gptheo1 - Chemistry 4610 Group Theory handout I Definition...

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1 Chemistry 4610 Group Theory handout I Definition of a Group: A set of elements G is said to form a group if in G there is defined an operation (called product and denoted by X) such that 1-for A, B elements of G, A X B is an element of G. In other words the product of A and B is also an element of G. (Rule of Closure). 2-for A, B and C elements of G such that A X (B X C) = (A X B) X C (Associative Rule) 3-There exists E, an element of G, such that A X E = E X A = A for all A in G. (Identity) 4-For every A, element of G there is exists an A -1 such that A X A -1 = A -1 X A (Inverse) These rules apply to group theory in general. In Chemistry the elements of a group are symmetry operations. Four Different Types of Symmetry Operations Proper Rotation- simple rotations about an axis passing through a molecule by an angle 2pi/n with designation C n . Reflection- reflection through a plane passing through the molecule. Designated by σ Inversion- reflection through a point in the molecule is called inversion and designated by i. Improper Rotation- the combination (in either order) rotation about an axis of 2pi/n and
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This note was uploaded on 12/17/2011 for the course CHM 4611/4610 taught by Professor Dr.r.lopezdelavega during the Fall '11 term at FIU.

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gptheo1 - Chemistry 4610 Group Theory handout I Definition...

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