課程名稱︰無機化學一
課程性質︰必修
課程教師︰林英智
開課學院：理學院
開課系所︰化學系
考試日期（年月日）︰104/12/02
考試時限（分鐘）：110分鐘
試題 :
Inorganic Chemistry - Midterm II
2015.12.2 Total score: 110 points in 2 pages
1. Give the point group of following molecules: NH3, BF3, CO2, H2O, CH4,
Fe(CO)5, CH2=C=CH2, C6H6 (benzene), (η5-C5H5)2Fe (staggered),
(η5-C5H5)2Fe (eclipse). (10 points)
2. List all symmetry operation of C3v, then derive the character table.
Find the irreducible representation of x, y, z, Rx, Ry, Rz, and xy, yz, zx.
(10 points)
3. For the electronic configuraion of carbon (2s)^2(2p)^2. Derive the term
symbols (spectroscopic terms). Find at least one wave equation for all
states (not all microstates). Hint use the orthogonal and normalization
relationship. (10 points)
4. How many stereoisomers are possible for a metal complex M(a)2bcde in
trigonal prism (三角錐), where a, b, c, d and e are five different
mono-dentate ligands. You should determine your result using the concept of
point groups. How many isomer are possible for six different ligands?
(10 points)
5. Explain the following terms in group theory: class, subgroup, orthoganility
theorem, similarity transform. (10 points)
6. Find the irreducible representation of all modes of molecular vibration for
BF3? Specify which of them are IR active and Raman active. (10 points)
7. (a) What is the point group of HI2Si-SiI2H, shown in the next page. List
all symmetry operations and construct the character table for this point
group. (b) Predict the number of IR- and Raman-active Si-I streching
vibrations. (10 points)
8. Apply the projection operator method to derive the group orbital SALCs for
three F atoms in BF3 on the basis of the irreducible represenations A1', E'
(for 2s orbitals) and A2" E" (for 2pz orbitals) (z axis is chosen to
perpendicular to the molecular plane). (10 points)
9. Describe and explain the different order of the energy levels for the
molecular orbitals for the homodiatonic molecules formed by elements
(Li-Ne) of the second period. Predict which are paramagnetic? (10 points)
10. (a) Use the term symbol to describe the ground state of the followed
molecules and molecular ions: H2, N2+, O2, B2, B2+.
(b) For the diatomic molecule B2* in a special excited state with the
electronic configuration (1π)1(1π*)1, namely, two electrons are in
different bonding and antibonding π orbitals, give appropriate term
symbols and check with the total number of microstates. (10 points)
11. (a) Consider a square pyramidal AB5 molecule. Using the C4v character
table below to determine all possible hybridization schemes for the
central atom A.
(b) Which of these would you expect to be most likely? (10 points)
D3h E 2C3 3C2 σh 2S3 3σv
A1' 1 1 1 1 1 1 x^2+y^2, z^2
A2' 1 1 -1 1 1 -1 Rz
E' 2 1 0 2 1 0 (x, y) (x^2-y^2, 2xy)
A1" 1 1 1 -1 -1 -1
A2" 1 1 -1 -1 -1 1 z
E" 2 -1 0 2 -1 0 (Rx, Ry) (xy, yz)
C4v E 2C4 C2 2σv 2σd
A1 1 1 1 1 1 z x^2+y^2, z^2
A2 1 1 1 -1 -1 Rz
B1 1 -1 1 -1 1 x^2-y^2
B2 1 -1 1 -1 1 xy
E 2 0 -2 0 0 (x, y) (Rx, Ry) (xz, yz)
A reminder for a C3 rotation along z axis: http://i.imgur.com/fT5rI7g.jpg