Chemistry Reference
In-Depth Information
example,. PBE. is. less. accurate. than. LDA. for. a. jellium. surface. [24],. a. traditional.
solid-state.model.system..In.general,.PBE.gives.lattice.constants.in.better.agreement.
with. experiments. than. LDA. does,. but. the. bulk. moduli. are. often. not. well. repro-
duced.[25]..A.newly.constructed.functional,.PBEsol.[26].is.mostly.based.on.fulill-
ing.constraints,.even.though.a.it.to.jellium.surfaces.as.in.the.AM05.construction.
is. used. [14].. PBEsol. and. AM05. both. improve. upon. LDA. and. PBE. for. solid-state.
applications.
By. allowing. additional. degrees. of. freedom. beyond. the. density. and. its. gradi-
ent,.further.constraints.can.be.satisied..This.leads.to.the.concept.of.meta-GGAs.
that.include,.for.example,.the.kinetic.energy.density.of.the.KS.orbitals..The.TPSS.
(Tao,.Perdew,.Staroverov,.Scuseria).[27].meta-GGA.functional.is.reported.to.give.
improved. results. over. PBE.. A. recent. comparison. of. many. GGAs. for. solids. has.
shown. that. in. many. contexts,. alternative. GGAs. outperform. PBE,. but. not. univer-
sally.[28].
6.3.4 e
mPirical
c
onStruction
,
the
BlyP
and
rPBe f
unctionalS
An. alternative. to. constraint-based. functional. construction. is. the. more. pragmatic.
approach. of. empirical. functionals.. The. governing. principle. is. that. good. exchange.
and.correlation.functionals.can.be.obtained.from.suitable.generic.expressions.itted.
to.known.energies..Traditionally,.this.approach.has.been.more.prevalent.in.chemistry.
than.in.solid-state.physics;.perhaps.due.to.the.more.readily.available.energy.data.on.
atoms.and.molecules.used.for.such.ittings.
One.of.the.most.widely.used.functionals.created.using.this.concept.is.the.BLYP.
(Becke,.Lee,.Yang,.Parr).functional..It.is.comprised.of.the.B88.exchange.functional.
[29]. and. the. LYP. correlation. functional. [30].. Both. of. these. functionals. use. its. to.
atomic.data.to.ix.free.parameters..The.BLYP.functional.has.proven.very.successful.
for.various.chemical.applications.[31]..However,.from.a.theoretical.standpoint,.LYP.
has.been.criticized.for.a.number.of.shortcomings:.(i).it.does.not.reproduce.LDA.in.
the. limit. of. uniform. density. and. (ii). it. gives. zero. correlation. energy. for. any. fully.
spin-polarized.system.
There. have. also. been. attempts. to. turn. constraint-based. functionals. into. a.
semiempirical.functional..Zhang.and.Yang.created.revPBE.by.reitting.one.of.PBE's.
parameters. to. atoms. ranging. from. Helium. to. Argon. [32].. Hammer,. Hansen,. and.
Nørskov.observed.that.the.reit.gave.improved.chemisorption.energies.[33].but.also.
that.this.improvement.could.still.be.achieved.without.giving.up.any.of.the.original.
PBE. constraints. by. changing. the. form. of. exchange.. The. result,. the. RPBE. func-
tional.[33],.is.not.overtly.empirical.in.the.sense.that.it.does.not.directly.involve.any.
its..However,.the.new.exchange.functional.form.was.chosen.because.it.reproduces.
relevant. behavior. of. the. exchange. of. revPBE,. which. was. itted. to. atoms.. Because.
of.this,.RPBE.does.not.improve.on.PBE.for.solid-state.systems..The.performance.
of.BLYP.and.RPBE.for.solid-state.systems.is.reported.in.Ref..[25]..Very.recently,.
inspired.by.the.fact.that.PBEsol.is.based.on.the.same.functional.form.as.PBE.with.
reit.parameters,.a.study.of.several.possible.functionals.based.on.the.PBE.form.has.
been.explored.[34].
Search WWH ::
Custom Search