CHEMISTRY 163, PROBLEM SET I
1) a) Find all the symmetry operations for cyclobutane which has a puckered conformation. You may wish to view the three-dimensional structure of the molecule using a chemical browser such as Chime. Three static images-A, B, and C-are also available.
b) Select any symmetry operation, X, other than the identity operation and demonstrate closure. That is, show that the product of X with every symmetry operation (including itself) generates another symmetry operation.
c) Determine the order of the group formed by the symmetry operations for cyclobutane.
d) Find at least one subgroup with an order great than two and demonstrate that the operations in this set do form a subgroup. Does the order of the subgroup have an allowed value? Explain.
e) Arrange the symmetry operations of cyclobutane into classes.
2) a) Derive the 3 x 3 matrices that express the transformations of the point (x,y,z) for the 12 operations of the point group D3h. (Hint: use the relations on pp. 33-34 of Cotton and the general relation between operators in the same class as a guide to obtain some of the matrices.)
b) Take the product of the matrix for C3 with the matrices for the following operations:
s h, S35, C2, and C32. Demonstrate that each product is a member of the group.3) a) Derive the character table for the group D3h.
b) Obtain the irreducible representation for the function z.
c) Obtain the characters for the nuclear motions of BF3 and reduce them to the irreducible representations. (Hint:
c (C3) = 0 and c (S3) = -2.)ps1_2002.htm, 15 Jan. 2002
