Reduction formula for point group C3h
Characters for molecular motions
| Motion |
E |
C3(z) |
(C3)2 |
 h |
S3 |
(S3)5 |
| Cartesian 3N |
45 |
0 |
0 |
15 |
0 |
0 |
| Translation (x,y,z) |
3 |
0 |
0 |
1 |
-2 |
-2 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
0 |
-1 |
2 |
2 |
| Vibration |
39 |
0 |
0 |
15 |
0 |
0 |
Decomposition into Irreducible representations
| Motion |
A' |
E' |
A'' |
E'' |
Total |
| Cartesian 3N |
10 |
10 |
5 |
5 |
30 |
| Translation (x,y,z) |
0 |
1 |
1 |
0 |
2 |
| Rotation (Rx,Ry,Rz) |
1 |
0 |
0 |
1 |
2 |
| Vibration |
9 |
9 |
4 |
4 |
26 |
Molecule Parameter
| Number of Atoms (N) |
15 |
| Number of internal coordinates |
39 |
| Number of independant internal coordinates |
9 |
| Number of vibrational modes |
26 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A' |
E' |
A'' |
E'' |
Total |
| Linear (IR) |
9 |
9 |
4 |
4 |
13 / 13 |
| Quadratic (Raman) |
9 |
9 |
4 |
4 |
22 / 4 |
| IR + Raman |
- |
9 |
- |
- |
9 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C3(z) |
(C3)2 |
h |
S3 |
(S3)5 |
| linear |
1 |
39 |
0 |
0 |
15 |
0 |
0 |
| quadratic |
2 |
780 |
0 |
0 |
132 |
0 |
0 |
| cubic |
3 |
10.660 |
13 |
13 |
860 |
5 |
5 |
| quartic |
4 |
111.930 |
0 |
0 |
4.578 |
0 |
0 |
| quintic |
5 |
962.598 |
0 |
0 |
20.958 |
0 |
0 |
| sextic |
6 |
7.059.052 |
91 |
91 |
85.204 |
19 |
19 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A' |
E' |
A'' |
E'' |
| linear |
1 |
9 |
9 |
4 |
4 |
| quadratic |
2 |
152 |
152 |
108 |
108 |
| cubic |
3 |
1.926 |
1.917 |
1.636 |
1.632 |
| quartic |
4 |
19.418 |
19.418 |
17.892 |
17.892 |
| quintic |
5 |
163.926 |
163.926 |
156.940 |
156.940 |
| sextic |
6 |
1.190.746 |
1.190.691 |
1.162.332 |
1.162.296 |
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