Tight Binding Methods for Metallic Systems - Metallic Systems: A Quantum Chemist's Perspective - page 245

The.binding.energy.per.atom.ploted.in.Figure.8.3.exhibits.oscillations.between.
even. and. odd. neutral. clusters,. and. the. oscillation. amplitudes. are. larger. at. smaller.
sizes,.in.qualitative.agreement.with.DFT.calculations.[55].
It. is. particularly. gratifying. to. observe. that. our. TB. model. also. reproduces. the.
ground.state.tetrahedral.structure.of.Au 20 ,.experimentally.determined.by.vibrational.
spectroscopy.[62]..The.tetrahedral.structure.corresponds.to.a.fragment.of.the.FCC.
structure.of.bulk.gold,.which.consists.only.of.surface.atoms.and.does.not.contain.any.
inner.atoms,.a.inding.that.also.agrees.with.DFT.calculations.[63].
The.results.discussed.in.this.work.show.that.including.the.on-site.orbital.popu-
lation. luctuation. in. the. total. energy. recovers. electronic. structure. effects. that. are.
important.for.the.proper.prediction.of.the.energetics.and.structural.properties.of.gold.
nanoclusters..This.constitutes.an.improvement.over.other.TB.parameterizations.and.
classical.empirical.potentials.that.fail.to.predict.the.correct.structures.and.relative.
energetics. of. gold. clusters,. despite. the. explicit. inclusion. of. the. structures. of. some.
clusters.in.the.parameterization.of.these.methods..The.perturbatively.corrected.TB.
model.introduced.in.this.work.is.particularly.important.in.the.case.of.homonuclear.
clusters,.where.charge-transfer.between.atoms.in.the.system.is.not.signiicant..For.
heteronuclear.systems,.charge-transfer.may.play.a.dominant.role.in.the.energy..But.
even.in.a.situation.of.strong.charge-transfer.interactions,.the.luctuation.of.the.on-
site.atomic.orbital.distribution.could.still.determine.the.global..minimum.as.long.as.
atomic.orbital.hybridizations.are.relevant.
8.5.2 o Ptical S Pectra
Metallic. nanoparticles. possess. unique. optical,. electronic,. chemical,. and. magnetic.
properties. that. are. strikingly. different. from. those. of. individual. atoms. as. well. as.
from. their. bulk. counterparts. [44].. Colloidal. solutions. of. noble. metals. like. silver.
and. gold. show. characteristic. colors. that. have. received. considerable. attention. [64]..
Gold.nanoparticles.have.attracted.considerable.attention.because.of.their.potential.
technological.applications..Much.interest.has.been.given.to.plasmon.resonances.of.
suspensions.of.quasi-spherical.gold.nanoparticles,.which.usually.have.a.violet.color..
However,.when.individual.gold.nanoparticles.come.into.close.proximity,.the.color.
changes.to.blue.[44]..The.change.in.color.that.follows.gold.nanoparticle.aggregation.
has.found.many.applications..These.systems.are.usually.studied.using.classical.Mie.
theory.. This. theory. has. traditionally. been. developed. for. calculation. of. the. extinc-
tion.spectra.of.single.particles.of.highly.symmetric.shapes..In.reality,.a.suspension.
of.particles.often.has.a.much.more.complex.structure..Also,.when.the.interparticle.
distance.is.very.small,.the.classical.theory.breaks.down.
Many. theoretical. methodologies. to. perform. frequency. domain. calculations. in.
the. context. of. DFT. have. been. suggested. in. the. literature.. All. of. these. have. their.
merits. and. shortcomings. [65].. If. the. SC-EHTB. method. described. in. the. previous.
section.is.interpreted.as.an.approximation.to.the.Kohn-Sham.energy,.then.the.use.
of. the. TB. approximation. in. conjunction. with. time-dependent. DFT. (TDDFT). is.
justiiable.for.the.calculation.of.excitation.energies.[66]..In.particular,.an.approach.
within.the.linear.response.TDDFT.(LR-TDDFT).has.been.developed.in.the.context.
of.SC-EHTB.[16].and.SC-DFTB.[35]..The.TB.approach.to.the.LR-TDDFT.is.based.