridanParry,A.V.;Grace,I.M.;Lambert, C.; Navarro, O.; Turner, M. L., "Extended conjugation inpoly(triarylamine)s:synthesis,structureandimpactonfield-effectmobility",JournalofMaterialsChemistryC2014,2,6520-6528.

5. Sprick,R.S.;Bonillo,B.;Clowes,R.;Guiglion,P.;Brownbill,N.J.;Slater,B.J.;Blanc,F.;Zwijnenburg,M.A.;Adams,D.J.;Cooper,A.I.,"VisibleLight-DrivenWater Splitting Using Planarized Conjugated Polymer Photocatalysts",AngewandteChemieInternationalEdition2016,55,1792-1796.

6. Jiang, J.-X.;Trewin,A.;Adams,D. J.;Cooper,A. I., "Bandgapengineering influorescent conjugatedmicroporous polymers",Chemical Science2011,2,1777-1781.

7. Brandt,J.;Schmidt,J.;Thomas,A.;Epping,J.D.;Weber,J.,"Tunableabsorptionand emission wavelength in conjugated microporous polymers bycopolymerization",PolymerChemistry2011,2,1950-1952.

8. Xu,Y.;Nagai,A.; Jiang,D., "Core-shellconjugatedmicroporouspolymers:anewstrategyforexploringcolor-tunableand-controllablelightemissions",ChemicalCommunications2013,49,1591-1593.

9. Liu, X.; Xu, Y.; Guo, Z.; Nagai, A.; Jiang, D., "Super absorbent conjugatedmicroporous polymers: a synergistic structural effect on the exceptionaluptakeofamines",ChemicalCommunications2013,49,3233-3235.


11. Wang, X. C.; Maeda, K.; Thomas, A.; Takanabe, K.; Xin, G.; Carlsson, J. M.;Domen, K.; Antonietti, M., "A metal-free polymeric photocatalyst forhydrogenproductionfromwaterundervisiblelight",NatureMaterials2009,8,76-80.



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14. Guiglion, P.; Butchosa, C.; Zwijnenburg, M., "Polymeric watersplittingphotocatalysts; a computational perspective on the water oxidationconundrum",JournalofMaterialsChemistryA2014,2,11996-12004.

15. Butchosa,C.;Guiglion,P.;Zwijnenburg,M.A.,"CarbonNitridePhotocatalystsforWater Splitting: A Computational Perspective",The Journal of PhysicalChemistryC2014,118,24833-24842.




19. Meier,C.B.;Sprick,R.S.;Monti,A.;Guiglion,P.;Zwijnenburg,M.A.;Cooper,A. I., "Structure-property relationships for covalent triazine-basedframeworks:theeffectofspacerlengthonphotocatalytichydrogenevolutionfromwater",submittedtoPolymer2017,

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CHAPTER6:

Contrastingtheoptical

propertiesofthedifferent

isomersofPPP

Inthischapter,Iwillstudyandcomparethetrendsinopticalpropertiesofthethree

isomersofoligophenylene(ortho-phenylene,meta-phenyleneandpara-phenylene)

usingacombinationofTD-DFT,withthreedifferentexchange-correlationpotentials

(B3LYP, BHLYP and CAM-B3LYP), and approximate Coupled Cluster Theory (RI-

CC2). By carefully investigating their structure, topology, and excited-state

electronic properties (absorption and fluorescence energies), I will highlight a

striking difference in behaviour between those three isomers, and propose an

explanationfortheoriginofthisobservedphenomenon.

Thecontentofthischapterhasbeentakenfromthefollowingpublishedwork:

Guiglion P.; ZwijnenburgM. A.; "Contrasting the optical properties of the

different isomers of oligophenylene"; Phys. Chem. Chem. Phys. 2015, 17, 17854-

17863.

CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP

140


Polyphenylene is perhaps one of the simplest conjugated polymers imaginable;

consistingofachainofaromaticphenyleneunitslinkedtogetherbysinglecarbon-

carbonbonds.Thissimplicityis,however,deceptiveaspolyphenylenecanoccurin

three different structural isomers; poly(ortho-phenylene) (o-phenylene),

poly(meta-phenylene) (m-phenylene) and poly(para-phenylene) (p-phenylene)

(seeFigure1).

Figure6.1:Structuresofthep-terphenyl(A),m-terphenyl(B)ando-terphenyl(C)oligomers.

The difference between these three isomers is the position of the carbon atom

throughwhichthephenyleneunitsarelinked;thisstructuralchangegivesriseto

significantly different optical properties. For example, experimentally, the

fluorescence spectrum of oligomers of p-phenylene is known to red shift with

increasingchainlength1-5whileforoligomersofo-phenylene,surprisingly,itshifts

totheblue.6-9Incontrast,m-phenyleneiseffectivelynon-conjugated10anditsoptical

propertiesarevirtuallyindependentofchainlength.

Thedifferencesintheopticalpropertiesofthesethreephenyleneisomersarenot

merely of academic interest. Polyphenylene, as outlined in Chapter 1, finds

applicationinlightemittingdiodes11andasaphotocatalyst12-16forthereductionof

protonstomolecularhydrogen(seeChapter3)andcarbondioxidetoformicacid,

bothinthepresenceofasuitableelectrondonor.Mostoftheseapplicationsinvolve

p-phenylene and it stands to reason that the other isomerswould give rise to a

differentperformanceinsuchapplications.Indeedastudythatexplicitlycompared


141

the ability of o-terphenyl, m-terphenyl and p-terphenyl oligomers to act as

photocatalyst for the reduction of carbon dioxide found that p-terphenyl was

significantlymoreactivethantheothertwoisomers,and interestinglyalsomore

activethanthep-phenylenepolymer.14

Elucidating theoriginof thestarklydifferentopticalpropertiesof the isomersof

suchaconceptuallysimplepolymerisclearlybothanacademicallyandpractically

relevantquestion.Notsurprisingly,thereisthusalargenumberofcomputational

studies on the optical3, 5-6, 8 and related structural9-10 properties of oligomers of

phenylene. Such studies generally focus on only one of the three isomers and

attempttocorrelateitsstructuralandopticalproperties.Inthischapter,Igoastep

further,andstudyoligomersofallthreeisomersofphenyleneonanequalfootingin

ordertouncovertheoverarchingstructuralandelectronicfeaturesthatexplainthe

deviation between the optical properties of the different isomers. In order to

minimise the chance of computational artefacts complicating the comparison

between the different isomers, I not only use TD-DFT to calculate the optical

propertiesof theoligomersbut also,wherepossible, approximate couple cluster

theory (see Chapter 2 for theoretical details). Finally, I carefully consider the

treatment of intramolecular dispersive interactions, which will prove to be

especiallycrucialinthecaseofo-phenylene.


