case I
Pt 0 Pt 0
Pt +0.2 Pt -0.2
Figure6.30: Dierentdissociationcurves.
forgeometry A(curvesI,II,and III)weregenerated fromsinglepointcalculationswithdierent
platinum-oxygenseparations. Thedierentelectronicstatesgeneratedinthis waywerestabilized
byshiftingthevirtualorbitals. ThismethodworkedonlypartiallyincaseIII.Atshortseparations
therepulsion ofthe6s electronsbytheoxygen atomsbecomessmallerand thereforetheyspread
morewidely. Thesystemhastwopossibilewaystorelax: Iteitheripstheelectronicstateof
plat-inumdimer,turningcaseAIII turnsintocaseAI,orcanfollowthepotentialcurve. Thisipping
isshownintheinsetingure6.30. Allthreecurvesconvergetothesamedissociation-point,where
the 6spopulationin the platinumdimer is 1.430. Comparingthose casesabridging position for
thewatermoleculeislesslikelythancaseAIsuggests.
ThePt
2 H
2
Oclusteratd
PtO
=10
Adiersnotonlyinthe6spopulationbutalsowithinthe
chargedistributionin thecluster. GeometryA caseI dissociatescorrectly into awater molecule
andaplatinumdimerwithunchargedatoms,whiletheinothercases(CI,GI, AIII)itdissociates
into adimer withchargedplatinumatoms(jq
Pt
j=0.2e) 5
.
Atadistanceof8
Afromthesurfacetheorientationofthewatermoleculerelativetothedimer
shouldbenegligible. Asmalldistortionoftheplaneofthewatermoleculeby1degreereducesthe
symmetry from C
2v to C
s
. In caseAI thetotal energydrops dramatically andcase AIconverts
into case AIII.Meanwhile, the charges on the platinum atoms increase to j0.2 ej. Such a large
increase cannot be explained physically with such a small distortion of the molecular geometry.
On the other hand, the conversion of geometry C (case CI) into geometry A (case III) hardly
changes the charge distribution and the total energy and no jump canbe observed despite the
breakofsymmetry. ThejumpfromcaseAItocaseAIII/caseCIcanbeexplainedbythemixing
of the 25 th
(a
1
symmetry, platinum
5d
+ water 3a
1
) and 23 rd
orbital (b
2
symmetry, HOMO,
5d
) molecular orbitals. The reverse step, the disentangling of the orbitals while changing from
C
s to C
2v
symmetry isnot possible. The mixed orbitalsdo notaprovide suitabledescriptionof
thePt
2 H
2
Osystemduetothephysicallyincorrectchargesontheplatinumatomsandthejump
betweengeometriesAandC/G(caseI)isnotphysicallyreasonableeither. Theexplanationofthis
behaviour is the mixing of twodierent electronic states with similar energies (near-degeneracy
eects [336a]). A moreappropriate theoreticalapproach isa multirefencecalculation. First test
CAS SCF(2,2)-calculations (complete active space SCF (section 2.3, page 22)) containing the
HOMOandsecondnextorbitaltotheLUMOoftheHartree-Fockcalculationyieldedgoodresults.
Noenergyshiftcan beobservedbetweenthegeometriesAandCandthechargeontheplatinum
atoms in geometry C become reasonablesmall (jq
Pt
j = 0.000041e). The6s populationis close
to itsmaximumvalue(1.828),which reducesthe bindingofthewatermolecule. Theinclusion of
further orbitals into the correlation space allows areasonable description of the chemical bond.
First test calculations showed 6
that the next important excitation contains occupied molecular
orbitalscontainingthewater3a
1
orbitalandvirtualorbitalsbuiltfromthewater1b
2
orbital. Such
an electronic excitation reduces the electron density in the congested centre of the molecule. A
completemultireference analysisofthePt
2 H
2
Osystemisbeyond thescopeofthiswork.
5
ChargedplatinumatomsareimpossibleforgeometryA(C2vsymmetry).Gaussian94complainsabout
anunsymmetricdensitymatrix,butallcalculations convergequickly.
6
Theimportantorbitalsfortheactivespacewerefoundwithasmallprogram,whichtestedalldouble
exciationsindividually. Onlytheenergeticallymostsignicant werechosenfortheactivespace.
*
Geometry E
Geometry C case VII
-0.867 -0.865 -0.863 -0.861 -0.859 -0.857 -0.855 -0.853 -0.851 -0.849 -0.847
0 20 40 60 80 100 120 140 160 180
Geometry G case V
Geometry D
*
*
*
Start
γ angle of rotation [deg]
(E TOT + 312) [H]
Figure6.31: RotationaroundthePtObond.
