Some Practical Considerations for Density Functional Theory Studies of Chemistry at Metal Surfaces - Metallic Systems: A Quantum Chemist's Perspective - page 170

. 2.. Electomorphism of KS particles ..By.electomorphism,.we.mean.interpret-

ing. KS. particles. as. electrons,. and. calculating. properties. with. formulae.
that. invoke. the. KS. orbitals. as. independent. electron. orbitals.. This. inter-
pretation,. strictly. speaking,. lies. outside. of. DFT,. and. can. yield. mislead-
ing. results.. A. prime. example. of. this. is. the. use. of. the. eigenvalue. band.
gap.between.occupied.and.unoccupied.KS.eigenstates.from.DFT.calcula-
tions.to.predict.the.fundamental.band.gap.in.solids..The.eigenvalue.gap,.
HOMO-LUMO. in. DFT. is. usually. (much). smaller. than. the. fundamental.
gap. measured. in. materials.. This. difference. is. often. described. as. a. fail-
ing. of. DFT,. the. so-called. band gap problem .. However,. local. density.
approximation. (LDA). (and. Perdew-Burke-Ernzerhof. functional. [PBE]).
give. excellent. structural. properties. for. silicon,. despite. a. KS. gap. that. is.
much. smaller. than. the. experimental. band. gap. [8].. Defect. energy. levels.
in.silicon,.charge.transition.energies.computed.as.differences.of.properly.
constructed.total.energy.calculations.of.different.charge,.indicate.a.range.
of. ionization. potentials. that. span. an. experimental. band. gap. and. are. not.
limited.by.the.KS.gap.[9]..This.seeming.contradiction.simply.relects.that.
DFT.is.a.ground-state.theory,.and.quantities.computed.from.ground-state.
energies—structures,. defect. levels—are. generally. quite. accurate,. while.
the. electron. orbital. interpretation. of. KS—KS. gap—is. faulty.. The. band.
structure. and. band. gap. deined. by. the. ideal. DFT. eigenvalue. spectrum.
from. the. exact. E XC . functional. may. be. signiicantly. different. from. the.
band. structure. and. band. gap. observed. in. experiment.. A. special. density.
functional. approach. would. be. needed. to. extricate. a. band. structure. from.
a. density. in. a. reliable. way;. it. would. need. to. explicitly. take. into. account.
the. nature. of. the. excitations. involved. in. promoting. an. electron. from. the.
valence.band.into.the.conduction.band.

Because.of.its.utility.and.computational.economy,.DFT.is.a.common.practical.tool.
and.researchers.often.need.to.glean.as.much.information.from.a.calculation.as.pos-
sible.. Where. an. explicit. density. functional. is. not. known,. or. hard. to. construct,. a.
researcher.might.have.to.appeal.to.noninteracting.particle.theory.for.results..A.good.
example. is. the. use. of. the. Kubo-Greenwood. formula. to. ind. the. conductivity. of. a.
material.based.on.KS.orbitals.[10]..This.approach.is.acceptable.with.the.following.
caveat:. the. results. extracted. in. this. fashion. are. no. longer. true. density. functional.
results.but.rather.are.based.on.an.MFT.interpretation.of.DFT.
An.MFT.approach.to.DFT.lies.outside.the.scope.of.the.original.HK.and.KS.formal-
isms..The.main.drawback.of.this.MFT.perspective.is.that.it.is.unclear,.which.many-
body.effects.have.already.been.accounted.for.in.the.DFT.potential..Improvement.of.
such.a.theory.can,.at.best,.be.made.on.empirical.evidence.and.on.analogies.to.wave.
function.theory,.while.moving.further.away.from.the.formal.exactness.based.on.a.
rigorous.KS.picture..Improving.the.extraction.scheme.without.improving.the.physics.
in. E XC .yields.less.predictive.results.
Response.theory.illustrates.the.conceptual.difference.between.interpreting.DFT.
as. an. exact. theory. versus. an. MFT.. In. the. exact. theory. picture,. the. excited. states.
of. a. quantum. system. can. be. extracted. by. examining.the. structure. of. the. response.