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references.therein)..The.static.polarizability.α.describes.the.induced.dipole.moments.
by.static.external.electric.ield.in.a.molecular.cluster..It.represents.one.of.the.most.
important.observables.for.the.study.of.the.electronic.structure.of.clusters,.since.it.is.
very.sensitive.to.the.delocalization.of.valence.electrons,.as.well.as.the.structure.and.
shape.. Despite. numerous. investigations. on. metal. clusters,. over. many. years,. static.
polarizabilitity.measurements.were.only.available.for.alkali-metal.clusters.such.as.
sodium,.lithium,.and.potassium.[188-191]..Because.of.their.particular.coniguration,.
homo-nuclear. alkali-metal. clusters. are. often. considered. to. be. the. simplest. metal.
clusters,. so. that. they. have. become. the. prototype. systems. for. understanding. size.
effects. in. metal. clusters.. The. experimental. work. of. Knight. et. al.. [188]. by. electric.
delection. techniques. has. shown. that. the. optical. properties. of. alkali. metal. aggre-
gates,.such.as.sodium.and.potassium.clusters,.follow.a.general.trend.toward.the.bulk.
value..Knight.et.al..have.also.shown.the.existence.of.a.pronounced.size.dependency.
in.the.polarizability.of.small.clusters..In.fact,.for.sodium.aggregates,.from.the.atom.
to. the. pentamer,. the. polarizability. per. atom. has. an. oscillating. behavior.. After. the.
pentamer,. it. decreases. to. a. minimum. for. the. octamer. and. it. increases. then. again.
for.the.nonamer..Potassium-cluster.polarizabilities.closely.follow.the.same.pattern.
[188]..Later.on,.Benichou.et.al..[189].have.measured.static.electric.polarizabilities.
of.lithium.clusters.up.to.22.atoms.by.delecting.a.well-collimated.beam.through.a.
static.inhomogeneous.transverse.electric.ield..In.order.to.avoid.any.systematic.error.
in.their.experiment,.Benichou.et.al..also.carried.out.measurements.of.sodium.cluster.
polarizabilities..The.values.they.obtained.were.in.close.agreement.with.those.previ-
ously.measured.by.Knight.et.al..[188]..The.work.of.Benichou.et.al..shows.that.the.
trend.of.the.polarizability.per.atom.of.small.lithium.clusters.differs.from.those.of.
small.sodium.and.potassium.clusters..In.fact,.a.sharp.decrease.by.about.a.factor.of.
two.from.the.monomer.to.the.trimer.is.observed..For.larger.sizes,.
n
.≥.4,.the.polar-
izability. per. atom. decreases. slowly.. For.
n
.≥.15,. a. marked. oscillation. is. observed..
The. sudden. transition. of. the. polarizability. from. atom. to. trimer. and. the. following.
slow.variation.were.interpreted.by.Benichou.et.al..[189].as.a.sign.that.the.electronic.
delocalization.already.appears.in.Li
4
.or.Li
5
.clusters..The.electronic.coniguration.of.
the.noble.metals.Cu,.Ag,.and.Au.is.characterized.by.a.closed.
d
.shell.and.a.single.
valence.electron.and.therefore.closely.related.to.that.of.the.alkali.metals..In.view.of.
this.prominent.characteristic,.clusters.of.noble.metals.are.expected.to.exhibit.certain.
similarities.to.alkali-metal.clusters.
Around.10.years.ago,.we.presented.the.irst.theoretical.study.of.an.all-electron.
gradient-corrected.density.functional.study.of.static.polarizability.and.polarizability.
anisotropy.for.copper.clusters.up.to.the.nonamer.[192]..The.calculations.of.polariz-
abilities. and. polarizability. anisotropies. were. performed. at. the. ground-state. struc-
tures.found.on.each.PES.with.the.expression
1
3
[
.
(9.77)
α
=
α
+
α
+
α
].
xx
yy
zz
.
The.obtained.results.of.the.static.polarizabilities.were.compared.with.experimental.
data. for. sodium. and. lithium. clusters.. All. details. concerning. the. computations. are.
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