Chemistry Reference
In-Depth Information
Figure 1.1
Example of spatially localized functions defined in the text.
Spatially localized functions are an extremely useful framework for thinking
about the quantum chemistry of isolated molecules because the wave functions
of isolated molecules really do decay to zero far away from the molecule.
But what if we are interested in a bulk material such as the atoms in solid
silicon or the atoms beneath the surface of a metal catalyst? We could still
use spatially localized functions to describe each atom and add up these func-
tions to describe the overall material, but this is certainly not the only way for-
ward. A useful alternative is to use periodic functions to describe the wave
functions or electron densities. Figure 1.2 shows a simple example of this
idea by plotting
f
(
x
)
¼ f
1
(
x
)
þ f
2
(
x
)
þ f
3
(
x
),
,
f
1
(
x
)
¼
sin
2
px
4
where
,
3
cos
2
px
1
f
2
(
x
)
¼
2
10
sin
2
(
px
)
1
f
3
(
x
)
¼
:
The resulting function is periodic; that is
f
(
x þ
4
n
)
¼ f
(
x
),
