Platinum-Water-Vacuum Interface
Dissertation
zur Erlangung des Doktorgrades
des Fachbereichs Chemie
der UniversitatHamburg
vorgelegtvon
Timm Lankau
aus Hamburg
Prof. Dr. K.Nagorny,Hamburg
Dr. I.L.Cooper,Newcastle
P.D.Dr. K.Drager,Hamburg
Die Quantensinddocheineho nungsloseSchweinerei.
Thesimplebilayermodel ofthe platinum-water-vacuuminterfacecanexplainmostexperimental
results,butfailsondetails. Ourworksuggeststhat cooperativee ects areveryimportantforthe
ne-structureoftheinterface. Theplatinum-water(chapter6)andthehydrogenbond(chapter3)
havebeenfoundto beverymuch alike. Intermolecularelectrontransferasobservedinthe water
trimerhasa strongin uence of theinterfacestructure and canmovethewatermolecules out of
theiridealpositions(chapter 8).
Our newwater-waterinteractionpotential(chapter 4)has beenused to explorethe potential
energysurfacesofthewatertrimer(chapter4)andhexamer(chapter8). Theresultsonthehexamer
suggestthataseamlesstransitionbetweentheplatinumsurfaceandtheicecrystalisnotpossible.
Structuressimilar to theQLL (Quasi Liquid Layer) have been observed, which canexplain the
lowverticaldipole moment of surfacewater, whilecooperativeforcescan be usedto explain the
seconddesorptionpeak(165K) inTDS (ThermalDesorptionSpectroscopy)experiments.
Theweakbondbetweenwaterandplatinumiscontrolledbytwoopposingforces: theCoulomb
repulsionbetweenthe6selectronsoftheplatinumcluster andtheoxygen atomand thebonding
interactionbetweenaplatinum5dorbitalandthefreeelectronpairofthewatermolecule. Ahigh
6spopulation, which repells the water molecule, createsat thesame time astrong bond among
theplatinumatoms. Itisthereforeimpossibletocreateasurfacemodelwithstrongintermetallic
bondsand astrongplatinum-waterbondatthesametime.
Thequalityofthesurfacemodeldependsstronglyonthe6spopulationandsoontheelectronic
stateof themetalcluster. The analysis ofthe platinum-waterbondwould havebeen impossible
without amodi cation of the Huckel theory (chapter 5), which wasused to selectsuitable
can-didatesas surfacemodelsand to understandthe electronicstructure ofthe platinumcluster and
electronmovementsduringtheformationoftheplatinum-waterbond.
The intermetallic bond in the platinum cluster is dominated by the 6s orbitals and the 5d
orbitals have to be considered in full detail only at active surfaceatoms. This assumption was
nallyproofedbythedevelopmentofanew1valenceelectronECP(E ectiveCorePotential)for
bulkandpassivesurfaceatoms (chapter7), which canbeusedtoreduce thecomputationalcosts
Ein einfaches Doppelschicht-Modell fur dasGrenzsystemPlatin-Wasserkann die meisten
experi-mentellen Ergebnisseerklaren, versagt aberbeider Interpretation von Details. In dieser Arbeit
werdenwirnachweisen,dacooperativeE ektesehrwichtigfurdieFeinstrukturderGrenzschicht
sind. Die Platin-WasserBindung und die Wassersto bruckenbindung sindeinander sehr
ahnlich
(Kapitel 6)undintermolekularerLadungstransfer,wieerauch imWassertrimerbeobachtetwird,
kanneinzelne WassermolekuleausihreridealenPositionbringen(Kapitel8).
UnserneuesWasser-Wasser-Wechselwirkungspotential(Kapitel4)wurdebenutzt,umdie
Ener-giehyper achedesWassertrimers(Kapitel4)unddesWasserhexamers(Kapitel8)zuuntersuchen.
DieErgebnissefurdasHexamerlassenvermuten,daseinnahtloser
Ubergangzwischender
Platin-ober ache und einem Eiskristall wie bisher angenommen nicht moglich ist. Strukturen,
ahnlich
einerzweidimensionalenSchicht ussigenWassersaufEis (engl. QLL,QuasiLiquidLayer),
wur-den an der Grenze zwischen Metall und Eis beobachtet. Solch ein Strukturmodell erklart den
kleinenAnteildesDipolmomentseinesWassermolekulsinderGrenzschichtsenkrechtzur
Metallo-ber ache,wahrenddieobenerwahntencooperativenKrafteerstmalseineDeutungfurdenzweiten
Desorptionspeak(165K) inTDS Experimenten(ThermalDesorptionSpectroscopy)bieten.
DieschwacheBindung zwischenPlatin undWasserkann mit zweieinanderwidersprechenden
Kraftenerklartwerden: DieCoulomb-Abstoungzwischenden6sElektronendesPlatinsunddem
negativgeladenem Sauersto imWassermolekul istdieerste Kraftund diezweite bindendefolgt
ausdem
UberlappeneinesfreienElektronenpaarsdesWassermolekulsmiteinemPlatin5dOrbital.
Einehohe6sBesetzungsdichte,diedasWassermolekulabstot,ezeugtabergleichzeitigeinestarke
Platin-Platin Bindung. EsgibtentwedereinestarkePlatin-Platin BindungimMetallclusteroder
einestarkeMetall-WasserBindung,aberniebeidesgleichzeitig.
Die 6sElektronendichte erwies sich alsSchlussel zu einem realitatsnahen Ober achenmodell.
Eine Modi kation derHuckel-Theorie(Kapitel5) half uns,dieelektronischeStruktur des
Platin-clustersunddieBewegungderElektronenwahrendderWasseradsorptionzuverstehen. Sowares
unsmoglich,gezieltnachgeeignetenKandidatenfurdieOber achenmodellenzusuchen.
DieMetall-MetallBindungimPlatinclusterwirdvonden 6sOrbitalendominiert, wahrenddie
5d Orbitale nur wichtig sind fur die Bindung des Wassermolekuls an ein aktivesOber
achena-tom. DieseAnnahmefuhrtezu derEntwicklung einesfunktionierenden1Valenzelektronen ECP
(E ectiveCorePotential), da inZukunft dieUntersuchunggroerOber achenmodelleerm
1 Introduction 1 1.1 GeneralIntroduction . . . 1 1.1.1 PropertiesofWater . . . 2 1.1.2 PropertiesofPlatinum . . . 4 1.1.3 LiteratureSurvey . . . 4 1.2 Thiswork . . . 10 2 Theory 15 2.1 Hartree-FockCalculations . . . 15
2.2 M ller-PlessetPerturbationTheory . . . 19
2.3 Con gurationInteractionandMulticon gurationSCFTheory . . . 22
2.4 BasisSetsandBasisSetSuperpositionError. . . 23
2.5 TheMorokumaEnergyDecompositionScheme . . . 26
2.6 Pseudopotentials . . . 30
2.6.1 NonRelativisticCorePotentials. . . 30
2.6.2 RelativisticQuantumMechanicsandCorePotentials . . . 34
2.7 Interactionsbetweendi erentelectronicstates . . . 38
2.7.1 IntersectionofPotentialEnergyCurves. . . 38
2.7.2 PhotoexcitationandIntersystemCrossings . . . 39
2.8 Dipole-DipoleInteractionand Polarisation . . . 40
3 QuantumChemistry ofsmall Water Clusters 45 3.1 TheWaterMolecule. . . 45
3.2 WaterDimer. . . 50
3.2.1 SinglePointCalculations. . . 50
3.2.2 PotentialCurvewithaFlexibleGeometry . . . 61
3.2.3 PotentialCurvewithaFixedGeometry . . . 65
3.2.4 CalculationoftheBSSE correctedgeometry ofthewaterdimer . . . 70
3.3 EnergyDecomposition . . . 72
3.4 WaterTrimer . . . 74
3.5 SummaryoftheQuantumMechanicalCalculations . . . 81
4 Classical Water-Water Interaction Potentials 85 4.1 Classi cationoftheDi erentPotentials . . . 85
4.3.1 An improvedmodel . . . 94
4.3.2 ApplicationofpotentialN onwatertrimers . . . 109
4.4 SummaryoftheCalculationwithaClassicalPotential . . . 114
5 Huckel calculations for the Analysisof Pt n 117 5.1 Theoryof theHuckel-approximationfortheplatinum6selectrons . . . 117
5.2 HuckelcalculationsforPt 3 . . . 119
5.3 AnalysisofthePt 5 pyramid . . . 121
5.3.1 HuckelcalcualtionsfotPt5. . . 122
5.3.2 Theinterfacebetweendi erentECPs . . . 123
5.3.3 5d-6sinteraction inPt 5 . . . 125
5.3.4 Therotationalbarrierin Pt 5 H 2 O . . . 126 5.3.5 SummaryonPt 5 . . . 128
5.4 HuckelCalculationsforPt 9 Cluster . . . 128
5.5 TwoSlabsPt 17 Cluster . . . 130
5.6 TheSecondNextNeighbour . . . 132
5.7 QuantitativeAnalysisoftheHMOCalculations . . . 135
5.7.1 ResultsforthePlatinumDimer . . . 135
5.7.2 ResultsforPlatinumPentamer(Pyramid) . . . 139
5.8 SummaryandConclusionsfromthe6sHuckelcalculations . . . 142
6 Platinum atomcalculations involving18 ValenceElectrons 145 6.1 Oneplatinumatom . . . 146
6.1.1 Theelectronicstatesofplatinum . . . 146
6.1.2 Platinumandasinglewatermolecule. . . 148
6.1.3 TheIn uenceofthePseudoPotential. . . 154
6.1.4 E ectoftheBSSE ontheplatinum-waterinteraction . . . 156
6.1.5 ThePlatinum-Hydrogeninteraction . . . 157
6.1.6 Summaryoftheresultsforsingleplatinumatom . . . 158
6.2 PlatinumDimer . . . 159
6.2.1 Theelectronicstructure oftheplatinumdimer. . . 159
