Reduction formula for point group C4h
Characters for molecular motions
| Motion |
E |
C4(z) |
C2 |
(C4)3 |
i |
(S4)3 |
 h |
S4 |
| Cartesian 3N |
99 |
1 |
-1 |
1 |
-3 |
-1 |
1 |
-1 |
| 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 |
93 |
-1 |
1 |
-1 |
-3 |
-1 |
1 |
-1 |
Decomposition into Irreducible representations
| Motion |
Ag |
Bg |
Eg |
Au |
Bu |
Eu |
Total |
| Cartesian 3N |
12 |
12 |
12 |
13 |
12 |
13 |
74 |
| Translation (x,y,z) |
0 |
0 |
0 |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
1 |
0 |
1 |
0 |
0 |
0 |
2 |
| Vibration |
11 |
12 |
11 |
12 |
12 |
12 |
70 |
Molecule Parameter
| Number of Atoms (N) |
33 |
| Number of internal coordinates |
93 |
| Number of independant internal coordinates |
11 |
| Number of vibrational modes |
70 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
Bg |
Eg |
Au |
Bu |
Eu |
Total |
| Linear (IR) |
11 |
12 |
11 |
12 |
12 |
12 |
24 / 46 |
| Quadratic (Raman) |
11 |
12 |
11 |
12 |
12 |
12 |
34 / 36 |
| IR + Raman |
- |
- |
- |
- |
12 |
- |
0* / 12 |
* 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 |
93 |
-1 |
1 |
-1 |
-3 |
-1 |
1 |
-1 |
| quadratic |
2 |
4.371 |
1 |
47 |
1 |
51 |
1 |
47 |
1 |
| cubic |
3 |
138.415 |
-1 |
47 |
-1 |
-145 |
-1 |
47 |
-1 |
| quartic |
4 |
3.321.960 |
24 |
1.128 |
24 |
1.320 |
24 |
1.128 |
24 |
| quintic |
5 |
64.446.024 |
-24 |
1.128 |
-24 |
-3.576 |
-24 |
1.128 |
-24 |
| sextic |
6 |
1.052.618.392 |
24 |
18.424 |
24 |
23.128 |
24 |
18.424 |
24 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
Bg |
Eg |
Au |
Bu |
Eu |
| linear |
1 |
11 |
12 |
11 |
12 |
12 |
12 |
| quadratic |
2 |
565 |
564 |
541 |
540 |
540 |
540 |
| cubic |
3 |
17.295 |
17.296 |
17.272 |
17.320 |
17.320 |
17.320 |
| quartic |
4 |
415.704 |
415.680 |
415.128 |
415.080 |
415.080 |
415.080 |
| quintic |
5 |
8.055.576 |
8.055.600 |
8.055.024 |
8.056.200 |
8.056.200 |
8.056.200 |
| sextic |
6 |
131.584.808 |
131.584.784 |
131.575.584 |
131.574.408 |
131.574.408 |
131.574.408 |
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