142


Thecomputational investigationof theopticalpropertiesofoligophenyleneswas

carried-out using a six-step approach. First, for every system, a conformational

searchwasperformedinordertofindthelowest-energyconformers.Second,the

singlet ground state (S0) of selected conformers was optimised using DFT17-18.

Third, for selected structures (trimer and hexamer), harmonic frequency

calculationswereperformedtoverifythatthestationarypointsobtainedintheS0

optimisation indeed correspond to ground-state minima. Fourth, the vertical

excitationenergiesoftheoligomerswerecalculatedusingbothTD-DFT19andthe

approximatecoupled-clusterssingles-and-doublesmethod20(CC2).Fifth, foreach

oligomer,thegeometryofthefirstexcitedstate(S1)wasrelaxedusingTD-DFTto

obtain theS1minimumenergystructureandpredict itsphotoluminescence(PL)

energy. Finally, for selected oligomers (trimer and hexamer), numerical TD-DFT

frequencycalculationswereperformedontheS1relaxedgeometriestoverifythat

theyindeedcorrespondtominima.

Fortheconformationalsampling(seeChapter2), theOPLS-2005forcefield21and

thelow-modesamplingalgorithm22wereemployed,asimplementedinMacromodel

9.9.23Iusedacombinationof10000MonteCarlosearchstepsandminimumand

maximumlow-modemovedistancesof3and20Årespectively.Allthestructures

located within an energy window of 200 kJ/mol relative to the lowest energy

conformerweresaved.

The DFT and TD-DFT calculations employed three different hybrid Exchange-

Correlation(XC)potentials;B3LYP24-27,BHLYP26andCAM-B3LYP28.Asmentioned

inChapter2,theB3LYPandBHLYPXCpotentialsinclude20%and50%Hartree-

Fock-likeexchange(HFLE)respectively,whereasthepercentageofHFLEinCAM-

B3LYP, a range separated XC-potential, changes from 19 to 65 with increasing

interelectronicseparation.Asaresult,theasymptoticbehaviouroftheCAM-B3LYP

XC-potential(thederivativeoftheXC-potentialwithrespecttotheinterelectronic

separationr)willbeclosertotheformal1/rdependenceoftheexactXC-potential.


143

Furthermore,inallTD-DFTcalculations,theTamm−DancoffapproximationtoTD-

DFT29wasused,whichfixesamongotherthingsproblemswithtripletinstabilities

present in full TD-DFT.29-30 Finally, in the case ofB3LYP,Grimme’sD3 empirical

dispersioncorrectionwasalsoemployed.31-33

IntheB3LYPandBHLYPcalculations,thedouble-ζDZP34basissetwasused,while

the CAM-B3LYP calculations typically employed the 6-31G** split-valence basis

set35.Alimitednumberofcalculationswithotherbasis-setssuchasthelargertriple-

ζdef2-TZVP36wereperformedforselectedsystemsinordertochecktheeffectof

thebasissetsizeontheresults.

TheCC2calculationswerecarried-outusingthefrozencoreapproximationandthe

resolution-of-the-identity (RI-CC2) approximation to the electron repulsion

integrals. The majority of RI-CC2 calculations, for reasons of computational

tractability,furtheremployedthesmalldef2-SV(P)34split-valencebasis.However

forsinglepointsonthesmallestoligomers,calculationswiththelargertriple-ζdef2-

TZVPP36basissetwerealsoperformed.

Finally, all B3LYP, BHLYP and RI-CC2 calculations were performed with the

Turbomole6.5code37-38.TheCAM-B3LYPcalculationsusedNWChem6.039except

inthecaseoftheTD-DFTS1relaxations,whichwereperformedusingGAMESS-US40

(version1October2010R1).


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6.3.1.Structuralmodels

Iwillstartwithabriefdiscussionoftheclassesofconformersconsideredforeach

isomerandtheircharacteristicstructuralfeaturesbeforemovingontoanin-depth

analysisof thepredictedabsorption (opticalgap)and fluorescence (fluorescence

energy)spectra.Oligomersofo-,m-andp-phenylenewerebuilt.Oligomerlengths

rangingfrom3(trimer)to8(octamer)phenylenerepeatunitswereconsidered.The

dimerisnotconsideredsinceitisthesameforo-,m-andp-phenylene;becauseof

thehighsymmetryofbenzene,thelabelso-,m-andp-onlybecomemeaningfulfor

oligomersof3unitsofphenyleneormore.

For each isomer, conformer searches were performed to find a number of low

energyconformers,withaspecificfocusonclassesoforderedconformers,thatwere

selected and subsequently re-optimised via DFT(+D), i.e. taking dispersion into

account. The latter selection includes for every oligomer-size the lowest energy

structure found by OPLS_2005, any ordered structures (see Figure 6.2), any

structures previously reported in the literature, and a number of less-ordered

structures.Thegroundstateenergydifferencesandvariationsinopticalgapvalues

between the different conformers are typically very small (less than 0.1 eV, not

shownhere).

The class of p-phenylene conformer of interest here are the lowest-energy

structures for each oligomer length. It consists of a linear backbone, and has

alternating torsion angles of approximately +37° and -37° (see Figure 6.2 A).

Another slightly higher-energy class of p-phenylene conformer also has a linear

backbone, butwith +37° torsion angles between each phenylene unit,making it

essentially helical. The latter structural difference, however, is of limited

significance in the context of this study, since the optical properties of both

conformers are generally very similar. The class of o-phenylene conformer of

interest are again the lowest-energy structures for each oligomer length (when


145

takingintoaccountthedispersioncorrection).Thisclassofconformerhasahelical

backbone,wherephenylenesstackeverythreeunits(seeFigure6.2B).

Form-phenylene, finally, three low-energy conformers are considered: the “flat”

lowest-energy conformer (see Figure 6.2 C), and two conformers with helical

backbones(“largehelix”and“smallhelix”,seeFigure6.2DandE).Allthosethree

m-phenyleneconformersyieldalmostidenticalopticalproperties(again,differing

bylessthan0.1eV,calculationsnotshownhere),andaretreatedcollectivelyinthe

remainderofthischapter.

