Reduction formula for point group C4h
Characters for molecular motions
| Motion |
E |
C4(z) |
C2 |
(C4)3 |
i |
(S4)3 |
 h |
S4 |
| Cartesian 3N |
39 |
5 |
-5 |
5 |
-3 |
-1 |
9 |
-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 |
33 |
3 |
-3 |
3 |
-3 |
-1 |
9 |
-1 |
Decomposition into Irreducible representations
| Motion |
Ag |
Bg |
Eg |
Au |
Bu |
Eu |
Total |
| Cartesian 3N |
6 |
4 |
4 |
5 |
2 |
7 |
28 |
| Translation (x,y,z) |
0 |
0 |
0 |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
1 |
0 |
1 |
0 |
0 |
0 |
2 |
| Vibration |
5 |
4 |
3 |
4 |
2 |
6 |
24 |
Molecule Parameter
| Number of Atoms (N) |
13 |
| Number of internal coordinates |
33 |
| Number of independant internal coordinates |
5 |
| Number of vibrational modes |
24 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
Bg |
Eg |
Au |
Bu |
Eu |
Total |
| Linear (IR) |
5 |
4 |
3 |
4 |
2 |
6 |
10 / 14 |
| Quadratic (Raman) |
5 |
4 |
3 |
4 |
2 |
6 |
12 / 12 |
| IR + Raman |
- |
- |
- |
- |
2 |
- |
0* / 2 |
* 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 |
33 |
3 |
-3 |
3 |
-3 |
-1 |
9 |
-1 |
| quadratic |
2 |
561 |
3 |
21 |
3 |
21 |
-1 |
57 |
-1 |
| cubic |
3 |
6.545 |
1 |
-55 |
1 |
-55 |
1 |
273 |
1 |
| quartic |
4 |
58.905 |
9 |
225 |
9 |
225 |
9 |
1.113 |
9 |
| quintic |
5 |
435.897 |
27 |
-531 |
27 |
-531 |
-9 |
3.969 |
-9 |
| sextic |
6 |
2.760.681 |
27 |
1.653 |
27 |
1.653 |
-9 |
12.817 |
-9 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
Bg |
Eg |
Au |
Bu |
Eu |
| linear |
1 |
5 |
4 |
3 |
4 |
2 |
6 |
| quadratic |
2 |
83 |
82 |
63 |
64 |
62 |
72 |
| cubic |
3 |
839 |
838 |
784 |
784 |
784 |
866 |
| quartic |
4 |
7.563 |
7.554 |
7.224 |
7.224 |
7.224 |
7.446 |
| quintic |
5 |
54.855 |
54.846 |
53.991 |
54.000 |
53.982 |
55.116 |
| sextic |
6 |
347.105 |
347.096 |
343.483 |
343.492 |
343.474 |
346.274 |
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