Tight Binding Methods for Metallic Systems - Metallic Systems: A Quantum Chemist's Perspective - page 237

or.Troullier-Martins),.local.and.non-local.functionals,.double.numerical.basis.sets,.
linear-scaling.methods.for.evaluating.band.structure,.spin-polarized.functionals,.a.
time-dependent.method,.and.a.molecular.dynamics.methods.using.various.thermo-
stats,.thermodynamic.integration.techniques.and.umbrella.sampling.

8.3.3 d enSity f unctional t ight B inding m ethod
The.DFTB.method.[10].and.its.later.self-consistent.charge.extension.(SCC-DFTB).
[11].are.computationally.eficient.approximations.to.the.fully.self-consistent.Kohn-
Sham.DFT.theory.based.on.the.work.of.Harris-Foulkes..This.method.has.been.suc-
cessfully.applied.to.a.wide.range.of.problems.in.the.ield.of.biomolecules,.surfaces.
and.interfaces,.as.well.as.point.and.extended.defects.in.solid-state.systems.[34]..
The. SCC-DFTB. method. is. based. on. the. second-order. expansion. of. the. Kohn-
Sham. total.energy. in.DFT. with.respect. to.charge. density. luctuations. of. Equation.
8.14..The.zeroth-order.approach.is.equivalent.to.the.standard.non-self-consistent.TB.
scheme

∑ (

dk

∑

. (8.22)

E = E k ( ) + U i j ( , ),

DFTB j

3

2 π )

j i > j

.

BZ

where.the.irst.term.on.the.right-hand.side.is.the.band.energy.that.depends.on.the.
reference.system,.and.the.second.term.is.the.pairwise.repulsive.contribution.that.
depends.on.the.interatomic.separation.between.two.atoms..The.most.important.dif-
ference.from.AITB.is.that.the.repulsive.potential.is.it.to.reproduce.points.on.the.
potential.energy.surface.of.a.set.of.reference.systems..In.this.sense.DFTB.is.not.
strictly.a.irst.principles.method.like.AITB..However,.as.in.AITB.the.Hamiltonian.
and.overlap.matrices.are.evaluated.using.the.DFT.method..The.atomic.references,.
which. provide. the. non-self-consistent. density,. are. chosen. from. the. neutral,. spin-
unpolarized.atoms.conined.by.a.repulsive.potential..In.DFTB,.three.center.inte-
grals.are.neglected,.thus.the.method.is.effectively.a.two.center.TB..The.absence.
of. three. center. terms. simpliies. the. parameterization. considerably. compared. to.
AITB.
Besides.the.usual.band.structure.and.short-range.repulsive.terms,.the.inal.approx-
imate.Kohn-Sham.energy.term.includes.a.Coulomb.interaction.between.charge.luc-
tuations..At.large.distances.this.accounts.for.long-range.electrostatic.forces.between.
two.point.charges.and.approximately.includes.self-interaction.contributions.from.a.
given.atom,.if.the.charges.are.located.on.the.same.atom..Due.to.the.SCC.extension,.
DFTB.can.be.successfully.applied.to.problems.where.deiciencies.within.the.non-
SCC. standard. TB. approach. become. obvious,. such. as. those. mentioned. in. Section.
8.3.2.
In.the.last.few.years,.the.DFTB.method.has.been.heavily.extended.to.allow.the.
calculation. of. optical. and. excited. state. properties.. The. GW. formalism. as. well. as.
time-dependent. DFTB. has. been. implemented. [35-37].. Furthermore,. DFTB. has.
been.used.to.calculate.the.Hamiltonian.for.electron.transport.using.Green's.function.
techniques.[38].