Some Practical Considerations for Density Functional Theory Studies of Chemistry at Metal Surfaces - Metallic Systems: A Quantum Chemist's Perspective - page 186

metals,.especially,.it.is.necessary.to.converge.the.bulk.calculations.with.respect.to.
k -point.sampling.[1]..The.fcc.calculations.were.performed.in.the.single-atom.rhom-
bohedral.primitive.cell,.sampling.the.Brillouin.zone.(BZ).with.regular.grids.ranging.
from.10 3 .to.24 3 .points.and.the.hcp.calculations.in.the.primitive.two-atom.cell,.using.
k -grids.ranging.from.10 2 .×.6.to.24 2 .×.15.points..(Note.there.is.no.special.signiicance.
to.the.multiplication.symbol.in.this.context,.10 2 .=.10.×.10.).With.BZ.sampling.of.16 3 .
(fcc).or.16 2 .×.10.(hcp),.the.energy.was.converged.to.∼1.meV/Er..The.lattice.parameter,.
a ,.was.converged.within.0.001.Å.and. c .to.0.002.Å..The.values.quoted.in.Table.6.2.
are.averages.obtained.from.the.BZ.samplings.from.this.convergence.and.better..The.
accuracy. of. the. stress-minimized. lattice. parameters. was. veriied. using. its. to. the.
potential.energy.curve.as.a.function.of.lattice.parameter..The.stress-minimized.and.
energy-minimized.lattice.parameters.for.the.fcc.calculations.agreed.to.better.than.
0.001.Å.
In.an.LCAO.code.like.SEQQUEST.that.implements.full.Pulay.corrections.for.the.
stress.formula,.this.quantitative.agreement.is.expected..With.plane-wave..calculations,.
cell.optimizations.using.stress-elimination.must.also.test.convergence.of.the.stress.
with. respect. to. the. energy. cutoff. (the. size. of. the. plane-wave. basis. set).. The. stress.
calculation.is.much.more.sensitive.to.incompleteness.in.the.plane-wave.basis.set.than.
is.the.total.energy.calculation,.and.to.converge.the.lattice.constants.using.the.stress.
requires.a.higher.energy.cutoff.than.is.necessary.to.converge.the.energy.[1].
One.will.do.calculations.with.both.the.LDA.and.PBE.functionals,.simply.to.get.a.
sense.of.the.magnitude.of.the.error.in.a.calculation.[1]..If.LDA.and.PBE.agree,.the.
calculation.is.more.likely.to.be.accurate,.as.the.different.constructions.of.LDA.and.
GGA.tend.to.expose.aspects.of.a.system.that.are.sensitive.to.errors..If.LDA.and.PBE.
results.disagree.signiicantly,.then.the.results.should.be.examined.with.a.skepticism,.
as.this.suggests.that.the.system.contains.physics.that.give.these.functionals.trouble.
Here,.the.preliminary.calculations.of.bulk.Er.indicate.that.LDA.will.likely.not.be.
useful.for.surface.studies..The.error.in.the.LDA.lattice.parameter.is.not.the.problem,.
deviations.of.4%.are.within.the.typical.errors..But,.the.nearly.equal.stability.of.the.
fcc.and.hcp.structures.will.be.a.problem..For.the.surface.calculations,.we.are.inter-
ested.in.surface.reconstructions.and.adsorbate-induced.relaxation..The.fcc.and.hcp.
differ.only.in.the.stacking.of.the.close-packed.planes.and.the.bulk.results.indicate.
that.stacking.could.easily.convert.from.hcp.to.fcc..The.1.meV/Er.energy.difference.
between.the.LDA.and.PBE.is.smaller.than.the.variation.with.BZ.sampling.for.either.
crystal,.so.that.there.are.local.environments.(such.as.a.surface).where.the.fcc.stack-
ing.might.be.lower.(artiicially).than.the.hcp.stacking..Hence,.for.the.purposes.of.the.
present.surface.study,.the.LDA.will.not.be.reliable..The.PBE.favors.the.hcp.structure.
by.25.meV/Er,.making.it.the.more.suitable.choice.
These.considerations.arise.frequently.for.metal.surface.calculations.and,.in.addi-
tion.to.providing.the.structural.parameters.necessary.to.construct.a.slab.model,.the.
bulk.calculations.are.also.useful.to.get.a.preliminary.assessment.of.the.applicability.
of.a.given.method..Among.the.better.known.examples.for.the.3d-transition.metals,.
particularly.for.iron,.the.computed.description.of.the.bulk.material.will.often.limit.
the.kind.of.simulation.that.one.can.do..While.PBE.predicts.the.bulk.Fe.to.be.mag-
netic. bcc ,.in.agreement.with.experiment,.the.LDA.ground.state.Fe.is.nonmagnetic.
fcc,.rendering.LDA.useless.for.practical.surface.studies.