Reduction formula for point group C4h
Characters for molecular motions
| Motion |
E |
C4(z) |
C2 |
(C4)3 |
i |
(S4)3 |
 h |
S4 |
| Cartesian 3N |
48 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| Translation (x,y,z) |
3 |
1 |
-1 |
1 |
-3 |
-1 |
1 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
1 |
3 |
1 |
-1 |
1 |
| Vibration |
42 |
-2 |
2 |
-2 |
0 |
0 |
0 |
0 |
Decomposition into Irreducible representations
| Motion |
Ag |
Bg |
Eg |
Au |
Bu |
Eu |
Total |
| Cartesian 3N |
6 |
6 |
6 |
6 |
6 |
6 |
36 |
| Translation (x,y,z) |
0 |
0 |
0 |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
1 |
0 |
1 |
0 |
0 |
0 |
2 |
| Vibration |
5 |
6 |
5 |
5 |
6 |
5 |
32 |
Molecule Parameter
| Number of Atoms (N) |
16 |
| Number of internal coordinates |
42 |
| Number of independant internal coordinates |
5 |
| Number of vibrational modes |
32 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
Bg |
Eg |
Au |
Bu |
Eu |
Total |
| Linear (IR) |
5 |
6 |
5 |
5 |
6 |
5 |
10 / 22 |
| Quadratic (Raman) |
5 |
6 |
5 |
5 |
6 |
5 |
16 / 16 |
| IR + Raman |
- |
- |
- |
- |
6 |
- |
0* / 6 |
* Center of inversion: Mutual Exclusion Principle
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C4(z) |
C2 |
(C4)3 |
i |
(S4)3 |
h |
S4 |
| linear |
1 |
42 |
-2 |
2 |
-2 |
0 |
0 |
0 |
0 |
| quadratic |
2 |
903 |
3 |
23 |
3 |
21 |
1 |
21 |
1 |
| cubic |
3 |
13.244 |
-4 |
44 |
-4 |
0 |
0 |
0 |
0 |
| quartic |
4 |
148.995 |
15 |
275 |
15 |
231 |
11 |
231 |
11 |
| quintic |
5 |
1.370.754 |
-26 |
506 |
-26 |
0 |
0 |
0 |
0 |
| sextic |
6 |
10.737.573 |
37 |
2.277 |
37 |
1.771 |
11 |
1.771 |
11 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
Bg |
Eg |
Au |
Bu |
Eu |
| linear |
1 |
5 |
6 |
5 |
5 |
6 |
5 |
| quadratic |
2 |
122 |
120 |
110 |
111 |
110 |
110 |
| cubic |
3 |
1.660 |
1.662 |
1.650 |
1.660 |
1.662 |
1.650 |
| quartic |
4 |
18.723 |
18.710 |
18.590 |
18.602 |
18.600 |
18.590 |
| quintic |
5 |
171.401 |
171.414 |
171.281 |
171.401 |
171.414 |
171.281 |
| sextic |
6 |
1.342.936 |
1.342.912 |
1.341.912 |
1.342.045 |
1.342.032 |
1.341.912 |
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