6.2.2 PlatinumDimerandWater . . . 163
6.2.2.1 In uenceofthegeometry . . . 163
6.2.2.2 Thewatermetalinteractionin Pt 2 H 2 O . . . 164
6.2.2.3 In uenceoftheelectronicstateoftheplatinumdimer . . . 167
6.2.2.4 Movementofwateronthesurface . . . 171
6.2.3 Summaryoftheresultsfortheplatinumdimer . . . 175
6.3 Theplatinumtrimer . . . 176
6.3.1 ElectronicstructureoftheequilateralPt 3 -cluster . . . 177
6.3.2 TheinteractionofwaterwithPt3-cluster. . . 178
6.3.2.1 Waterbound tothehollowsiteonthecluster . . . 178
6.3.2.2 Waterbound ontop . . . 181
6.3.2.3 Pt3surfacemodelforthePt(100) surface . . . 183
6.3.3 SummaryoftheresultsforPt 3 . . . 185
5
6.4.1 ElectronicstructureofthePt
5
-pyramid. . . 187
6.4.2 TheinteractionofthePt 5 -pyramidwithwater. . . 187
6.4.2.1 Dissociation . . . 189
6.4.2.2 Rotation. . . 190
6.4.2.3 Wagging . . . 191
6.4.3 Summaryoftheresultsfortheplatinumpyramid . . . 191
6.5 ThePt 9 -cluster . . . 192
6.6 Theelectronicstructureofthemetalcluster asafunctionofitssize . . . 195
6.7 EHTcalculationsonthePt n H 2 Osystem . . . 197
6.8 Summaryofthecalculationswitha18valenceelectronsplatinumatom. . . 199
7 Calculations with 1-Valence Electronper Platinum 203 7.1 Numericalpropertiesforthenew1-electronECP . . . 204
7.1.1 NumericalResultsforthe6sorbital . . . 205
7.1.1.1 The6sWavefunction . . . 205
7.1.1.2 Radial6sDensity. . . 207
7.1.1.3 Simpli cationoftheRadial6sElectron DensityFunction . . . . 208
7.1.1.4 Thequestforthenew6sWavefunction . . . 209
7.1.2 NumericalResultsforthePt6pOrbital . . . 210
7.1.3 NumericalResultsforthePt6dorbital . . . 211
7.1.4 Summaryandcompilationofall1electronproperties . . . 213
7.2 Principlequestions abouta1electronECP. . . 215
7.2.1 Isitpossibleto usethemethod fromHay andWadt? . . . 216
7.2.2 Whichconditionshasagaussiantypewavefunctionto ful ll? . . . 216
7.2.3 Isapositiveeigenvalueforthe6dorbitalphysicallyreasonable? . . . 217
7.2.4 HowdoesGaussian94calculatetheenergyof theorbitals?. . . 218
7.2.5 Underwhichconditionsisglobal minimumpossible? . . . 219
7.2.6 HowdoesGaussiancalculatetheECP? . . . 219
7.2.7 WhathappensiftheECPvanishesasrbecomesin nite? . . . 221
7.2.8 Whichform hasanECPwithalocalenergyminimumford-electrons? . . 222
7.2.9 Isitpossibleto createalocalminimumwithtwoormorefunctions? . . . 226
7.3 Howdescribethe6delectron? . . . 230
7.3.1 WhatproblemsareconnectedwiththeECPbyZuritaetal.? . . . 230
7.3.2 What'snext? . . . 234
7.3.3 HowdoesU core L controllthedimer'sproperties? . . . 236
7.3.4 Howstrongisthein uence ofU core L onthePtH bond? . . . 239 7.3.5 HowdoesU core L changetheelectronicstructureofPt 5 ? . . . 240
7.3.6 Whathappensiftwodi erentECPsinteract witheachother? . . . 241
7.3.7 IstheLanL1MBclusterasuitablesurfacemodel? . . . 244
8.1 Formationof(H 2 O) 3 onPt(111). . . 252 8.1.1 Introduction . . . 252 8.1.2 ComputationalProcedure . . . 253
8.1.3 ResultsandDiscussion . . . 254
8.1.4 Conclusions . . . 262
8.2 (H 2 O) 6 onaVirtualMetalSurface . . . 265
8.2.1 Introduction . . . 265 8.2.2 ComputationalProcedure . . . 267 8.2.3 WaterDimer. . . 268 8.2.4 WaterTrimer . . . 270 8.2.5 WaterHexamer . . . 271 8.2.5.1 TheModel . . . 271
8.2.5.2 Thefreewaterhexamer . . . 273
8.2.5.3 Theconstrainedhexamer . . . 273
8.2.5.4 Variationofthesurfacelatticeconstant . . . 275
8.2.6 Discussion . . . 280
8.2.7 FinalConclusions . . . 284
9 Final Conclusionsand Further Proceedings 285 10 Bibliography 295 10.1 Citedliterature . . . 295
10.2 Programsusedforthiswork . . . 311
11 Appendix 313 11.1 Abbriviations . . . 313
11.2 BasissetandECPSusedwith inthiswork . . . 316
11.3 SelectedWaterMonomerData. . . 319
11.4 ResultsfromSingle PointCalculationsfortheWaterDimer . . . 320
11.5 In uenceoftheBSSEontheMonomer'sGeometry . . . 323
11.6 ChangingW3andBendingtheHydrogenBond . . . 326
11.7 EnergiesoftheMorokumaEnergyDecompostion fortheWaterDimer . . . 326
11.8 Di erentwater-waterinteractionpotentialsfromtheliterature . . . 329
11.9 GeometryoptimisationofwaterclusterswithinpotentialN. . . 341
11.9.1 Direct conversion . . . 342
11.9.1.1 TrimerI . . . 342
11.9.1.2 TrimerII . . . 343
11.9.1.3 TrimerIII . . . 344
11.9.1.4 TrimerIV . . . 345
11.9.2 Conversionofrotationalinto cartesiancoordinates . . . 345
11.9.3 Optimisationof(H 2 O) 6 . . . 348
11.10 TheC++Gaussian 94interface . . . 348
11.11 HuckelcalculationsforPt 9 . . . 354
11.12 HuckelcalculationsforPt 17 . . . 355
1.1 Structureofice 1h. . . 3
1.2 Idealbilayerstructure. . . 5
1.3 Scienti cenvironmentofthiswork. . . 11
2.1 In uenceoftheBSSEontheinteractionenergy. . . 25
2.2 Formationofatrimer. . . 26
2.3 Interactionandmixing ofthemonomer'sorbitals. . . 28
2.4 Dipole-dipole interaction.. . . 42
3.1 Sketchofthemolecularorbitalsofwater.. . . 48
3.2 Geometryofthewaterdimer. . . 50
3.3 Variablesofthedimer. . . 51
3.4 Compositionofthewaterdimer'sMOs.. . . 55
3.5 In uenceoftheelectrostaticinteractionsontheorbital energies.. . . 55
3.6 MO5a'ofthewaterdimer. . . 56
3.7 MO6a'ofthewaterdimer. . . 56
3.8 MO7a'ofthewaterdimer. . . 56
3.9 MO8a'ofthewaterdimer. . . 56
3.10 Electrondensityin thesymmetryplane. . . 56
3.11 Formationofthewaterdimer. . . 57
3.12 InteractionenergyandBSSE. . . 62
3.13 Minimain gure3.12. . . 62
3.14 Energycomposition,notBSSE corrected.. . . 62
3.15 Changingofr OH withd OO . . . 62
3.16 Changingofchargesduringdimerisation. . . 62
3.17 Correlationenergyvs. d OO . . . 62
3.18 Geometryofapossibleionpair. . . 63
3.19 Energyduringtheprotontransfer. . . 65
3.20 Protonchargeduringprotontransfer.. . . 65
3.21 Chargretransferq duringprotontransfer. . . 65
3.22 Interactionenergywithrigidgeometries. . . 66
3.23 Detailsfrom gure3.22. . . 66
3.24 Comparisonofthechargetransfer. . . 66
3.25 Di erencebetweena exibleandarigidmonomergeometry. . . 67
3.26 Detailsfrom gure3.25. . . 67
3.29 Repulsionbetweenwatermolecules. . . 69 3.30 Oxygen-oxygenrepulsiona OO . . . 69 3.31 Hydrogen-Hydrogenrepulsiona HH . . . 69
3.32 Local minimumof H-Hrepulsion. . . 69
3.33 Arti cialBSSEminimumofa HH . . . 69
3.34 BSSEcorrectedminimumgeometry. . . 71
3.35 GeometryoftrimerI. . . 74
3.36 GeometryoftrimerII. . . 74
3.37 GeometryoftrimerIII. . . 74
3.38 GeometryoftrimerIV. . . 74
3.39 ThreepossibleconformersoftrimerIIIwiththeirMP2energiesin Hartree. . . 76
3.40 3a'orbital oftrimerI. . . 80
3.41 FormationoftrimerIIIfrom dimers. . . 80
4.1 Geometriesofwatermonomersfordi erentinteractionpotentials.. . . 86
4.2 Local minimumof theBNS-a OO curve. . . 90
4.3 DampingfunctionfortheCoulombinteraction. . . 90
4.4 In uence ofthedamping.. . . 90
4.5 CompositionoftheCoulombenergy. . . 90
4.6 OHinteractionenergiesinOH . . . 92
4.7 PolarisationenergyoftheCFMSmodel. . . 92
4.8 Dimerisationcurve-TIPS2. . . 93
4.9 OOrepulsion-TIPS2. . . 93 4.10 HH repulsion-TIPS2. . . 93 4.11 Variationof -TIPS2. . . 93 4.12 Variationof -TIPS2. . . 93 4.13 H 2 Ogeometryfortheclassicalpotential . . . 96
4.14 Sketchesofselecteddimergeometries.. . . 99
4.15 Dimerisationcurve-Pot. E. . . 100
4.16 OOrepulsion-Pot. E. . . 100
4.17 HH repulsion-Pot. E. . . 100
4.18 Variationof -Pot. E.. . . 100
4.19 Variationof -PotE. . . 100
4.20 Di erentrepulsionfunctions.. . . 100
4.21 PotentialenergysurfacepotentialEfor and ; d OO =2.8514 A/minima.. . . 101
4.22 PotentialenergysurfacepotentialEfor and ; d OO =2.8514 A/maxima. . . 101
4.23 Energypro le,path1-5-3,Pot. E. . . 102
4.24 Energypro le,path4-1,Pot. E.. . . 102
4.25 Energycomposition,path1-5-3,Pot. E. . . 102
4.26 Energycomposition,point5,Pot. E. . . 102
4.27 Dimerisationcurve-Pot. N. . . 105
4.28 OOrepulsion-Pot. N. . . 105
4.29 HH repulsion-Pot. N. . . 105
4.32 PotentialenergysurfaceofpotentialNfor and ;d
OO
=2.9834
A/minima. . . . 106
4.33 PotentialenergysurfaceofpotentialNfor and ;d OO =2.9834 A/maxima. . . . 106
