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contracted. Gaussian. basis. sets. tuned. to. the. particular. PP. and. functional. for. bulk.
periodic.systems.
6.4.4  P SeudoPotentialS
PPs,.perhaps.better.known.in.the.molecular.quantum.chemistry.community.as.effec-
tive.core.potentials.(ECPs),.are.commonly.used.in.periodic.DFT.codes.to.remove.the.
explicit.treatment.of.core.electrons..The.focus.on.the.chemically.active.valence.elec-
trons.reduces.the.number.of.electrons.and.the.size.of.the.basis.sets.required.in.a.calcu-
lation,.dramatically.reducing.the.computational.cost..While.nominally.performing.the.
same.role.in.chemistry.and.solid-state.physics,.the.practical.generation.and.use.of.PPs.
is.quite.different.in.the.two.communities..The.ECPs.of.quantum.chemistry.are.typi-
cally.constructed.from.HF.atoms.and.are.accompanied.by.Gaussian-based.contracted.
basis.sets.to.accommodate.their.use.in.the.prevalent.codes.in.chemistry..A.good.deal.
of.chemistry.concerns.itself.with.irst-row.atoms.and.does.not.require.or.use.ECPs..
Solid-state. codes. are. generally. concerned. with. heavier. atoms. in. the. periodic. table,.
requiring.PPs.to.make.any.but.the.smallest.calculations.computationally.tractable.
One. surprising. fact. for. chemists. using. solid-state. codes. is. that. it. is. common-
place.to.use.PPs.for.atoms.without.core.electrons—even.for.a.hydrogen.atom!.This.
practice. is. dictated. by. computational. considerations.. The. cusp. of. the. 1s. orbital. of.
the.hydrogen.atom.at.the.nucleus.cannot.be.reproduced.with.any.reasonably.sized.
plane-wave. basis,. and. the. pseudized. orbitals. are. needed. to. make. the. computation.
tractable..The.goal.of.PP.construction.is.to.create.a.smooth.nodeless.pseudo-orbital.
that. quantitatively. reproduces. the. electronic. behavior. of. the. full-potential. orbital..
Such.a.construction.can.be.made.from.any.valence.orbital,.even.if.it.lacks.core.elec-
trons..With.carefully.converged.calculations.that.treat.the.cusp.accurately,.we.were.
unable.to.identify.any.meaningful.differences.in.results.comparing.a.hydrogen.PP.to.
a.bare-core.hydrogen.
One.should.not.use.HF.PPs.in.DFT.calculations.and,.indeed,.it.is.not.advisable.
to. use. a. PP. generated. using. one. functional. in. DFT. calculations. with. a. different.
functional.[1]..The.results.can.be.unpredictable..Mismatching.functionals.in.the.PP.
and.calculation,.just.as.mismatching.experimental.lattice.parameters.and.theoretical.
lattice. parameters. in. slab. models,. can. produce. unphysical. results.. A. further. com-
plication. is. that. the. functionals. that. are. used. in. solid-state. calculations. vary. and.
preferred.functionals.change.over.time,.and,.therefore,.PPs.need.to.be.reconstructed.
frequently..The.practice.of.PPs.use.in.solid-state.systems.is.not.as.systematized.as.
in.quantum.chemistry..One.does.not.have.libraries.of.accepted.PP..Instead.of.being.
distributed.as.collated.sets.of.ECP+basis.over.atoms,.PPs.used.in.solid-state.calcula-
tions. are. distributed. as. codes. that. implement. speciic. methods. for. generating. PPs.
and.it.is.often.left.to.the.user.to.fashion.their.own.PP.for.a.speciic.calculation.
Two.well-established.methods.for.PP.construction.include.the.norm-conserving.
PP.due.to.Hamann.[52],.considered.by.many,.including.us,.to.be.the. gold standard .
of.PP.in.DFT,.and.the.somewhat.softer.(smoother),.therefore,.more.computationally.
tractable.PP.of.Troullier.and.Martins.(TM).[53]..PPs.using.the.Hamann.construction.
are.generally. hard ,.involving.more.rapid.variations.in.the.resulting.valence.pseudo-
orbitals,. thereby. achieving. better. transferability.. The. softer. TM. PP. compromise.
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