Figure6.2:TopandsideviewsofB3LYPoptimisedgroundstategeometriesofthelowestenergyconformersofp-quinquephenyl(A)ando-quinquephenyl(B),aswellasthreelowenergyconformersofm-quinquephenyl(flatstructure:C;largehelix:D;

smallhelix:E).


146

6.3.2.Predictingtheeffectofisomertypeandoligomerlengthonopticalgaps

Thevariationoftheopticalgap(assimilatedtothelowestverticalexcitationenergy,

as explained in previous chapters) with the oligomer length for the different

phenyleneisomersisshowninFigure6.3.

Figure6.3:OpticalgapvaluesasafunctionofoligomerlengthforthedifferentphenyleneisomerscalculatedwithTD-B3LYP(A),BHLYP(B),CAM-B3LYP(C)andRI-

CC2(D).

Ascanbeseen,TD-DFTusingallthethreedensitypotentialsconsidered(B3-LYP,

BH-LYP and CAM-B3LYP), aswell as RI-CC2, generally yield the same qualitative

trends. Moreover, quantitatively, the predictions of RI-CC2 lie in between those

obtainedusingTD-B3YLPandTD-CAM-B3LYP.Theeffectofincreasingthebasis-set

qualityintheDFTcalculationstodef2-TZVPfinallyisverysmall(seeTable6.1).For

p-phenylene, a pronounced red shift in the optical gapwith increasing oligomer

lengthisobserved,aspreviouslyreportedintheliterature1,3-5(seealsoTable6.1).


147

Table6.1:ComparisonbetweenTD-B3LYPpredictedopticalgaps(ineV)ofp-phenyleneoligomers,inthegasphaseanddichloromethane(DCM,εr=8.93)and

experimentaldata.4Valuesinbracketsareobtainedwiththelargerdef2-TZVPbasis-set.

aSubstitutedatbothchainendswithisopropylgroupsinparaposition.Experimentaldatatakenfromreference4

Ortho-phenylenesshowsimilarbehaviour,againinlinewithliterature6,8-9.However

inthiscase,useofGrimme’sdispersioncorrection31-33toDFT(DFT-D3)isneeded

toaccuratelydescribeVanderWaalsinteractions(arene-areneπ-stacking)between

the phenylene units, due to their spatial proximity. Calculations on o-phenylene

withouttheuseofDFT-D3incontrastpredictthattheopticalgapfirstdecreases

then increases and ultimately decreases again with increasing oligomer length.

Finally, form-phenylene, increasing the oligomer length does not result in any

significant change in the calculated optical gaps beyond the trimer, again in

agreementwithliterature10wheretheyaredescribedas“conjugationbreakers”.

Finally,theeffectiveconjugationlengthofo-,m-,andp-phenylenewascalculatedin

the case of TD-B3LYP using the methodology of Meier and co-workers41, as

describedinChapter3.Amongthethreeisomers,p-phenyleneispredictedtohave

thelongesteffectiveconjugationlength(~20repeatunits,λ∞≈370nm,E∞≈3.35

eV),followedbyo-phenylene(~10units,λ∞≈293nm,E∞≈4.23eV),andultimately

m-phenylene(~6units,λ∞≈276nm,E∞≈4.49eV).Theherepredictedp-ando-

phenylene conjugation lengths are larger than the values obtained from

experimentalspectra(9and~4respectively)butthecalculationsandexperiment

agreeontherelativeconjugationlengthsofthedifferentisomers.7,41Theconsistent

difference in the absolute magnitude of conjugation lengths between the

calculations and experiment is probably due to a combination of three factors.


148

Firstly, our calculations ignore thermal effects that might reduce the effective

conjugationlength,secondly,experimentallythespectraofmanylongeroligomers

donot showwell-definedpeaks,and thirdly, thegeneral insolubilityof thesame

oligomers in most solvents means that experimental spectroscopy is inherently

limitedtoshortoligomers.

6.3.3.Linkingstructure,topology,andopticalgap

NaïveconsiderationsbasedonHückelorperturbationtheorywouldsuggest that

the optical gap of phenylene oligomers and polymers is linked to the overlap

between the π-systems of adjacent phenylene units and that the predominant

structuralparametercontrolling thisoverlap is the interphenylene torsionangle.

Flatstructureswithtorsionanglesof~0°areexpectedtohavemaximumπ-systems

overlapand,asaresult,smallopticalgapvalueswhilestructureswithtorsionangles

approaching90°shouldhavelarge(r)opticalgapvaluesnotdissimilartothatofthe

monomer.Forthecasewheretorsionanglesdonotchangemuchwiththeoligomer

length,trueforallsystemsstudiedhereexcepto-phenylenewhenoptimisedwith

standardDFTinsteadofdispersioncorrectedDFT+D,onewouldthusexpecttosee

thisalsoreflectedinthetrendsofopticalgapwitholigomerlength.Morespecifically,

onewouldexpectfortheopticalgaptosmoothlydecreasewitholigomerlengthin

anapproximate1/nfashion,andthelongoligomerlimitoftheopticalgap(E0∞)of

different isomers to be smallest for the isomerwith the smallest torsion angles.

Indeed p-phenylene oligomers have consistently smaller average torsion angles

thano-phenyleneoligomers(37°versus50°,seeFigure6.4,whenconcentratingon

the DFT+D optimised geometry in the case of o-phenylene) and steadily lower

opticalgapvaluesandalongereffectiveconjugationlength.


149

Figure6.4:TD-B3LYPpredictedaverageground(right)andexcitedstate(left)interphenylenetorsionanglesasafunctionofoligomerlengthforthedifferent

phenyleneisomers.

Also,aD2hversionofthep-phenylenetrimer,atransitionstatewithtwoimaginary

frequenciesbut90°torsionangles,ispredictedbyTD-B3LYPtohaveamuchlarger

opticalgapthanthep-phenylenetrimerminimumenergygeometry(5.28vs.4.49

eV),whichliesratherclosetothatpredictedforbenzene(5.51eV).Theonlyminor

issuewiththisnaïvetheoreticalpictureisthatvisualisationoftheorbitalsrelevant

fortheopticalgap(e.g.HOMOtoLUMOexcitationinthecaseofp-phenylene,see

Figure6.5),aswellastheexcitedstate-groundstatedensitydifferences,suggestthat

thenaïvepicturemightbeslightlytoosimple.WhiletheHOMOistypicallylocalised

on the constituent phenylene units and has π-like character, the LUMO is

predominantlylocalisedalongtheinterphenylenebonds(π-like)withminorπ*-like

contributionsonthephenyleneunits.

