Computational Investigations of Metal Oxide Surfaces - Metallic Systems: A Quantum Chemist's Perspective - page 203

thermodynamically. would. be. accessed. for. pure. zirconia. within. the. relevant. tem-
perature/pressure.cycle.
Metal. oxides. of. interest. are. often. in. the. form. of. thin. ilms.. Depending. on. the.
size,.thickness,.and.other.factors,.these.frequently.present.electronic.band.structure.
differences.from.the.bulk.crystalline.material.stable.facets..Generally,.for.electronic.
structure. calculations,. a. crystalline. facet. is. chosen. that. meets. one. or. more. of. the.
following.criteria:

•. It.is.known.to.be.an.experimentally.relevant.surface.

•. It.is.shown.to.be.the.lowest.energy.facet.after.comparing.the.energetics.of.

several.low.index.surfaces.

•. It. presents. the. appropriate. surface. termination. for. comparison. with. the.

experiment,. or. it. avoids. models. presenting. complications,. such. as. polar.
surfaces,. or. it. presents. a. small. surface. area,. and. thus. is. computationally.
more.tractable.

Accordingly,.determining.the.appropriate.facet.choice.in.a.computer.model.may.
be.inluenced.by.the.desired.application.as.well.as.the.computational.resources.
Although.a.variety.of.techniques.could.be.employed.to.investigate.metal.oxides,.
the.primary.focus.of.this.chapter.will.be.on.applications.employing.density.functional.
theory. (DFT). 4,5 . DFT. applications. have. become. ubiquitous. across. both. solid. state.
and.molecular.applications,.frequently.being.used.in.both.descriptive.and.predictive.
capacities.because.such.calculations.may.provide.physical.insights.that.complement.
what.can.be.explored.through.experiment.and.allow.a.level.of.control.in.structural.
modiications.that.may.be.challenging.or.even.impossible.to.explore.via.experimen-
tal. techniques. alone.. Although. a. few. applications. of. Orbital. Free. DFT. (OFDFT).
have.been.performed, 6,7 .this.primarily.remains.an.area.of.ongoing.development.and.
research. 8-11 .The.Kohn-Sham.(KS).implementation.of.DFT.is.employed.in.almost.all.
applications.since.the.KS-DFT.implementation.allows.an.exact.form.for.the.kinetic.
energy. functional. in. which. one-electron. orbitals. are. introduced.. The. form. of. the.
exchange-correlation. functional. is. not. known. exactly. and. must. be. approximated..
The. primary. distinction. between. these. exchange-correlation. functionals. is. local.
density. approximation. (LDA). versus. generalized. gradient. approximation. (GGA).
functionals..Within.the.GGA.functional.family,.many.varieties.have.been.proposed.
with. this. being. an. active. area. of. theoretical. development. for. over. two. decades. 12 .
The.functional.that.results.in.closest.agreement.with.the.experiment.may.depend.on.
the. application. of. interest,. with. the. Becke-Lee-Yang-Parr-type. (BLYP). function-
als.proving.popular.for.many.molecular.applications,.while.others.(LDA.and.GGA.
functionals.discussed.in.more.detail.in.other.chapters.and.in.reviews.mentioned.here).
are.frequently.used.in.solid-state.physics.calculations.
One.issue.that.is.particularly.challenging.in.the.electronic.structure.calculations.of.
metal.oxide.surfaces.and.surface.reactions.is.the.choice.of.a.model.system..Choosing.
a.model.of.suficient.complexity.to.capture.the.necessary.physics.must.be.balanced.
with.computational.constraints.for.system.size.and.complexity..Surface.models.can.
be.divided.into.two.main.categories,.namely,.cluster.and.periodic.models..Figure.7.1.
displays.schematics.of.cluster.and.periodic.models.for.surface.reactions.