4.34 Detailsofminimum3,Pot. N. . . 107
4.35 Energypro lepath1-5-3,Pot. N. . . 107
4.36 Energycompositionpath1-5-3,Pot. N. . . 107
4.37 Energycompositionpoint5,Pot. N. . . 107
4.38 Reactionpath1-5-3,Pot. E. . . 107
4.39 Reactionpath1-5-3,Pot. N. . . 107
4.40 Geometryofthecyclictrimers. . . 111
4.41 Formationofacyclictrimer. . . 113
4.42 Ringclosureof (H 2 O) 3 . . . 113 4.43 Globalminimumof(H 2 O) 3 . . . 113 4.44 Transitionstate.. . . 113
4.45 Potentialenergyfunction. . . 113
5.1 Pt 3 cluster. . . 120
5.2 Pt 3 Huckelorbital energies. . . 121
5.3 Pt 5 pyramid, topview. . . 122
5.4 VariationofthebondintegralH .. . . 124
5.5 Variationof ofthetopatom. . . 124
5.6 5d-6sinteractioninPt 5 . . . 126 5.7 Mirrorplanesin Pt 5 H 2 O. . . 127
5.8 Mixingofthenonbonding6s orbitals. . . 127
5.9 Rotationin Pt 5 H 2 O/singletstate. . . 127 5.10 Rotationin Pt 5 H 2 O/tripletstate. . . 127 5.11 Pt 9 cluster,topview. . . 128
5.12 Pt 17 cluster,topview. . . 131
5.13 Surfacemodelcluster. . . 133
5.14 E ectofthesecond nextneighbour( =0.2). . . 133
5.15 S calculatedwithG94andthebest t. . . 138
5.16 EHTresultsforPt 0 2 . . . 138
6.1 Electronicstatesofaplatinumatom . . . 148
6.2 HFresultsforPt H 2 O. . . 149 6.3 HFresultsforPt H 2 O. . . 149
6.4 Platinumstatescloseto negativecharge. . . 149
6.6 Pt H 2 Ogeometry. . . 150 6.5 FormationofPt H 2 O. . . 151 6.7 6a'orbitalofPt H 2 O. . . 152 6.8 7a'orbitalofPt H 2 O. . . 152 6.9 10a'orbitalofPt H 2 O. . . 152
6.10 Movementofthetotalelectrondensity. . . 152
6.11 Waterwagglemovement. . . 154
2
6.14
6s
orbital(LUMO) inthe 1 S 1 Sdimer. . . 160 6.15 6s orbital(HOMO)inthe 3 D 3 D dimer. . . 160 6.16 Dissociationofthe 1 S 1 Sdimer. . . 162 6.17 Dissociationofthe 1 S 3 D dimer. . . 162
6.18 Di erentgeometriesforPt 2 H 2 O. . . 163
6.19 GeometryA:Bondingorbitala 1 symmetry. . . 165
6.20 GeometryA:Bondingorbitalb 2 symmetry. . . 165 6.21 Zero 5d -3a 1 overlap. . . 165
6.22 GeometryC:Bondingorbital(water3a 1 ). . . 166
6.23 GeometryC:Bondingorbital(water1b 1 ). . . 166
6.24 GeometryG:Bondingorbital(water3a 1 ). . . 166
6.25 GeometryG:Bondingorbital(water1b 1 ). . . 166 6.26 ElectronmovementinPt 2 H 2 O. . . 167 6.27 Dissociationofgeometry A. . . 169 6.28 Dissociationofgeometry C. . . 169 6.29 Dissociationofgeometry G. . . 169
6.30 Di erentdissociationcurves. . . 169
6.31 RotationaroundthePtObond. . . 171
6.32 Waggingofthewatermolecule. . . 171
6.33 Pt 2 -GeometryA toD. . . 171
6.34 ShiftalongthePtPtbond, startgeometryA,distance. . . 172
6.35 ShiftalongthePtPtbond, startgeometryA,energy. . . 172
6.36 ShiftalongthePtPtbond, startgeometryA,wagging. . . 172
6.37 ShiftalongthePtPtbond, startgeometryC,length. . . 172
6.38 ShiftalongthePtPtbond, startgeometryC,energy. . . 172
6.39 WaggingoftheH 2 Oingeometry A,bondlength. . . 173
6.40 WaggingoftheH 2 Oingeometry A,totalenergy. . . 173
6.41 GeometryCto F,6spopulation. . . 174
6.42 GeometryCto F,totalenergy. . . 174
6.43 Connectionbetweendi erentgeometriesandstates.. . . 175
6.44 HuckelresultsforequilateralPt 3 . . . 177
6.45 ThehollowsiteofPt(111). . . 180
6.46 DissociationenergiesHF/MP2. . . 180
6.47 RHFenergyandHF6spopulation. . . 180
6.48 MP2energyandMP26spopulation. . . 180
6.49 MP2energyandgroundstatecoeÆcient. . . 180
6.50 Rotationofthehollowsitewater. . . 180
6.51 GeometryIV. . . 181
6.52 GeometryII.. . . 181
6.53 GeometryIII. . . 181
6.54 Dissociationofgeometry II. . . 182
6.55 RotationofH 2 Oin geometryII.. . . 182
6.56 Movementofthewatermolecule. . . 182
6.57 RotationofH 2 Oin geometryIII. . . 182
3 2
6.59 Huckelorbitalenergies. . . 183
6.60 GeometryofPt 5 H 2 O. . . 186
6.61 HuckelresultsforPt 5 . . . 187 6.62 Bondingorbitalin Pt 5 H 2 O(H 2 O3a 1 ). . . 189 6.63 Bondingorbitalin Pt 5 H 2 O(H 2 O1b 1 ). . . 189 6.64 DissociationPt 5 H 2 O.. . . 189 6.65 RotationofH 2 OaroundthePtObondin Pt 5 H 2 O. . . 190 6.66 WaggingofH 2 OinPt 5 H 2 O. . . 190 6.67 OptimizedPt 9 H 2 O.. . . 192 6.68 Bondingorbitalin Pt 9 H 2 O(H 2 O3a 1 ). . . 193 6.69 Bondingorbitalin Pt 9 H 2 O(H 2 O1b 1 ). . . 193
6.70 Bandstructureofsmallplatinumcluster.. . . 196
6.71 Pt 5 H 2 Obindingenergy(EHT). . . 197
6.72 ChargeonPt5in Pt 5 H 2 Ofordi erentvaluesofd PtPt (EHT). . . 197
6.74 EHTresultsfotPt n H 2 O(n=1,2,5). . . 198
6.75 EHTresultsforPt 9 H 2 O.. . . 198
6.73 TotallysymmetricEHMOsin Pt 5 H 2 O . . . 198
7.1 6sorbital,LanL2ECP,cutalongthexaxis. . . 206
7.2 6sorbital,5d 9 6s 1 ,di erentECPs,cutalongthexaxis. . . 206
7.3 Radial6selectrondensityfordi erentECP. . . 207
7.4 Replacementpolynominalsfordi erenttransitionpoints(r 0 ). . . 208
7.5 New6s wavefunction, nalversion. . . 209
7.6 New6s radialelectrondensity, nalversion. . . 209
7.7 6pradialdensityfunction (LanL2). . . 212
7.8 6ptargetradialfunctionandbest t. . . 212
7.9 OriginalLanL26pradialdensityand thenewone. . . 212
7.10 Newandoriginalradial6pwavefunction. . . 212
7.11 6d xz radialelectrondensity. . . 214
7.12 Di erent6d xz radialfunctions.. . . 214
7.13 Radial6d xz electrondensity(4 gaussians). . . 214
7.14 6d xz wavefunctioncutalongtheXZ axis.. . . 214
7.15 6d xz densityfunctions. . . 214
7.16 Test ofequation 7.29withGaussian94.. . . 218
7.17 Globalminimumwithapositiveenergyeigenvalue. . . 218
7.18 Plotofequation7.39,V max =1.0.. . . 221
7.19 Plotofequation7.39, =0.1. . . 221
7.20 Individualenergycontributions;equation7.39, =0.1,V max =2.5. . . 222
7.21 ECPwithlocalminimum;E T =0.23, =0.12, =0.016,d=2:5310 5 . . . 222
7.22 Localminimumforn=6,7and8. . . 224
7.23 Minimumenergydi erencefora nitepotential. . . 224
7.24 asafunctionofE. . . 226 7.25 R versusd A . . . 227
A A 7.28 R asafunctionofd A and A . . . 230
7.29 Fitforthenewfterm(test2).. . . 232
7.30 Fitforthenews-f term(test2). . . 232
7.31 Fitforthenewp-fterm(test2). . . 232
7.32 Fitforthenewd-fterm(test2). . . 232
7.33 Dimerisationenergyfromtest1andtest3.. . . 232
7.34 Fitforthenews-dterm(test3). . . 233
7.35 Fitforthenewp-dterm(test3). . . 233
7.36 U core L in the3di erenttests. . . 233
7.37 6sorbital. . . 235 7.38 6porbital. . . 235 7.39 6dorbitals.. . . 235 7.40 Gaussian94input. . . 236 7.41 2 nd testforU core L ( =0.02).. . . 237 7.42 Order2: E TOT foranoptimizedbondlengthof2.3578 A. . . 237
7.43 In uence ofd A onthebondlengthfor xedvaluesof A .. . . 238
7.44 In uence ofd A onthedimer'senergyfor xedvaluesof A . . . 238
7.45 Order3: Optimizedbond lengthis2.3578 A.. . . 238
7.46 In uence ofd A ontheoptimizedbond length . . . 238
7.47 Twoenergydiscontinuitiesobservedfor =0.42a.u.. . . 239
7.48 In uence ofU core L onthepotentialenergysurface( =0.42).. . . 239
7.49 PtHbondlength. . . 239 7.50 TotalenergyE TOT ofPtH. . . 239 7.51 CollapsofPtH ( A =0.46). . . 240
7.52 BondlengthandE TOT inPt + 5 . . . 241
7.53 Chargeonthetopplatinumanddipole momentin Pt + 5 . . . 241
7.54 E TOT oftheLanL1MBcluster. . . 243
7.55 ChargesontheLanL1MBcluster. . . 243
7.56 Dipole momenttheLanL1MBcluster. . . 244
7.57 Dissociationcurves. . . 245
7.58 In uence ofthesymmetry. . . 245
7.59 Rotationalbarriere-unsymmetriccase.. . . 246
7.60 Rotationalbarriere-symmetriccase. . . 246
7.61 RotationalbarriereatMP2level. . . 247
7.62 Dissociationat MP2level. . . 247
8.1 FragmentofthePt(111)surfacewithwaterbilayer. . . 253
8.2 Platinumand awaterdimer -principal geometries. . . 255
8.3 ClusterI:Pt 2 (H 2 O) 3 . . . 256 8.4 ClusterII:Pt 3 (H 2 O) 3 . . . 257 8.5 ClusterIII:Pt 3 (H 2 O) 3 . . . 258 8.6 ClusterIV:Pt 2 (H 2 O) 3 . . . 258
8.7 ClusterVandclusterVI . . . 259
8.10 Waterdimer. . . 269
8.11 C 3h Watertrimer.. . . 270
8.12 WaterHexameronthevirtualSurface(d1=2.8 A). . . 272
8.13 Waterdimersinthesurface-constrainedhexamer. . . 273
8.14 Freewaterhexamer. . . 274