Figure6.5:HOMOandLUMOforthep-quaterphenyloligomer.


150

ThecaseofusingstandardDFTwhendescribingo-phenylene,wheretheopticalgap

is predicted to decrease, increase and decrease again (Figure 6.3) is a more

complicated.Thefactthato-phenyleneformshelicalstructureswithclosecontact

between non-directly adjacent phenylene units means that a more accurate

description of non-covalent dispersion interactions is required than available in

standard DFT. As a result, while DFT and dispersion-corrected DFT+D predict

essentiallyidenticalstructuresandopticalgapvaluesforp-andm-phenylene,their

predictionsdifferconsiderablyforo-phenylene.AscanbeseeninFigure6.4,useof

standardDFTresultsinthepredictionthattheaverageinterphenylenetorsionangle

of o-phenylene increases with oligomer length rather than stay constant.

Consequently, the trend in the optical gap for o-phenylene and plain DFT is a

convolution of two trends; the decrease in optical gapwith increasing oligomer

lengthandtheincreaseintheopticalgapwithincreasingtorsionangle.Itshouldbe

notedherethattheeffectofthedispersioncorrectionispurelystructuralandsingle

point TD-DFT vertical excitation energy calculations with DFT and DFT+D give

identicalresults.

Whichbringsustothenon-conjugatednatureofm-phenyleneoligomers.Fromthe

averageinterphenylenetorsionanglevaluesform-phenyleneinFigure6.4,itisclear

thatthislackofconjugationisnotduetothetorsionanglebeingcloseto90°.Asa

matteroffact,theaveragetorsionanglevaluesforo-phenyleneoligomersareonly

veryslightlylargerthanthoseofp-phenyleneoligomers.Havingruledoutthatthe

lackofdirectgeometricaloverlap is theoriginof the lackof conjugation,wecan

consider alternative explanations. The most promising of such an alternative

explanations is the proposal by Hong and co-workers10 that the lack of overlap

between theπ-systemsof adjacent phenyleneunits arises from the fact that the

frontierorbitalscontributingtothisexcitationonlyhavesmallcoefficientsonthe

metacarbonatoms.Indeed,usingDFTwefindthatforthedimertheatomsinmeta

positionwithrespecttotheinterphenylenebondhaveamuchlowercontribution

tothefrontierorbitalsthantheatomsthatlieinparaororthopositions.Similarly,in

thevalencebondperspectiveofvanVeenandco-workers,42m-phenyleneiscross-

conjugated,43-44 meaning that one cannot conceive a direct pathway involving

alternatingdoubleandsinglebondsbetweenmorethantwophenyleneunits(see


151

Figure 6.6), while the other two phenylene isomers are omniconjugated, and

possesssuchpathways.

Figure6.6:Directpathwaysofalternatingdoubleandsinglebondsinp-ando-terphenyl

(A&C)andabsenceofsuchapathwayinm-terphenyl(B).

Both explanations thus suggest that the origin of the lack of conjugation inm-

phenyleneoligomers inatopologicalratherthanageometric feature.Asaresult,

while the optical gap of p- and o-phenylene can be controlled by changing the

interphenylene torsion angle by tuning of the steric bulk of substituents, this

strategydoesnotworkform-phenylene.

The break in conjugation when introducing m-phenylene units, finally, can

convenientlybeobservedbymodellinganoligomerconsistingoftwop-phenylene

regions(3or4units,dependingontheperspective)separatedbyam-phenylene

segmentinthecentreofthemolecule(seeFigure6.7).ForthisoligomerstheTD-

B3LYPpredictedopticalgap(4.06eV)isverysimilartotheopticalgapofanisolated

p-phenylenetetramer(4.11eV)andmuchlargerthanthevalueforthep-octamer

(3.58 eV). This effect can also be observed from the electron density difference

between the ground and the excited state, which shows that the lowest energy

singletexcitationonlyinvolvestothepara-chainends(seeFigure6.7).

Figure6.7:TD-B3LYPground-excitedstatedensitydifferenceplotforanoligomerconsisting

oftwop-phenyleneregionsseparatedbyam-phenylenesegmentinthecentreofthemolecule(negativedensitydifferenceinblue,positivedensitydifferenceinred).


152

6.3.4. Investigating the effect of excited state localisation on fluorescence

energies

Justasfortheopticalgap,allthemethodcombinationsusedgenerallyagreeonthe

trends of fluorescence energieswith respect to oligomer length for the different

phenyleneisomers(seeFigure6.8).However,asexpectedfromtheliterature2-3,7-8

these predicted trends are very different from one isomer to the other. Them-

phenyleneisomersarepredictedtohavethehighestfluorescenceenergies,ofthe

order of 3.8 eV in the case of TD-B3LYP, and show effectively no variation in

fluorescenceenergywitholigomerlength.

Figure6.8:FluorescenceenergyvaluesasafunctionofoligomerlengthforthedifferentphenyleneisomerscalculatedwithTD-B3LYP(A),BHLYP(B),CAM-B3LYP

(C)andRI-CC2(D).

Thefluorescenceenergiesofp-phenyleneisomers,incontrast,showadistinctred

shiftwithincreasingoligomerlength,whilecalculationspredictaratheruniqueblue


153

shiftinfluorescenceenergiesfortheo-phenyleneisomers.Theonlystructurewhere

there is contention about the description is o-terphenylene. Here, TD-DFT

calculationswith all XC-potentials considered predict an excited stateminimum,

whileRI-CC2findswhatappearstobeaconical intersectionbetweentheground

andlowestexcitedstatepotentialenergysurface,whereallthreephenylenerings

enduplyinginapproximatelythesameplane.

Havingdiscussedthetrendinfluorescencewitholigomerlength,Iwillnowmoveon

to an in-depth discussion of the differences in excited state relaxation and

fluorescence between the different phenylene isomers. Here, the focus is on the

resultsobtainedusing(TD-)B3LYPbut,whereinsightful,thepredictionsofexcited

staterelaxationcalculationsusingtheotherXC-potential,aswellasRI-CC2,willalso

bereferredto.ConcentratingfirstontheStokesshiftanditscontributionsduetothe

stabilisation of the excited state (Excited State Stabilisation Energy, ESSE) and

destabilisationofthegroundstate(GroundStateDestabilisationEnergy,GSDE,see

Figure6.9),weobserveagradualincreaseforp-phenyleneintheStokesshiftwith

oligomer length, and the contributions of the ESSE are roughly 25% larger than

thoseoftheGSDE.

