Exploring the Borderland between Physics and Chemistry: Theoretical Methods in the Study of Atomic Clusters - Metallic Systems: A Quantum Chemist's Perspective - page 385

2 .

±

(11.4)

f ( ) r = φ ( ) r

.

where.ϕ( r ‾ ).is.the.frontier.molecular.orbital,.and.the.sign.±.means.the.HOMO.or.
LUMO,.respectively..A.condensed.form.of.this.function.using.the.integration.of.the.
proper.Fukui.function.over.its.own.basins.has.been.proposed.as.a.better.alternative.
than.using.population.analysis.[55]..In.Ref..[53].this.condensed.form.has.been.used.to.
study.the.reaction.of.hydrogen.atom.with.silicon.clusters..The.theoretical.predictions.
of.the.sites.of.most.probable.attack.have.been.conirmed.by.computational.simula-
tions.where.the.genetic.algorithm.has.been.used.to.ind.the.most.stable.clusters.of.
Si n H..Given.that.the.chemical.potential,.deined.as.the.negative.of.the.absolute.elec-
tronegativity,.has.a.value.of.−7.25.eV.for.the.hydrogen.atom.and.is.in.the.range.of.
−4.5.to.−5.0.eV.for.silicon.clusters,.it.is.expected.that.the.silicon.clusters.will.donate.
charge.to.the.hydrogen.atom.and.therefore.the.Fukui.function.should.be.calculated.
with.the.square.of.the.HOMO.
On.the.left.column.in.Figure.11.6.the.geometrical.structures.of.the.clusters.of.Si 3 ,.
Si 4 ,.Si 5 ,.and.Si 7 .have.been.depicted,.while.in.the.right.column.the.respective.Fukui.

0.25 0.25

Si 3 C 2v

2

1

0.23 0.23

3

Si 4 D 2h

2

0.14

0.14

0.33

0.33

1

3

4

Si 5 D 5h

4 0.30

1

0.30 0.30

3

5

2

Si 7 D 5h

0.10
0.10

1

0.10

0.10

0.10
0.10

5 7 2

6

0.10

0.10

0.10 0.10

4 3

FIGURE 11.6 Geometries. of. the. clusters. of. Si 3 ,. Si 4 ,. Si 5 ,. and. Si 7 . and. the. corresponding.
Fukui.function.isosurface.(on.the.right).