Symmetry

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Symmetry
Reflection
Translation
Slide rotation (Sn)
Rotation
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Lecture 36 Character Tables The material in
this lecture covers the following in Atkins.
15 Molecular Symmetry
Character tables 15.4
Character tables and symmetry labels
(a) The structure of character tables
(b) Character tables and orbital
degeneracy (c) Characters and
operators Lecture on-line
Character Tables (PowerPoint)
Character tables (PDF) Handout for this lecture
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Audio-visuals on-line Symmetry (Great site on
symmetry in art and science by Margret J.
Geselbracht, Reed College , Portland Oregon)
The World of Escher  Wallpaper Groups  The 17
plane symmetry groups 3D Exercises in Point
Group Symmetry
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A rotation through 180 about the
internuclear axis leaves the sign
of a s orbital unchanged
but the sign of a p orbital is changed.
In the language introduced in this lectture
The characters of the C2 rotation are 1 and -1
for the s and p orbitals, respectively.
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In a group GE,A,B,C,..., we say that two
elements B and C are conjugate to each other if
ABA-1 C, for some element A in G.
An element and all its conjugates form a class.
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We have in general
Thus C3 and C3-1 form a class of dimension 2
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Elements conjugated to sv ?
In general
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The px,py, and pz orbitals on the central atom
of a C2v molecule and the symmetry elements of
the group.
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What you must learn from this lecture
1. You are not expected to derive any of the
theorem of group theory. However, you are
expected to use it as a tool
2.. You must understand the different parts of a
character table for a symmetry group (a) Name of
symmetry group (b)Classes of symmetry operators
(c) Names of irreducible symmetry
representations. (d) The irreducible characters
3. For simple cases you must be able to deduce
what irreducible representation a function or a
normal mode belongs to by the help of a
character table.
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Symmetry operations in the same class are
related to one another by the symmetry
operations of the group. Thus, the three mirror
planes shown here are related by threefold
rotations, and the two rotations shown here are
related by reflection in sv.
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Typical symmetry -adapted linear combinations
of orbitals in a C 3v molecule.