Tight Binding Methods for Metallic Systems - Metallic Systems: A Quantum Chemist's Perspective - page 243

2

DFT (PW92)
DFT (LDA)

NRL-TB
This work

1

0

-1

-2

1 2 3 4 5 6

Distance (Å)

FIGURE 8.1 Binding.energy.per.atom.as.a.function.of.atomic.distance.for.gold.dimer.

through.a.comparison.of.photoelectron.spectroscopy.(PES).data.with.calculated.den-
sities.of.states.[56].
In. order. to. compute. the. geometry. of. the. lowest. energy. neutral. gold. cluster.
(assumed.in.this.work.to.be.close.to.the.global.minimum),.we.make.use.of.the.basin.
paving.optimization.technique,.which.has.been.demonstrated.to.work.quite.well.in.
the. optimization. of. cluster. structures. [57].. The. method. is. based. on. the. combina-
tion.of.the.optimization.strategies.used.by.basin.hopping.[58].and.energy.landscape.
paving.[59].
The.global.minima.of.neutral.gold.cluster.structures.obtained.in.this.work.(with.
and.without.the.energy.correction.to.the.NRL-TB.Hamiltonian).are.shown.in.Figure.
8.2.. In. this. igure,. our. optimized. geometries. are. compared. with. results. obtained.
with.different.DFT.calculations.previously.reported.in.the.literature.[45,46,60,61]..In.
addition,.the.variation.of.the.binding.energy.per.atom.as.a.function.of.the.cluster.size.
for. all. global. minima. cluster. conigurations. found. by. our. perturbatively. corrected.
TB.model.is.presented.in.Figure.8.3.
The.results.in.Figure.8.1.show.that.the.uncorrected.NRL-TB.Hamiltonian.pre-
dicts.a.smaller.equilibrium.distance.and.a.larger.binding.energy.when.compared.to.
DFT.calculations,.even.with.LDA.results,.while.the.perturbatively.corrected.version.
of.the.same.TB.Hamiltonian.substantially.reduces.these.differences..This.illustrates.
the.importance.of.taking.the.on-site.population.luctuation.into.account.in.the.TB.
total.energy.calculation.
The.most.remarkable.of.the.results.depicted.in.Figure.8.2.is.that,.while.the.uncor-
rected. NRL-TB. Hamiltonian. predicts. planar. global. minima. up. to. n .=.20,. the. per-
turbatively.corrected.NRL-TB.Hamiltonian.shows.a.transition.between.a.2D.global.
minimum.to.the.3D.structure.at. n .=.12,.in.excellent.agreement.with.previous.DFT.
calculations.[55].
With. the. exception. of. Au 3 ,. Au 7 ,. and. Au 10 ,. the. global. minima. for. small. cluster.
sizes. ( n .<.12). predicted. by. the. uncorrected. NRL-TB. are. similar. the. global. min-
ima.predicted.by.the.corrected.one,.but.as.the.size.increases,.signiicant.structural.