8.15 EnergyofFormationE HEX ofthewaterhexamerunder surfaceconstraints. . . 275
8.16 PairinteractionenergiesE DIM inthewaterhexamer(classicalpotential). . . 277
8.17 Height(h)ofringasfunctionofsurfacelatticeconstantd1. . . 277
8.18 Anglew1 asafunction ofsurfacelatticeconstantd1. . . 278
8.19 Anglew2 asafunction ofsurfacelatticeconstantd1. . . 278
8.20 Anglew3 asafunction ofsurfacelatticeconstantd1. . . 280
9.1 Modelfortheplatinum-waterinteraction. . . 288
11.1 Variablesofthewaterdimer.. . . 326
11.2 BendingofW3. . . 326
11.3 Test oftheBNSwater-waterinteractionpotential. . . 330
11.4 Test oftheST2water-waterinteractionpotential. . . 331
11.5 Test oftheRowlinsonwater-waterinteractionpotential. . . 332
11.6 Test oftheDernalandFowler water-waterinteractionpotential. . . 333
11.7 Test oftheTIPS2water-waterinteractionpotential. . . 334
11.8 Test oftheTIP4Pwater-waterinteractionpotential. . . 335
11.9 Test oftheSPC water-waterinteractionpotential.. . . 336
11.10 Test oftheSPC/Ewater-waterinteractionpotential. . . 337
11.11 Test oftheTIPSwater-waterinteractionpotential. . . 338
11.12 Test oftheTIP3Pwater-waterinteractionpotential. . . 339
11.13 Test oftheCFMS water-waterinteractionpotential(I).. . . 340
11.14 Test oftheCFMS water-waterinteractionpotential(II). . . 341
11.15 Pt 9 cluster,topview. . . 354
11.16 Pt 17 cluster,topview. . . 356
1.1 Propertiesofwater. . . 2
1.2 Propertiesofice. . . 3
1.3 Propertiesofplatinum. . . 4
1.4 MultilayerPeaks . . . 6
2.1 In uenceoftheexcitationonthecorrelationenergyofwater. . . 23
2.2 Expectation valueofhr 2 iin bohrfordi erenturaniumorbitals. . . 37
3.1 Optimizedwatergeometries. . . 46
3.2 Compilationofthemainresultsforwater. . . 47
3.3 Harmonicvibrationalfrequenciesofwatercalculatedwith aDZPbasisset.. . . 49
3.4 Thermodynamicpropertiesofwater. . . 49
3.5 RHFresultsforwater. . . 50
3.6 GroundstatecoeÆcientsfromdi erentcorrelationcalculations. . . 50
3.7 Resultsforthewaterdimerfrom previousworks. . . 51
3.8 Optimizedgeometriesforthewaterdimer. . . 53
3.9 Remarkstotable 3.8 . . . 54
3.10 In uenceoftheBSSEontothemonomer'sgeometry. . . 54
3.11 Comparissonwiththeliterature.. . . 59
3.12 Calculatedharonic frequenciesofthewaterdimer[cm -1 ]. . . 60
3.13 Frequencyshiftscausedbythedimerisationofwater. . . 60
3.14 Correlationlevelandd OO , =0 Æ . . . 63
3.15 Comparisonofdi erentionpairsanddimer atL3=1.0 A. . . 64 3.16 ResultsforH 3 O + andOH . . . 64
3.17 In uenceoftheBSSEonthevariablesofthewaterdimer. . . 68
3.18 Minimumgeometryandenergyatthedi erentsteps. . . 71
3.19 FinalparameterforV CH . . . 72
3.20 Energycompositionnear theminimumin kcal/mol. . . 72
3.21 De nitionofthetrimergeometries. . . 75
3.22 Geometricaldetailsofthetrimers.. . . 75
3.23 Previouslypublishedresultsforthewatertrimer. . . 76
3.24 Analysisoftheinteractionenergy. . . 77
3.25 ElectronaÆnityandionisation energyofwater. . . 78
3.26 Correlationofchargetransferandstability.. . . 79
3.27 E NPA inkcal/mol . . . 81
4.2 PotentialsA-F. . . 97
4.3 Optimizedgeometriesofbothminimaonthedimer'spotentialenergysurface. . . 97
4.4 ErrorsforpotentialE . . . 98
4.5 Stationarypointsin gure4.21. . . 99
4.6 Characteristicpointsof gure4.22,d OO =2.8514 A. . . 103
4.8 Characteristicpointsof potentialN(referto gure4.32and4.33fordetails). . . 104
4.7 ErrorsforpotentialN. . . 104
4.9 ParameterforpotentialN. . . 109
4.10 Variancesof potentialN. . . 109
4.11 AbsolutvaluesforpotentialN.. . . 109
4.12 Globalminimafordimers. . . 109
4.13 OptimisationoftrimersI toIVusingpotentialN. . . 110
4.14 Compostionofthetrimerisationenergycomposition duringtheoptimisation. . . 111
4.15 Z-matricesforcyclicwatertrimers. . . 112
5.1 HMOsfortheequilateraltriangle.. . . 120
5.2 HMOsfortheright-angledtriangle. . . 121
5.3 HuckelorbitalsforPt5. . . 123
5.4 PopulationanalysisPT + 5 . . . 123
5.5 CoeÆcientsofthemolecularorbitalsinPt 9 . . . 129 5.6 ChargesonthePt 9 cluster. . . 129 5.7 6spopulationinthePt 9 cluster. . . 129
5.8 OccupiedorbitalsofthePt17clusterandpopulationanalysis. . . 131
5.9 ChargesonthePt 17 cluster. . . 132
5.10 Q cent ondi erntmetalcluster.. . . 132
5.11 OrbitalenergiesanddegeneraciesoftheHMOcalcualtions. . . 135
5.12 HuckelparametersfromECP-FHcalculationsonPt 0 2 andPt + 2 . . . 138
5.13 ResultsfromECP-HFcalculations. . . 139
6.1 ECPsusedin chapter6. . . 146
6.2 Energiesfrom di erentquantum chemistrycodesforplatinum. . . 147
6.3 platinumwateradduct-equilibrium geometries . . . 149
6.4 Platinumwateradduct-extremaofasystematicchangeof . . . 154
6.5 Comparisonofdi erentECPs. . . 155
6.6 BSSEin 1 Pt H 2 Oat MP2level. . . 156 6.7 ParametersforV BSSE . . . 156 6.8 Propertiesof 2 + PtHfordi erentECPs . . . 157
6.9 MullikenPopulationfromLanL2DZcalculations. . . 157
6.10 Propertiesoftheplatinumdimer. . . 161
6.11 1 S 1 Sdimer andwater. . . 164
6.12 3 D 1 S dimerandwater. . . 164
6.13 ChargesandchargetransferinPt 2 H 2 O. . . 167
6.14 Theplatinum-waterbondasafunction ofthe6spopulation . . . 168
6.15 MullikenoverlappopulationinPt 2 H 2 O. . . 174
3 6.17 MP26spopulationin Pt 3 . . . 178 6.18 Overlappopulationin Pt 3 . . . 178
6.19 OptimizedstructuresforPt 3 H 2 O.. . . 182
6.20 Geometriesfortheright-angledPt 3 -triangle. . . 185 6.21 OptimizedPt 5 H 2 Ocluster. . . 188
6.22 Localminimain thePt5H2Odissociation. . . 190
6.24 GroundstatecoeÆcientc 0 versuscluster size. . . 193
6.23 ElectronicpropertiesofthePt 9 H 2 Ocluster. . . 194 6.25 SmallPt n Cluster,singuletwavefunction,MP2optimizedstructure. . . 195
7.1 simp inGaussian94inputformat. . . 210
7.2 Resultsforthenew6pwavefunction. . . 211
7.3 LanL2eigenvalues. . . 216
7.4 6dorbitalwithaaugmentedbasisset. . . 217
7.5 Localminumcreatedwithvariousexponetsn. . . 225
7.6 Resultsford A .. . . 228
7.7 Parametersof Zuritas'sECP. . . 231
7.8 Einergyeigenvaluesform test1. . . 231
7.9 Resultsfrom test2. . . 232
7.10 Resultsfrom test3. . . 232
7.11 Mullikenpopulationatthetopin Pt + 5 . . . 240 7.12 Pt + 5 propertiescalculatedwithasecondorderECPfunction.. . . 241
7.13 Pt 5 pyramidewithdi erentECPatthetop. . . 242
7.14 OrbitalcoeÆcientsinPt 5 . . . 243
8.1 SelectedresultsforPt H 2 O. . . 254 8.2 ResultsforPt (H 2 O) 2 . . . 255
8.3 SelectedValuesforlargerplatinum-waterclusters . . . 263
8.4 Water-Waterinteractionparameters. . . 268
8.5 Calculatedpropertiesofthewaterdimer.. . . 269
8.6 Calculatedpropertiesoftheplanarfpppgwatertrimer. . . 271
8.7 Globalminimaofthepotentialenergycurvesfortheconstrainedwaterhexamer. . . 276
8.8 MultilayerPeaks. . . 283
9.1 Pt n H 2 Owithdi erentECPs. . . 292
11.1 DZPbasissetforH 2 O. . . 316
11.2 TZVPbasissetforH 2 O. . . 316
11.3 LanL2DZPtbasisset. . . 317
11.4 LanL1MBPtbasisset. . . 317
11.5 LanL2DZPtECP. . . 317
11.6 LanL1MBPtECP. . . 318
11.7 NewbasissetforPt. . . 318
11.8 NewECPforPt. . . 318
11.11 Dimerwithastraighthydrogenbond(W3=90 Æ
). . . 321
11.12 Dimers withabendedhydrogenbond. . . 322
11.13 Dimerwitha xedwatergeometry (r
OH =0.9572 A,^ HOH =104.52 Æ ). . . 323
11.14 In uence oftheBSSE onthemonomer'sgeometry(I). . . 324
11.15 In uence oftheBSSE onthemonomer'sgeometry(II). . . 324
11.16 In uence oftheBSSE onthemonomer'sgeometry(III). . . 325
11.17 In uence oftheBSSE onthemonomer'sgeometry(IV). . . 325
11.18 Morokumaenergydecomposition(d
OO
)-allenergiesin kcal/mol. . . 327
11.19 Morokumaenergydecomposition( )-allenergiesin 10 3
Hartree. . . 328
11.20 Morokumaenergydecomposition( )-allenergiesin10 3
Hartree. . . 329
11.21 BasissetforthePt
9
Huckelcalculation. . . 354
11.22 BasissetforthePt
17
Huckelcalculation. . . 357
11.23 Functionsusedforthecalculationof
R
. . . 359
11.24 FunctionsusedforthecalculationofE 00
Introduction
1.1 General Introduction
Waterisprobablyoneofthemostcommonandbestanalysedchemicalsubstancesonthisplanet.
