Computational Investigations of Metal Oxide Surfaces - Metallic Systems: A Quantum Chemist's Perspective - page 204

(A) (B) (C)

FIGURE 7.1 Possible.model.surfaces.for.studying.a.chemical.reaction.on.a.metal.or.metal.
oxide.surface..(A).shows.a.“cluster.model,”.(B).displays.a.periodic.model.with.a.small.surface.
area,.and.(C).displays.a.periodic.model.with.a.larger.surface.area..Some.advantages.and.dis-
advantages.of.each.model.are.discussed.in.the.text.

Cluster.models.of.surfaces.may.have.the.advantage.of.modeling.an.isolated.sur-
face.event.using.a.relatively.small.number.of.atoms..However,.especially.for.metallic.
surfaces,.terminating.the.edges.of.the.cluster.in.a.way.that.maintains.the.appropriate.
electronic. structure. in. the. region. of. interest. is. not. trivial.. Inserting. a. metal. oxide.
cluster.into.a.point.charge.array.may.provide.a.means.of.alleviating.some.of.the.difi-
culties.associated.with.correctly.terminating.a.surface,.but.careful.testing.is.required.
to.ensure.that.size.effects.do.not.introduce.unphysical.behavior. 13,14
Periodic.models.have.the.advantage.of.avoiding.artiicial.surface.edge.termina-
tions.needed.in.cluster.models.that.can.impact.the.surface.band.structure..A.major.
concern.with.periodic.models.used.in.simulating.surface.reactions.is.the.adsorbate.
interactions. with. their. periodic. images. if. the. surface. area. of. the. unit. cell. is. too.
small..Although.such.a.model.may.capture.some.features.of.a.high.coverage.regime,.
predictions.and.direct.linkage.to.experiments.may.be.complicated.by.the.enforced.
periodicity. with. the. small. unique. surface. area. of. the. model,. whereas. the. experi-
mental. conditions. may. relate. to. very. low. coverage. and. depend. on. defect. sites. 15,16 .
Conversely,.increasing.the.surface.area.of.the.unit.cell.is.accompanied.by.a.signii-
cantly. increased. computational. cost..Once.again,.careful. testing. may.be. required,.
although.the.general.“rule.of.thumb”.separations.on.the.order.of.10.Å.between.peri-
odic. images. may. be. used.. For. applications. with. periodic. interfaces,. the. issue. of.
lattice. misit. between. the. two. materials. can. be. a. signiicant. issue. in. determining.
the.size.of.the.interface.cell.that.must.be.employed.to.avoid.unphysical.strain.due.to.
enforced.periodicity.of.commensurate.lattices.in.the. xy .plane..In.catalytic.applica-
tions,. it. may. be. step. edges. or. defect. sites. that. are. key. to. functionality. rather. than.
the.clean.periodic.surface..Properly.including.such.sites.in.a.periodic.model.is.chal-
lenging.since.the.limiting.system.size.necessitates.either.a.clean.periodic.surface.or.
the.creation.of.a.very.high.defect.density,.which.may.not.correspond.to.the.physical.
system.
A. vast. number. of. DFT. calculations. on. metal. oxides. have. been. performed. to.
date,.and.it.is.certain.that.this.number.will.continue.to.increase.with.correspond-
ing.increases.in.computing.power.and.improvements.in.techniques.allowing.much.
faster.theoretical.calculations.and.more.complex.systems.to.be.addressed..It.would.
not.be.possible.to.provide.a.comprehensive.review.of.all.computational.metal.oxide.
studies,. but. we. wish. to. highlight. a. few. applications. that. are. interesting. in. their.
own. right,. and. which. provide. examples. of. the. breadth. of. applications. that. exist..
Accordingly,.in.Section.7.2,.we.present.a.summary.of.Al 2 O 3 .calculations.from.early.