Figure6.9:VariationintheESSEandGSDEwitholigomerlengthforp-phenylene(left),m-phenylene(centre),ando-phenylene(right,N.B.:differentenergyscale).


154

For o-phenylene, in contrast, though in line with the blue shift observed in the

fluorescence energy, the Stokes shift decreaseswith increasing oligomer length,

however,notassmoothlyasforp-phenylene.Useof(TD-)B3LYP+D(whichisnot

necessarily a panacea in this case, because the parameters of the dispersion

correctionshouldinprinciplebedifferentforthegroundandexcitedstate,butare

not in practice) also yields slightly different results than obtained when using

standard(TD-)B3LYP.

Bothmethods,however,doagreethatfortheshortero-phenyleneoligomers,the

GSDEisconsiderablylargerthantheESSE,whileforthelongeroligomerstheyare

ofsimilarmagnitude.Finally,theStokesshiftofthem-phenyleneoligomersis,just

like their optical gap and fluorescence energy, virtually independentof oligomer

lengthandisthesmallestinmagnitudeofallthreeisomers;justasforp-phenylene,

theESSEcontributionisapproximately25%largerthanthatduetoGSDE.Overall,

itisclearthattheStokesshiftdoesnotmerelyfinditsorigininthestabilisationof

theexcitedstatebutalsohasa largecomponentduetothedestabilisationof the

groundstate,attheexcitedstateminimumenergygeometry.

Figure6.10:VariationoftheTD-B3LYPcalculatedexcitedstateinterphenylenetorsionangles(left)andgroundstate-excitedstateinterphenylenetorsionangledifference(right)alongtheoligomer,forthedifferentp-phenyleneoligomers.

A structural comparison of TD-B3LYP geometries shows that in the case of p-

phenyleneoligomers,themaindifferencesbetweenthegroundandrelaxedexcited

stateminimumenergystructuresresponsibleforthefluorescenceare:(i)adecrease


155

intheinterphenylenetorsionanglesrelativetothoseinthegroundstate(seeFigure

6.4 in the previous section, and Figure 6.10 above) and (ii) a para-quinone like

distortionof thebond lengths (seeFigure6.11).Bothdistortionsare inall cases

symmetricallydelocalisedover thewholechainwith the largestdistortion in the

centre.

Figure6.11:Para-quinonebondlengthdistortionforthep-phenylenetetramer.

Foro-phenylene,asimilarreductionintorsionanglesrelativetothegroundstateis

observed(seeFigure6.4intheprevioussection,andFigures6.12and6.13below)

butnowcombinedwithanorthoratherthanapara-quinonelikedistortionofthe

bondlengths(aspreviouslydiscussedbyHartley,8seeFigure6.14).Interestingly,

thereductionofthetorsionangleandtheortho-quinonelikedistortionofthebond

lengthsgotogetherwithtwoothertypesofdistortionsthatareessentiallyunique

to the excited state minimum of o-phenylene oligomers. Firstly, (i) there is a

significantdistortionoftheplanarityofthephenyleneunitand,secondly,(ii)after

excitedstaterelaxations,theinterphenylenebondstypicallydonotlie(anymore)in

thesameplaneaseitherofthephenyleneunitstheyconnect.


156

Figure6.12:VariationoftheTD-B3LYP+Dcalculatedexcitedstateinterphenylenetorsionanglesalongtheoligomerforthedifferento-phenyleneoligomers.

Figures6.13:VariationoftheTD-B3LYP(left)andTD-B3LYP+D(right)calculatedgroundstate-excitedstateinterphenylenetorsionangledifferencealongthe

oligomerforthedifferento-phenyleneoligomers.

Bothoftheselatter“planarity”distortionsaretoacertainextentalreadypresentin

the ground state structure of o-phenylene oligomers but become magnified

enormouslyafterexcitedstaterelaxation.Atell-talesign,finally,of(ii)isthatthe

magnitudeofthetorsionanglebetweentwophenyleneunitsisdifferentdepending

onwhichpairofatomsarechosen(beyondthosedirectlyinvolvedinthephenylene-

phenylene bond) to represent the interphenylene torsion angle, by up to

approximately20°(seetorsionangles1-2-3-4and1’-2-3-4’inFigure6.15).Taking


157

thisintoaccount,thevaluesreportedinFigure6.4andFigures6.12and6.13are

thusaveragesofthetwouniqueanglechoices.

Figure6.14:Ortho-quinonebondlengthdistortionfortheo-phenylenetetramer.

Figure6.15:Thetwouniquetorsionanglechoices1–2–3–4and1’-2-3-4’.

Thenumberofphenyleneunitsinvolvedinthedistortionandthedegreetowhichit

ispredictedtobesymmetricdifferwitholigomerlength,andtheuseofdispersion

correction with TD-B3LYP+D predicts that the excited state minima remain

symmetricaluptotheheptamer,wheretheexcitedstateismostlikelydelocalised

over thewhole oligomer length. Themaximumdistortion relative to the ground

statestructureisforalltheseoligomersinthecentreofthechainandtheflattest

torsion angles generally occur at either endof the oligomer. For the octamer, in

contrast,TD-B3LYP+Dpredictsanasymmetricexcitedstateminimum,wherethe

excitedstateappearstolocaliseononesideoftheoligomer.UseofplainTD-B3LYP

yieldssymmetricexcitedstateminimawithadelocalisedexcitedstate,foroligomers

up to and including the pentamer, and asymmetric structures for the longer

oligomers,wheretheexcitedstatehaslocalisedononesiteofthechain(similarto


158

thatoftheTD-B3LYP+Doctamerexcitedstateminimum).Theincreaseofselected

torsionanglesfarawayfromwheretheexcitedstatelocalisesinasymmetricexcited

stateminima (i.e. torsionangles thatareactually larger than in thegroundstate

structure,aspreviouslyobservedbyHartley8)isonlyobservedinmycalculations

intheabsenceofdispersioncorrection.RI-CC2calculations,finally,onlynumerically

tractableforuptothepentamer,yieldsymmetricexcitedstateminima,similarto

thosefoundwithTD-B3LYP+DandplainTD-B3LYP.

For m-phenylene, finally, excited state relaxation results in an extremely well

localised excited state (see Figure 6.4 in the previous section, and Figure 6.16

below). In line with the lack of conjugation in this isomer, already discussed

previously,onlytwoadjacenttorsionanglesandtheassociatedtwointerphenylene

bonddistancesarealwayssignificantlydistorted.

