Reduction formula for point group C4h
Characters for molecular motions
Motion |
E |
C4(z) |
C2 |
(C4)3 |
i |
(S4)3 |
h |
S4 |
Cartesian 3N |
72 |
0 |
0 |
0 |
0 |
0 |
24 |
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 |
66 |
-2 |
2 |
-2 |
0 |
0 |
24 |
0 |
Decomposition into Irreducible representations
Motion |
Ag |
Bg |
Eg |
Au |
Bu |
Eu |
Total |
Cartesian 3N |
12 |
12 |
6 |
6 |
6 |
12 |
54 |
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 |
5 |
5 |
6 |
11 |
50 |
Molecule Parameter
Number of Atoms (N) |
24 |
Number of internal coordinates |
66 |
Number of independant internal coordinates |
11 |
Number of vibrational modes |
50 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
Ag |
Bg |
Eg |
Au |
Bu |
Eu |
Total |
Linear (IR) |
11 |
12 |
5 |
5 |
6 |
11 |
16 / 34 |
Quadratic (Raman) |
11 |
12 |
5 |
5 |
6 |
11 |
28 / 22 |
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 |
66 |
-2 |
2 |
-2 |
0 |
0 |
24 |
0 |
quadratic |
2 |
2.211 |
3 |
35 |
3 |
33 |
1 |
321 |
1 |
cubic |
3 |
50.116 |
-4 |
68 |
-4 |
0 |
0 |
3.104 |
0 |
quartic |
4 |
864.501 |
21 |
629 |
21 |
561 |
17 |
24.081 |
17 |
quintic |
5 |
12.103.014 |
-38 |
1.190 |
-38 |
0 |
0 |
158.424 |
0 |
sextic |
6 |
143.218.999 |
55 |
7.735 |
55 |
6.545 |
17 |
914.641 |
17 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
Ag |
Bg |
Eg |
Au |
Bu |
Eu |
linear |
1 |
11 |
12 |
5 |
5 |
6 |
11 |
quadratic |
2 |
326 |
324 |
236 |
237 |
236 |
308 |
cubic |
3 |
6.660 |
6.662 |
5.868 |
5.884 |
5.886 |
6.644 |
quartic |
4 |
111.231 |
111.212 |
105.044 |
105.062 |
105.060 |
110.924 |
quintic |
5 |
1.532.819 |
1.532.838 |
1.492.925 |
1.493.213 |
1.493.232 |
1.532.531 |
sextic |
6 |
18.018.508 |
18.018.472 |
17.787.896 |
17.788.203 |
17.788.184 |
18.014.920 |
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