Chemistry Reference
In-Depth Information
TABLE 8.1
Five Lowest Excitation Energies (in eV) for Gold Dimer at a Distance
of 2.55 Å
Expt. (a)
This Work
TDDFT/LDA (b)
TDDFT/PW91 (c)
TDDFT/B3LYP (d)
2.44
2.40
2.39
2.47
2.79
3.18
2.69
2.70
2.82
2.93
3.91
3.60
3.70
3.87
3.20
5.95
5.20
5.49
5.28
5.50
6.26
6.01
6.14
5.74
5.80
(a).
Klotzbuecher,.W.E..and.Ozin,.G.A.,.
Inorg. Chem
.,.19,.3767,.1980;.Idrobo,.J.C..et.al.,.
Phys.
Rev. B
.,.76,.205422,.2007..(b).Wang,.X.J..et.al.,.
J. Mol. Struct
..(
THEOCHEM
),.9,.221,.2002..
(c).Lian,.K.Y..et.al.,.
J. Chem. Phys
.,.30,.174701,.2009..(d).Datta,.S.,.
Superlatt. Microstruct
.,.
28,.253,.2000.
the.atomic.length..The.strength.of.these.two.modes.indicates.that.they.are.collective.
in.character;.however,.there.are.no.experimental.measurements.available.for.these.
resonances.
To.assess.the.quality.of.the.methodology,.in.Table.8.1.we.present.the.ive.lowest.
excitation. energies. in. the. gold. dimer. and. compare. them. with. experimental. values.
[71,72]. and. TDDFT. calculations. at. various. levels. of. theory:. TDDFT/PW91. [73],.
TDDFT/B3LYP. [74],. and. TDDFT/LDA. [75].. The. bond. distance. in. these. calcula-
tions.was.ixed.at.2.55.Å..In.all.cases.the.computed.values.are.lower.than.the.experi-
mental.ones..The.LDA.results.are.closer.to.experimental.values.than.the.B3LYP.and.
PW91.TDDFT.results,.with.an.average.error.of.6.3%..The.differences.are.6.6%.for.
PW91.and.11%.for.B3LYP.
In. order. to. cover. the. experimentally. interesting. excitation. modes,. we. compute.
the.excitation.energies.up.to.7.eV.for.gold.chains.between.2.and.50.atoms..Even.with.
the.present.approximations,.as.the.chain.length.increases,.one.has.to.include.more.
and.more.occupied.and.virtual.Kohn-Sham.states.to.cover.the.desired.energy.range..
For.50.gold.atoms,.at.least.500.occupied.and.2000.virtual.orbitals.are.necessary.to.
cover.an.energy.window.of.7.eV..Of.course.this.requires.an.amount.of.computational.
power.that.is.prohibitive.for.large.systems.
The.computed.excitation.energies.and.dipole.strengths.for.gold.chains.of.2-50.
atoms.are.shown.in.Figure.8.5..The.chains.studied.have.a.ixed.internuclear.separa-
tion.of.2.89.Å.as.used.in.Ref..[16].for.TDDFT.calculations..For.the.gold.dimer.at.the.
same.separation.two.comparable.peaks.occur.at.2.34.and.4.91.eV,.with.the.second.
peak.at.twice.the.strength.of.the.irst..Even.if.the.spectra.become.more.complex.as.
the.number.of.atoms.increases,.at.energies.of.less.than.7.eV,.as.in.the sodium.chain,.
two.main.peaks.are.clearly.seen..In.all.cases.these.peaks.correspond.to.σ(6s).→.σ*.
(6p).transitions,.with.a.small.mixing.with.5d(σ).orbitals..These.two.peaks.are,.in.
most. cases,. two. times. stronger. than. other. 5d,. or. π.→.π*. transitions.. The. smaller.
.absorption has.a.maximum.strength.at.16.gold.atoms.and.decreases.quickly.with.
increasing. chain. length.. As. the. length. of. the. chain. increases,. the. spectrum. at.
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