Chemistry Reference
In-Depth Information
ensure.that.the.surfaces.are.suficiently.far.apart.to.support.the.conclusions.of.the.
simulation.
Third,.periodically.replicated.slabs.can.interact.with.one.another,.either.directly.
through. overlap. of. the. densities,. or. through. long-range. Coulombic. potentials.. To.
remove.direct.overlap,.the.slabs.need.to.be.separated.by.suficient.distance.so.that.
the.surface.densities.die.off.to.near-vacuum.and.have.little.overlap..Computational.
cost. considerations. intrude. here,. the. size. of. the. basis. set. and,. therefore,. the. com-
putational. cost,. increases. with. increasing. volume,. with. the. additional. cost. mostly.
devoted. to. reproducing. a. vacuum. region.. Hence,. any. slab. calculations. should. test.
that. the. slabs. are. suficiently. separated. that. they. do. not. quantitatively. affect. sur-
face. processes.. Simulations. of. surface. chemistry. mostly. involve. adsorbates. and.
interactions.between.them,.so.the.construction.of.the.intervening.vacuum.in.a.slab.
model. should. anticipate. suficient. slab. separation. to. accommodate. adsorbates. and.
ensure.those.adsorbates.will.not.interact.with.adjacent.periodic.images.of.the.slab..
The.separation.distance.between.the.top.layer.of.atoms.on.one.surface.of.slab.and.
the. .bottom.surface.of.the.next.slab.should.be.longer.than.the.sum.of.the.range.of.the.
basis.sets.on.the.two.surfaces.for.a.local.orbital.basis..Our.experience.is.that.a.10.Å.
separation.between.atoms.in.different.slabs.is.the.minimum.required.to.adequately.
isolate.metallic.slabs;.however,.more.than.15.Å.is.almost.certainly.wasteful.
If.the.slab.is.polar,.convergence.of.computed.properties.with.slab.separation.is.
very.slow..A.dipole.across.a.polar.slab.interacts.with.all.of.the.slab.periodic.images..
For. clean. metal. surfaces,. slab. dipoles. are. not. a. signiicant. issue,. as. metals. do. not.
often.sustain.the.localized.charge.polarizations.necessary.to.generate.a.signiicant.
dipole.in.a.slab..However,.adsorption.of.electronegative.species,.such.as.oxygen,.on.
surfaces.induces.signiicant.charge.transfer,.creating.a.surface.dipole.on.the.metal.
surface.. Furthermore,. there. is. a. lot. of. interest. in. the. chemistry. in. the. presence. of.
electric.and.magnetic.ields.recently,.and.computational.studies.that.investigate.the.
effects.of.external.ields.in.slab.calculations.are.becoming.more.common..A.nonpo-
lar.metal.slab.becomes.polar.in.the.presence.of.an.applied.external.ield.
An.external.electric.ield.is.typically.incorporated.into.a.DFT.slab.calculation.in.
the.form.of.a.sawtooth.potential.normal.to.the.slab,.as.illustrated.in.Figure.6.4..The.
discontinuity.in.the.potential.is.placed.in.the.middle.of.vacuum,.and.the.gradient.in.
the.potential.across.the.slab.imposes.a.static.external.ield..This.potential.gradient.
induces.the.electrons.in.the.slab.to.polarize,.creating.a.slab.dipole..For.plane-wave.
slab. methods,. this. application. of. an. external. electric. ield. has. a. second. unwanted.
consequence..With.suficient.vacuum.inserted.into.the.slab.model.to.isolate.the.peri-
odic.slabs.from.one.another,.the.potential.at.the.vacuum.boundary.between.the.slabs.
can.become.deep.enough.that.it.is.deeper.than.the.binding.energy.of.the.electrons.
in.the.slab..With.local.orbital.DFT.methods,.this.is.not.a.great.concern,.as.there.is.
no.basis.set.support.in.the.vacuum.region.that.would.allow.this.vacuum.occupation..
With.plane-wave.calculations,.the.basis.set.treats.all.regions.in.the.super-cell.equally,.
allowing.this.artiicial.well.to.become.populated..Applying.external.electric.ields.
needs.to.be.done.with.extra.care.and.monitored.carefully.to.ensure.this.model.arti-
fact.does.not.corrupt.the.calculation.[44].
One. common. trick. to. remove. an. adsorption-induced. dipole. is. to. take. advan-
tage. of. the. symmetry. that. often. exists. in. a. metal. slab. model. and. do. equivalent.
Search WWH ::
Custom Search