Some Practical Considerations for Density Functional Theory Studies of Chemistry at Metal Surfaces - Metallic Systems: A Quantum Chemist's Perspective - page 194

These.total.energies.must.be.consistent.with.each.other,.that.is,.generated.with.the.
same. functional,. method,. and. computational. algorithms.. For. example,. one. would.
not. use. a. CO. energy. obtained. in. a. molecular. quantum. chemistry. code. in. the. cal-
culation.of.the.adsorption.energy.with.a.slab.result.from.a.periodic.DFT.code..The.
numerical.implementation.of.different.codes.may.be.incompatible.and.even.the.same.
DFT.functional.can.differ.from.code.to.code..The.energy.of.the.isolated.CO.mol-
ecule.must.be.computed.in.the.same.code,.using.the.same.basis.(e.g.,.energy.cutoff.in.
a.plane-wave.code).and.numerical.quadratures.as.in.the.slab.calculation.
Note.that.an.isolated.molecule.such.as.CO.in.a.periodic.code.is.represented.as.
a.very.diffuse.3D.crystal.of.molecules..The.periodic.slab.models.need.to.be.sepa-
rated.by.suficient.vacuum.to.isolate.the.repeating.slabs.from.one.another.along.one.
dimension,. to. isolate. the. molecule. requires. suficient. vacuum. in. all. three. dimen-
sions..In.the.molecular.calculation,.dipole,.quadrapole,.and.higher.moments.between.
periodically. replicated. molecules. affect. the. energy,. and. either. the. energy. must. be.
extrapolated.using.larger.super-cells.with.more.vacuum.or.the.offending.multipolar.
interactions.explicitly.removed.[46,64].
Once. this. computational. infrastructure. is. in. place. and. the. numerical. aspects. of.
the.calculations.are.explicitly.controlled,.one.has.only.to.deal.with.the.limitations.of.
DFT.in.the.calculations..This.present.example,.CO/Pt(111).is.a.classical.example.of.a.
failure.of.DFT.for.surface.chemistry.[65]..Feibelman.recounts.multiple.computational.
methods.implementing.LDA.and.GGA.that.attempt.to.compute.adsorption.of.CO.on.
Pt(111).and.fail..Experimentally,.it.has.been.observed.that.CO.adsorbs.directly.atop.
a.surface.Pt.atom,.but.many.prevalent.functionals.favor.the.triangular.site.midway.
between.three.surface.Pt.atoms..The.DFT.functionals.do.very.well.for.the.bulk.plati-
num,.but.do.poorly.for.chemisorption.of.CO.on.platinum..The.B3LYP.functional.does.
quite.well.for.irst.row.chemistry.but.does.poorly.for.many.bulk.metals..The.present.
example,.CO/Pt(111),.remains.an.unsolved.problem.for.DFT.calculations.and,.there-
fore,.any.DFT.simulation.of.chemistry.at.a.Pt.surface.involving.CO.is.suspect..The.
CO/Pt.“puzzle”.[65].is.among.the.most.prominent.manifestations.of.this.problem,.but.
any. molecular. chemistry. at. surfaces. should. be. thoroughly. validated. against. estab-
lished.data.before.more.sophisticated.simulations.are.undertaken.
It. is. not. uncommon. for. DFT. to. fail. for. a. crucial. aspect. of. a. surface. chemistry.
problem..In.the.Er.example.above,.the.LDA.failed.to.reproduce.bulk.Er.properties,.
but.the.GGA-PBE.functional.succeeded.and.was.able.to.give.reasonable.results..For.
cases.like.the.CO/Pt(111),.both.the.LDA.and.PBE.fail.and.an.alternative.approach.
must.be.taken.
Among.the.3d.transition.metals.and.particularly.for.the.oxides.of.these.metals,.
standard. DFT. frequently. fails.. A. recent. development. proposed. to. circumvent. this.
problem. is. the. DFT+ U . approach. [66]. where. the. interactions. among. the. 3d. elec-
trons. in. the. DFT. treatment. are. modiied. by. an. empirical. U . parameter. in. order. to.
obtain. a. better. description. of. the. bulk. system.. This. method. enables. applications.
that.would.otherwise.need.to.be.abandoned.with.standard.DFT.approaches..Being.
outside.of.formal.DFT,.this.approximation.needs.to.be.approached.with.as.much,.or.
more,.skepticism.than.DFT.calculations..The.LDA+ U .method.can.ix.some.errors.
of. the. bulk. problem. but. perhaps. at. the. cost. of. exacerbating. others.. Validation. of.