Theoceans, whichcover70.8% ofthe planet'ssurface,store 97.3%of allwater(1.38510 9
km 3
).
Platinumontheother hand is veryrare (0.01ppm[1]). This workso focuses ontheinteraction
betweenthecommonandthenoble.
Platinum is a very important catalysist. The rst reaction studied in detail, which served
for the de nition of acatalysis, wasthe hydrogen combustion (2 H
2 +O 2 ! 2 H 2 O) [2{5]. A
stoichometricmixtureofhydrogenandoxygendoesnotreactuntilasmalldoseofplatinumpowder
isadded. Then, themixturereactsvividly andanexplosion canbeobserved. Theplatinumdust
loweredthebarrierofactivatione ectivelyforthereactiontostart.
Today,oneofthemostimportantapplicationsofplatinumisthepuri cationofexhaustfumes
frommotorvehicles[6]. Platimumcatalysistheoxidationofcarbonmonoxidandhydrocarbonsto
carbondioxide,butmoreimportantisthereductionof nitrogenoxides.
2CO + 2NO ! N
2
+ 2CO
2
Water is next to carbon dioxide the most important product of the combustion and large
amountsofwaterarealsoatthesurfaceoftheplatinumcatalysist.
C x H 2x+2 + 3x+1 2 O 2 ! xCO 2 + (x+1)H 2 O
Thesewatermoleculescompetewiththeotheroxidesintheexhaustfumesforactivesurfacesites
onthecatalystandhavesoamajorimpactonthequalityofthecleaningprocess. Electrochemical
experiments showed, that the rate of the O
2
reduction and H
2
ionisation reaction on platinum
electrodesdependsstonglyontheorientationofthewatermolecules [7].
Regardingthe economicaland environmental importance of theplatinum-waterinteraction it
isnotsurprising,thattheworkonthistopicstartedearlyand rstresultshavebeenpublishedby
General Motors[8].
Theoreticalworkaspublished withinthisthesiswillhelp ustounderstandtheinteraction
be-tweenplatinumandwaterbetter,whichwillhopefullyendinthedevelopmentofbettercatalysists
BernalandFowlershowed,thatthestructureofanindividualwatermoleculedoesnotchange
much with the phase of the substance [9]. The free water molecule has C
2v
symmetry and the
structure ofthe moleculecanbe explainedwellwiththe VSEPRmodel (V alence ShellElectron
PairRepulsion)[10{12]. Theoxygenatom(sp 3
hybridisation)hasatetrahedralenvironment:Two
sp 3
hybridorbitalsform thebondsto thehydrogen atoms(r
OH
)whilethe remainingtwohybrid
orbitalsfromtheloneelectronpairs. Theloneelectronpairs,needingslightlymorespacethanthe
chemicalbonds, force thehydrogen atoms closerto eachother and thebond angle ! is therefore
smallerthanthatfoundin anidealtetrahedreon(109.47 Æ
).
Waterisachemicalsubstancewith
extraor-property value ref.
M 18:0151 g/mol [1] r OH 0:9572 A [16] ! 104:52 deg [16] 1:85 D [17] I X 2:9376 10 40 g 1 cm 2 [16] I Y 1:0220 10 40 g 1 cm 2 [16] I Z 1:9187 10 40 g 1 cm 2 [16] 1:45 A 3 [15] E ION 11:53 eV [15] E AFF 1:07 eV [15] E HO H 498 kcal/mol [15] E O H 427:5 kcal/mol [15] T F 0:0 Æ C [1] T B 100:0 Æ C [1]
Table1.1: Propertiesofwater.
dinaryphysicalproperties(table1.1). The
boil-ing(T
B
)and thefreezingpoint(T
F
)aremuch
higher than the values for the other hydrogen
chalcogenids (eg H 2 S: -85.6 Æ C and -60.3 Æ C).
Thehightransitiontemperaturesarecausedby
stronghydrogen bondsamong the water
mole-cules[13]. Di erentelectronegativitiesfor
oxy-gen(3.5)andhydrogen(2.1)causepolar
oxygen-hydrogen bonds and so create a large dipole
moment (). Coulomb forces can be used for
a rst attemp to explain the strong hydrogen
bond between a positively charged hydrogen
atomandaloneelectronpairontheoxygen,but
quantumchemistryprovidesfarbettermethods
(chapter3,page45).
The covalenthydrogenbonds [14] canform
arigid,tetrahedralnetworkand sothebasisof
ice. Thisnetworkkeepsthewatermoleculesfurtherapartthanin theliquidphase,wherethermic
motionsallowthe watermolecules to collideand formso distorted microcluster. Thedensityof
thelowpressureice phasesIhandIc (table1.2)isthereforesmallerthanthedensityoftheliquid
(=0.99978gcm -3
atthetriplepoint[15]). Thestructureofthesetwoicephasescanbeexplained
wellwithasetofrulesoriginallydevelopedbyBernal,FowlerandPauling(BFPrulesorice
rules)[9,13]:
Thewatermoleculeinice resemblesthewatermoleculein thegasphase.
Eachwatermoleculeis orientedsothatits twohydrogenatoms aredirected approximately
toward two of the four oxygen atoms which surround it tetrahedrally, forming hydrogen
bonds.
Onlyonehydrogenatomispositionedbetweeneachneighbouringoxygen-oxygenpair.
Underordinaryconditionstheinteractionofnon-adjacentmoleculesisnotsuchastostabilize
appreciably any one of the many con gurations satisfying the preceding conditions with
Only theoxygens of the water molecules are drawn anddi erentgrey shadesin gure1.1 mark
di ernt layers of water molecules in the crystal. The structure of ice Ih canbe visilized by the
condensationof waterhexamers. These waterhexamer are ringsin thechair conformation. One
hexamerismarkedlightgreyasanexamplein thecentreofthe gure.
Paulingsuggested1935,thatnexttothe
hexag-Figure1.1: Structureofice1h. [18] onalice phase(iceIh)withanother icephasewitha
cubiccrystal system(ice Ic)should bepossible[13].
Ice Ic can created by the condensationof water
va-pors between 120 Æ
C and 140 Æ
C [1]. Table 1.2
showsacompilationofthestrcturalcharacteristicsof
bothlowpressureice phases.
InbothicephasesIcandIharethepositionsofthe
hydrogens disordered. The hydrogen is attached to
eitherwatermoleculesharingahydrogenbond. The
bonds among the water molecules oscilate therefore
betweenhydrogenbondingandcovalency,depending
onthe distance of the hydrogen from theoxygen atom 1
. If the ice crystal is cooled to very low
temperatures,themovementofthehydrogensfreezesandthehydrogensstayinrandompositions.
ice phase Ih Ic
crystalsystem hexagonal cubic
spacegroup P63/mmc Fd3m
celldimensions a
[pm] a=450 c=732 a=635
moleculesperunitcell 4 8
nearestneighbours 4 4
distanceto thenextneighbour[pm] 275 275
O O Oangle[deg] 109.3,109.6 109.6
hydrogenposition disordered disordered
Density a [gcm -3 ] 0.93 0.94 a 110K,athmosphericpressure
Table1.2: Propertiesofice. [18]
Protonorderedicephasesarepossibleandstillsubjectofcurrentresearch[19,20]. Acomplete
ordering of protons can be used to align the dipole momentsof the water molecules parallel to
eachother (ferroelectricity) [1, 21]. Ferroelectric ice phasesshowa spontaneous polarisation and
strongelectric eldscan beobservedbetweenoppositesidesoftheice crystal.
OneofthemanywaystoobtainferroelectriciceistheepitaxialgrowthonPt(111)[20,22]. The
platinumsurfaceisbelivedtoordertheprotonsinthe rstlayerofwater. Carefulcondensationof
1
Protontransfer similarto theGrotthus mechanism [23, 24] isimpossibleinice between30to 190
K [25]. The potential, in which the proton moves, is not periodic, since the proton structure inice is
disordered,andlongdistanceprotontunnelingfortheGrotthusmechanismdemandsaperodicpotential.
ProtontransferiniceisthemovementofaDdefect(twohydrogenatomsareononeoxygen-oxygenbond)
ferroelectricbulkicephasehasbeenreached. WitekandBuchshowed,thatonlythe rstbilayer
gowthswith orientatedhydrogensand that theprotons in thesecond layerarenotorientated to
minimizetheelectrostaticenergy[26]andbreaksothestandardrulesforhydrogenbonds[27].
1.1.2 Properties of Platinum
Three countriescover98%of theworldsdemand forplatinummetals (South Africa45%,former
UdSSR 45%,Canada8%). OnlytheMerensky-MineinSouth Africa(SouthAfricacovers65%of
theworldsplatinumdemand.) isexploitedforplatinumsolely,ineveryothercaseistheplatinum
re nedfrom impuritiesofotherores[1].