Figure6.16:VariationoftheTD-B3LYPcalculatedexcitedstateinterphenylenetorsionangles(left)andgroundstate-excitedstateinterphenylenetorsionangledifference(right)alongtheoligomer,forthedifferentp-phenyleneoligomers.

Thedistortionintermsofintraphenylenebonddistancechanges(seeFigure6.17)

is limited to the threephenyleneunitsaround these torsionanglesanddoesnot

followasimplepattern,perhapsbecausethereisnosuchthingasameta-quinone

likedistortion.


159

Figure6.17:Bondlengthdistortionforthem-phenylenetetramer.

6.3.5.Instabilityofo-terphenyl

This brings us to a reflection on the description of excited state relaxation ino-

terphenylbyTD-DFTandRI-CC2.AstheRI-CC2methodisknowntostrugglewith

thedescriptionofconicalintersectionsduetotheirinherentmulti-referencenature,

andastheD1diagnostic45thatprobesforpossiblemulti-referenceissuewithinthe

contextofRI-CC2indeedsoarsatthispointto0.26,onemustbecarefulnottoover

interpret theRI-CC2result foro-terphenyl.However,o-terphenyl isanexception

amongst the (o-)phenylene oligomers, as it is known experimentally to undergo

photocyclisationto4a,4b-dihydrotriphenylene(DHT)viaaconicalintersection46-47

rather than display fluorescence,8 shedding doubt on the TD-DFT excited state

optimisationresultsforthisparticularstructure.

Theobserved instability isprobably related to the fact that thepatternofbond-

lengthelongationsandcontractionsassociatedwiththeexcitedstateortho-quinone

likedistortionissimilartothebondlengthpatterninthegroundstatestructureof

DHT.The longero-phenyleneoligomersalsodisplay the sameortho-quinone like

distortion,butthestericrepulsionswiththerestoftheoligomermeansthatinthese

cases, a section of three adjacent phenylene units cannot become approximately

coplanar,rulingoutcyclisationandexplainingwhythesestructuresarefluorescent

instead.


160

6.3.6.Understandingthefundamentaldifferencebetweeno-andp-phenylene

Thisinvestigationleavestwopertinentinterrelatedquestionstoconsider;(i)why,

forshorteroligomers,isthefluorescenceenergyofp-phenylenelargerthanthatof

o-phenyleneoligomers,and(ii)why,foro-phenylene,doesthefluorescenceenergy

increase with oligomer length rather than decrease as generally observed for

polymers?Bothissuesareknown,asaresultoftheRI-CC2calculations,nottobe

artefactsoftheuseofTD-DFToraparticularXC-potential.

Focussing first on the question of the origin of the difference betweeno- andp-

phenylene, it is clear that this cannot be simply related to themagnitude of the

excitedstateinterphenylenetorsionangle.Comparingoligomersofsimilarsize,the

torsion angles in the excited state structure of o-phenylene are consistently

significantlylargerthanthatofp-phenylene(seeFigures6.4,6.10and6.12).Asthe

excited state for these smaller oligomers is always delocalised, onewould thus,

based on the link between torsion angle and π-systems overlap, naively have

expected the fluorescence energy of o-phenylene to be larger than that of p-

phenylene.Similarly,forshorto-andp-phenyleneoligomers,thechangeintorsion

anglebetweenthegroundandexcitedstateissimilarinmagnitudebuttheStokes

shift(anditsESSEandGSDEcomponents)ismuchlargerinthecaseofo-phenylene

than for p-phenylene oligomers of the same size. Also, the excited state

interphenylenebonddistancesofo-andp-phenyleneoligomersofthesamesizeare

verysimilar(seeFigure6.18),suggestingnolinkbetweenthisstructuraldegreeof

freedomandthefactthefluorescenceenergyofp-phenyleneislargerthanthatofo-

phenyleneeither.Finally,partialexcitedstateoptimisationofdimericclusterscut

fromtheo-phenylenetrimerandtetramerexcitedstateminima,whereallatomsbut

thenewlyaddedoneortwoterminatinghydrogenatomsareheldfixed,havelarger

fluorescenceenergiesthanthefullyoptimiseddimer.Theplanaritydistortionsthus

alsocannotexplainthelowo-phenylenefluorescenceenergies,atleastnotfordimer

fragments.


161

Figure6.18:Variationinaverageexcitedstateinterphenylenebondlengthwitholigomerlength,foro-andp-phenylene.

Havingeffectivelyruledoutmoststructuralexplanations, itthusstandstoreason

thatthelowerfluorescenceenergiesofshorto-phenyleneoligomersrelativetotheir

p-phenylenecounterpartsmustfinditsoriginintheinherentelectronicstructureof

o-phenyleneingeneral,andthepresenceofanortho-ratherthanapara-quinonelike

distortion inparticular, as theopticalgapappearswellbehaved.Support for this

hypothesis comes from the observation that, independent of the XC-potential

employed and oligomer length, the difference between the Kohn-Sham orbital

energy gap for the pair(s) of orbitals responsible for the lowest energy TD-DFT

excitationanditsTD-DFTenergyisalwaysconsiderablylargerforo-phenylenethan

for p-phenylene. For example, in the case of TD-B3LYP, the energy difference

betweentheKohn-Shamgapandthe lowestTD-B3LYPexcitationenergyisof the

orderof0.1-0.2eVforthep-phenyleneoligomerexcitedstateminimaand0.4-0.6

eVfortheiro-phenylenecounterparts. In linearresponseTD-DFTtheKohn-Sham

gapisthezeroth-orderapproximationtothelowestTD-DFTexcitationenergy,with

allhigher-ordercorrectionsduetoacombinationofthecontributionsoftheHartree

andXCkernel(fxc,thefunctionalderivativeoftheXC-potentialwithrespecttothe

density48).The largerdifferencebetweentheKohn-Shamgapand lowestTD-DFT

excitationenergy foro-phenyleneoligomers thussuggest that theHartreeand fxc

correction ismuch larger foro-phenylene than forp-phenyleneand that the two

oligomers indeed fundamentally differ in their many-body electronic structure

beyondsimplytheconstitutingKohn-Shamorbitals.


