Tight Binding Methods for Metallic Systems - Metallic Systems: A Quantum Chemist's Perspective - page 234

Stated. in. this. way,. non-self-consistent. calculations. are. limited. to. problems.
in. which. δ n . is. small.. However,. for. many. important. problems. the. last. term. is. not.
negligible..For.example,.in.systems.with.strong.charge.transfer.between.atoms.it.is.
hard.to.imagine.that.a.summation.of.atomic-like.densities.is.a.good.approximation..
Another.example.is.the.spin.polarized.case.that.frequently.occurs.in.metallic.sys-
tems.in.which.it.is.crucial.to.consider.the.inclusion.of.changes.to.the.density.via.a.
self-consistent.procedure..To.this.end,.a.number.of.self-consistent.TB.schemes.have.
been.proposed.in.the.literature.[11,30].

8.3 MODERN TIGHT BINDING
Modern.TB.methodologies.are.based.on.DFT..In.this.section,.we.take.a.tour.of.three.
of.the.most.cited.methods:.the.NRL.total.energy.TB.method.[7],.the.AITB.method.
[8,9],.and.the.DFTB.method.[10,11]..A.comparison.of.these.methods,.using.the.case.
of.gold.clusters,.is.given.in.a.subsequent.section..However,.it.is.important.to.note.that.
the.method.which.is.most.appropriate.will.depend.strongly.on.the.particular.appli-
cation.and.the.particular.system..We.emphasize.in.each.case.the.connection.of.the.
method. with. the. Harris-Foulkes-Haydock. [5,6]. methodology. exposed. in. Section.
8.2.2.

8.3.1 nrl t ight B inding t otal e nergy m ethod
In. this. section. we. will. concentrate. on. the. TB. method. developed. at. the. NRL. by.
Cohen,.Mehl,.and.Papaconstantopoulos.[7,28,31]..Even.though.the.NRL-TB.method.
is.not.a.direct.descendant.of.the.Harris-Foulkes-Haydock.method,.but.is.more.“clas-
sical”.in.nature,.the.methodology.is.based.on.the.Kohn-Sham.DFT.formulation,.and.
for.this.reason.it.is.presented.in.this.section.
In. the. Kohn-Sham. DFT. method. the. total. energy. is. given. by. Equation. 8.10.. It.
was.shown.above.that.this.equation.is.closely.related.to.the.TB.formulation..Note.
that.the.repulsion.potential.of.TB.methods.is.related.to.the.double.counting.of.the.
Hartree. potential,. the. exchange-correlation,. and. the. ion-ion. repulsion.. The. value.
of. the. repulsion. potential. depends. upon. the. choice. of. the. zero. of. energy. for. the.
Kohn-Sham.potential,.which.is.arbitrary..In.general,.the.zero.of.energy.is.chosen.to.
coincide.with.the.Fermi.level.energy..In.the.formulation.of.the.NRL-TB.methodol-
ogy.the.Kohn-Sham.potential.is.shifted.by.an.amount.equal.to

[ ] , . n

N

(8.16)

V

0 =

E

REP

.

e

where
E REP .is.the.repulsion.potential
N e .is.the.number.of.electrons.in.the.unit.cell

Since. this. shift. is. applied. to. the. Kohn-Sham. eigenvalues,. the. total. energy. of. the.
system.becomes