Platinumisasilverwhite,ductilemetalwitha
cu-property value number 78 isotopes 6 mass 195.08g/mol con guration [Xe]4f 14 5d 9 6s 1 electronegativity 2.2 d Pt Pt 2.77 A T F 1769 Æ C T B 4170 Æ C E ION 9.0eV
Table1.3: Propertiesofplatinum[1].
bicclosedstructureandcanbedissolvedeasilyinaqua
regiaand slowly in hydrochloricacidin the presence
ofair. PtCl 2 4 + 2e ! Pt + 4Cl E 0 =0:75V PtCl 2 6 + 2e ! PtCl 2 4 + 2Cl E 0 =0:77V
Platinumdissolves also readily in fused alkali oxides
andspeciallyinalkaliperoxides. Itisalsoattackedby
uorineandchlorineatredheat andreactsalsowith
elemetal P, Si, Pb, As, Sb, S and Se under reducing
conditions.
Pt(0)compoundsarewellknownandthesynthesis
ofmanyclustercompoundswithdirectplatinum-platinumbondsstartsfromPt(PPh
3 )
4
[28].Huge
amountsof molecularhydrogencanbesolvedin platinumand themetalactivatesthe
hydrogen-hydrogenbond,which explainsitscatalyticactivityinhydrogenationreactions.
Platinumis chemicallymuchmorereactivethancommonly asumed: Morethan70
oxidation-reductionreactionsarecatalyzedbyplatinumanditisnowpossibletopredictcatalytic activities
from thethermochemicalpropertiesofthereactingcouples[29].
1.1.3 Literature Survey
Theplatinum-waterinterfacehasbeenexaminedwithvariousexperimentaltechniquesrangingfrom
UHV (Ultra High V acuum) to electrochemicalexperiments. Bothexperimentsdi er principally
in the number of water molecules. But, it is possible to vary the electric eld at the surface
systematicallyin electrochemicalexperimentsand notin UHV experiments. Theelectric eld at
the surface is varied in UHV experiments by the coadsorption of polar or ionic species, which
makesthe ne tuning of the eld strength diÆcult. On the other hand, UHV experimentsgive
informationsonthemicroscospicscale,whereaselectrochemicalexperimentsgiveintegralvaluesfor
thedoublelayer[30]. Variousstructuremodelshavebeenproposedfortheelectrochemicalbilayer
toexplainthevalueofthedi erentialcapacityasafunctionoftheexcesscharge,butthenumber
ofexperimentalparametersadjustedtoreproduceexperimentaldataquaestionsthevalidityofthe
model[24,30{33].
Weaver et al. exploited the similarityof both experimental methods forthe analysisof the
1. Ebene
2. Ebene
Bilayer - Zelle
Platin - Zelle
Figure1.2: Idealbilayerstructure.
means ("UHV electrochemical modeling") [34, 35]. They showed, that both methods complete
eachother verywell.
Early UHV experiments [36, 37] on the adsorption of water on platinum(111) reported a
p( p 3 p 3)R30 Æ
surfacestructure of adsorbed water molecules and suggestedthe formation of
iceorderedin domainsof30 40
Ain lenght.
A waterbilayerstructure [38,39]( gure 1.2)hasbeenproposed asthe basisof thegrowthof
iceonhexagonalmetallatices. Theicephaseonplatinumisbelievedtohavethesamehexagonal
symmetryasthesurfaceandthewaterhexamermarkedin gure1.1formsthebasisofthebilayer
structure[40]. Thestructureofthiswaterbilayersisgenerallyexplainedin termsofanextension
to surfaces [39] ofthe Bernal-Fowler-Paulingrules (ice rules)[9, 13]. Speci cally [39],each
watermoleculeis assumedbound byat leasttwobonds (which may be hydrogen bonds toother
watermoleculesoroxygenlonepairbondstothesurface)whilemaintainingatetrahedralbonding
con guration. Thewaterisassumedboundto thesurfaceviaonelonepairorbital ontheoxygen
andallfreelonepairorbitalsonoxygenstaynearlyperpendiculartothesurface.Inanidealin nite
bilayer,allwatermoleculeshavetheirdipolemomentspointingawayfromthesurface(" ipup"),
whereasina nitecluster,watermoleculeswhose dipolemomentspointtowardthesurface(" ip
down") mayoccurat theedge of thecluster [39, 41, 42]. Experimental results[43] suggestthat
theedgesofice-likeclustersonPt(111)areconstructedfrom ipupmoleculestogetherwithwater
moleculeswith oneOHbondparallel tothemetalsurface,in contrastto the op downgeometry
predicted at the edges by the BFP rules. Such a water species has been observed on Pt(100)
[44] and experimental evidence suggests that such aspecies may also exist on Pt(111) [45, 46].
It has notbeen possibleto rule outsuch a structure byapplication of ultraviolet photoelectron
spectroscopy(UPS)toPt[6(111)(100)][37].
Doering and Madey [39] concludedusing the surfaceextended ice rule set, that the
small-est stable water cluster on a hexagonal metal surface should be the water nonamer. Such an
(H
2 O)
9
clusterhasbeenobservedonRu(0001)aspartofp(6 p 36 p 3)R0 Æ superstructure[39,47],
whereasexperimentalresultssuggest,thatthesmallestclusterpossibleonplatinum(111)isa
three-dimensionalwatertrimer[45].
In the initial stages of growth, awater moleculehas twopossible adsorption sites: attached
eitherdirectlyaboveaplatinumonthesurfaceortoawatermoleculealreadyboundtothesurface
[46,48]. Thecoexistenceofbothspecies(i.e. awatermoleculedirectlyboundtothesurfaceanda
watermoleculeattachedtoanotherwatermolecule)iscommonlyexplainedintermsoftheenergy
of isolated bonds, although the importance of cooperative forces has been suggested previously
[42,45,49]. Thestrengthoftheplatinum-waterbondcorrespondstothatoftwotothreehydrogen
platinum(111) surfaceallow us to distinguishdi erentwater species, but thediscussion remains
controversial.ThemostrecentdatafromOgasawara etal. [56]showsthreeprominentpeaksat
155K,165Kand200K.The rstpeak(at155K)wasassignedtoicesublimation,thesecond(at
165K) to waterin thesecond adsorptionlayerand thethird (at200K) to waterdirectly bound
to thesurface. Whilethe rst twopeaks havebeen positively identi ed, theorigin of the third
remainsamatterofdiscussion[53,54]. Theformationofthesecondpeakat165Kcanbeobserved
at coveragesas low as0.13to 0.27monolayer(ML),where 1ML refersto oneidealbilayer[39].
TheseTDSresultsareconsistentwithotherexperimentalresults[43,45,46,48,57,58],whichalso
supporttheformationofwaterclustersatlowsurfacecoverage.
Thesecondpeak 2
(165K)isthemultilayerpeakintheTDS
surface ltm T [ A] [K] Ni(111) +0:19 170 Cu(111) +0:08 150 Rh(111) 0:16 190 Ru(0001) 0:19 212-220 Re(0001) 0:28 180 Pt(111) 0:30 170 Ag(111) 0:50 150
Table1.4: MultilayerPeaksdata
fromrefs. [38,47] spectrum. A watermoleculefrom thetopshouldthereforebe
in achemicalenvironmentsimilar toaniceIhcrystal.
Di er-ences in the desorptiontemperaturehaveto betherefore the
result ofthe latticedistortion of theice crystal,becausethis
moleculehasnodirectcontactwiththemetalunderneath. A
measure for this distortion is thelattice-mismatch (ltm)
(ta-ble 1.4). A negative value indicates the contraction of the
ice lattice and apositive its expansion. The highest
desorp-tiontemperatureshouldthereforebefoundforthemetalwith
thesmallestvaluefor thelattice-mismatch (copper), but was
foundforruthenium. Thisshiftofthemaximumpeakposition
andthehigherbondingenergycomparedwithicesublimation
suggest, that the simplebilayermodel from Doering and Madey may need furtherre nement
[42,59].
Thetheoretical work published on the metal-waterinterface canbeseperatedinto two main
groups: The rst group focuses on electrochemicalaspects of thesubject. Molecularmechanics
(MC)andmoleculardynamics(MD)calculationsareusedtomodeltheplatinum-electrolyte
inter-face. The secondapproachconcentratesmoretheUHV aspects. Quantum chemical calculations
on various level of theory examine the interaction of one water molecule with a metal cluster
[54,60{72].
Bothquantumchemistryandexperimentagreethatthewatermoleculeisonlyslightlydisturbed
uponadsorptiononPt(111)[41,45,46,48,58,73{75]anddissociationhassofaronlybeenobserved
experimentallyonpre-coveredsurfaces[76{79],whichallowsustouserigidwatergeometrieswithin
thecomputationalsimulations.
FirstquantumchemicalresultshavebeenpublihedbyHollowayandBennemannusingthe
EHT (Extended Huckel Theorie) for the calculation(1980, [64]). Theyused a Pt
5
pyramid to
modelthesurfaceandreportedabondingenergyof0.5 eVwiththewatermoleculein anon-top
position withaplatinum-oxygendistance of 2.3
A. These calculationsservedasthebasisforthe
developmentforclassicalplatinum-waterinteractionpotentialusedforMDcalculations.
EightyearslaterEstiuetal. [65]reportedanewsetofEHTcalculationswithadi erntsetof
Huckelparametersand largermetalclusters (Pt
18 , Pt
19
andPt
25
). Theplatinum-waterdistance
2
Theprecisevalueofthedesorptiontemperaturedependsslightlyontheexperimentalconditions
was xedat1.7Aasaresultofearliercalculations(bondingenergy=0.94eV[60]). Theyreported
bondingenergiesof0.42eVforthePt(111)surfaceand0.57eVforPt(100). Inbothcaseswasthe
watermoleculein anon-toppositionwithitsmolecularplaneperpendicularto thesurface.
