Chemistry Reference
In-Depth Information
precisely,.the.change.of.those.spacings.from.their.bulk.values..A.inely.tuned.surface.
probe,.EXAFS.can.detect.changes.in.interlayer.spacings.of.less.than.0.1%..A.typical.
interlayer.spacing.at.a.surface.changes.by.∼5%.for.a.close-packed.surface.and.more.
for.open.surfaces..Assuming.a.2%.deviation.of.lattice.parameter,.a.slab.calculation.
using.the.experimental.lattice.parameter.would.have.a.surface.area.∼4%.larger.than.
the.LDA.ideal.surface.area..With.the.lateral.dimensions.of.the.slab.ixed,.the.only.
means.that.the.atoms.within.the.slab.have.to.recover.the.LDA.equilibrium.volume.is.
to.expand.the.slab.normal.to.the.surface.∼4%.to.compensate.for.the.error.in.the.sur-
face.lattice.parameter..Note.that.the.resulting.error.normal.to.the.surface.is.roughly.
double.the.error.imposed.parallel.to.the.surface.and.that.typical.DFT.deviations.from.
experimental.lattice.parameters.cause.interlayer.compensations.as.large.as.typically.
observed.surface.relaxations.
However,.unless.the.same.calculation.can.be.performed.for.the.bulk.metal,.the.
theoretical.interatomic.spacings.between.the.metal.substrates.are.unknown,.and.the.
choice.of.an.arbitrary.spacing.can.lead.to.spurious.results.
If. substrate. atoms. participate. notably. in. the. chemistry,. it. is. imperative. to. use.
interatomic. spacings. in. the. substrate. that. are. consistent. with. theoretical. lattice.
parameters.obtained.using.the.same.method.
6.4.3 c
omPutational
m
ethodS
A. prerequisite. for. any. slab. calculation. is,. of. course,. to. choose. the. computational.
method..The.most.common.choice.for.periodic.calculations.is.plane-wave.basis,.pseu-
dopotential.(PP).codes,.and.numerous.codes.are.widely.available,.from.commercial.
codes.such.as.VASP.or.CASTEP.to.open.source.codes.such.as.ABINIT.or.PWSCF.
Full-potential,. all-electron. codes. such. as. WIEN2K,. RSPT,. or. the. newly. emerg-
ing. open. source. EXCITING. enable. explicit. treatment. of. core. electrons. with. a. cor-
responding. increase. in. computational. cost.. Linear. combination. of. atomic. orbitals.
(LCAO). approaches. are. most. commonly. used. for. molecular. calculations.. Periodic.
LCAO.codes,.such.as.CRYSTAL,.use.contracted.Gaussian.basis.sets,.and.SIESTA.
uses.with.a.numerical.atomic.orbital.basis.set,.may.be.familiar.to.practicing.computa-
tional.chemists..LCAO.codes.often.have.signiicant.computational.cost.advantages.for.
periodic.calculations.over.the.more.common.plane-wave.codes.at.the.expense.of.hav-
ing.a.less.lexible.and.less.complete.basis.sets..In.bulk.calculations,.the.requirement.
that.the.LCAO.basis.sets.avoid.linear.dependence.limits.which.basis.sets.can.be.used..
Different.codes.have.different.features.that.are.particularly.useful.for.a.given.applica-
tion,.desired.computational.performance,.or.availability.of.needed.atomic.potentials.
For. purposes. of. illustrating. the. construction. of. slab. models. below,. we. use.
SEQQUEST.[48],.a.general.purpose.DFT.code.using.PPs.and.a.contracted.Gaussian.
basis.set.in.an.LCAO.approach.to.periodic.DFT.calculations..SEQQUEST.is.based.
on.a.computational.method.speciically.developed.for.slab.calculations.of.metal.sur-
faces.[40,41].and.has.capabilities.speciically.designed.to.properly.treat.reduced-sym-
metry.problems.such.as.molecules,.slabs.[49],.and.defects.in.bulk.periodic.systems.
[42]. in. a. periodic. super-cell. approximation.. Hence,. it. is. particularly. well-suited.
to. slab-surface. calculations.. It. uses. standard,. norm-conserving. PPs. [50,51]. taken.
from. an. extensive. library. of. atomic. potentials. accompanied. by. highly. optimized.
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