推 lancer1668 :傳說中的第10題呢XD? 06/27 02:40
課程名稱︰化學鍵
課程性質︰化學系選修
課程教師︰王瑜
開課學院：理學院
開課系所︰化學系
考試日期（年月日）︰2009.06.19
考試時限（分鐘）：13:20~15:10，110分鐘
是否需發放獎勵金：是
試題 :
1. Give the point group for each of the following molecules: PCl3; Co(en)3 2+;
C6H6; B(OH)3; 1,3-dichlorobenzene; Fe(C5H5)2 (ferrocene); trans- and cis-
Mo(CO)4Cl2; CH2O (formaldehyde)
2. Indicate all the symmetry elements of C3v and D4h.
3. Work out the irriducible representations of C-C σ- and π- bonds of
cyclobutadiene (C4H4) in D4h.
4. What are the respective irriducible representations of C-H; C-Cl bonds in
chloroform CHCl3?
5. Which irriducible representation does the following vibration modes of
water belongs to?
Ｏ Ｏ Ｏ
／ ＼ ／ ＼ ↗ ＼
／↘ ↙＼ ↙ ↘ ／ ↘
Ｈ Ｈ Ｈ Ｈ Ｈ Ｈ
bending sym. stretching asym. stretching
6. Show the crystal field splittings of s, p and d-orbitals in Oh; D4h; C3v;
C2v.
7. Compare the crystal field stabilization energies (CFSE in Dq) for metal d-
orbitals between high spin and low spin configurations for Mn2+ (d5); Fe2+
(d6); Co2+ (d7); Ni2+ (d8) in Oh. Which ones are likely to have Jahn-Teller
distortion?
8. Fe(CN)6 4- belongs to Oh; illustrate the d(t2g)-π* back bonding of
NC-Fe-CN, what effect will such bonding do to Fe-C and C-N bonds? Explain
why this back bonding will give strong bond.
9. How many bonds can d-d orbitals form in a M2 species? Illustrate each bond.
C2v│ E C2 σv(xz) σv'(yz)│ │
──┼──────────────┼───┼──────
A1 │ 1 1 1 1 │ z │x2, y2, z2
A2 │ 1 1 -1 -1 │ Rx │xy
B1 │ 1 -1 1 -1 │x, Ry │xz
B2 │ 1 -1 -1 1 │y, Rx │yz
C3v│ E 2C3 3σv │ │
──┼─────────┼───────┼─────────
A1 │ 1 1 1 │ z │ x2+y2, z2
A2 │ 1 1 -1 │ Rz │
E │ 2 -1 0 │(x,y) (Rx,Ry) │(x2-y2,xy) (xz,yz)
(C4^2)
D4h│E 8C3 6C2 6C4 3C2 i 6S4 8S6 3σh6σd │ │
──┼────────────────────┼────┼─────
A1g│1 1 1 1 1 1 1 1 1 1 │ │x2+y2, z2
A2g│1 1 1 -1 -1 1 1 1 -1 -1 │ Rz │
B1g│1 -1 1 1 -1 1 -1 1 1 -1 │ │ x2-y2
B2g│1 -1 1 -1 1 1 -1 1 -1 1 │ │ xy
Eg│2 0 -2 0 0 2 0 -2 0 0 │(Rx,Ry) │ (xz,yz)
A1u│1 1 1 1 1 -1 -1 -1 -1 -1 │ │
A2u│1 1 1 -1 -1 -1 -1 -1 1 1 │ z │
B1u│1 -1 1 1 -1 -1 1 -1 -1 1 │ │
B2u│1 -1 1 -1 1 -1 1 -1 1 -1 │ │
Eu│2 0 -2 0 0 -2 0 2 0 0 │ (x,y) │
(C4^2)
Oh│E 8C3 6C2 6C4 3C2 i 6S4 8S6 3σh6σd │
──┼────────────────────┼─────┼──────
A1g│1 1 1 1 1 1 1 1 1 1 │ │x2+y2+z2
A2g│1 1 -1 -1 1 1 -1 1 1 -1 │ │
Eg│2 -1 0 0 2 2 0 -1 2 0 │ │(2z2-x2-y2,x2-y2)
T1g│3 0 -1 1 -1 3 1 0 -1 -1 │(Rx,Ry,Rz)│
T2g│3 0 1 -1 -1 3 -1 0 -1 1 │ │(xy,yz,zx)
A1u│1 1 1 1 1 -1 -1 -1 -1 -1 │ │
A2u│1 1 -1 -1 1 -1 1 -1 -1 1 │ │
Eu│2 -1 0 0 2 -2 0 1 -2 0 │ │
T1u│3 0 -1 1 -1 -3 -1 0 1 1 │(x,y,z) │
T2u│3 0 1 -1 -1 -3 1 0 1 -1 │ │
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