Reduction formula for point group C4h
Characters for molecular motions
| Motion |
E |
C4(z) |
C2 |
(C4)3 |
i |
(S4)3 |
 h |
S4 |
| Cartesian 3N |
21 |
3 |
-3 |
3 |
-3 |
-1 |
5 |
-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 |
15 |
1 |
-1 |
1 |
-3 |
-1 |
5 |
-1 |
Decomposition into Irreducible representations
| Motion |
Ag |
Bg |
Eg |
Au |
Bu |
Eu |
Total |
| Cartesian 3N |
3 |
2 |
2 |
3 |
1 |
4 |
15 |
| Translation (x,y,z) |
0 |
0 |
0 |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
1 |
0 |
1 |
0 |
0 |
0 |
2 |
| Vibration |
2 |
2 |
1 |
2 |
1 |
3 |
11 |
Molecule Parameter
| Number of Atoms (N) |
7 |
| Number of internal coordinates |
15 |
| Number of independant internal coordinates |
2 |
| Number of vibrational modes |
11 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
Bg |
Eg |
Au |
Bu |
Eu |
Total |
| Linear (IR) |
2 |
2 |
1 |
2 |
1 |
3 |
5 / 6 |
| Quadratic (Raman) |
2 |
2 |
1 |
2 |
1 |
3 |
5 / 6 |
| IR + Raman |
- |
- |
- |
- |
1 |
- |
0* / 1 |
* 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 |
15 |
1 |
-1 |
1 |
-3 |
-1 |
5 |
-1 |
| quadratic |
2 |
120 |
0 |
8 |
0 |
12 |
0 |
20 |
0 |
| cubic |
3 |
680 |
0 |
-8 |
0 |
-28 |
0 |
60 |
0 |
| quartic |
4 |
3.060 |
4 |
36 |
4 |
72 |
4 |
160 |
4 |
| quintic |
5 |
11.628 |
4 |
-36 |
4 |
-144 |
-4 |
376 |
-4 |
| sextic |
6 |
38.760 |
0 |
120 |
0 |
300 |
0 |
820 |
0 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
Bg |
Eg |
Au |
Bu |
Eu |
| linear |
1 |
2 |
2 |
1 |
2 |
1 |
3 |
| quadratic |
2 |
20 |
20 |
13 |
12 |
12 |
15 |
| cubic |
3 |
88 |
88 |
75 |
80 |
80 |
97 |
| quartic |
4 |
418 |
414 |
367 |
358 |
358 |
389 |
| quintic |
5 |
1.478 |
1.478 |
1.393 |
1.422 |
1.418 |
1.523 |
| sextic |
6 |
5.000 |
5.000 |
4.765 |
4.720 |
4.720 |
4.895 |
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