M
ulleretal. usedtheKohn-Shamshemewithalocaldensityapproximation[70]toperform
cluster calculations(Pt
10 H
2
O) on theadsorption of water onPt(111) [54, 63, 68]. This group
reported a bonding energy of 0.53 eV with a platinum-oxygen distance of 2.5
A. M
uller
pro-posedalsoaquantumchemicalmodelfortheplatinum-waterbond[68] basingonhisworkonthe
aluminium-waterinteraction [70],which waslaterused byRibarsky et al. for thecopper-water
bond[71]: The3a
1
and the 1b
1
orbitals, which do notcontributemuch to thebonds within the
watermolecule,interactwith lledplatinum5dorbitals. ThelowlyingLUMOinteractsthenwith
both lled orbitalsresultingfromtheplatinum-wateroverlapandlowerssothetotalenergy. The
occupationoftheformeremptyLUMOleadstoanchargetransferfromthewatermoleculetothe
metalcluster. Thisinteractionmodelisthequantumchemicalequivalenttotheelectrostatic
polar-isationandtheauthors thereforecalltheLUMOapolarisationfunction. Theygivethefollowing
equationforthepolarisationenergyE
E = hPOLj ^ VjLi 2 POL L (1.1)
jPOLiistheLUMO,whichactsas apolarisationfunction,andjLithefreeelectronpairofthe
watermolecule. Twoprincipalfeaturesoftheplatinum-waterbondfollowfromequation1.1,which
arenotmentionedinreference68:
1. ThebindingenergyofthewatermoleculedependsonitsorientationrelativetojPOLi,since
E is proportionalto the square of the overlapbetweenthe platinum5d orbitals and the
freeelectronpairofthewatermoleculehPOLj ^
VjLi.
2. E isinverselyproportionalto theenergydi erencebetweenbothorbitals. Thelargerthe
cluster becomes, the smaller becomes the HOMO-LUMO gap and so the energy di erence
betweenjPOLiand L,because
L
isindependentoftheclustersize.
Theimportanceof polarisationfor theplatinum-waterbondsuggests,that cooperativeforces
are important for the structure and energy of theplatinum-water interface. The signi cance of
hydrogen bonding and polarisatione ects hasbeendiscussed previously [45, 56, 64, 68, 71, 75],
but, to ourknowledge, hasnot been studied in great detail. Kutnetsov et al. published 1989
CNDO/2 (Complete Neglect of Di erential Overlap) for water clusters bonded to 1b (Cu, Ag,
Au)and2bgroup(Zn, Cd,Hg)elements[67].
Modernquantumchemicalcalculationsontheplatinum-waterinterfacesuggestthatthe
molec-ularplaneof thewatermoleculelies parallelto thesurface[54, 63,68]. These resultsagree with
workfunctionmeasurements[45,52, 58,73] onwater-coveredplatinumsurfaces,which showthat
that acontribution of about 0.2 D of the water dipole moment (free watermolecule 1.84 D) is
normaltosurface[58],butcontradicttheicerulesforsurfaces,whichexplainverywellotherUHV
dataliketheLEED(LowEnergyElectron Di raction)results. Theorientationofthehydrogens
inwatermoleculewithadirectbondtothemetalsurfaceunderneathshouldthereforeberegarded
asunsetteled.
Thenumberofatomsandmoleculesintheelectrochemicalinterfaceinhibitstheapplicationof
quantumchemicalmethodsandotherhavetobeused. MonteCarlosimulations(MC)[80{83]and
mirror images for the simulation of themetal-water interaction. They assumed an ideal, highly
polarizablemetal surface. The image charges had thereforethe samesize asthe charges onthe
watermolecules(TIPS2potentialforbulkwater),butweredi erentinsign. Thesecalcualtionsfor
anunchargedmetalwallresultedinerroneouswaterorienationscloseto thewall. The rstlayer
watermoleculesbondedwithonehydrogenatomtothemetalsurfacewhiletheotherpointedinto
the bulk water. Despite this principle problem these calculations indicate that polarisationand
manybodye ectswithinthemetalhaveasigni cantin uenceonthestructureofthemetal-water
interface, while Kohlmeyer et al. [84] published molecular dynamics calculationsshowing that
theinclusion ofpolarisationintothewater-waterinteractionpotentialhasonlylittlein uenceon
the results of the siumulation. MC calculations with a more elaborate set of potential energy
functions [80,81]reproducecorrectlytheorientationof the rstlayerwatermoleculesclosetoan
unchargedcopperwall.
MD calculations [84{102] form the second group of computational methods applied to the
electrochemical metal-water interface. The potential energy functions used for the metal-water
interaction canbesubdividedinto twogroups: First,potentialsexploiting electrochemicale ects
suchasmirrorchargesandsecond,potentialstryingto mimicchemisorptiondatafrom quantum
chemicalcalculations.
Hautmanetal. [91]publishedMDcalculationsforunchargedmetalwallsusingthe rstgroup
of metal-waterpotentialswith apeculiar result: Although the rstpeakof thehydrogendensity
lies0.2
Aclosertothemetalsurfacethanthe rstpeakoftheoxygendensity(ref. 91 g. 2)the
dipole momentsofthewatermoleculespointpreferentiallyawayfrom thesurface(ref. 91 g. 3).
The authors explain this e ect with the largercharge (factor 2) on theoxygen atoms thanon
thehydrogenatomsresultingin anoverallnegativechargeat themetalsurface.
ZhuandRobinson[92]reportedMDcalculationsofwaterbetweentwosolid,insulatingwalls.
Theinteractionbetweenthewallandthewatermoleculesisdescribedwithagas-crystalpotential
excluding mirror charges. They conclude form their calculations that thewater molecules close
to the surface orientate the hydrogen atoms towards the solid and notinto the bulk water. In
a second paper Zhu and Philpott[93] showed, that theorientation of thewater molecules
to-wardsthesurfacedependsstronglyonthechosenpotentialenergyfunctionsnowincludingmirror
charges. Theycompare twopotentialenergyfunctions foravarietyof metalsurfaces di eringin
an anisotropicLennard-Jonesenergy term (V
an
) actingon the hydrogens. Thepotentialenergy
functions containingV
an
resultin watermoleculesbondingtoaPt(100)surfaceviaonehydrogen
atomsimilartothebondinggeometriesreportedbyGardneretal. [82,83]whereasthepotential
energyfunction withoutV
an
producesnoplatinum-hydrogenbonds.
ThesecondclassofMDcalculationsusesindividualpotentialenergyfunctionsforthehydrogen
atoms and the oxygen atom to calculate the metal-water binding energy. The parameters of
thesefuctionshavebeenchosenbyHeinzingerandSpohr[94{96]toreproduceExtended-Huckel
results[64]andexperimentaldata. Later, thesepotentialenergyfunctions havebeenextendedby
Berkowitzetal. aboutasurfaceterm,whichincludesthesymmetryofthemetalsurface[97,98].
Spohrs[94{96,99{101]resultsfortheunchargedplatinum-waterinterfacemaybesummarized
asfollows:
Theoxygenandthehydrogenatomdensityshowstrongoszilationsclosetothesurface,but
watermolecules closetothe surface. These twopeakssuggesttheexistence ofwaterlayers
similarto thebilayerstructureobservedforwaterinUHV experiments.
Thewatermoelcules,whichcause the rstpeak in thoxygen atomdensitypro le(directly
attached tothesurface), stayattheirposition duringtheMD run,whereasmoleculesfrom
thesecondpeakarelesstightbound andmovefreelywithinthelayer[102].
Atlowcoveragesofwater()thewatermoleculesinthe rstlayerareorientatedinatilted
position withtheir dipolemoment pointingawayfrom thesurface(# =75 Æ
, # istheangle
between the surface normal and the dipole moment). Both hydrogen atoms of the water
molecule are at the samedistance from the surface[95]. Such anorientationof the water
molecules is expected for a bonding bonding mechanism viaa lone electronpair, which is
surprising,sincetheplatinum-waterpotentialfavoursanadsorptiongeometrywiththewater
moleculesdipolemomentperpendiculartothesurface 3
. Astronghydrogenbondingnetwork
isassumedtostabilizethisgeometry. Thesameprinciplegeometrye ectshavebeenobserved
bySpohr[100,101]alsoforHg(111).
Asincreasesfrom0.2to0.8movethehydrogenatomscloserotthesurfaceuntil nallythe
molecularplaneofthewatermoleculeisparallel tothesurface.
Theelectrochemicalresultssuggest,thathydrogenbondingwithintheinterfaceisessentialfor
avaliddescriptionoftheplatinum-waterinterface. Thetransition betweenbothelectrochemistry
and UHV experiments is done by the reductionof thewater molecules used for the simulation.
Insteadofbulkwatercomenowsmallwaterclustersintofocus. Liuetal. [103]pointedout,that
water-waterinteractionpotentials,which reproducewellthepropertiesof bulkwatertend tofail
onsmallwaterclusters.
The water dimer is probably thebest analysed watercluster of all. It wasnotonly the rst
watercluster subjectof ab initio calculations[104] butis alsocommonlyused asbenchmarktest
fornewcalculations. It isthereforepossibleto ndreferencevaluesin theliteratureforthewater
dimeroneverypossibleleveloftheory[105{131]. Theglobalminimumhasalineargeometrywith
C
S
symmetry withthe nonbonding hydrogens onoppositesites ofthe oxygen-oxygenbond. The
optimizedoxygen-oxygendistanceisabout3
Aandthebondingenergyabout5kcal/mol.
Sch
utzet al. suggestedanameningsystemforthenon-bondinghydrogensinthecyclicwater
trimer,whichfully describesthegeometryof thecluster[132]: Thenonbondinghydrogencanbe
either above (up, "u"), parallel to (planar, "p") or under (down, "d") the oxygen plane, while
thebondinghydrogens restin the oxygen plane. Ifthe oxygen planebisects thewatermolecule,
thegeometry ismarked withan"b". Theglobalminimumof thepotentialenergy surfaceof the
watertrimerhasacyclicgeometry. Earlycalculationsonthewatertrimersuggest,thatthefuuug
water trimer is less stable than the ideal linearstructure [133], but already the fpppg trimer is
morestable thanthelinearone. Thelineartrimeragaintransformssmoothlyintoacyclicfuudg
geometry,whichmarksthe globalminimum[128,131,132,134{150]. Thegeometry ofthe water
3
Thisorientationre ects the results of the Huckel calculations usedfor thecreation of the potential
energy functions. The Huckel calculations for Pt
5 H
2
O favour the same geometry and the observed
equilibriumgeometrymaybetheresultofthemissinginteractionsbetweensurfaceatomsandthehydrogens
(2 n
n!2,wherenisthenumberofwatermolecules inthecluster)[103,150{156].
