Chapter 4, Problem 4.21P

Ethylene has ${\text{D}}_{\text{2h}}$ symmetry.
a. List all the symmetry operations of ethylene.
b. Write a transformation matrix for each symmetry operation that describes the effect of thatoperation 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 ${\text{D}}_{\text{2h}}$ irreduciblerepresentations.
e. Show that your irreducible representations are mutually orthogonal.