Chemistry Reference
In-Depth Information
We. have. chosen. to. organize. the. chapter. in. a. way. that. should. put. the. proper-
ties. front. and. center.. Following. the. next. section,. which. will. deine. and. describe.
succinctly. the. methodologies. and. software. of. interest,. the. following. sections. are.
each.devoted.to.a.particular.property,.in.rough.order.of.dificulty..For.each,.we.will.
attempt.to.give.a.sense.of.the.main.hurdles.that.had.to.be.overcome.in.previous.work,.
examples.of.leading-edge.research.in.the.current.time.frame,.and.a.sense.of.what.is.
needed.to.extend.the.horizons.even.further.in.the.future.
9.2 
METHODOLOGY
9.2.1  B aSic  dft
By.now,.DFT.is.familiar.to.the.vast.majority.of.theoretical.and.computational.chem-
ists.and.is.used.by.many.hundreds.of.researchers.everyday..Many.good.monographs.
and.review.articles.may.be.consulted.[1-7]..We.will.limit.ourselves.here.to.a.brief.
overview.of.the.foundations.of.DFT.and.to.some.of.the.options.available.for.convert-
ing.the.formalism.into.practical.methodologies.and.computer.codes.
The.cornerstone.paper.of.DFT.comes.from.1964.with.the.proof.by.Hohenberg.and.
Kohn.[8].that.the.energy.of.a.nondegenerate.ground.state.is.entirely.ixed.by.the.elec-
tron.density..To.elaborate.this.proof,.we.assume.that.two.different.external.potentials.
v ( r ). and. v ′( r ). can. be. generated. from. the. same. nondegenerate. ground-state. density.
ρ( r ),.which.determines.the.number.of.electrons.in.the.system.by.simple.quadrature..
As.a.consequence,.two.different.Hamiltonians. H ˆ .and. H ˆ. ′.with.different.eigenfunc-
tions. Ψ  and. Ψ′. would. exist,. where. Ψ. and. Ψ′. would. yield. the. same. density. ρ( r )..
Taking.Ψ′.as.a.trial.function.for. H ˆ ,.we.obtain
ˆ
ˆ
ˆ
ˆ
E
<
Ψ
ʹ
|
H
Ψ
ʹ =
Ψ
ʹ
|
H
ʹ
Ψ
ʹ +
Ψ
ʹ
|
H H
−
ʹ
Ψ
ʹ
0
∫
= ʹ +
E
ρ r
( )[ ( )
v
r
− ʹ
v
( )]
r
d
r
.
.
(9.1)
0
.
On.the.other.hand,.taking.Ψ.as.a.trial.for. H ˆ ′.yields
ˆ
ˆ
ˆ
ˆ
ʹ <
E
Ψ
|
H
ʹ
Ψ
=
Ψ
|
H
Ψ
+
Ψ
|
H
ʹ
−
H
Ψ
0
∫
=
E
+
ρ
( )[
r
v
ʹ
( )
r
−
v
( )]
r
d
r
0
∫
=
E
−
ρ
( )[
r v
( )
r
− ʹ
v
( )]
r
d
r
.
.
(9.2)
0
.
Adding.(9.1).and.(9.2).yields.the.contradiction
+ ʹ < ʹ +
E
E
E
E
. .
(9.3)
.
0
0
0
0
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