Chemistry Reference
In-Depth Information
PAAHC,.and.PVP..In.the.same.study,.Hori.et.al..report.that.the.measured.magne-
tization.is.strongly.size.dependent,.increasing.with.particle.diameter.at.the.smaller.
nanoparticle. sizes,. peaking. at. approximately. 3.nm. for. Au-thiol. nanoparticles,. and.
subsequently.decreasing.with.increasing.nanoparticle.size,.keeping.with.the.fact.that.
as.the.Au.nanoparticle.size.increases,.its.coniguration.approaches.that.of.the.bulk.
lattice.[63]..Additionally,.a.closely.related.phenomenon.has.been.observed.in.gold.
surfaces:.the.occurrence.of.magnetism.when.organic.molecules.are.self-assembled.
as. monolayers. on. a. surface. [64].. The. observed. magnetism. has. been. attributed. to.
charge.transfer.between.the.organic.layer.and.the.metal.substrate.[64].
These.effects.are.somehow.intriguing.given.that.gold.is.a.diamagnetic.metal,.but.
perhaps.not.totally.unexpected..A.close.examination.of.Stoner's.model.[65].suggests.
that.the.emergence.of.“unexpected”.magnetic.ordering.in.transition.metal.clusters.
in.conined.spaces.at.the.nanoscale.is.possible..In.this.model,.the.paramagnetic.sus-
ceptibility.χ.is.determined.by.the.density.of.d-states.at.the.Fermi.level.
N
(
E
F
).and.the.
exchange.function.
J
:
μ μ
2
N E
JN E
(
)
0
B
F
F
χ
=
)
.
(11.5)
(
1
−
(
.
where
μ
0
.is.the.permeability.of.free.space
μ
B
.is.the.Bohr.magneton.(9.27.×.10
−24
.J/T)
The. spatial. coninement. produces. a. narrower. d-band. and. eventually. the. center. of.
the. band. is. shifted. closer. to. the. Fermi. level.. For.
JN
(
E
F
).>.1,. the. term. 1−
JN
(
E
F
). in.
Equation.11.5.becomes.negative,.consequently.generating.ferromagnetic.instability.
and.thus.a.magnetic.order.
Several. previous. experimental. studies. have. shown. that. the. onset. of. magne-
tism.at.the.nanoscale.occurs.in.a.complicated.way.with.clusters.frequently.having.
unusual.magnetic.properties.not.clearly.related.to.the.strength.and.orientation.of.
the. metal. bulk. magnetization.. Stern-Gerlach. molecular-beam. delection. experi-
ments.[66-71].with.bare.clusters.of.transition.metals.show.either.high-ield.delec-
tion. indicative. of. superparamagnetism. or. symmetric. broadening. indicative. of.
locked.moment.behavior..These.clusters.exhibit.susceptibilities.signiicantly.larger.
in.magnitude.than.those.expected.based.on.the.extrapolation.of.the.susceptibility.
of.the.bulk.solids..It.is.worth.mentioning.also.that.molecules.comprising.a.large.
number. of. coupled. paramagnetic. centers. capped. by. ligands. (e.g.,. Mn
12
. and. Fe
8
.
families). are. known. to. show. unambiguous. evidence. of. quantum. size. effects. in.
magnets.[72].
Magnetism.in.bare.(uncapped).gold.nanoclusters.has.been.explored.in.our.group.
[73].from.a.spin-dependent.DFT.perspective.with.scalar.relativistic.effects.included.
via.the.use.of.pseudopotentials..In.this.study,.three.different.DFT.exchange-corre-
lation.energy.functionals.were.used:.the.Perdew,.Burke,.and.Ernzerhof.[74].gener-
alized. gradient. approximation. (PBE). and. the. hybrid. functionals. B3LYP. [75]. and.
PBE1PBE. [76].. In. addition,. two. different. basis. sets. were. chosen:. a. single. valence.
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