Environmental Engineering Reference
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where w denotes the width of the band and 1
c
its center. We consider two such bands: a
wide sp-band centered at the Fermi level for simplicity and a narrow d-band of arbi-
trary width w
d
and center 1
c
, and assume that each band couples to a reactant level with
a certain constant: D
sp
for the sp-band and D
d
for the d-band. Thus, we obtain for the
chemisorption function D,
"
#
1
=
2
2
1
w
0
u(w
0
1
2
)
D(1)
¼
D
sp
1
"
#
1
=
2
2
1
1
c
w
d
u[w
d
(1
1
c
)
2
]
þ
D
d
1
(2
:
17)
For the explicit calculations presented below, we have chosen a width w
0
¼
10 eV for
the sp-band, and a coupling strength D
sp
¼
0
:
2 eV, and have varied the parameters for
the d-band. The level shift L(1) is obtained from the second part of (2.7). The resulting
functions are illustrated in Fig. 2.12.
Figure 2.13 shows the effect that a d-band has on the density of states of a level
positioned at its center. When the interaction is weak, the level is just broadened.
However, when the interaction is strong, the level is split into a bonding orbital
(with respect to the metal) and an antibonding orbital, which lie below and above
the d-band, respectively. The same effects can be observed when the level lies orig-
inally above or below the d-band (Fig. 2.14). For a weak interaction, the level just
Figure 2.12
Chemisorption functions for the model metal band structure.
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