Chemistry Reference
In-Depth Information
KS-DFT Choices
E
XC
,
V
XC
= δ
E
XC
/δφ
• Gaussians
• Slaters
• Numerical functions
• Plane waves
• APW etc.
• Exact
• Fitting
• Multipoles
• PP
• ECP
• MCP
⎛
⎜
1
2
⎞
⎟
ϕ
(
)
2
KS
KS KS
− ∇
+
V
+
V
+
V
=
ε
ϕ
C
XC
PP
i
i
i
• L(S)DA
• GGA
• Hybrid
• AC
• LAP, TAU
(meta-GGA)
• OEP
FIGURE 9.1
Kohn-Sham.equations.and,.symbolically,.some.of.the.technical.options.that.
may.be.introduced.
δ ρ
δρ
J
[ ( )]
( )
r
r
δ
E
[ ( )]
( )
ρ
r
XC
v
[ ( )]
ρ
r
=
v r
( )
+
+
.
(9.9)
s
δρ
r
.
.
The.orbital.approach.to.DFT.is.the.workhorse.of.the.myriad.applications.of.DFT,.
from.condensed.matter.physics.to.chemistry,.materials.science,.biology,.and.other.
ields..Figure.9.1.gives.a.symbolic.overview.of.different.implementation.options.for.
the.Kohn-Sham.method..Even.though.it.represents.an.independent.particle.approach,.
and. the. equations. are. still. exact,. the. dificulty. lies. in. inding. good. approximate.
exchange-correlation.functionals.and.the.corresponding.functional.derivatives,.the.
exchange-correlation.potentials.
As.we.will.see.in.the.following.sections,.great.progress.has.been.made.in.inding.
eficient. and. accurate. algorithms. for. solving. the. KS. equations. and. implementing.
them.in.user-friendly.software.suites..DFT.has.become.a.major.part.of.mainstream.
quantum.chemistry,.and.this.was.relected.in.the.awarding.of.the.1998.Nobel.Prize.in.
Chemistry.to.Walter.Kohn.along.with.John.Pople,.relecting.the.need.for.both.solid.
foundations.and.software.that.is.accessible.to.essentially.all.practicing.chemists.(and.
also.physicists,.biologists,.materials.scientists,.etc.).
9.2.2 x
α
S
cattered
-W
ave
m
ethod
The.earliest.applications.of.DFT.to.molecular.systems,.including.metal.clusters,.were.
performed.in.the.1970s,.not.within.the.formal.DFT.framework.but,.rather,.within.a.
parallel.line.of.research.that.originated.in.solid-state.physics,.notably.in.the.school.
of. John. C.. Slater.. As. early. as. 1951,. Slater. [10]. had. formulated. an. “approximate.
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