Some Practical Considerations for Density Functional Theory Studies of Chemistry at Metal Surfaces - Metallic Systems: A Quantum Chemist's Perspective - page 185

Er.atom.has.a.4f 12 .5d 0 .6s 2 .ground-state.coniguration..Erbium.metal.has.a.hexagonal.
close-packed.(hcp).structure.with.lattice.constants. a .=.3.56.Å.and. c .=.5.59.Å.
Lanthanides.can.be.problematic.for.DFT.calculations.as.they.possess.a.partially.
illed.4f-shell..This.is.particularly.true.for.PP.codes..Many.codes.might.not.have.PPs.
available.for.Er.or.the.default.potential.might.never.have.been.validated..Hence,.PP.
availability.may.limit.the.choice.of.computational.method.
If.an.Er.PP.does.not.exist,.one.must.be.constructed..The.4f-shell.is.the.irst. f -shell.
to. be. occupied. and,. therefore,. the. orbitals. have. very. sharp. spatial. variations. that.
violate.the.underlying.motivation.of.PP.codes,.namely,.that.all.the.resulting.valence.
orbitals. are. smooth.. Fortunately,. the. 4f-orbitals,. being. the. irst. f-shell. and,. hence,.
largely.unscreened,.are.so.short.ranged.that.the.interaction.with.the.outer.valence.
electrons.is.quite.small..These.4f-electrons.are.chemically.inert,.and.the.oxidation.
state. in. chemical. environments. is. mostly. ixed;. to. a. good. approximation. in. most.
chemical.environments.(with.the.exception.of.the.bare.atom),.the.erbium.atom.can.be.
well.approximated.as.having.11.f-electrons,.and.3.valence.electrons..For.our.applica-
tion,.we.are.not.interested.in.magnetic.properties,.so.the.presence.of.the. f -electrons.
in.the.valence.is.unnecessary.and.we.use.this.observation.to.justify.putting.the.4f 11 .
electrons.into.the.core.of.the.PP..Computing.bulk.properties.of.Er.indicates.that.the.
5p 6 .semi-core.states.need.to.be.treated.as.valence.electrons.and.that.a.partial.core.
correction.was.needed.to.incorporate.the.nonlinear.effects.of.the.density.from.the.
other. core. electrons. [59].. The. tuning. of. these. aspects. of. the. PP. closely. follows. a.
process.described.elsewhere.for.constructing.a.strontium.PP.[1]..The.basis.set.is.of.
double-ζ.quality.with.s-.and.d-orbitals.and.a.single-ζ.function.for.the.semi-core.5p 6 .
electrons.plus.a.second,.single-Gaussian.p-function.for.polarization.of.the.valence.
electrons.[59].
The.next.steps.are.to.verify.that.the.computational.model.is.sound.and.validate.
that.it.gives.reasonable.results.for.the.systems.of.interest..The.immediate.quantities.
of.interest.are.the.bulk.lattice.parameters..Using.SEQQUEST.and.the.PP.described.
above,.the.results.for.the.hcp.ground-state.structure.and.the.fcc.closed-packed.struc-
ture.obtained.from.stress-optimized.DFT.calculations.are.presented.in.Table.6.2..For.

TABLE 6.2
Er Crystal Properties from DFT
Bulk Er

Experiment LDA-CAPZ GGA-PBE

hcp
a .(Å)

3.559 3.437 3.578

c .(Å) 5.587 5.375 5.560

c/a 1.570 1.564 1.554

V .(Å 3 ) 30.64 27.49 30.83

fcc
a .(Å)

n/a 4.769 4.957

V .(Å 3 ) n/a 27.12 30.45

B .(GPa) n/a 46.5 43.8

ϕ E fcc .(meV) >0 +0.8 +25.2