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Chemistry 416
Symmetry and the Interaction of Orbitals or States
All orbitals
and states
must have the symmetry of one of the
irreducible representations of the point group of the molecule.
This holds for all orbitals of the central atom (if there is
one), and for any symmetryadaptedlinear
combinations of orbitals (SALCs).
For two orbitals or two states to interact, they must have the
same symmetry (the same irreducible representation).
Any two orbitals or states that have the same symmetry will
likely interact and mix.
The overlap of two orbitals is given by
±
²
1

²
2
³
´
µµµ²
1
*
²
2
dx
dy
dz
The respresentation for [
²
1
¶
²
2
] is the representation of
²
1
times the
representation of
²
2
.
When we integrate over all space, the integrand
²
1
¶
²
2
must have a
1
symmetry or else the integral will be zero.
Here’s why:
What if the integrand didn’t have a
1
symmetry, and changed
sign about some mirror plane?
Then when we integrate over
all space, the result from one side of the mirror will cancel
the result on the other side.
For
²
1
¶
²
2
to be a
1
,
²
1
must have the same representation as
²
2
.
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View Full Document Chem416
Energies and Spectroscopies
3x10
8
10
Hz
cm
NMR
100 cm
1 Å
10
3x10
3x10
3x10
3x10
2
10
12
14
16
1
1
100
3x10
20
3x10
18
10
10
8
10
6
10
4
1 cm
0.1 mm
IR
1 micron
EPR
100 nm
0.01 Å
Vis
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