UCL Discovery - UCL Discovery · 3 Abstract In this Ph.D. project, I introduce a new computational...
Transcript of 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
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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
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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
11
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
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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
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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).
CHAPTER1:Introduction
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
CHAPTER1:Introduction
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,
CHAPTER1:Introduction
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).
CHAPTER1:Introduction
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.
CHAPTER1:Introduction
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
CHAPTER1:Introduction
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
CHAPTER1:Introduction
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
CHAPTER1:Introduction
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.
CHAPTER1:Introduction
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
CHAPTER1:Introduction
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.
CHAPTER1:Introduction
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
CHAPTER1:Introduction
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).
CHAPTER1:Introduction
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.
CHAPTER1:Introduction
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.
CHAPTER1:Introduction
31
Figure1.16:DFToptimised3DstructuresofselectedCTFclusters:TP3(1),PT2P4(2),TP3T3P6(3)andPT2P4T4P8(4).Thenomenclaturereflectsthedendrimericnatureofthemolecules:TandPstandfortriazineandphenylene,respectively.
CHAPTER1:Introduction
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
CHAPTER1:Introduction
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.
CHAPTER1:Introduction
34
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32. Hong,Z.;Shen,B.;Chen,Y.;Lin,B.;Gao,B.,"EnhancementofphotocatalyticH2 evolution over nitrogen-deficient graphitic carbon nitride", Journal ofMaterialsChemistryA2013,1,11754-11761.
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.
CHAPTER1:Introduction
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.
CHAPTER1:Introduction
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 .
CHAPTER2:Theoreticalfoundations
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 .
CHAPTER2:Theoreticalfoundations
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.
CHAPTER2:Theoreticalfoundations
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
CHAPTER2:Theoreticalfoundations
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.
CHAPTER2:Theoreticalfoundations
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.
CHAPTER2:Theoreticalfoundations
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-
CHAPTER2:Theoreticalfoundations
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
CHAPTER2:Theoreticalfoundations
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.
CHAPTER2:Theoreticalfoundations
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.
CHAPTER2:Theoreticalfoundations
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-
CHAPTER2:Theoreticalfoundations
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)
CHAPTER2:Theoreticalfoundations
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
CHAPTER2:Theoreticalfoundations
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.
CHAPTER2:Theoreticalfoundations
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).
CHAPTER2:Theoreticalfoundations
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.
CHAPTER2:Theoreticalfoundations
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
CHAPTER2:Theoreticalfoundations
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.
CHAPTER2:Theoreticalfoundations
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,
CHAPTER2:Theoreticalfoundations
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).
CHAPTER2:Theoreticalfoundations
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.
CHAPTER2:Theoreticalfoundations
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).
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
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
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
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.
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
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.
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
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
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
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)
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
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
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
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
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
71
ofaniminiumspecies,whichinthepresenceofwater isthenhydrolysedtoform
diethylamine(DEA)andacetaldehyde(seeFigure3.3).
Figure3.3:Degradationoftriethylamineintodiethylamineandacetaldehyde,viatwo
1-electronoxidationsteps(TEAH+referstoprotonatedTEA).
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
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
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
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.
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
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.
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
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
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
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
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
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.
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
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
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
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)
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
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.
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
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.
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
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
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
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.
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
84
Table3.5:Basis-seteffectsonadiabaticandfreeenergy(Gvib/rot/trans)correctedstandardreductionpotentialsofwater,hydrogenperoxideandsacrificialelectron
donors.CalculatedusingB3LYP(allvaluesinV,pH=0)
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
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.
CHAPTER3:PredictingPPP’sthermodynamicabilitytosplitwater
86
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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
4.1.MotivationandLiteraturereview
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
CHAPTER4:Confrontingtheoreticalpredictionstoexperimentaldata
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
CHAPTER4:Confrontingtheoreticalpredictionstoexperimentaldata
93
materials. Finally, I will examine what a comparison of experimental and
computationally predicted potentials teaches us about conjugated polymers as
watersplittingphotocatalysts.
CHAPTER4:Confrontingtheoreticalpredictionstoexperimentaldata
94
4.2.Computationalmethodology
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.
CHAPTER4:Confrontingtheoreticalpredictionstoexperimentaldata
95
4.3.Resultsanddiscussion
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.
CHAPTER4:Confrontingtheoreticalpredictionstoexperimentaldata
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.
CHAPTER4:Confrontingtheoreticalpredictionstoexperimentaldata
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.
CHAPTER4:Confrontingtheoreticalpredictionstoexperimentaldata
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
CHAPTER4:Confrontingtheoreticalpredictionstoexperimentaldata
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.
CHAPTER4:Confrontingtheoreticalpredictionstoexperimentaldata
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
CHAPTER4:Confrontingtheoreticalpredictionstoexperimentaldata
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.
CHAPTER4:Confrontingtheoreticalpredictionstoexperimentaldata
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*.