162

Whichbringsus,finally,tothequestionoftheoriginofthecharacteristicblueshift

of the fluorescence energies of o-phenylene oligomers with increasing oligomer

length. Focussing on the oligomers with symmetric excited state minima and

delocalised excited states, it is clear that the torsion angles of the excited state

minimasteadilyincreasewitholigomerlengthforo-phenylene(e.g.intermsofthe

averagetorsionangleforTD-B3LYP+D,anincreasefrom23°forthetrimerto40°

forthehexamer,seeFigure6.4).Forp-phenylenethere isalsoan increase inthe

excitedstatetorsionanglewitholigomerlengthbutthemagnitudeofthechangeis

considerablysmallerthanforo-phenylene(e.g.intermsoftheaveragetorsionangle

forTD-B3LYPanincreasefrom10°forthetrimerto17°forthehexamer,seeFigure

6.4).Ifoneassumesthatthechangeoffluorescenceenergywitholigomerlengthis

abalancebetweentwocompetingeffects(thedecrease inexcitationenergywith

increasing oligomer length and the increase in excitation energywith increasing

torsionangle),thenitappearsthatdifferenttermsdominateforo-phenyleneandp-

phenylene.Forp-phenyleneoligomers,theincreaseintorsionanglewitholigomer

size is relatively small and the decrease in excitation energy with increasing

oligomerlengthdominates,resultingintheconventionalredshiftinfluorescence

energy with oligomer length, while for o-phenylene oligomers, the increase in

excitationenergywithincreasingtorsionangledominates,givingrisetotherather

uniqueblueshiftwitholigomerlength.

The large change in torsion angle with increasing o-phenylene oligomer length,

finally,isprobablyrelatedtoanincreaseinstericrepulsionduetoagrowthofthe

number of intraoligomer close arene-arene π-stacking contacts with increasing

oligomerlength(i.e.0,1,2and3forn=3,4,5and6respectively).Suchclosearene-

areneπ-stackingcontactsarecompletelyabsentinp-phenyleneoligomersandall

other “straight” conjugated polymers, while for helical structures their effect

probablydecreaseswithincreasingsizeofthepitch(4inthecaseofo-phenylene),

explainingwhyablueshiftinfluorescenceenergywithincreasingoligomerlength

issuchararephenomenon.


163

6.4.Conclusions

In conclusion, I showed through a combination of TD-DFT and approximate

correlated wavefunction RI-CC2 calculations that the three isomers of

oligophenylene, while chemically similar, display quite different absorption and

especially fluorescence properties. More specifically, both TD-DFT and RI-CC2

predict that all m-phenylene oligomers essentially have the same fluorescence

signature,whilethefluorescenceenergyofp-phenyleneoligomersdecreaseswith

oligomer length, and that ofo-phenylene increases. In the caseofm-phenylene I

discuss that the lack of change in fluorescence energywith oligomer length is a

topologicalfeatureofthebondinginphenylene,whilethedifferencebetweeno-and

p-phenylene arises from a combination of steric and electronic factors. I further

showthattheseelectronicfactors,interestingly,resultinthefluorescenceofsmall

o-phenyleneoligomerstobesignificantlyredshiftedrelativetotheirp-phenylene

counterparts.

Followingonfromthat,Iarguethattherarityofablueshiftinfluorescenceenergy

withincreasingoligomerlength,asobservedforo-phenyleneoligomers,isprobably

related to the absence of close intraoligomer arene-arene π-stacking contacts in

mostotheroligomersandpolymers.Finally, Ihypothesisethatthereasonthato-

terphenyl experimentally photocyclises to 4a,4b-dihydrotriphenylene while the

longero-phenyleneoligomersdonot,andarefluorescent,isduetothefactthatthe

stericbulkofthelongeroligomersdonotallowfortheplanarisationrequiredfor

cyclisation.


164

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CHAPTER7:

Summaryandperspectives

Inthisthesis,Iintroducedanewcomputationalapproachbasedon(TD-)DFTthat

canbeusedtosystematicallycalculatethestandardreductionpotentialsoftarget

conjugated oligomers and polymers, in order to assess their relevance aswater

splitting photocatalysts. Unlike other methods based on static DFT, this

methodology takes into account electronic excitations, considers both charge

carriersandexcitons,andisthereforemorerealisticwhenmodellingprocessesthat

involve chemical systems in their excited state. It is computationally simple to

implement,tractableforrelativelysmallmolecularclusters(upto~200atoms),and

yieldsexploitablepredictionswithinshorttimescales(afewhourstoafewdays).

Thisapproachcanbeusedtorapidlyscreenfornewpromisingphotocatalystsfor

water splitting, possibly with high throughput. However, as it only takes

thermodynamiceffectsintoconsideration,andneglectsimportantkineticprocesses

thathappen inmaterials (e.g. excitondissociation, transportof recombinationof

charge carriers) as well as some of their intrinsic properties (e.g. wettability,

porosity,surfacearea,interfaces,defects),itsrealstrengthresidesinitsabilityto

consistently rule out materials that are inherently bad choices for such an

application,beforesynthesisingandcharacterisingthem(i.e.thatdonotandwill

never,accordingtoourcalculations,havesufficientthermodynamicforcetodrive

protonreduction, likepoly(p-phenylene),orwateroxidation, likepolypyrrole,on

their own). Predictions of the (relative) photocatalytic activity of a material

therefore largely remain out of reach. Additionally, one must be careful when

employingthiscomputationalmethodologytostudysystemswherecharge-transfer

ormultipleexcitationsarelikelytooccur,situationsinwhich(TD-)DFTisknownto

struggle.

CHAPTER7:Summaryandperspectives

169

Thismethodologywas then tested; the calculated standard reduction potentials

werecomparedtoexperimentalresultsfromIP/EAmeasurementsintheliterature,

andthepredictedperformanceofsomeoligomersandpolymerswasconfrontedto

photocatalytic measurements by our collaborators, the Cooper Group, at the

University of Liverpool. Overall, despite the lack of consistent and reliable

measurements, especially for IP*/EA*, a good fit was found for IP values, and a

decent fit for EA values, for samplesmeasured in the solid state, although such

accuracymightbeduetoerror-cancellationamongthetheoreticaltoolsused.Apoor

fit,however,wasfoundforthepotentialsofp-phenyleneandfluoreneoligomersin

gasphaseandsolution.Someoftheopticalpropertiesofp-phenylene(absorption

onset)werealsocomparedtoexperimentalresultsfromtheliterature,withavery

goodfit.

I then applied themethodology to awide range of clustermodels of oligomers.

