Environmental Engineering Reference
In-Depth Information
Fig. 1.5.
Radial wavefunctions for
α
-Ce metal, calculated by Skriver
from the self-consistent atomic-sphere potential, at the energies
C
nl
of the
centres of the associated bands. Since these wavefunctions are normalized
within the unit cell, the effective masses
µ
nl
are inversely proportional
to the value of
R
l
(
C
nl
,S
) at the Wigner-Seitz radius, and this probabil-
ity, and the consequent overlap between wavefunctions on neighbouring
sites, therefore determines the corresponding band width.
Augmenting these partial waves by suitably-chosen regular solutions
of Laplace's equation, we define the energy-dependent
mun-tin orbitals
⎧
⎨
R
l
(
ε, r
)+
p
l
(
ε
)(
r/S
)
l
;
r<S
χ
lm
(
ε,
r
)=
i
l
Y
lm
(
r
)
(1
.
3
.
3)
⎩
(
S/r
)
l
+1
;
r>S
,
which are continuous and differentiable if
p
l
(
ε
)=
D
l
(
ε
)+
l
+1
,
(1
.
3
.
4)
D
l
(
ε
)
− l
where the
logarithmic derivative
is
D
l
(
ε
)=
S
R
l
(
ε, S
)
R
l
(
ε, S
)
.
(1
.
3
.
5)
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