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328 10MOLECULAR SYMMETRY
are the same as S1, and centres of inversion, which are the same as S2.�e table
in Section 10A.2(e) on page 393 shows that a molecule belonging to Th pos-
sesses S6, i, and σh symmetry elements, so such a molecule may not be chiral .
Similarly the table in Section 10A.2(e) on page 393 shows that a molecule be-
longing to Td possesses S4 and σd symmetry elements, so such a molecule
may not be chiral .
Solutions to problems
P10A.2 �emolecules are shown in Fig. 10.8 along with some of their key symmetry el-
ements. For clarity the sulfur atoms have been omitted and not all symmetry el-
ements are shown.�e point group of each species is determined using the �ow
diagram in Fig. 10A.7 on page 391. �en, as explained in Section 10A.3(a) on
page 394, molecules belonging to Cn , Cnv, or Cs may be polar while molecules
belonging to all other point groups are not.
F
F F
F
F
F
C4
i
C4C4
F
F F
F
Cl
F
C4
F
F F
F
Cl
Cl
C4
i
SF6 SF5Cl trans-SF4Cl2
Oh, not polar C4v, polar D4h, not polar
F
F Cl
Cl
F
F
C2
F
F Cl
Cl
Cl
F
C3
Cl
F Cl
Cl
F
F
C2
cis-SF4Cl2 fac-SF3Cl3 mer-SF3Cl3
C2v, polar C3v, polar C2v, polar
Figure 10.8
P10A.4 �ere are �ve distinct geometric isomers which are shown in Fig. 10.9 together
with their point groups and some of their symmetry elements. For clarity not
all symmetry elements are shown.
As explained in Section 10A.3(b) on page 395 a molecule is only chiral only if it
does not possess an Sn axis; this includes mirror planes σ , which are equivalent
to S1, and centres of inversion i, which are equivalent to S2. Of the �ve isomers
only the all-cis isomer, which possesses no symmetry elements apart from the
identity and therefore belongs to the point group C1, is chiral.