CHAPTER4:Confrontingtheoreticalpredictionstoexperimentaldata
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.
CHAPTER4:Confrontingtheoreticalpredictionstoexperimentaldata
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.
CHAPTER4:Confrontingtheoreticalpredictionstoexperimentaldata
105
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22. Miyamae,T.;Yoshimura,D.;Ishii,H.;Ouchi,Y.;Seki,K.;Miyazaki,T.;Koike,T.;Yamamoto,T.,"Ultravioletphotoelectronspectroscopyofpoly(pyridine-2,5-diyl),poly(2,2′-bipyridine-5,5′-diyl),andtheirK-dopedstates",TheJournalofChemicalPhysics1995,103,2738-2744.
23. Liao,L.S.;Fung,M.K.;Lee,C.S.;Lee,S.T.;Inbasekaran,M.;Woo,E.P.;Wu,W.W.,"Electronicstructureandenergybandgapofpoly(9,9-dioctylfluorene)investigatedbyphotoelectronspectroscopy",AppliedPhysicsLetters2000,76,3582-3584.
24. Hwang,J.;Kim,E.-G.;Liu,J.;Brédas,J.-L.;Duggal,A.;Kahn,A.,"PhotoelectronSpectroscopic Study of the Electronic Band Structure of Polyfluorene andFluorene-Arylamine Copolymers at Interfaces", The Journal of PhysicalChemistryC2007,111,1378-1384.
25. Sohn,Y.;Stuckless,J.T.,"Bimolecularrecombinationkineticsandinterfacialelectronic structures of poly[2-methoxy-5-(2-ethyl-hexyloxy)-p-phenylenevinylene]ongold studiedusing two-photonphotoemissionspectroscopy",TheJournalofChemicalPhysics2007,126,174901.
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27. Kanai, K.; Miyazaki, T.; Suzuki, H.; Inaba, M.; Ouchi, Y.; Seki, K., "Effect ofannealingontheelectronicstructureofpoly(3-hexylthiophene) thin film",PhysicalChemistryChemicalPhysics2010,12,273-282.
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28. Baik,M.-H.;Friesner,R.A.,"ComputingRedoxPotentialsinSolution: DensityFunctional Theory as A Tool for Rational Design of Redox Agents", TheJournalofPhysicalChemistryA2002,106,7407-7412.
29. Uudsemaa, M.; Tamm, T., "Density-Functional Theory Calculations ofAqueousRedoxPotentialsofFourth-PeriodTransitionMetals",TheJournalofPhysicalChemistryA2003,107,9997-10003.
30. Shimodaira,Y.;Miura,T.;Kudo,A.;Kobayashi,H.,"DFTMethodEstimationofStandard Redox Potential ofMetal Ions andMetal Complexes", Journal ofChemicalTheoryandComputation2007,3,789-795.
31. Roy,L.E.; Jakubikova,E.;Guthrie,M.G.;Batista,E.R., "CalculationofOne-Electron Redox Potentials Revisited. Is It Possible to Calculate AccuratePotentials with Density Functional Methods?", The Journal of PhysicalChemistryA2009,113,6745-6750.
32. Nayak,P.K.;Periasamy,N.,"Calculationofionizationpotentialofamorphousorganicthin-filmsusingsolvationmodelandDFT",Org.Electron.2009,10,532-535.
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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.
CHAPTER5:BeyondPPP;screeningforsuitablephotocatalysts
111
5.1.MotivationandLiteraturereview
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
CHAPTER5:BeyondPPP;screeningforsuitablephotocatalysts
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
CHAPTER5:BeyondPPP;screeningforsuitablephotocatalysts
113
Amongthosedifferenttypesofmaterials,Iwillaimatfindingthemostpromising
candidatesforsolar-drivenwatersplitting,i.e.photocatalyststhathavedeep(very
positive)IPandEA*,andshallow(verynegative)EAandIP*,alwaysbearinginmind
theadditionalconstraintthattheabsorptiononsetoftheidealmaterialshouldbe
smallenoughforittoabsorbvisiblelight,andlargeenoughforittodrive,atleast
thermodynamically,ideallyboththeprotonreductionandthewateroxidationhalf-
reactions.
CHAPTER5:BeyondPPP;screeningforsuitablephotocatalysts
114
5.2.Resultsanddiscussion
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.
CHAPTER5:BeyondPPP;screeningforsuitablephotocatalysts
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
CHAPTER5:BeyondPPP;screeningforsuitablephotocatalysts
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
CHAPTER5:BeyondPPP;screeningforsuitablephotocatalysts
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
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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.
CHAPTER5:BeyondPPP;screeningforsuitablephotocatalysts
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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
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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
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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
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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-
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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.
CHAPTER5:BeyondPPP;screeningforsuitablephotocatalysts
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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)
CHAPTER5:BeyondPPP;screeningforsuitablephotocatalysts
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).
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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
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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.
