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10 Molecular symmetry
10A Shape and symmetry
Answers to discussion questions
D10A.2
symmetry operation symmetry element
identity, E the entire object
n-fold rotation n-fold axis of symmetry, Cn
re�ection mirror plane, σ
inversion centre of symmetry, i
n-fold improper rotation n-fold improper rotation axis, Sn
D10A.4 Amolecule may be chiral (optically active) only if it does not possess an axis of
improper rotation, Sn .
Solutions to exercises
E10A.1(b) From the table in Section 10A.2(c) on page 393 a molecule belonging to the
point group D3h, such as BF3 (Fig. 10.1), possesses
• the identity E
• a C3 axis perpendicular to the plane of themolecule and passing through
the boron atom
• three C2 axes , each passing through the boron and one of the �uorine
atoms
• a horizontal mirror mirror plane σh in the plane of the molecule
In addition
• the elementsC3 and σh jointly imply the presence of an S3 axis coincident
with the C3 axis
• the presence of the C3 axis and three C2 axes jointly imply the presence of
three vertical mirror planes σv , each containing the C3 axis and passing
through the boron and one of the �uorines