Reduction formula for point group C3h
Characters for molecular motions
| Motion |
E |
C3(z) |
(C3)2 |
 h |
S3 |
(S3)5 |
| Cartesian 3N |
60 |
0 |
0 |
6 |
0 |
0 |
| Translation (x,y,z) |
3 |
0 |
0 |
1 |
-2 |
-2 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
0 |
-1 |
2 |
2 |
| Vibration |
54 |
0 |
0 |
6 |
0 |
0 |
Decomposition into Irreducible representations
| Motion |
A' |
E' |
A'' |
E'' |
Total |
| Cartesian 3N |
11 |
11 |
9 |
9 |
40 |
| Translation (x,y,z) |
0 |
1 |
1 |
0 |
2 |
| Rotation (Rx,Ry,Rz) |
1 |
0 |
0 |
1 |
2 |
| Vibration |
10 |
10 |
8 |
8 |
36 |
Molecule Parameter
| Number of Atoms (N) |
20 |
| Number of internal coordinates |
54 |
| Number of independant internal coordinates |
10 |
| Number of vibrational modes |
36 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A' |
E' |
A'' |
E'' |
Total |
| Linear (IR) |
10 |
10 |
8 |
8 |
18 / 18 |
| Quadratic (Raman) |
10 |
10 |
8 |
8 |
28 / 8 |
| IR + Raman |
- |
10 |
- |
- |
10 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C3(z) |
(C3)2 |
h |
S3 |
(S3)5 |
| linear |
1 |
54 |
0 |
0 |
6 |
0 |
0 |
| quadratic |
2 |
1.485 |
0 |
0 |
45 |
0 |
0 |
| cubic |
3 |
27.720 |
18 |
18 |
200 |
2 |
2 |
| quartic |
4 |
395.010 |
0 |
0 |
930 |
0 |
0 |
| quintic |
5 |
4.582.116 |
0 |
0 |
3.396 |
0 |
0 |
| sextic |
6 |
45.057.474 |
171 |
171 |
12.386 |
11 |
11 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A' |
E' |
A'' |
E'' |
| linear |
1 |
10 |
10 |
8 |
8 |
| quadratic |
2 |
255 |
255 |
240 |
240 |
| cubic |
3 |
4.660 |
4.650 |
4.592 |
4.584 |
| quartic |
4 |
65.990 |
65.990 |
65.680 |
65.680 |
| quintic |
5 |
764.252 |
764.252 |
763.120 |
763.120 |
| sextic |
6 |
7.511.704 |
7.511.613 |
7.507.568 |
7.507.488 |
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