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Symmetry Translation Rotation Reflection Slide rotation (S n )

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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 orbital unchanged but the sign of a orbital is changed. In the language introduced in this lectture: The characters of the C 2 rotation are +1 and -1 for the and orbitals, respectively.

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In a group G={E,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 C 3 and C 3 -1 form a class of dimension 2

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In general Elements conjugated to v ?

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The p x,p y, and p z orbitals on the central atom of a C 2v molecule and the symmetry elements of the group.

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What you must learn from this lecture 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 1. You are not expected to derive any of the theorem of group theory. However, you are expected to use it as a tool 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 v.

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Typical symmetry -adapted linear combinations of orbitals in a C 3v molecule.

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