Tight Binding Methods for Metallic Systems - Metallic Systems: A Quantum Chemist's Perspective - page 226

requirements.is.made,.and.the.inal.results.depend,.often.strongly,.on.the.physical.
and. theoretical. models. used.. The. choice. of. physical. and. theoretical. model. is. an.
intensely.personal.one,.and.there.is.frequently.no.best.approach.that.should.be.taken..
One.researcher.may.believe.that.all.physical.problems.can.be.reduced.to.systems.of.
a.few.tens.of.atoms,.which.are.then.studied.at.the.highest.level.of.accuracy.available..
Another.possibility.is.the.simpliication.of.the.physical.model.in.favor.of.accuracy..
This.simpliication.comes.with.the.drawback.that.it.is.often.very.dificult.to.obtain.
a. direct. interpretation. of. the. results.. For. many. problems. of. interest,. especially. in.
biomolecular.and.nanomaterial.sciences,.this.level.of.simpliication.is.not.possible..
The.description.of.a.physical.system.in.these.disciplines.may.require.the.inclusion.
of.hundreds.(or.even.thousands).of.atoms..In.these.cases,.the.expense.of.the.required.
calculations. at. high. levels. of. theory. is. prohibitive.. Researchers. then. resort. to. the.
use. of. approximate. theories. which. involve. a. tradeoff. between. accuracy. and. com-
putational.expense..In.the.ield.of.materials.science,.the.most.commonly.employed.
approximation.for.describing.solids.is.tight.binding.(TB).[1-3]..In.the.last.decade,.the.
number.of.TB.methodologies.has.increased.more.than.any.other.approximate.elec-
tronic.structure.method..A.number.of.TB.methods.have.been.introduced.for.metallic.
systems,.and.it.is.for.this.reason.that.we.give.a.survey.of.some.of.these.methods.in.
this.chapter.
Review.of.the.literature.on.applications.of.TB.theory.in.metallic.systems.is.a.for-
midable,.if.not.impossible,.task..For.this.reason,.we.focus.on.two.areas:.(i).a.survey.
of.TB.methodologies.that.include.d-electrons.rather.than.on.TB.studies.of.metallic.
systems,.and.(ii).a.discussion.of.some.of.our.own.work.on.the.structure.and.optical.
properties.of.gold.clusters.as.a.means.to.illustrate.various.aspects.of.TB.theory.
To.describe.the.TB.methodology,.we.summarize.some.of.the.most.inluential.TB.
methodologies,.explore.their.strengths.and.weaknesses,.and.highlight.the.theoretical.
challenges. in. their. development.. We. review. the. essential. physics. contained. in. the.
various. approximations. used. to. describe. metal. systems. from. the. TB. perspective..
Throughout.this.chapter,.TB.methods.are.grouped.into.two.categories:.classical.TB.
methods.and.the.density.functional-based.TB.
The.study.of.classical.TB.techniques.begins.with.the.seminal.work.of.Slater.and.
Koster.that.constitutes.the.birth.of.the.TB.method.[4]..This.method,.and.extensions.
to.it,.are.very.well.described.in.many.topics.on.solid-state.theory.[1-3].as.it.is.the.
simplest.way.to.understand.the.band.structure.of.solid.metals.and.semiconductors..
Classical.TB.methods.are.used.as.itting.and.interpolation.schemes.rather.than.as.
quantitative. computational. tools.. Their. simplicity. allows. analytical. results. to. be.
produced. for. a. number. of. systems;. thus. it. has. been. used. extensively. to. provide. a.
qualitative.understanding.of.a.wide.range.of.electronic.structure.problems.[3]..The.
most.important.improvement.to.the.original.Slater-Koster.method.came.at.the.end.
of.the.1980s.with.the.advent.of.the.calculation.of.TB.parameters.directly.from.irst.
principles.density.functional.theory.(DFT).calculations.[5,6]..The.connection.with.
DFT.was.fully.exploited.in.a.new.generation.of.very.successful.TB.methodologies..
Prominent.examples.of.this.aproach.are.the.Naval.Research.Laboratory.TB.method.
(NRL-TB).[7],.the. ab initio .TB.method.(AITB).[8,9].and.the.density.functional.TB.
(DFTB).method.[10,11]..These.methods.have.become.routine.in.the.solid-state.litera-
ture.and.the.computer.codes.that.implement.them.are.available.from.their.developers.