Density Functional Calculations of Metal Clusters: Structure, Dynamics, and Reactivity - Metallic Systems: A Quantum Chemist's Perspective - page 316

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Li-Exp.

2 3 4 5

Number of atoms

6 7 8 9

FIGURE 9.25 Experimental.mean.polarizability.per.atom.of.Li n .( n .=.2-9)..Values.are.from.
Ref..[189]..(Reprinted.from.Calaminici,.P..et.al.,. J. Chem. Phys .,.113(6),.August.8,.2199,.2000..
With.permission.)

The. values. of. the. experimental. polarizability. per. atom. of. sodium. clusters. are.
those. reported. by. Knight. et. al.. [188],. while. the. experimental. polarizability. data.
of.lithium.clusters.are.those.reported.by.Benichou.et.al..[189]..The.comparison.of.
Figures.9.23.through.9.25.shows.that.the.calculated.polarizability.per.atom.of.copper.
clusters,.going.from.the.atom.to.the.nonamer,.presents.the.same.trend.as.experimen-
tally.observed.by.Knight.et.al..[188].for.sodium.clusters..However,.the.mean.polariz-
ability.per.atom.of.copper.clusters.is.about.three.times.smaller..This.result.indicates.
that.in.copper.clusters,.the.electrons.are.more.strongly.attracted.by.the.nuclei.than.
in.the.sodium.clusters..Therefore,.their.electronic.structure.is.more.compact..We.are.
conident.that.the.reliability.of.the.absolute.values.for.the.calculated.polarizabilities.
of.the.copper.clusters.is.in.the.same.range.as.for.the.previously.studied.sodium.clus-
ters.[193]..Thus,.deviations.of.less.than.10%.for.the.absolute.values.can.be.expected..
The.theoretical.prediction.of.the.trend.of.the.mean.polarizabilities.per.copper.atom.
is.believed.to.be.reliable..In.fact,.it.was.conirmed.by.several.other.theoretical.stud-
ies.[194-196].too..However,.the.experimental.work.of.Knickelbein.[197].on.copper.
cluster. polarizabilty. has. shown. large. discrepancies. between. the. experimental. and.
theoretical.polarizability.value.of.Cu 9 ..Further.experimental.and.theoretical.studies.
are.needed.to.resolve.this.mismatch.

9.5.2 t ranSition m etal S yStemS (f e , n i )
In. the. previous. section,. we. showed. that. the. electronic. structure. of. small. copper.
clusters. is. more. closely. related. to. that. of. sodium. rather. than. to. that. of. lithium.
clusters.. However,. generally,. the. TMs. are. characterized. by. an. open. d . shell,. and,.
therefore,. the. prediction. of. their. electronic. properties. is. even. more. complicated..
Moreover,.these.calculations.also.provide.a.means.of.testing.computational.meth-
ods.and.are,.therefore,.very.interesting.for.theoreticians..From.a.theoretical.point.of.
view,.the.calculation.of.properties.of.iron-.and.nickel-containing.systems.presents.
a. challenging. goal. for. any. quantum. chemical. methodology.. The. investigation. of.