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محتاجكم ضرورى
1. The transformation matrices for the C4v point group are shown below:
1 0 0 1 0 0 -1 0 0 0 1 0 0-1 0 0 1 0 0-1 0 -1 0 0
0 1 0 0–1 0 0 1 0 1 0 0 -1 0 0 -1 0 0 1 0 0 0-1 0
0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1
E 1 2 3 4 C4 C43 C2
Use these transformation matrices and the Great Orthogonality Theorem to derive a partial C4v character table (you should be able to give 2 irreducible representations and the dimensions of all irreducible representations). Clearly explain each step that you perform. Assume that 1 and 2 are in a class, 3 and 4 are in a class, and C4 and C43 are in a class. You MUST show your work to receive credit.
2. Use the appropriate character table to determine the symmetry species (irreducible
representation) for each of the following orbitals.
(a) dz2 (C5) (b) dx2-y2 (D4d) (c) s (D6d) (d) dz2 (Td)
3. What information does B2g give in the D4h character table?
4. Decompose the following reducible representation in the D3h point group.
E 2C3 3C2 h 2S3 3v
red 17 -1 -1 -3 9 -1
5. For the species in problem #1 of Problem set #4,
(a) List which species are chiral
(b) List which species have a dipole moment
6. Determine the irreducible representation to which the fxyz orbital belongs in the C4v point
group.
7. Consider a trigonal prismatic AX6 molecule having D3h symmetry (see below). With s, p, and
d orbitals available, what hybridization schemes are possible for the A atom? HINT:
perform the symmetry operations on the sigma bonds.
8. How many IR CO stretching bands does the trans- Fe(CO)4Cl2 have? (HINT: D4h point
group)
9. For the tetrahedral (Td) sulfate ion, SO42-, answer the following questions. The reducible
representation of SO42- using the cartesian coordinate system at each atom as a basis set is:
E 8C3 3C2 6S4 6d
xyz 15 0 -1 -1 3
(a) Give the irreducible representations of all vibrational modes that would be IR active.
(b) Give the irreducible representations of all vibrational modes that would be Raman
active.
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