-0.87 -0.865 -0.86 -0.855 -0.85 -0.845 -0.84
0 20 40 60 80 100 120 140 160 180
Geometry G
Geometry D
Geometry C
γ - 90 deg [deg]
(E TO T + 312) [H]
Figure6.32: Waggingofthewatermolecule.
6.2.2.4 Movementof wateron the surface
Asshownintheprevioussectiontheelectronicstateoftheplatinumdimerdependsonthe
oxygen-platinum distance. This section considers of the connection between dierent geometries
corre-spondingto thesame(orsimilar)oxygen-platinumdistances.
Figures 6.31 and 6.32 show that allclusters with C
s
symmetry can be easily interconverted.
Figure6.31showsthetotalenergyasfunctionoftherotationaroundthePtObond. Thegeometries
C,E andD arejoined byastraightline. Thesecond curveshowsthesameplotforgeometry G.
GeometryG is only energetically morestable than the other clusters in a small conformational
region. Figure 6.32 shows the total energy as a function of the angle of the water molecular
plane and the PtO bond. The curve starting from geometry G represents the global minimum
in only a small section of the conformational space. The geometries C and D are separated by
a small maximum. With increasing 6s population (changing from singlet state to the triplet)
the water-platinum bond becomes weaker. The relativeheight of the maximum is reduced and
the interconversionofgeometries C and D becomes morelikely. Thisexplains the conversionof
geometryDintogeometryCduringtheoptimisationofthetripletstateofgeometryD(subsection
6.2.2.1).
Figures 6.34 and 6.35 show the conversion of geometry A (case
Pt Pt 2 O
H H
d
a γ
d’
Figure 6.33: Pt
2
-Geo-metryAto D.
I) into geometry D, starting from geometry A. The distance from
the surface(PtPt bond) seemsto be shorter in geometry A despite
thesmallerbinding energy. Figure6.34showsthattheeectivePtO
distanceislonger dueto themolecule'sgeometry. TheeectivePtO
distanceandthebindingenergyagreewellwiththosevaluesobtained
in the previous sections. Figure 6.35 shows the total energy of the
clusteras thewatermoleculemovesfromgeometry A intogeometry
D. Figure6.36showsthevariationofthe anglebetweenthe
surface-oxygenbondd (seegure6.19forthedenition of d)andthewater
molecularplane asafunction ofthedistancefromthecentre. The
water molecule moves smoothly into its nal position as the water
moleculeapproachesitsdestination.
Figures6.37and6.38showtheresultsofthesamecalculationstartingfromgeometry C.The
distancefromthesurfacerstshrinksandthenincreases,whilethePtObondincreasescontinuously
1.7 1.75 1.8 1.85 1.9 1.95 2 2.05 2.1 2.15 2.2
Geo A 0.2 0.4 0.6 0.8 1 1.2 Geo D
distance to Pt 2 = d’
distance from the surface = d
length [Å]
distance from the center of the Pt-Pt bond [Å]
Figure 6.34: ShiftalongthePtPtbond, start
geometry A,distance.
-0.850 -0.848 -0.846 -0.844 -0.842 -0.840 -0.838 -0.836 -0.834 -0.832
Geo A 0.2 0.4 0.6 0.8 1 1.2 Geo D
E TOT [H]
distance from the center of the Pt-Pt bond [Å]
Figure 6.35: ShiftalongthePtPtbond,start
geometry A,energy.
60 80 100 120 140 160 180
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Start at ge ometry A Geometry A
Start a t geo metry C
Geometry D Geometry C
Geometry H
distance from the center of the Pt-Pt bond [Å]
γ [deg]
Figure 6.36: ShiftalongthePtPtbond, start
geometry A,wagging.
1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7
Geo H 0.2 0.4 0.6 0.8 1 1.2 Geo C
distance from the surface distance to Pt-2
length [Å]
distance from the center of the Pt-Pt bond [Å]
Figure 6.37: ShiftalongthePtPtbond,start
geometry C,length.
-0.865 -0.860 -0.855 -0.850 -0.845 -0.840 -0.835 -0.830 -0.825
0 0.2 0.4 0.6 0.8 1 1.2 1.4
shallow minimum 0.8 kcal/mol Geometry H
Geometry C
distance from center of the Pt-Pt bond [Å]
(E TOT + 312) [H]
Figure6.38: ShiftalongthePtPtbond, start
geometryC,energy.
