Tight Binding Methods for Metallic Systems - Metallic Systems: A Quantum Chemist's Perspective - page 236

A. similar. expression. exists. for. the. non-diagonal. overlap. integrals.. A. total. of. 93.
(or.97).parameters.are.required.to.produce.the.irst.principles.database..Parameters.
for.the.NRL-TB.method.are.available.at.http://cst-www.nrl.navy.mil/bind/.and.the.
program.is.available.upon.request.from.its.authors.
In. Section. 8.4. we. explore. the. performance. of. this. methodology. for. the. global.
optimization.of.gold.clusters.and.propose.an.improvement.
8.3.2 A b I nItIo t ight B inding m ethod
We. begin. this. section. by. describing. the. formalism. of. Sankey. and. Niklewski. [8],.
following.the.variant.due.to.Horsield.[9],.and.in.Section.8.3.3.we.discuss.the.for-
malism.due.to.Frauenheim.et.al..[10,11]..In.contrast.with.the.NRL-TB.method,.these.
.methods.are.derived.from.the.Harris-Foulkes-Haydock.formalism.[5,6].
The. method. of. Sankey. and. Niklewski,. known. as. the. ab initio . TB. method.
(AITB),. is. simply. an. effort. to. implement. the. non-self-consistent. version. of. the.
Harris-Foulkes.functional.in.its.full.form..The.method.is.a.recipe.for.constructing.
an. input. charge,. evaluating. and. tabulating. the. Hamiltonian. and. overlap. elements.
(including.three.center.contributions),.and.calculating.the.repulsive.potential.from.
the.Coulombic.double.counting.terms.without.any.empirical.itting.(for.this.reason.
the. method. is. termed. ab initio ).. A. number. of. technical. details. make. this. method.
very.interesting.
Since.numerous.self-consistent.calculations.on.molecules.and.solids.have.shown.
that.the.electron.densities.in.these.structures.are.better.approximated.as.a.superposi-
tion.of.compressed.atomic.densities,.the.basis.set.and.the.charge.density.in.AITB.are.
calculated.from.orbitals.in.which.the.radial.function.is.conined.to.some.maximum.
radius..This.is.equivalent.to.conining.the.pseudo-atoms.in.an.ininite.square.well.
potential..Compression.of.the.pseudo-atoms.is.a.crucial.step.for.the.success.of.any.
DFT-based.TB..The.three.center.integrals.are.tabulated.as.a.function.of.three.vari-
ables:.the.bond.length,.the.distance.and.the.angle.between.the.bond.center.and.the.
site.on.which.the.potential.is.centered,.and.an.angle.
The. formalism. of. Horsield. [9]. is. an. extension. of. the. Sankey. and. Niklewki.
method.[8]..The.important.difference.is.the.calculation.of.the.pseudo-atomic.basis,.
and.the.way.in.which.the.exchange.and.correlation.integrals.are.handled..A.minimal.
basis.set.was.found.to.be.inadequate.for.accurate.descriptions.of.luorocarbons,.but.
a. double. numerical. basis. gives. better. agreement. with. DFT. calculations.. Thus. the.
orbitals.were.taken.from.the.neutral.atom.and.a.positive.ion.in.a.conined.potential.
of.the.form. r 6 ,.instead.of.an.iniinite.square.well..The.integrals.are.evaluated.in.real.
space.using.the.partition.function.[32,33],.in.contrast.with.the.method.of.Sankey.and.
Niklewki.in.which.the.integrals.are.evaluated.in.reciprocal.space..The.key.point.in.
this.approach.is.the.use.of.a.sub-linear.dependence.of.the.functional.on.the.charge.
densities,.rather.than.on.the.density.
This.method.has.been.applied.to.crystals.and.clusters.such.as.amorphous.silicon,.
silicon.clusters,.silicon.surfaces,.carbon.clusters,.and.a.number.of.semiconductor.sys-
tems.[34]..The.AITB.program.is.implemented.and.available.in.the.Fireball.suite.of.pro-
grams.by.the.Lewis.research.group.at.http://www.ireball-dft.org/web/ireballHome..
The. actual. implementation. includes:. norm-conserving. pseudopotentials. (Hamann.