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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
CHAPTER5:BeyondPPP;screeningforsuitablephotocatalysts
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
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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
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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
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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
CHAPTER5:BeyondPPP;screeningforsuitablephotocatalysts
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.
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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
CHAPTER5:BeyondPPP;screeningforsuitablephotocatalysts
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.
CHAPTER5:BeyondPPP;screeningforsuitablephotocatalysts
137
5.4.References
1. Schwarz,C.;Bässler,H.;Bauer,I.;Koenen,J.-M.;Preis,E.;Scherf,U.;Köhler,A., "Does Conjugation Help Exciton Dissociation? A Study on Poly(p-phenylene)sinPlanarHeterojunctionswithC60orTNF",AdvancedMaterials2012,24,922-925.
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.
10. 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.
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.
12. Liu,J.;Liu,Y.;Liu,N.;Han,Y.;Zhang,X.;Huang,H.;Lifshitz,Y.;Lee,S.-T.;Zhong,J.; Kang, Z., "Metal-free efficient photocatalyst for stable visible watersplittingviaatwo-electronpathway",Science2015,347,970.
CHAPTER5:BeyondPPP;screeningforsuitablephotocatalysts
138
13. Zhang,G.;Lan,Z.-A.;Lin,L.;Lin,S.;Wang,X.,"OverallwatersplittingbyPt/g-C3N4 photocatalysts without using sacrificial agents", Chemical Science2016,7,3062-3066.
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.
16. 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.
17. 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.
18. Jiang,X.;Wang,P.;Zhao,J.,"2Dcovalenttriazineframework:anewclassoforganicphotocatalyst forwatersplitting", JournalofMaterialsChemistryA2015,3,7750-7758.
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,
20. Chizu,S.;Yoshiaki,T.;Takeshi,Y.;Makoto,K.;Shuji,D.,"Recentprogressofhigh performance polymer OLED and OPV materials for organic printedelectronics",ScienceandTechnologyofAdvancedMaterials2014,15,034203.
21. Li,G.;Zhu,R.;Yang,Y.,"Polymersolarcells",NatPhoton2012,6,153-161.22. Matsuoka,S.;Kohzuki,T.;Kuwana,Y.;Nakamura,A.;Yanagida,S., "Visible-
light-induced photocatalysis of poly(pyridine-2,5-diyl). Photoreduction ofwater,carbonylcompoundsandalkeneswithtriethylamine",JournaloftheChemicalSociety,PerkinTransactions21992,679-685.
23. Maruyama, T.; Yamamoto, T., "Effective Photocatalytic System Based onChelating π-Conjugated Poly(2,2'-bipyridine-5,5'-diyl) and Platinum forPhotoevolutionofH2fromAqueousMediaandSpectroscopicAnalysisoftheCatalyst",TheJournalofPhysicalChemistryB1997,101,3806-3810.
24. Bi, J.; Fang,W.; Li, L.;Wang, J.; Liang, S.; He, Y.; Liu,M.;Wu, L., "CovalentTriazine-BasedFrameworksasVisibleLightPhotocatalystsfortheSplittingof Water", Macromolecular Rapid Communications 2015, DOI:10.1002/marc.201500270.
25. TeachtheMechanism.teachthemechanism.com.26. Sui,Y.;Liu, J.;Zhang,Y.;Tian,X.;Chen,W.,"Dispersedconductivepolymer
nanoparticles on graphitic carbon nitride for enhanced solar-drivenhydrogenevolutionfrompurewater",Nanoscale2013,5,9150-9155.
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
6.1.MotivationandLiteraturereview
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
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
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.
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
142
6.2.Computationalmethodology
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.
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
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).
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
144
6.3.Resultsanddiscussion
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
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
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).
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
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).
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
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.
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
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.
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
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.
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
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
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
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).
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
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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
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
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).
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
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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
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
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.
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
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
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
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
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
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.
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
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.
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
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.
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
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.
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
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.
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
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.
CHAPTER6:ContrastingtheopticalpropertiesofthedifferentisomersofPPP
164
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44. Gholami, M.; Tykwinski, R. R., "Oligomeric and polymeric systems with across-conjugatedpi-framework",Chemicalreviews2006,106,4997-5027.
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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*
CHAPTER7:Summaryandperspectives
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,
CHAPTER7:Summaryandperspectives
171
is striking the correct balance between computational cost, the ability to
consistentlycalculateallthedesiredproperties,andaccuracy.
1. Liu,J.;Liu,Y.;Liu,N.;Han,Y.;Zhang,X.;Huang,H.;Lifshitz,Y.;Lee,S.-T.;Zhong,J.; Kang, Z., "Metal-free efficient photocatalyst for stable visible watersplittingviaatwo-electronpathway",Science2015,347,970.
2. Zhang,G.;Lan,Z.-A.;Lin,L.;Lin,S.;Wang,X.,"OverallwatersplittingbyPt/g-C3N4 photocatalysts without using sacrificial agents", Chemical Science2016,7,3062-3066.
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