Reduction formula for point group C3h
Characters for molecular motions
| Motion |
E |
C3(z) |
(C3)2 |
 h |
S3 |
(S3)5 |
| Cartesian 3N |
93 |
0 |
0 |
9 |
0 |
0 |
| Translation (x,y,z) |
3 |
0 |
0 |
1 |
-2 |
-2 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
0 |
-1 |
2 |
2 |
| Vibration |
87 |
0 |
0 |
9 |
0 |
0 |
Decomposition into Irreducible representations
| Motion |
A' |
E' |
A'' |
E'' |
Total |
| Cartesian 3N |
17 |
17 |
14 |
14 |
62 |
| Translation (x,y,z) |
0 |
1 |
1 |
0 |
2 |
| Rotation (Rx,Ry,Rz) |
1 |
0 |
0 |
1 |
2 |
| Vibration |
16 |
16 |
13 |
13 |
58 |
Molecule Parameter
| Number of Atoms (N) |
31 |
| Number of internal coordinates |
87 |
| Number of independant internal coordinates |
16 |
| Number of vibrational modes |
58 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A' |
E' |
A'' |
E'' |
Total |
| Linear (IR) |
16 |
16 |
13 |
13 |
29 / 29 |
| Quadratic (Raman) |
16 |
16 |
13 |
13 |
45 / 13 |
| 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 |
87 |
0 |
0 |
9 |
0 |
0 |
| quadratic |
2 |
3.828 |
0 |
0 |
84 |
0 |
0 |
| cubic |
3 |
113.564 |
29 |
29 |
516 |
3 |
3 |
| quartic |
4 |
2.555.190 |
0 |
0 |
3.030 |
0 |
0 |
| quintic |
5 |
46.504.458 |
0 |
0 |
14.742 |
0 |
0 |
| sextic |
6 |
713.068.356 |
435 |
435 |
68.068 |
19 |
19 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A' |
E' |
A'' |
E'' |
| linear |
1 |
16 |
16 |
13 |
13 |
| quadratic |
2 |
652 |
652 |
624 |
624 |
| cubic |
3 |
19.024 |
19.008 |
18.850 |
18.837 |
| quartic |
4 |
426.370 |
426.370 |
425.360 |
425.360 |
| quintic |
5 |
7.753.200 |
7.753.200 |
7.748.286 |
7.748.286 |
| sextic |
6 |
118.856.222 |
118.855.995 |
118.833.520 |
118.833.312 |
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