作者firepeter (碰碰碰碰碰)
看板NTU-Exam
标题[试题] 99下 陈振中 化学数学二 期末考
时间Wed Jun 22 16:20:26 2011
课程名称︰化学数学二
课程性质︰化学系选修
课程教师︰陈振中
开课学院:理学院
开课系所︰化学系
考试日期(年月日)︰2011/6/22
考试时限(分钟):120min
是否需发放奖励金:是
试题 :
Mathematics for Chemistry(II) Final Exam 2011.6.22
Section A (70%)
1.(12%) Write down the characters of the representations of the following direct
products, and determine the irreducible representations which comprise them for
group D4h:
A1u x A1u A1g x B1g B2u x Eg Eg x Eu
2.(20%) Consider the group C3v. Let the C3 axis coincide with the z-axis. Write
out the complete matrices for all irreducible representations for this group.
Derive from these the character table.
3.(16%) Derive the following character table and determine the irreps
transformed by the five d-orbitals.
Character table for D3h group
──────────────────────────────────────
| | E |2C3 |3C2'|σh |2S3 |3σv|linear, rotations | quadratic |
──────────────────────────────────────
|A1'| | | | | | | | |
──────────────────────────────────────
|A2'| | | | | | | Rz | |
──────────────────────────────────────
|E' | | | | | | | (x.y) | |
──────────────────────────────────────
|A1"| | | | | | | | |
──────────────────────────────────────
|A2"| | | | | | | z | |
──────────────────────────────────────
|E" | | | | | | | (Rx,Ry) | |
──────────────────────────────────────
4.(22%) Suppose we have a planar molecule as shown below
p1 p2
=======
| |
←── p3|=====|p4 ● z
x | |
=======
p5 p6
|
|y
↓
(a) Using the Huckel MO approximation, determine the MOs of the symmetry B1u
and their energies.
(b) Some of the Huckel molecular orbitals are schematically illustrated, where
positive and negative coefficients of the orbitals are represented by unshaded
and shaded circles, respectively. Note that only the upper lobes of the p
orbitals are shown.
‧=====‧ ●=====● 。=====‧ ‧=====‧ ○=====● 。=====‧
| | | | | | | | | | | |
●=====● |=====| ○=====● ○=====○ |=====| ●=====○
| | | | | | | | | | | |
‧=====‧ ○=====○ 。=====‧ ‧=====‧ ●=====○ 。=====‧
ψ1 ψ2 ψ3 ψ4 ψ5 ψ6
Classify each of these orbitals relative to the point group of the molecule
(i.e. determine the corresponding irrep of each orbital).
Section B (30%)
1.(10%) It has been said that the first point, i.e. t=0, of time domain data
will determine the value of the overall intrgral of the frequency domain
spectrum. Prove the statement using Fourier transformation theory.
2.(20%) Consider the hypothetical dicyclobutadiene organometallic sandwich
compound (C4H4)2M of D4h symmetry:
_________
ψ3/ /ψ2
/ / (PS:每个ψ都是一个p轨域...实在是太难画了 所以就这样罗)
/ / (PS:每个p轨域靠近M的那端为+ 远离M的那端为-)
/________/ ↑
ψ4 ψ1 |
z| y ↗
● M /
_________
ψ1'/ /ψ4' \
/ / x ↘
/ /
/________/
ψ2' ψ3'
(i) Construct all the symmetry adapted orbitals from the ligand pπ orbitals.
You must normalized all the SALCs.
(ii)Mathch all the metals s, p, and d orbitals with all the ligand symmetry
orbitals to obtain bonding, antibonding, and non-bonding molecular orbitals.
Indicate all the bond types(σ,π,δ,nonbonding)
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 140.112.7.214
1F:推 a3225737 :太精美了= = 06/22 22:47
2F:→ firepeter :被你称赞是我的荣幸 06/22 23:04
3F:推 a3225737 : = = 06/23 00:15