Exploring the Borderland between Physics and Chemistry: Theoretical Methods in the Study of Atomic Clusters - Metallic Systems: A Quantum Chemist's Perspective - page 381

-52.070

-52.075

-52.080

-52.085

-52.090

-52.095

-52.100

0 5,000 10,000

Step number

15,000 20,000

FIGURE 11.4 The.quenching.route.in.the.optimization.of.the.Li 7 + .cluster.

clusters..It.starts.with.a.relatively.large.population.of.geometrical.structures.that.is.
chosen.randomly.and.enclosed.in.a.very.small.volume..Then,.using.standard.geom-
etry.optimization.procedures,.one.proceeds.to.relax.the.structures.by.following.the.
force.(negative.gradient)..Since.at.the.beginning.all.the.atoms.are.very.close.to.each.
other,. the. repulsive. forces. among. them. are. very. large. and. consequently. they. tend.
to.“explode,”.landing.in.distant.parts.of.the.hypersurface..By.starting.with.a.large.
population,. one. can. be. certain. to. explore. a. large. portion. of. the. hypersurface.. By.
optimizing. individual. structures,. the. procedure. produces. different. local. minima.
including,.hopefully,.the.global.minima..The.method.is.very.simple.to.implement,.
but.curiously.has.not.been.adopted.by.the.chemistry.community..In.the.implementa-
tion.developed.in.Ref..[39],.1000 N .random.structures.were.generated,.where. N .is.the.
number.of.atoms.in.the.cluster..These.were.conined.to.a.volume.proportional.to.the.
covalent. radius. of. the. atom. and. the. structures. were. optimized. using. the. semiem-
pirical.MSINDO.method.[26]..The.optimized.structures.where.then.optimized.at.a.
higher.level.of.theory.
In.this.way,.more.than.70.different.isomers.of.Li n .( n .=.3-20).have.been.found.[39]..
In.Table.11.3,.the.symmetry.of.the.reported.structures.is.compared.with.other.work.
[40,41]..More.than.50.new.structures.are.reported..The.big.bang.methodology.has.
been.also.applied.to.sodium.and.potassium.clusters.[39].
The. three. methodologies. discussed. in. this. section. are. all. based. on. the. use. of.
stochastic.techniques..In.each.of.the.methods.there.is.no.guarantee.of.reaching.the.
global.minimum,.and.one.should.perform.the.minimization.various.times.with.dif-
ferent.starting.structures.to.be.sure.that.a.consistent.set.of.minimum-energy.isomers.
is.obtained..In.general,.the.choice.of.which.method.to.use.is.more.a.matter.of.conve-
nience,.especially.with.respect.to.the.computational.facilities,.than.a.formal.decision.
based.on.theoretical.grounds..In.the.cases.discussed.here,.a.detailed.comparison.of.
the. small. members. of. the. series. indicates. that. the. three. methodologies. discussed.
above.are.able.to.locate.the.lowest.energy.isomers.and.the.differences.lie.more.in.
the. eficiency. of. the. implementation. rather. than. in. some. formal. advantage. of. the.
method.