Reduction formula for point group C3h
Characters for molecular motions
| Motion |
E |
C3(z) |
(C3)2 |
 h |
S3 |
(S3)5 |
| Cartesian 3N |
90 |
0 |
0 |
30 |
0 |
0 |
| Translation (x,y,z) |
3 |
0 |
0 |
1 |
-2 |
-2 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
0 |
-1 |
2 |
2 |
| Vibration |
84 |
0 |
0 |
30 |
0 |
0 |
Decomposition into Irreducible representations
| Motion |
A' |
E' |
A'' |
E'' |
Total |
| Cartesian 3N |
20 |
20 |
10 |
10 |
60 |
| Translation (x,y,z) |
0 |
1 |
1 |
0 |
2 |
| Rotation (Rx,Ry,Rz) |
1 |
0 |
0 |
1 |
2 |
| Vibration |
19 |
19 |
9 |
9 |
56 |
Molecule Parameter
| Number of Atoms (N) |
30 |
| Number of internal coordinates |
84 |
| Number of independant internal coordinates |
19 |
| Number of vibrational modes |
56 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A' |
E' |
A'' |
E'' |
Total |
| Linear (IR) |
19 |
19 |
9 |
9 |
28 / 28 |
| Quadratic (Raman) |
19 |
19 |
9 |
9 |
47 / 9 |
| IR + Raman |
- |
19 |
- |
- |
19 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C3(z) |
(C3)2 |
h |
S3 |
(S3)5 |
| linear |
1 |
84 |
0 |
0 |
30 |
0 |
0 |
| quadratic |
2 |
3.570 |
0 |
0 |
492 |
0 |
0 |
| cubic |
3 |
102.340 |
28 |
28 |
5.770 |
10 |
10 |
| quartic |
4 |
2.225.895 |
0 |
0 |
53.853 |
0 |
0 |
| quintic |
5 |
39.175.752 |
0 |
0 |
423.516 |
0 |
0 |
| sextic |
6 |
581.106.988 |
406 |
406 |
2.907.424 |
64 |
64 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A' |
E' |
A'' |
E'' |
| linear |
1 |
19 |
19 |
9 |
9 |
| quadratic |
2 |
677 |
677 |
513 |
513 |
| cubic |
3 |
18.031 |
18.012 |
16.101 |
16.092 |
| quartic |
4 |
379.958 |
379.958 |
362.007 |
362.007 |
| quintic |
5 |
6.599.878 |
6.599.878 |
6.458.706 |
6.458.706 |
| sextic |
6 |
97.335.892 |
97.335.657 |
96.366.708 |
96.366.537 |
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