Lecture 34: Symmetry Elements

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Lecture 34 Symmetry Elements The material in
this lecture covers the following in Atkins. 15
Molecular Symmetry The symmetry elements
of objects 15.1 Operations and symmetry
elements 15.2 Symmetry classification of
molecules (a) The groups
C1,Ci, and Cs (b) The groups
Cn,Cnv, and Cnh (c) The
groups Dn,Dnh, and Dnd Lecture on-line
Symmetry Elements (PowerPoint)
Symmetry Elements (PDF) Handout
for this lecture
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Group Theory
Some of the symmetry elements of a cube. The
twofold, threefold, and fourfold axes are
labelled with the conventional symbols.
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(b) an H2O molecule has a twofold (C2) axis.
Both have other symmetry elements too.
(a) An NH3 molecule has a threefold (C3) axis
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Symmetry Operation
Inversion
Reflection
Rotation
noisrevnI
Reflection
or a line
a point
a plane
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Point Groups
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2. n-fold rotation
(b) an H2O molecule has a twofold (C2) axis.
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3. Reflection plane
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4. The inversion center
A regular octahedron has a centre of inversion
(i).
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The improper rotation axis
(a). A CH4 molecule has a fourfold improper
rotation axis (S4) the molecule is
indistinguishable after a 90 rotation followed
by a reflection across the horizontal plane,
but neither operation alone is a symmetry
operation.
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The improper rotation axis
(b) The staggered form of ethane has an S6 axis
composed of a 60 rotation followed by a
reflection.
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The presence of a twofold axis and a horizontal
mirror plane jointly imply the presence of a
centre of inversion in the molecule.
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A molecule with n twofold rotation axes
perpendicular to an n-fold rotation axis belongs
to the group Dn.
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A molecule with a Mirror plane perpendicular
to a Cn axis, and with n twofold axes in the
plane, belongs to the group Dnh.
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1. Given a molecule, you should be able to
identify the different symmetry elements
(Cn,sv,sh,sd,i,Sn, etc. )
2. Having identified the symmetry elements of a
molecule, you should be able to establish the
point group to which the molecule belong