Chemistry Reference
In-Depth Information
in. the. range. of. nanoparticles,. between. 1. and. 100.nm,. and. thin. ilms. have. shown.
unexpected.properties.and.have.found.use.in.areas.such.as.catalysis.and.magnetic.
storage.[1,4,5].
The. presence. of. dangling. bonds. (unsatisied. valences). on. the. surface. makes.
clusters. chemically. very. active.. In. general,. clusters. may. split. or. combine. with.
other.particles.more.rapidly.than.normal.molecules..This.means.that.they.are.much.
more.reactive,.and.therefore,.more.dificult.to.stabilize.for.study.in.the.laboratory.
with. conventional. methods.. Hence,. most. experimental. measurements. are. carried.
out. in. the. gas. phase. at. low. pressures. and. require. sophisticated. instrumentation..
Experimental.dificulties.are.one.of.the.main.reasons.that.theoretical.work.on.clus-
ters. is. so. valuable.. As. an. added. beneit,. research. in. this. ield. has. united. chem-
ists. and. physicists,. both. experimental. and. theoretical,. to. study. a. huge. variety. of.
phenomena.in.a.very.detailed.and.synergistic.manner..One.of.the.irst.successful.
attempts.to.rationalize.an.experimental.observation.of.cluster.phenomena.was.the.
explanation.of.the.existence.of.magic.numbers.in.the.abundance.spectrum.of.alkali.
metal.clusters.[6],.which.was.concurrently.explained.by.the.very.simple.theoreti-
cal.jellium.model.[7,8]..Magic.numbers.arise.as.a.consequence.of.illing.molecular.
orbitals.to.form.a.closed-shell.species.like.the.atomic.noble.gases,.giving.them.extra.
stabilization.energy.with.a.large.HOMO-LUMO.gap..However,.it.was.also.realized.
early.on.that.to.explain.the.variation.of.most.of.the.properties.of.a.given.cluster.with.
respect.to.the.number.of.atoms,.it.is.necessary.to.use.theoretical.models.that.take.
into.account.the.quantum.nature.of.the.electronic.structure.[9]..Fortunately,.around.
the.same.time.DFT.emerged.as.a.robust.and.eficient.methodology.to.perform.cal-
culations.of.the.electronic.structure.of.atoms,.molecules,.and.clusters.of.moderate.
size.[10,11].
We.briely.discuss.some.key.steps.that.most.researchers.perform.in.conducting.
theoretical. studies. of. atomic. clusters.. This. chapter. does. not. provide. a. systematic.
study.(or.review).of.this.topic.but.a.short.description.of.our.own.and.related.research..
It. is. set. out. in. ive. sections,. beginning. with. this. introduction.. In. Section. 11.2,. we.
use. DFT. calculations. to. describe. clusters. as. entities. that. lie. between. atoms. and.
solids. with. unique. properties. depending. on. their. size,. chemical. nature,. and. sym-
metry..Section.11.3.describes.several.methods.of.inding.different.stable.isomers.of.
a.given.cluster..There.are.various.stochastic.methodologies.and.evolutionary.algo-
rithms.currently.used.for.this.task;.we.shall.discuss.the.genetic.algorithm,.simulated.
annealing,.and.the.so-called.“big.bang”.methods..The.chemical.bonding.and.reac-
tivity.of.clusters.are.discussed.in.Section.11.4..We.present.the.ELF.as.a.very.robust.
tool.to.understand.chemical.bonding.in.clusters.and.the.Fukui.function.as.an.effec-
tive.means.of.predicting.their.chemical.reactivity..Finally,.in.Section.11.5.we.discuss.
some. interesting. properties. of. clusters. such. as. the. magnetic. moment. observed. in.
clusters.and.surfaces.of.gold,.a.typically.diamagnetic.metal,.from.a.theoretical.point.
of.view.
11.2 CLUSTERS: BETWEEN ATOMS AND BULK
Recently,. the. study—both. experimental. and. theoretical—of. the. transition. from.
atomic.and.molecular.clusters.to.bulk.solids.has.become.accessible.for.almost.any.
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