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superconducting.quantum.interface.device.(SQUID).magnetometer.[34].or.magnetic.
force.microscopy.[35].
10.1.3  c omPutational  m ethodS for  tmc
Computational. studies. of. nanoparticles. have. developed. into. an. important. part. of.
cluster.science,.which.contributes.information.that.often.complements.experimental.
studies.. These. studies. can. be. separated. into. two. groups:. those. investigating. equi-
librium. (static. or. very. low. temperature). properties. and. those. studying. dynamical.
properties..Finding.the.most.stable.structure.for.a.given.cluster.size.and.composition.
[36-38].and.describing.its.electronic.and.magnetic.properties.[39].are.the.basic.goals.
of. equilibrium. calculations.. Transitions. between. structural. motifs,. phase. changes.
[40-42],. diffusion,. collision,. segregation,. and. growth. kinetics. are. related. to. the.
dynamical.properties.of.interest..Both.types.of.calculations.are.extremely.interesting.
and.challenging.
A. critical. consideration. in. any. theoretical. investigation. is. the. means. by. which.
intra-.and.interatomic.interactions.are.described..The.cluster.coniguration.energy.
as.a.function.of.atomic.coordinates,.for.example,.the.potential.energy.surface.(PES).
is. determined. by. describing. intra-. and. interatomic. forces.. The. methods. for. com-
putation. of. the. PES. range. from. simple. atom-atom. model. potentials. (such. as. the.
Morse.potential).and.many-body.semiempirical.methods.(such.as.embedded.atom.
method. [EAM]. or. the. Sutton-Chen. potential). to. parameter. free. ab. initio. calcula-
tions..First.principles.methods.like.density.functional.theory.(DFT).[43].can.provide.
suficiently.high.accuracy.to.be.applied.to.a.wide.variety.of.systems.with.sizes.up.to.
a.few.hundred.atoms.for.symmetric.structures.[44],.whereas.semiempirical.methods.
are. less. computationally. intensive. but. exhibit. accuracy,. which. is. strongly. system.
dependent. [3,4,6,15].. The. accuracy. of. the. irst. principles. methods. highly. depends.
on.the.choice.of.basis.set.and.the.method.used.for.the.description.of.the.electronic.
interactions.
A.complete.exploration.of.the.PES.by.means.of.irst.principles.methods.is.pres-
ently. not. feasible. even. for. clusters. containing. a. few. tens. of. atoms,. while. simply.
guessing. the. most. stable. structures. of. TMCs. is. very. dificult. and. nontrivial. [15]..
Thus,.large.databases.of.possible.cluster.structures.constructed.by.a.much.more.com-
plete. sampling. of. the. PES. with. semiempirical. potentials. are. used. as. the. starting.
point.for.further.ab.initio.calculations.
Since. TMCs. have. many. valence. electrons,. close-lying. states. and. mostly. open.
d -shells,. a. treatment. of. electron. correlation. is. required.. Additionally,. relativistic.
effects.become.important.for.the.heavier.transition.metals..DFT.is.one.of.the.most.
effective. and. widely. used. methods. in. the. study. of. TMCs.. While. highly. accurate.
multi-determinant.quantum.chemical.methods.[45].can.treat.about.a.dozen.atoms,.
modern.DFT.methods.[44,46].can.describe.clusters.with.up.to.a.few.hundred.atoms..
In. a. recent. review,. Alonso. [47]. has. reported. electronic. and. atomic. structures. and.
magnetism. of. bare. TMCs. noble. metal,. nickel,. iron,. niobium,. titanium,. vanadium,.
and.chromium.clusters.
In.this.chapter,.by.focusing.on.size-selected.clusters.consisting.of.up.to.a.few.tens.
of.atoms,.that.is,.in.the.size.regime.where.properties.change.drastically.by.addition.
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