Some Practical Considerations for Density Functional Theory Studies of Chemistry at Metal Surfaces - Metallic Systems: A Quantum Chemist's Perspective - page 180

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FIGURE 6.4 A.schematic.depiction.of.how.an.electric.ield.is.applied.to.a.slab.super-cell.
and. the. associated. hazard.. An. electric. ield. is. applied. to. a. slab. super-cell. in. the. form. of. a.
“sawtooth”.potential.from.one.end.of.the.super-cell,.across.the.slab.and.to.the.other.end.of.
the.super-cell..The.thicker.the.super-cell,.the.deeper.the.sawtooth.potential.at.the.boundary.
between.the.cells,.in.the.middle.of.the.vacuum..If.the.super-cell.is.thick.enough,.the.attrac-
tive.potential.of.the.edge.of.the.sawtooth.will.artiicially.extract.electrons.from.the.slab..This.
artifact.must.be.avoided.for.a.meaningful.calculation.
adsorption.on.both.sides.of.the.slab..The.adsorption-induced.dipole.on.one.side.of.
the.slab.then.exactly.cancels.the.adsorption-induced.dipole.on.the.other.side.of.the.
slab.. This. is. often. effective. in. removing. the. dipole. problem. but. risks. exacerbat-
ing. the. interaction. between. the. two. sides. of. the. same. slab.. An. adsorption. strong.
enough. to. generate. a. signiicant. dipole. will. more. deeply. perturb. the. slab.. A. slab.
thick.enough.to.keep.that.perturbation.from.reaching.the.far.side.of.the.slab.may.
not.be.thick.enough.to.prevent.interaction.with.duplicated.adsorption.on.the.other.
surface.of.the.slab..Hence,.while.adsorption.on.two.sides.removes.a.slab.dipole,.a.
thicker.slab.might.be.needed.to.remove.the.extended.interaction,.requiring.a.more.
expensive.calculation.
This. duplicated. adsorption. is. an. unnecessary. expense.. A. better. approach. is. to.
explicitly.remove.the.periodic.effects.of.the.slab.dipole.layer,.either.by.introducing.
a.counter-dipole-layer.in.the.middle.of.vacuum.between.the.slabs.[45],.or.a.mixed-
dimension.Poisson.solver.that.explicitly.solves.the.2D.Poisson.equation.for.the.dipole.
layer.[46]..These.kinds.of.ixes.for.the.slab.dipole.problem.are.implemented.in.many.
DFT.codes,.but.it.should.not.be.assumed.that.they.are,.or.that.they.are.implemented.
correctly.. Any. simulation. that. involves. a. polar. surface. should. be. checked. for. this.
dipole. correction. by. assessing. the. convergence. of. the. computed. quantities. with.
respect.to.the.amount.of.vacuum.separation.between.slabs..It.should.be.noted.that.
the.original.theory.[45].for.correcting.the.slab.dipole.had.a.subtle.error.that.was.only.
identiied.and.repaired.several.years.later.[47]..Hence,.even.if.the.code.in.question.