Exploring the Borderland between Physics and Chemistry: Theoretical Methods in the Study of Atomic Clusters - Metallic Systems: A Quantum Chemist's Perspective - page 379

Ly

Lx

Lz

(a) 4.313 eV (c) 4.297 eV

(b) 4.310 eV (d) 4.275 eV

FIGURE 11.3 Geometries.of.the.four.most.stable.isomers.of.Si 60 .and.their.respective.BE.

in.eV.

there.does.not.seem.to.be.any.correlation.with.the.dipole.polarizability.or.with.the.
HOMO-LUMO.gap.[22].
Using.the.same.methodology.as.in.Ref..[29],.the.following.larger.silicon.clusters.
were.studied:.Si 40 ,.Si 46 ,.and.Si 60 .(the.last.one.was.included.in.this.study.due.to.its.
possible. similarity.to. C 60 ).. Figure. 11.3. shows. the. four. most. stable. isomers. of. Si 60 ..
Structure.(b).corresponds.to.the.structure.reported.in.Ref..[30]..However,.the.calcu-
lations.of.Ref..[29].show.that.at.this.level.of.theory,.the.structure.has.ive.imaginary.
frequencies.. All. of. the. structures. in. Figure. 11.3. are. very. close. in. binding. energy.
making.it.dificult.to.predict.the.most.stable.isomer..However,.it.is.clear.that.for.the.
Si 60 .cluster.there.is.no.cage.structure.similar.to.the.fullerene.structure.observed.for.
carbon.atom.clusters..In.addition,.it.is.observed.that.the.silicon.cluster.structures.are.
more.prolate.in.shape.than.their.carbon.counterparts.
As.discussed.in.Ref..[29],.one.signiicant.weakness.of.the.methodology.consists.
of. the. use. of. a. semiempirical. method,. MSINDO,. to. evaluate. the. atomic. clusters..
For.example,.silicon.clusters.of.the.endohedral.type,.where.some.silicon.atoms.are.
hypervalent,.are.not.properly.described.given.that.the.semiempirical.methodology.is.
not.parametrized.to.treat.hypervalent.silicon.atoms.

11.3.2 S imulated a nnealing
In.this.section,.we.discuss.simulated.annealing.techniques.[31,32].as.implemented.
by.Perez.et.al..[33]..In.this.methodology.the.system.is.allowed.to.evolve.inside.a.box.
of.a.given.length..The.method.is.initialized.with.randomly.selected.cluster.geom-
etries,. and. the. energy. of. each. atomic. cluster. is. calculated. using. some. quantum.
chemical.method..In.this.case,.the.energy.is.evaluated.at.each.step.at.the.HF/Lanl2z.
level.of.theory..Every.generated.structure.is.then.subject.to.one.or.more.acceptance.