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Point Symmetry Operations (Form "Groups" (Matrix Rep (Characters…
Point Symmetry Operations
Change nothing about the object
Form "Groups"
4 RULES
Identity
Invere
Closure
Associativity
Matrix Rep
correspond to each symmetry operator in group
Follow 4 rules under matrix multiplication
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square matrix
Need to form a basis
A set of objects that obey the symmetry operations IN THE group
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Functions
SYMMETRY ADAPTED FUNCTIONS
Linear combination of functions
Reduce Matrix Representation
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To Irreducible Rep
2 more items...
Vectors
Cartesian axes
Linear Combinations of cartesian disblacements
Normal modes of vibration
Reduce the matrix representation
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Etc
Infinite
Characters
Sum of diagonal elements
DOES not change under linear combination of basis functions
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Chatacter Tables
Tables corresponding to the point group
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Defines symmetric, antisymmetric and non-symmetric behavior of basis set