Chemistry Reference
In-Depth Information
groups in a compound, so that bands observed here can be assigned to the C
O stretching
modes.
For example, the trigonal bipyramidal pentacarbonyl-iron complex [Fe(CO)
5
]shownin
Figure 5.10 belongs to the
D
3h
point group. The complex contains 11 atoms, and so a full
vibrational analysis would require 3
11 = 33 basis vectors. However, if we are only
interested in the C O bond stretching modes, then a suitable basis set would only require
the five C O bond vectors shown in Figure 5.10. The basis vectors have been drawn to the
side of the C
×
O bonds for clarity, but should be treated as lying directly along each bond.
O
b
1
C
b
4
O
b
2
C
b
3
Fe
C
O
C
O
C
b
5
O
Figure 5.10
The trigonal bipyramidal complex [Fe(CO)
5
], point group D
3h
. A suitable basis
for obtaining the irreducible representations of the carbonyl stretching modes is shown.
The set of total characters form a reducible representation which is summarized in the
first row of Table 5.7. These are obtained by considering an example operation from each
class in turn:
Tab l e 5 . 7
The reduction formula is applied to the basis
of five C O bonds in the
D
3h
complex [Fe(CO)
5
], shown
in Figure 5.10.
D
3h
E
2
C
3
3
C
2
σ
h
2
S
3
3
σ
v
h
=
12
521303
g
c
χ
(
C
)
C
n
i
A
1
5433094 2
A
2
54
χ
i
(
C
)
−
330
−
9
0
0
E
10
−
4
0
6
0
0
12
1
A
1
543
−
30
−
9
0
0
A
2
54
−
3
−
3092 1
E
10
−
4
0
−
6000 0
The identity operator, as always, leaves all basis vectors unchanged, and we simply
count the number in the basis to arrive at a character of 5.
The
C
3
axis contains the two basis vectors on the axial carbonyl ligands, and so these
remain in place after any
C
3
rotation. However, the equatorial ligands are moved by either
