Reduction formula for point group C4
Characters for molecular motions
Motion |
E |
C4 |
C2 |
(C4)3 |
Cartesian 3N |
15 |
5 |
-5 |
5 |
Translation (x,y,z) |
3 |
1 |
-1 |
1 |
Rotation (Rx,Ry)* |
2 |
0 |
-2 |
0 |
Vibration |
10 |
4 |
-2 |
4 |
* Linear molecule
Decomposition into Irreducible representations
Motion |
A |
B |
E |
Total |
Cartesian 3N |
5 |
0 |
5 |
10 |
Translation (x,y,z) |
1 |
0 |
1 |
2 |
Rotation (Rx,Ry)* |
0 |
0 |
1 |
1 |
Vibration |
4 |
0 |
3 |
7 |
* Linear molecule
Molecule Parameter
Number of Atoms (N) |
5 |
Number of internal coordinates |
10 |
Number of independant internal coordinates |
4 |
Number of vibrational modes |
7 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A |
B |
E |
Total |
Linear (IR) |
4 |
0 |
3 |
7 / 0 |
Quadratic (Raman) |
4 |
0 |
3 |
7 / 0 |
IR + Raman |
4 |
- |
3 |
7 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C4 |
C2 |
(C4)3 |
linear |
1 |
10 |
4 |
-2 |
4 |
quadratic |
2 |
55 |
7 |
7 |
7 |
cubic |
3 |
220 |
8 |
-12 |
8 |
quartic |
4 |
715 |
11 |
27 |
11 |
quintic |
5 |
2.002 |
20 |
-42 |
20 |
sextic |
6 |
5.005 |
29 |
77 |
29 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A |
B |
E |
linear |
1 |
4 |
0 |
3 |
quadratic |
2 |
19 |
12 |
12 |
cubic |
3 |
56 |
48 |
58 |
quartic |
4 |
191 |
180 |
172 |
quintic |
5 |
500 |
480 |
511 |
sextic |
6 |
1.285 |
1.256 |
1.232 |
Literature
- J.K.G. Watson, J. Mol. Spec. 41 229 (1972)
The Numbers of Structural Parameters and Potential Constants of Molecules
- X.F. Zhou, P. Pulay. J. Comp. Chem. 10 No. 7, 935-938 (1989)
Characters for Symmetric and Antisymmetric Higher Powers of Representations:
Application to the Number of Anharmonic Force Constants in Symmetrical Molecules
Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement