Chemistry Reference
In-Depth Information
Taking.in.account.all.of.these.approximations,.the.EHTB.total.energy.expression.of.
Equation.8.14.is.written.as
⎛
⎞
occ
∑ ∑
1
2
∑
∑
∑
⎟
+
∑
U
αβ
αβ
*
⎜
⎟
0
2
E
2
C C H
+
δ δ γ
q q
+
δ
P
Γ
.
(8.32)
μ
i
vi
μ
v
α
β αβ
μ
v
μ
v
⎜
⎝
⎠
i
μ
v
αβ
α
(
μ
> ∈
v
)
α
.
Applying.the.variational.principle.to.Equation.8.32,.we.obtain.a.Kohn-Sham-like.
equation,.
HC = ESC
,.with.Hamiltonian.elements.of.the.form.[16]
⎧
∑
−
VSIE
+
γ δ
q
if
μ
=
v
,
μ α
∈
,
⎪
⎪
μ
αβ
β
β
.
(8.33)
H
=
P
Γ
if
μ
≠
v
,
μ α
∈
,
v
∈
α
,
⎨
μ
v
μ
v
μ
v
⎪
⎪
⎪
1
2
∑
0
H
+
S
(
γ
γ
)
δ
q
if
μ
≠
v
,
μ α
∈
,
v
∈
β
.
μ
v
μ
v
αξ βξ
ξ
⎩
.
ξ
Since.the.elements.of.the.Hamiltonian.of.Equation.8.33.depend.on.the.density.matrix.
through.the.atomic.charges.and.the.off-diagonal.one.center.elements,.these.equations.
must.be.solved.iteratively.until.SCC.is.achieved..One.important.contribution.of.this.
version.of.the.EHTB.is.the.incorporation,.through.the.use.of.spectroscopic.Slater-
Condon.parameters,.of.the.on-site.off-diagonal.elements.of.the.Coulomb-exchange-
correlation. coupling. matrix,. in. a. fashion. similar. to. that. employed. in. the. Zerner's.
semiempirical.intermediate.neglect.of.differential.overlap.(ZINDO).method.[41,42].
8.5 GOLD CLUSTERS
Gold. nanoclusters. and. gold-based. complexes. are. currently. under. active. investiga-
tion. in. various. areas. of. nanoscience. and. nanotechnology. due. to. some. remarkable.
physical.and.chemical.properties.of.gold.that.appear.only.at.the.nanoscale.[43,44]..
Gold.has.been.shown.to.exhibit.surprising.mechanical.properties.at.the.nanoscale.
by.forming.stable.nanowires.with.quantized.electrical.conductivity,.which.has.great.
relevance.to.atomic.junctions.[18]..Optical.absorption.by.gold.nanoparticles.depends.
sensitively.on.size,.and.this.property.can.be.used.in.labeling.applications.or.in.devis-
ing. precision. therapies. for. selective. imaging. and. destruction. of. cancer. cells. [19]..
Although.totally.inert.as.bulk.solids,.gold.nanoparticles.can.be.surprisingly.active.
as.catalysts.in.oxidation.and.hydrogenation.reactions..As.a.consequence,.there.exist.
many.theoretical.studies.on.the.electronic.structure.of.gold.nanoclusters.[19].
Hakkine. and. Landman. investigated. neutral. and. anionic. gold. clusters,. Au
2-10
,.
using. DFT. with. scalar-relativistic.
ab initio
. pseudopotentials. and. the. generalized.
gradient.approximation.(GGA).[45]..Wang.et.al..studied.low-energy.conformers.of.
gold.clusters.with.sizes.from.2.to.20.atoms.[46],.and.Walker.performed.DFT.calcula-
tions.on.neutral.and.cationic.gold.clusters.with.up.to.9.atoms.[47].
In. this.section,. we. present. a. systematic. investigation. of. the. applicability. of. TB.
methods.to.describe.the.physics.of.small.gold.clusters.
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