Reduction formula for point group C3h
Characters for molecular motions
| Motion |
E |
C3(z) |
(C3)2 |
 h |
S3 |
(S3)5 |
| Cartesian 3N |
102 |
0 |
0 |
0 |
0 |
0 |
| Translation (x,y,z) |
3 |
0 |
0 |
1 |
-2 |
-2 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
0 |
-1 |
2 |
2 |
| Vibration |
96 |
0 |
0 |
0 |
0 |
0 |
Decomposition into Irreducible representations
| Motion |
A' |
E' |
A'' |
E'' |
Total |
| Cartesian 3N |
17 |
17 |
17 |
17 |
68 |
| Translation (x,y,z) |
0 |
1 |
1 |
0 |
2 |
| Rotation (Rx,Ry,Rz) |
1 |
0 |
0 |
1 |
2 |
| Vibration |
16 |
16 |
16 |
16 |
64 |
Molecule Parameter
| Number of Atoms (N) |
34 |
| Number of internal coordinates |
96 |
| Number of independant internal coordinates |
16 |
| Number of vibrational modes |
64 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A' |
E' |
A'' |
E'' |
Total |
| Linear (IR) |
16 |
16 |
16 |
16 |
32 / 32 |
| Quadratic (Raman) |
16 |
16 |
16 |
16 |
48 / 16 |
| IR + Raman |
- |
16 |
- |
- |
16 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C3(z) |
(C3)2 |
h |
S3 |
(S3)5 |
| linear |
1 |
96 |
0 |
0 |
0 |
0 |
0 |
| quadratic |
2 |
4.656 |
0 |
0 |
48 |
0 |
0 |
| cubic |
3 |
152.096 |
32 |
32 |
0 |
0 |
0 |
| quartic |
4 |
3.764.376 |
0 |
0 |
1.176 |
0 |
0 |
| quintic |
5 |
75.287.520 |
0 |
0 |
0 |
0 |
0 |
| sextic |
6 |
1.267.339.920 |
528 |
528 |
19.600 |
16 |
16 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A' |
E' |
A'' |
E'' |
| linear |
1 |
16 |
16 |
16 |
16 |
| quadratic |
2 |
784 |
784 |
768 |
768 |
| cubic |
3 |
25.360 |
25.344 |
25.360 |
25.344 |
| quartic |
4 |
627.592 |
627.592 |
627.200 |
627.200 |
| quintic |
5 |
12.547.920 |
12.547.920 |
12.547.920 |
12.547.920 |
| sextic |
6 |
211.226.768 |
211.226.496 |
211.220.224 |
211.219.968 |
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