5. The most stable structure for N₂O4 is planar and belongs to the D2h point group, which has the character table shown below. D2h E C₂(X) C₂(V) C₂ (2) i o(xy) o(yz) o(x2) Ag 1 1 1 1 1 1 1 1 B1g 1 1 -1 -1 1 1 -1 -1 1 -1 -1 1 -1 1 1 -1 1 1 -1 -1 1 1 1 -1 -1 -1 1 -1 -1 -1 1 -1 -1 -1 1 -1 -1 1 -1 1 1 B2g B3g Au B1u 1 B2u 1 B3u 1 1 -1 1 -1 1 -1 -1 1 -1 1 1 -1 5.1 How many translational degrees of freedom does N₂04 have? 5.2 How many rotational degrees of freedom does N₂04 have? 5.3 How many normal modes of vibration does N204 have? x², y², z² xy 5.5 How many of the vibrational modes of N₂04 are IR-active? XZ yz 5.6 How many of the vibrational modes of N₂O4 are Raman-active? Z y X Rz Ry Rx 3. 5.4 The displacement vectors for the atoms of N₂O4 span 3Ag + 3B1g + 2B2g + B3g + Au + 2B1u + 3B2u + 3B3u. What are the symmetry species of the normal modes of vibration? 00

5. The most stable structure for N₂O4 is planar and belongs to the D2h point group, which has the character table shown below. D2h E C₂(X) C₂(V) C₂ (2) i o(xy) o(yz) o(x2) Ag 1 1 1 1 1 1 1 1 B1g 1 1 -1 -1 1 1 -1 -1 1 -1 -1 1 -1 1 1 -1 1 1 -1 -1 1 1 1 -1 -1 -1 1 -1 -1 -1 1 -1 -1 -1 1 -1 -1 1 -1 1 1 B2g B3g Au B1u 1 B2u 1 B3u 1 1 -1 1 -1 1 -1 -1 1 -1 1 1 -1 5.1 How many translational degrees of freedom does N₂04 have? 5.2 How many rotational degrees of freedom does N₂04 have? 5.3 How many normal modes of vibration does N204 have? x², y², z² xy 5.5 How many of the vibrational modes of N₂04 are IR-active? XZ yz 5.6 How many of the vibrational modes of N₂O4 are Raman-active? Z y X Rz Ry Rx 3. 5.4 The displacement vectors for the atoms of N₂O4 span 3Ag + 3B1g + 2B2g + B3g + Au + 2B1u + 3B2u + 3B3u. What are the symmetry species of the normal modes of vibration? 00

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter13: Introduction To Symmetry In Quantum Mechanics

Section: Chapter Questions

Problem 13.31E: Structural isomers can have very different point groups. There are three isomers of dichlorobenzene....

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5. The most stable structure for N₂O4 is planar and belongs to the D2h point group, which
has the character table shown below.
D2h E
C₂(X) C₂(V) C₂ (2)
i o(xy) o(yz) o(x2)
Ag
1
1
1
1
1
1
1
1
B1g
1
1
-1
-1
1
1
-1
-1
1
-1
-1
1
-1
1
1 -1
1
1
-1
-1
1
1
1
-1
-1
-1
1
-1
-1
-1
1
-1
-1 -1
1
-1
-1
1
-1 1
1
B2g
B3g
Au
B1u
1
B2u
1
B3u 1
1
-1
1
-1
1
-1
-1
1
-1
1
1
-1
5.1 How many translational degrees of freedom does N₂04 have?
5.2 How many rotational degrees of freedom does N₂04 have?
5.3 How many normal modes of vibration does N204 have?
x², y², z²
xy
5.5 How many of the vibrational modes of N₂04 are IR-active?
XZ
yz
5.6 How many of the vibrational modes of N₂O4 are Raman-active?
Z
y
X
Rz
Ry
Rx
3.
5.4 The displacement vectors for the atoms of N₂O4 span 3Ag + 3B1g + 2B2g + B3g + Au + 2B1u
+ 3B2u + 3B3u. What are the symmetry species of the normal modes of vibration?
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