1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2
0 20 40 60 80 100 120 140 160 180
Geometry A Geometry H
wagging angle γ [deg]
distance from the surface [Å]
Figure6.39: WaggingoftheH
2
Oingeometry
A,bondlength.
-0.834 -0.832 -0.83 -0.828 -0.826 -0.824 -0.822 -0.82 -0.818 -0.816 -0.814 -0.812
0 20 40 60 80 100 120 140 160 180
-6.1 -6.08 -6.06 -6.04 -6.02 -6 -5.98 -5.96
65 70 75 80 85 90
E TO T - 312.82 H [mH]
γ [deg]
geometry H
wagging angle γ [deg]
(E TOT + 312) [H]
area of the inset
Figure6.40: WaggingoftheH
2
Oingeometry
A,totalenergy.
(gure 6.37). Unlike the previouscases geometry C doesnot change into geometry A, but into
geometry H, where theoxygen atom rests directly abovethe centre of the PtPt bond while the
hydrogen atoms are tilted downwardsand pointtowardsthe neighbouring platinumatom. The
secondplotingure6.36displaysthetiltangleofthewatermolecularplaneduringthismovement.
The geometry still has C
s
symmetry and the platinums carry opposite charge. The electronic
structure and the symmetryof geometry Chave been conserved during the calculation. During
this movement the water moleculepasses through a shallow minimum (0.8 kcal/mol relativeto
geometryC,gure6.38).
Thenextseries ofcalculationsdescribesthemovementofthewatermoleculein geometriesA
andH.Duringthesecalculationswechangedtheanglebetweenthebondbetweenthesurfaceand
the water molecular plane , while the bond lengthd wasallowedto relax at a constant a= 0
(gure 6.33). The resultsof these calculationsare summarized in gures 6.39and 6.40. Figure
6.39showstheoptimizeddistanceto thesurfaceduring therotation. Thebond distancechanges
smoothlythe rotational angle. Only theslopeof thecurveat small valuesof rotational angle is
suspicious. Symmetry demands that the bond length should change smoothlyoverthe 0degree
pointandthecurveshouldnothaveacusp. Thesameisobservedfortheenergy(gure6.40). At
zerodegreestheclusterhas againC
2v
symmetry,but theplatinumatoms arechargeddierently
(j q
Pt
j=0.172e). Theinsetin gure6.40showsthelocal energymaximum,whichmakesadirect
transformation from geometry A into geometry C impossible, because asmall activation energy
hastobeovercomeandthesoftwarefollowsthepathoflowestenergy.
Finally, the transformation from geometry C into geometry F viageometry G wasanalyzed.
Figures6.42showsthelengthoftheplatinum-oxygenbondandthepopulationofthe6sorbitals.
The shortest equilibrium length was observed for geometry C (90 Æ
). At this point the total 6s
population has its highest value. As geometry C changes into geometry G this bond becomes
longerandsimultaneouslyincreasesthetotal6spopulation. Theenlargeddistancetotheoxygen
atomreducestherepulsionbetweenthe6selectronsandtheoxygenandresultsahigherpopulation
ofthe6sband. Atthebottomofgure6.41the6spopulationsoftheindividual platinumatoms
aredisplayed. ForPt-Pt-Oanglesabove140 Æ
thetotal6spopulationremainsconstant,whilethe
6spopulationof theindividual platinumatoms changes continuously. This movementof the 6s
electrondensitydemonstratesthepossibilityofintermetallicchargetransferincooperativeforces.
0.6 0.8 1 1.2 1.4 1.6 1.8 2
90 100 110 120 130 140 150 160 170 180
bond length total 6s population
6s population on Pt1
6s population on Pt2
6s population
Pt-Pt-O angle [deg]
2.12 2.11 2.10 2.09 2.08 2.07 2.06 2.05 2.04
Pt-O bond length [Å]
Figure6.41: GeometryCtoF,6spopulation.
-0.867 -0.866 -0.865 -0.864 -0.863 -0.862 -0.861 -0.860 -0.859
(E TOT + 312) [H]
Pt-Pt-O angle [deg]
90 100 110 120 130 140 150 160 170 180
charge transfer [e]
0.22
0.21
0.20
0.19
0.18
0.17
0.16
0.15
energy charge transfer
Figure6.42: GeometryCtoF,totalenergy.
