Ethylene has D2h symmetry.
a. List all the symmetry operations of ethylene.
b. Write a transformation matrix for each symmetry operation that describes the effect of that operation on the coordinates of a point x, y, z.
c. Using the characters of your transformation matrices, obtain a reducible representation.
d. Using the diagonal elements of your matrices, obtain three of the D2h irreducible representations.
e. Show that your irreducible representations are mutually orthogonal.
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