Firstly, for PPP, it confirmed the material’s thermodynamic ability for to drive

hydrogenevolution,butshowedthat it is fundamentallyunlikelytodriveoxygen

evolution for thermodynamic reasons. Secondly, for a range of linear oligomers,

calculationsshowedthatoligomerscanbedesignedandtheirshapeandchemical

functionschanged,totunetheiropticalpropertiesandthermodynamicpotentialsto

desired levels, by adjusting the electron-rich or electron-poor character of its

monomers.Thirdly,movingonto2Dand3Dmolecularclusters(CTFsandCMPs),it

confirmedthattheoptical/fundamentalgaps, intrinsicallytiedtothepositionsof

IP/IP* and EA/EA* levels, can have a dramatic influence on the overall

photocatalyticperformanceofasystem(e.g.somematerialsmightabsorbalarger

partofthevisiblespectrumthanothers,orabsorbatverydifferentwavelengths,e.g.

UVvs.visible).Finally,consideringtheparticularcaseofcarbonnitride,althoughit

had been experimentally unable to drive overall WS, the computational

methodologypredictedthatcarbonnitridehadsuitablethermodynamicpotentials

to drive both water splitting half-reactions, which was finally achieved

experimentallyinthelastcoupleofyears.1-2

Throughoutthethesis,theroleofexcitonswasemphasised,asthecomputational

approachpredictedthatmanyoligomersrelevanttowatersplittinghadIP*andEA*


170

valuesthatwerewellpositioned,i.e.thatexcitonsthemselvescouldoftendrivethe

protonreductionand/orwateroxidationhalf-reactionsdirectly.Theobservation

that excitons in conjugated polymers are so strongly bound (i.e. often have high

excitonbindingenergies)thattheydonotspontaneouslyfallapartinthebulk,was

confirmed through comparison to experimental results.Therefore, in such cases,

chargecarriersmustbegeneratedbythedissociationofexcitonsatan interface,

suchasthepolymer-solutioninterface,orapolymer-polymerinterfaceinthecase

ofheterogeneousmaterials.Anareaofpolymerphotocatalysisthatdeservesspecial

attentionandcouldbenefitfromacombinedcomputationalandexperimentaleffort,

is indeedthephysicsandchemistrythatunderlietheelectron–holeseparationin

heterostructuresandtheoriginoftheiractivityfortheoverallsplittingofwater.

Finally,Istudiedtheopticalpropertiesofthethreeisomersofoligophenylene(and

theirmainconformers)bysubmittingthemtothesamecomputationalsetup.Ished

some light on the relationship between their molecular structure and their

absorptionandfluorescenceenergies.Firstly,bothortho-andpara-phenyleneare

well behaved, to the extent that their absorption onsets decreasewith oligomer

length,whereasmeta-phenyleneshowsnovariationinabsorptionenergies,dueto

“cross conjugation” leading to very localised excitations. Secondly, the three

oligomersshowverydifferentfluorescencefeatures:para-phenylenefluorescence

energiesunsurprisinglydecreasewitholigomerlength,whileformeta-phenylene,

oligomer lengthhasno influence,stilldue tocross-conjugation,but interestingly,

fluorescence blue-shifts for ortho-phenylene, due to increasingly larger

interphenylenetorsionangleswithinitsmolecularbackbone,intheexcitedstate.

Computationaltoolsprovetobeofcriticalimportance,especiallywhencoupledto

experimental techniques;bothapproachesmustgohand-in-hand.Theycanoffer

invaluable insight into the molecular structure of materials, which cannot

necessarilybeaccessedbymeasurementalone(whenpolymersarechallengingto

synthesise or characterise, e.g. insoluble, highly cross-linked polymers, which is

often the case for materials presented in this thesis), but these computational

methods,asattractiveastheymaybe,dorequiresomeexperimentalvalidationto

betestedandimproved.Thebiggestchallenge,asoftenincomputationalchemistry,


171

is striking the correct balance between computational cost, the ability to

consistentlycalculateallthedesiredproperties,andaccuracy.



Acknowledgements

IwouldliketoexpressmysinceregratitudetomyPhDsupervisor,Martijn,forhis

availability,support,andguidancethroughoutmyproject,bothonatechnicaland

psychologicallevel.Ihugelybenefitedfromhisadvice,keyinsights,andhealthydose

ofscepticism.Withouthim,manyaspectsoftheworkcarriedoutinthisthesiswould

havebeenimpossible.

Iwouldalsoliketothankmysecondarysupervisor,Furio,forhisvaluablecomments

especiallyatthebeginningofmyproject,thathelpedmeredefinepartofthefocus

ofmyproject,andhowtobestcommunicatemyresults.

IamgratefultoallpastandpresentmembersoftheZwijnenburggroup.Enrico,with

whomIsharedmanytypicalaspectsofthePhDstruggle, fortakingmeunderhis

wing and helping me make sense of the arcane of quantum and computational

chemistry, for the countless philosophical discussions we’ve had, and all the

unforgettable moments spent together. Cristina, for her collaboration, her

unwavering optimism and easygoingness, and her geek side to which I happily

related. Milena, for stimulating discussions and mutual psychological support.

Adriano,forhishelpandcollaboration.

IamalsogratefultothefollowingUCLstaff:Jörg,forhiscontinuoustechnicalhelp;

Saïdforhisfriendlinessandavailability;MartinVickersandJeremyCockcroft for

happilyhelpingmeprintpostersatthelastminuteonseveraloccasions.

IwouldliketothankallmycollaboratorsattheUniversityofLiverpool,especially

Seb,DaveandAndy,fromtheexperimentalside,forworkingwithushandinhand,

and for the interesting discussions that helped shapemy project.With a special

mention to Kim, now at Imperial’s College, who broadened my perspectives by

Acknowledgements

173

givingmeanopportunitytodiscovernewcodes,andtosharpenmyPythonskills.

Allthebestforthefuture!

To Shereif, Yoshi and Yasmine. To Abdul, Maxime, Alberto, and Ester. To Linda,

Larisa,andPete.ToJürgen,Lucy,RalphandJane.ToGarouiandHugo.Thankyou

guyssomuchforalltheawesomemoments!YouarethereasonwhyIwillnever

forgetmyLondonexperience.

Lastbutnotleast,IwouldliketoexpressmydeepestgratitudetomyloveStephanie,

andtomyparentsCharlesandChristine,fortheirunconditionallove,andinvaluable

support.ThanksforbelievinginmewhenIfelthelpless,forbearingwithme,and

fordoingallyoucould tokeepmemotivatedduring those fouryearsofupsand

downs.

Pierre

ucl discovery - ucl discovery · 3 abstract in this ph.d. project, i introduce a new computational...

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