Chemistry Reference
In-Depth Information
The.DFTB.code.is.available.from.its.authors.at.http://www.dftb-plus.info/.and.is.
maintained.by.the.Bremen.Center.for.Computational.Materials.Science..The.DFTB.
methodology. is. also. included. in. some. popular. electronic. structure. codes. such. as.
Gaussian.(http://www.gaussian.com/).and.molecular.modeling.codes.such.as.Amber.
(http://www.ambermal.org/).. A. number. of. parameters. are. available. at. http://www.
dftb.org/,.including.parameters.for.bio.and.organic.molecules,.solids.and.surfaces,.
organic-inorganic. hybrid. systems,. chalcogenide. glasses,. transition. metals. in. bio-
logical.systems,.rare.earths,.and.zinc.oxide.with.organic.molecules.
8.4 SELF-CONSISTENT EXTENDED HUCKEL TIGHT BINDING
The.self-consistent.extended.Huckel.tight.binding.(SC-EHTB).method.is.an.approxi-
mation. to. the. second-order. expansion. of. the. Kohn-Sham. DFT. total. energy. of.
Equation. 8.14.. Here,. we. consider. only. closed. shell. systems;. however,. extension. to.
the.open.shell.case.is.straightforward.
To. derive. the. EHTB. formalism,. the. Kohn-Sham. orbitals. are. expanded. into. a.
basis. of. Slater-type. orbitals,
.
ψ
=
∑
.
.
The. elements. of. the. Kohn-Sham
.
Hamiltonian.are.calculated.using.the.EH.approximations.[12]:.the.diagonal.elements.
are.taken.as.the.valence.state.ionization.energies.(VSIE).and.the.off-diagonal.ele-
ments.are.calculated.using.the.Wolfsberg-Helmholtz.formula,
C
φ
i
μ
i
μ
μ
1
2
(
)
∫
ˆ
ˆ
ˆ
ˆ
.
(8.23)
0
0
0
0
H
=
φ
H dr
φ
=
K
H
+
H S
,
μ
v
μ
v
EH
μμ
vv
μ
v
.
where
S
μ
v
.is.the.overlap.integral.over.the.atomic.basis.set.and.the.Wolfsberg-Helmholtz.
constant
K
EH
.is.evaluated.as.the.weighted.distance.expression.of.Calzaferri.and.Kamber.
[39].and.Calzaferri.and.Rytz.[40]
Turning.now.to.the.second.term.of.Equation.8.14.within.the.frame.of.the.basis.expan-
sion.employed.here,.the.density.luctuation.δρ.is.given.by
∑
∑
*
( )
δρ
( )
r
=
δ
P
φ
r
φ
( ),
r
.
(8.24)
μ
v
μ
v
μ
v
.
where
∑
2
0
0
δ
μ
P
=
(
C C
−
C C
).
.
(8.25)
v
μ
i
vi
μ
i
vi
.
i
δρ.(Equation.8.24).is.decomposed.into.atom-centered.expansion.by.employing.the.
following.approximation,
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