Reduction formula for point group C3h
Characters for molecular motions
| Motion |
E |
C3(z) |
(C3)2 |
 h |
S3 |
(S3)5 |
| Cartesian 3N |
87 |
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 |
81 |
0 |
0 |
9 |
0 |
0 |
Decomposition into Irreducible representations
| Motion |
A' |
E' |
A'' |
E'' |
Total |
| Cartesian 3N |
16 |
16 |
13 |
13 |
58 |
| Translation (x,y,z) |
0 |
1 |
1 |
0 |
2 |
| Rotation (Rx,Ry,Rz) |
1 |
0 |
0 |
1 |
2 |
| Vibration |
15 |
15 |
12 |
12 |
54 |
Molecule Parameter
| Number of Atoms (N) |
29 |
| Number of internal coordinates |
81 |
| Number of independant internal coordinates |
15 |
| Number of vibrational modes |
54 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A' |
E' |
A'' |
E'' |
Total |
| Linear (IR) |
15 |
15 |
12 |
12 |
27 / 27 |
| Quadratic (Raman) |
15 |
15 |
12 |
12 |
42 / 12 |
| IR + Raman |
- |
15 |
- |
- |
15 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C3(z) |
(C3)2 |
h |
S3 |
(S3)5 |
| linear |
1 |
81 |
0 |
0 |
9 |
0 |
0 |
| quadratic |
2 |
3.321 |
0 |
0 |
81 |
0 |
0 |
| cubic |
3 |
91.881 |
27 |
27 |
489 |
3 |
3 |
| quartic |
4 |
1.929.501 |
0 |
0 |
2.781 |
0 |
0 |
| quintic |
5 |
32.801.517 |
0 |
0 |
13.221 |
0 |
0 |
| sextic |
6 |
470.155.077 |
378 |
378 |
59.229 |
18 |
18 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A' |
E' |
A'' |
E'' |
| linear |
1 |
15 |
15 |
12 |
12 |
| quadratic |
2 |
567 |
567 |
540 |
540 |
| cubic |
3 |
15.405 |
15.390 |
15.240 |
15.228 |
| quartic |
4 |
322.047 |
322.047 |
321.120 |
321.120 |
| quintic |
5 |
5.469.123 |
5.469.123 |
5.464.716 |
5.464.716 |
| sextic |
6 |
78.369.183 |
78.368.985 |
78.349.428 |
78.349.248 |
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