Chemistry Reference
In-Depth Information
asserts.a.proper.treatment.of.periodic.slab.dipole.layers,.the.correctness.and.effec-
tiveness.of.the.implementation.should.be.veriied.in.test.calculations.
In.summary,.the.use.of.a.super-cell.slab.model.in.periodic.DFT.calculations.for.
surface.processes.complicates.the.study.of.surfaces..Reconstructing.the.appropriate.
boundary. conditions. needed. for. the. reduced-dimensional. surface. simulation. from.
codes.that.are.designed.with.3D.periodicity.and.juggling.the.compromises.that.must.
be.made.as.a.consequence,.are.issues.that.constrain.how.to.approach.a.given.simu-
lation.. These. are. issues. that. do. not. arise. in. typical. molecular. quantum. chemistry.
calculations,. but. become. crucial. for. simulations. of. chemistry. on. surfaces.. These.
broader.issues.go.into.the.design.of.a.slab.model.and.dictate.the.boundary.conditions..
Construction.of.a.speciic.slab.model.within.a.given.DFT.code.involves.manipulat-
ing.a.wide.array.of.input.options,.subject.to.the.constraints.given.by.the.boundary.
conditions.imposed.by.the.slab.model..This.is.the.subject.of.the.following.sections.
6.4.2 B
ulk
l
attice
P
arameterS
and
S
laB
m
odelS
The.initial.step.in.fashioning.a.viable.slab.model.for.a.surface.is.to.obtain.the.proper-
ties.of.the.bulk.metal.within.the.same.computational.methodology..The.immediate.
need.for.constructing.a.slab.model.is.the.optimized.bulk.structure—the.computed.
lattice.parameters.and.positions.of.the.atoms.in.the.unit.cell.of.a.perfect.crystal..This.
step.is.also.important.to.assess.the.insensitivity.of.the.results.to.increases.in.the.qual-
ity.of.computational.parameters.
From.the.perfect.crystal,.one.generates.an.initial.ideal.model.by.truncating.a.bulk.
crystal.along.crystal.symmetry.planes.to.create.a.slab..The.lateral.dimensions.of.the.
slab—those.along.the.surface—are.ixed.in.any.slab.calculation..The.surface.lattice.
parameter.should.be.set.to.its.bulk.value.to.satisfy.the.requirement.that,.as.the.thick-
ness.of.the.slab.increases,.the.center.of.the.slab.approaches.the.perfect.crystal.bulk.
material..If.this.condition.is.not.satisied,.the.
ideal
.positions.of.the.atoms.will.not.
correspond.to.the.perfect.truncated.bulk.atoms.and.this.law.in.the.model.construc-
tion. will. lead. to. an. artiicially. reconigured. surface—a. reconstruction. dictated. by.
improperly.applied.boundary.conditions.rather.than.the.creation.of.a.surface.
It. is. plausible. but. questionable. to. use. experimental. lattice. parameters. to. place.
the. atoms. for. a. model. surface.. The. problem. with. this. approach. is. that. theoretical.
lattice.parameters.rarely.match.experiment..The.typical.computed.DFT.bulk.lattice.
parameter. differs. by. 2%-3%. from. experiment:. LDA. usually. too. small. and. GGA.
usually.too.large..Using.an.experimental.lattice.parameter.for.an.LDA.slab.calcula-
tion.places.the.atoms.on.the.surface.farther.apart.than.the.optimal.LDA.distances..
This.expansion.in.the.surface.area.then.causes.an.overall.contraction.in.the.lattice.in.
the.direction.normal.to.the.surface,.as.the.system.attempts.to.reestablish.a.volume.
per.atom.closer.to.the.calculated.equilibrium.volume..Because.the.surface.dimen-
sion.is.ixed,.this.contraction.is.expressed.as.a.shrinking.of.the.distances.between.
the.interatomic.layers.at.the.surface..It.is.not.possible.to.separate.the.motion.of.atoms.
responding.to.this.boundary.condition.from.the.relaxation.of.the.atoms.caused.by.
the.creation.of.the.surface.or.the.chemical.interaction.with.an.adsorbing.molecule.
Using. extended. x-ray. absorption. ine. structure. (EXAFS). it. is. possible. to. mea-
sure.with.very.high.accuracy.the.interlayer.spacings.of.atoms.at.a.surface,.or.more.
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