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SOLUTIONSMANUAL TO ACCOMPANY ATKINS' PHYSICAL CHEMISTRY 405
0 5 10 15 20 25 30
0.0
0.2
0.4
0.6
0.8
1.0
h0/m
T
ε = 200 mol−1 dm3 cm−1
ε = 100
ε = 50
ε = 25
Figure 11.15
v /cm−1~
h
0
 /m
Figure 11.16
product always includes the totally symmetric irreducible representation and it
is this symmetry species which needs to be combined with the anti-symmetric
spin function for two spin-paired electrons.
(a) Ethene belongs to the point group D2h: assume that the molecule lies
in the xy-plane, with the C–C bond along x. �e π bonding molecular
orbital transforms in the same way as the cartesian function z, that is as
B1u. �e π∗ anti-bonding molecular orbital transforms in the same way
as the cartesian function xz, that is as B2g. �e excited state (π)1 (π∗)1
therefore has symmetry B1u × B2g = B3u (the direct product is found by
multiplying together the characters of the two irreducible representations,
as described in Section 10C.1(a) on page 407).