Reduction formula for point group C3h
Characters for molecular motions
Motion |
E |
C3(z) |
(C3)2 |
h |
S3 |
(S3)5 |
Cartesian 3N |
27 |
0 |
0 |
3 |
0 |
0 |
Translation (x,y,z) |
3 |
0 |
0 |
1 |
-2 |
-2 |
Rotation (Rx,Ry,Rz) |
3 |
0 |
0 |
-1 |
2 |
2 |
Vibration |
21 |
0 |
0 |
3 |
0 |
0 |
Decomposition into Irreducible representations
Motion |
A' |
E' |
A'' |
E'' |
Total |
Cartesian 3N |
5 |
5 |
4 |
4 |
18 |
Translation (x,y,z) |
0 |
1 |
1 |
0 |
2 |
Rotation (Rx,Ry,Rz) |
1 |
0 |
0 |
1 |
2 |
Vibration |
4 |
4 |
3 |
3 |
14 |
Molecule Parameter
Number of Atoms (N) |
9 |
Number of internal coordinates |
21 |
Number of independant internal coordinates |
4 |
Number of vibrational modes |
14 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A' |
E' |
A'' |
E'' |
Total |
Linear (IR) |
4 |
4 |
3 |
3 |
7 / 7 |
Quadratic (Raman) |
4 |
4 |
3 |
3 |
11 / 3 |
IR + Raman |
- |
4 |
- |
- |
4 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C3(z) |
(C3)2 |
h |
S3 |
(S3)5 |
linear |
1 |
21 |
0 |
0 |
3 |
0 |
0 |
quadratic |
2 |
231 |
0 |
0 |
15 |
0 |
0 |
cubic |
3 |
1.771 |
7 |
7 |
37 |
1 |
1 |
quartic |
4 |
10.626 |
0 |
0 |
114 |
0 |
0 |
quintic |
5 |
53.130 |
0 |
0 |
246 |
0 |
0 |
sextic |
6 |
230.230 |
28 |
28 |
598 |
4 |
4 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A' |
E' |
A'' |
E'' |
linear |
1 |
4 |
4 |
3 |
3 |
quadratic |
2 |
41 |
41 |
36 |
36 |
cubic |
3 |
304 |
300 |
291 |
288 |
quartic |
4 |
1.790 |
1.790 |
1.752 |
1.752 |
quintic |
5 |
8.896 |
8.896 |
8.814 |
8.814 |
sextic |
6 |
38.482 |
38.466 |
38.280 |
38.268 |
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