Thetotalenergy(gure6.42)oftheclusterdoesnotfollowthe6spopulation,buthasadistinct
minimumclosetogeometryG(135 Æ
). Figure6.42alsodisplaysthechargetransferfromthewater
molecule to the platinum dimer. The charge transfer decreases steadily during the motion and
exhibitsnootherfeatures. Theglobalminimumofthetotalenergyat140 Æ
isclosetogeometryG.
Atthispeakthetotal6s populationreacheditsmaximumwhilethechargetransferisstillhigh.
Table 6.15shows theMulliken overlappopulation
geo MOPPtPt MOPPtO
90 Æ
C 0.120739 0.072887
135 Æ
G 0.303253 0.059046
140 Æ
| 0.311012 0.054689
180 Æ
F 0.256784 0.040784
Table 6.15: Mulliken overlappopulation
in Pt
2 H
2 O.
of selectedbonds in thePt
2 H
2
Osystemduring the
transformation of geometry C into geometry F. The
platinum-platinum bond becomes stronger, while the
platinum-oxygen bond simultaneously becomes
wea-ker.
This interplay of 6s-electron density and charge
transferwithin theplatinum-waterbondexplainswhy
the water molecule bonds strongly to the platinum
dimer with small charge transferin geometry G. It is not a change in binding mechanism, but
achangein the6s-population,whichcompensatesfortheweakbond(seesubsection6.2.2.1). The
6s population changes again as the bond betweenthe water molecule and the dimer breaks. In
geometry Cthe6spopulationincreasesby0.037. Thisincreasereectsthereducedrepulsion
be-tweenthe6s electronsand oxygen. This smalldierence indicates that mostof theextracharge
fromthewatermoleculehastobestoredinthe5d-band. GeometryGismorecomplicated: the6s
populationdecreasesby0.365during thedissociation. Thisextra6spopulationin thePt
2 H
2 O
complescanbeexplained bythehigher contributionof the6sorbitals tothe bonds betweenthe
watermoleculeand theplatinumto compensate forthelonger bond, asthe 6sorbitalsare more
widelyspreadingthanthe5d.
Figure6.43showstheconnectionsbetweendierentgeometries andelectronic states. Double
headed arrows indicate two way connections, while single headed arrows indicate one way
con-nections. It is possible to go from a totallycovalent platinum dimer without water (end of the
dissociationcurvefor geometry A, case I,gure 5.30)to a partially ionic bonded dimer (end of
the dissociation curves for the geometries G and C, gure 5.30), but not the other way round.
Foragivengeometry (e.g. geometry A)twodissociationpathways exist to dierent end points,
whichcannotbetransformedintoeachother. MoreadvancedcalculationslikeCAS-SCFwouldbe
requiredforamorephysicaldescriptionofthewaterplatinuminteraction.
Geo H Geo E
Geo C Geo F Geo G Pt 0 -- Pt 0 Geo A Geo D
Pt +0.2 -- Pt -0.2
Figure6.43: Connectionbetweendierentgeometriesandstates.
6.2.3 Summary of the results for the platinum dimer
Theplatinum-platinum bond isdominated bythe6sorbitals. The strengthof themetallic bond
andthereforethetotalenergyoftheclusterincreaseswiththeoccupationofthe6sorbitals(table
6.10). Electroncorrelationis essentialforthe correctdescriptionofthis bond. ThecoeÆcient of
thegroundstate(c
0
)intheMller-Plessetcalculationis0.95andsmallerthenthevalueforwater
(0.97). Atrstsight,theinuenceofelectroncorrelationseemstobesmallenoughtoproceedwith
this method. The existenceofenergetically closeelectronic statesmakesthe application ofmore
advancedmethodsnecessary. FirstCASSCFcalculationsyieldedawavefunctionwithaverysmall
contributionsfromthegroundstate(c
0
=0.8). Thisresultindicatesthattheinuenceisnotsmall
andtheMller-Plessetapproachtoelectroncorrelationisinappropriate. MC-SCFcalculations,on
theother hand,are costlyand notsimple(Root ippinghasbeenobserved withPt
2
[336b]). In
thiswork wethereforecontinueto useMller-Plessetcalculationsdespitetheknownproblems,to
getaninitial ideaoftheroleofcorrelationeects.