18stationarypointshavebeenfoundonthepotentialenergysurfaceof thewatertrimer[142,
145]. Thefpppgtrimerhasaslightlysmallerbondingenergythanthefuudg(E<0.5kcal/mol)
[132] and is a stationary pointwith aHessian index of 3. Most of thepublished resultsfocuses
onthefuudgtrimerandonlyfewarticlesconcentrateonthefpppg[132,140,142,144,157{159],
despitethefact,thatthefpppgandthefudpgtrimerarepossibleintermediatesinthemovement
ofthehydrogens[132].
Thecomputational analysis of watercluster gained moreinterest recently, becausethese
mi-crocrystalscanbeusedtoinvestigatephasetransitions[160]. But,thetransitionfromsmallwater
cluster to largeris notstraight forwardand thewaterhexamer seperates thewater clusters into
twodomains.
Twoprinciples control the structure of water clusters: First, the numberof hydrogen bonds
in the cluster should be ashigh aspossiblefor a maximum energy gain. And second, repulsive
interactionsbetweennonbondinghydrogensandgeometricalstrainswithin thewaterringsshould
be as low as possible at the same time. Small water cluster (H
2 O)
n
with n 5 5 are therefore
commonly assumed to becyclic planar [103, 128,133, 161{170], while large clusters with n = 7
havethree dimensional structures [160,170{178]. Thewater hexamer markstheborder between
both regions and is the smallest water cluster with a three dimensional equilibrium structure.
Severalgeometrieswithsimilarenergies(E<1kcal/mol)havebeenfoundforthewaterhexamer
[128,148,149,179{182]. Themultitude ofenergeticallysimilarisomersmakesthewaterhexamer
anewbenchmarksystemformethods,whicharegoingtobeapplied tolargerclusters.
Althoughthecyclic water hexamerforms thebasisof theice structure[18, 183,184]andhas
beenobservedasastructuralelementin liquidwater[185],hasthemoststablewaterhexamer in
the gas pase a cage structure [186, 187]. The energy di erencebetweenthe cyclic and the cage
hexamer is small and it has not been possible to observethe free hexamer experementaly until
recently[187].
Quantumchemicalcalculations[128,148,149,179{182,188]onthecyclicwaterhexameragree
reasonably well on the geometry of the cluster, but disagree heavily on the total energy of the
cluster. The moststable ring hasa "chair"conformation(S
6
symmetry) with straighthydrogen
bonds and the oxygen-oxygen distance between direct neighbours varies between 2.708
A and
2.855
A. Themain propertiesof thecluster's geometry canbereproduced withsimple methods,
whereasreliableenergycalculationsrequiresophisticatedones. Published valuesforthebonding
energyofthecyclicwaterhexamervarybetween 37.99kcal/moland 56.00kcal/mol(withone
exception: 66.66kcal/mol[181])dependingonthelevelofcomputation.
1.2 This work
Twocomputerexperimentsareusedcommonlyforthesimulationoftheplatinum-waterinterface:
First,quantumchemicalcalculationswithasinglewatermoleculeandsecond,moleculardynamics
simulationswith various potential energy functions. Between theese two extremes is this work
placed: Acomputationalanalysisofwaterclustersattachedtoaplatinumsurface.
Figure 1.3 shows, howthe calculationof water clusters on aplatinum surface(Pt
n (H
2 O)
m
in thecenterof thesketch)is embededin its scienti cenvironment. As mentionedin section1.1
Pt
n
-(H
2
O)
m
6s electron
density
cooperative forces
in the water cluster
cooperative forces
in the Pt-H
2
O bond
Transformation
possible ?
natural geometry
under surface conditions
quantum chemistry
Pt
n
-H
2
O
quantum chemistry
Pt
n
quantum chemistry
(H
2
O)
m
classical interaction
potentials (H
2
O)
m
molecular dynamics
electrochemistry
potential ener
gy functions
potential energy functions
bulk properties vs. small cluster
polarisation
strong vs. weak bonds
Figure1.3: Scienti cenvironmentofthis work.
[101]. Thepotentialenergy functionused forthesecalculationsbase onextendedHuckel
calcula-tionsusing aPt
5 H
2
Opyramid withthe watermoleculeat the topassurfacemodel (Pt(100)).
Suchaclusterhasnoothersurfaceatomsthantheonebondingthewatermoleculeandthe
repre-sentationoftheinteractionsbetweenthewatermoleculeandthenon-bondingsurfaceatomsseems
tobepoorfortheequilibriumgeometry. Anotherproblemarisesfromthewater-waterinteraction
potential usedfor thesimulation. Most ofthe usedpotentialshavebeenoptimizedto reproduce
properties of bulk water. Many-body forces are important for bulk water, where an individual
watermoleculeisevenlysurroundedbyotherwatermoleculesandthewatermolculecantherefore
bethought captured in a homogenous matrix. Simple, pair wise additive interaction potentials
cansimulate agreat share of these forces bytheir parametrisation and good bulkvalues canso
beeasilycomputed. Inasmallclusterisawatermoleculenotevenlysurroundedbyitspeers and
'bulkpotentials'failthereforetoreproducethepropertiesofsmallwatercluster.
Thisworkstartedwithaquantumchemicalrevisionofthewaterdimerandtrimertoobtaina
setofbasisdataforsmallwatercluster. Aselectionofclasicalwater-waterinteractionpotentials,
used byother groupsformolecular dynamics simulations,wasunable to reproducethe quantum
chemicalresults.
Quantum chemical calculationson large water clusters are computationally expensive and a
classicalwater-waterinteractionpotentialwouldallowusto ndgoodstartinggeometriesforthe
quantumchemicalanalysis. Therefore,wecreatedanewwater-waterinteraction potential,which
inludespartiallycooperativeforces byitsparametrisation.
tronicstateofthecluster,asthebondbetweenthemetalatomsisformedmainlyviathe6sorbitals,
whointeractwiththepartially lled 5dband.
Thequantumchemicalinvestigationoftheplatinum-waterbondshowed,thatthisbonddepends
also on the 6s population in the metal cluster, but in the other direction: A strong
platinum-platinumbondandastrongplatinum-waterbondexcludeeachother.Theconstructionofaworking
surfacemodelproofedtherefore tobe much morecomplicated thanexpected. Polaristion e ects
causedbytheelectricdipole eld ofthewatermoleculecanleadto asuddenredistributionofthe
6selectronsandchange sotheelectronicstructureoftheclusteraswellasthetotalenergy.
Atthispointwestartedthedevelopmentofourown1-valenceelectronECPforplatinum. The
aim was not so much the reduction of the computational costs but to minimize the number of
electronic states close to the ground state. As the density of electronic states becomes smaller,
suddenchangesoftheelectronicstructureoftheclusterbecomelesslikelyandthescanningofthe
potentialenergysurfaceeasier.
Both,the1-andthe18valenceelectronECPcalculations,wouldhavebeenmuchmorediÆcult
withouttheapplicationoftheHuckeltheorytotheplatinum6sorbitals. Huckeltheoryallowedus
toidentifysuitableelectronicstatesforthesurfacemodelandtounderstandtheelectronmovements
within thecluster.
The platinum-water bond was found to be similar to the hydrogen bond in water clusters
and cooperativee ects are therefore likely tobefound in the interactionbetweenwater andthe
platinumsurface. Inspired by Ogasawara weusedPt
3 (H
2 O)
3
asmodel fortheadsorption of
wateronPt(111)[42,56]. Thesecalculationsshowedthatcooperativee ects,similartothee ects
observedinthewatertrimer,haveastrongin uenceonthegeometryandtheenergyofthewater
cluster.
Cooperative forces in the platinum-water bond can turn a water molecule out of its ideal
orientation. Doering andMadey suggestedawaterbilayersimilarto thestructureof ice Ihto
grow on the metal surface [39]. In this model every water molecule is tetrahedraly surrounded
by bonding partners and the hydrogens of the water molecules directly attached to platinum
pointawayfrom thesurface. Ourquantumchemicalcalcualtionsontheotherhand showed,that
the energy to movethe hydrogens upordown is verysmall and the prefered angle betweenthe
molecular plane of the water molecule and the platinum-oxygen bond depends strongly on the
chosenmethod for thecomputation. We used thereforeour ownclasical water-waterinteraction
potentialto analysethepreferdgeometry ofawaterhexamerunder surfaceconditions.
Thefollowinglist sumarizestheindividual chaptersofthisworkandtheircontents.
Chapter1 containstheliteraturesurveyaswellasanintroductionto thiswork.
Chapter2 compiles briefsummaries of themethods used for this work. Theories, who are
notdescribedinstandardquantumchemistrytextbooks,aredescribedingreater
detailthanproceduresandformulae,whicharepartof thosetextbooks.
Chapter3 focusesonthequantumchemistryofsmallwaterclusters. Thewaterdimerserved
asbenchmarktestforthecomputationalmethod(DZPbasisset,MP3,fullBSSE
correction),whichwaslaterusedfortheanalysisofcooperativeforcesinthewater
throughthepotentialenergysurfaceofthewaterdimer andselectedpointsfrom
thetrimersurface(chapter3)and rstapplicationsofthenewpotential.
Chapter5 demonstratestheapplicationoftheHuckeltheorytotheanalysisofsmallplatinum
clusters. Theresultsofthesecalculationsarelaterusedin thechapters6and7.
Chapter6 isacompilationofthequantumchemicalcalculationsforPt
n andPt n H 2 O(n=
1,2,3,5,9)usingtheLanL2DZECP(18velenceelectrons)fromHayandWadt
[189]. Thischapterexaminesthecorrelationoftheplatinum-waterbondstrength
andtheelectronic stateofthemetalcluster.
Chapter7 summarizesthe development ofa new 1valence electronECP for platinum and
itsapplication fortheanalysisofPt
5 H
2 O.
Chapter8 combinesallresultsobtainedsofarandfocussesonwaterclustersontheplatinum
surface. The rst section of Chapter 8combines the resultsfrom chapter 3 and
6forthe analysis ofcooperativee ects in Pt
3 (H
2 O)
3
while the second section
usestheresultsfromthechapters4,6and7toinvestigatethewaterhexameron
avirtualmetalsurface.
Chapter9 isthesummary ofsummariesandsuggestsfurtherproceedings.
Chapter10 liststheliteraturereferencesandprogramsusedforthiswork
Chapter11 Appendix
Attention: The atomic energy unit Hartree is abbreviated with 'H'
