Chemistry Reference
In-Depth Information
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
(a)
80
70
60
50
40
30
20
10
0
0
5
10
15
20 25
Number of atoms
30
35
40
45
50
(b)
FIGURE 8.5  (a).Longitudinal.plasmon.excitation.energy.and.(b).dipole.oscillator.strength.
as.a.function.of.the.number.of.gold.atoms.in.a.linear.chain.
low.energy.is.dominated.by.a.single.absorption.that.is.redshifted..In.general,.the.
.average. location. of. these. peaks. moves. toward. lower. energies. as. the. number. of.
atoms.increases.
There.are.some.similarities.between.spectra.observed.in.gold.and.sodium.chains..
Even.though.the.gold.spectra.are.more.complicated.due.to.the.presence.of.5d.orbit-
als,.the.main.features.appearing.in.both.cases.are.produced.by.longitudinal.absorp-
tions.of.σ.symmetry..In.particular,.we.note.the.appearance.of.two.main.absorptions.
whose. location. and. strength. depend. on. the. size. of. the. chain.. We. expect. this. type.
of. transition. to. be. dominant. in. most. noble. metal. chains.. It. is. well. known. that. 5d.
orbitals. are. more. localized,. and. their. lower. transition. is. of. tranverse. π. symmetry.
with.small.oscillator.strength..In.both.cases,.the.lower.energy.absorptions.that.domi-
nate.the.small.chains.are.more.localized.on.the.ends.of.the.chain,.while.the.large.
energy.absorptions.that.dominate.the.large.chains.tend.to.localize.on.the.center.of.
the.chains..In.the.gold.chains,.these.three.transitions.are.at.much.lower.energy.than.
in.sodium.and.are.better.separated.
Previous. calculations. of. gold. and. silver. chains. were. performed. up. to. a. maxi-
mum.of.20.atoms.and.generally.possess.a.single.longitudinal.mode.whose.frequency.
depends.on.chain.length..This.dispersion.is.comparable.to.that.of.a.propagating.plas-
mon.in.a.1D.electron.gas.model..However,.as.the.size.increases,.other.absorptions.
appear. as. seen. in. the. present. methodology.. Also,. the. longitudinal. excitations. of. s .
symmetry.are.nearly.unaffected.by.the.5d.orbital.hybridization.as.the.interband.d-p.
transition.only.operates.in.transverse.excitations.of.π.symmetry.
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