The following conclusionscould bedrawnfrom the Pt
2 H
2
Ocalculationsneglectingthe
ad-vancedcorrelationproblem:
1. As shown previouslyfor Pt
1 H
2
O the interaction between water and the metal decreases
with increasing 6s population (table 6.14). The principal problem, strong metallic bonds
versus strong water metal interactions, remains unsolved. Since the intermetallic bonds
contributemorestronglytothetotalenergythanthewater-metalbond,excitedmetalstates
arenecessaryforthecorrectdescriptionofthebond.
2. Theinteractionofthewatermoleculewiththeplatinumdimerreducestheoverallsymmetry
oftheproblem. Metalorbitals,whichwerepreviouslywellseparatedbysymmetry,cannow
interact. This additionaloverlapresultsin anincreaseofthe6spopulation,which weakens
thewater-metalbond. Evenverysmalldistortionsoftheinitialgeometry(e.g. 0.01 Æ
inbond
angles)canbreakthesymmetry 7
. Thisbreakcausesanincreaseinthe6spopulation,which
resultsinunphysicaljumps betweenpotentialenergysurfaces. Those jumpscanbeavoided
withcostlyMC-SCFcalculations.
3. A smoothtransition between electronic states generated with the method described above
are possible(Figures 6.43),but not alwaysin both directions. It is diÆcultto constructa
smoothpotentialenergysurfacecoveringthewholeofconformationspace.
4. The valenceorbitals of thewater moleculebond to anyorbital withcorrect symmetry and
energy. Duringtheformationofthebondthemolecularorbitalsofthefreedimermixtoform
7
Even ata distance of 100
A the water molecule is symmetricallypresent. A simpleHF calculation
doesnotconvergetothe 1
S 1
Sdimerasobservedforthefreedimer,butnottothe 3
D 3
Ddimer.
(a) Thepresenceofthewatermoleculereducesthesymmetry(seeabove).
(b) Thewater moleculepolarizes theplatinum cluster and creates a holein the 5d band
fortheformationofthebond. Theoccupationoftheformerlyemptyplatinumorbitals
withelectronsisthequantum chemicalequivalentofpolarisation(gure2.3,page28).
Theinterplayofpolarisationand 6spopulationisillustratedforgeometry A: The6s
popu-lationof thefreedimer shouldbeaslowaspossibleforastrongbond to formbetweenthe
dimer and water. Thehigherthe 6spopulation, theweakertheadsorption becomes (table
6.14)duetostrongrepulsionbetweenthe6selectronsandtheoxygen. Thefreedimercreated
bythe dissociation of case AI(gure 6.30)has atotal 6spopulationof 0.279. Duringthe
formationof thebond betweenthedimerand thewatermoleculeelectrondensity(0.174 e)
movesfrom thewatermoleculeinto the5d-band ofthedimer. Electrondensitymust
there-foremoveintothe6s orbitals. Theobserved6spopulation(1.021)istwiceaslarge,asthis
estimatepredicts(0.279+0.174=0.453). Theextra0.568electronsstabilize theclusterby
symmetry-allowedorbitalmixing inboththemetal-metalandmetal-oxygenbond. Ahigher
occupationofthe6sorbitalsisnotpossible,sincesymmetryforbidsthecorrespondingorbital
interactions. Theexactposition ofthewatermoleculemirrorsthedelicatebalancebetween
electrostaticrepulsion,6spopulationin termsofmetalclusterstabilityandpolarisation.
5. Theelectronsin the 6s orbitals areverymobile andcan movefreelyin the cluster (gures
6.26and6.41). Thisexibilityoersthepossibilityoffarreachingchargetransferandsofor
cooperativeforces inthewater-platinuminteraction.
6. Acomparisonofthedierentgeometriesshows,that
(a) thebridgingpositionsforthewatermoleculeareenergeticallyunfavourable.
(b) the interaction of the hydrogen atoms with the surface platinum atoms contributes
signicantlytothetotalinteraction energy.
(c) thesymmetryandshapeoftheavailablemetalorbitalscontrolthesite ofadsorbtion.
(d) thesecond layer (geometries Fand G) is also important forthe binding of the water
molecule.
An ideal surface model should therefore be build from at least two slabs of platinum and
at the surface there should be a suÆcient numner of platinum atoms to interact with the
hydrogens(section6.5(page192)onPt
9 ).
6.3 The platinum trimer
The smallest physically realistic Pt
3
-cluster is the equilateraltriangle. This cluster represents a
small sectionof thePt(111)surfaceand socanopperateasasurfacemodel. A second cluster,a
trianglewitha90 Æ
angle,poorlydescribesthePt(100) surface,and sothissectionfocusesonthe
equilateraltriangle.