Reduction formula for point group C3v
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3 v |
| Cartesian 3N |
120 |
0 |
8 |
| Translation (x,y,z) |
3 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
| Vibration |
114 |
0 |
8 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
Total |
| Cartesian 3N |
24 |
16 |
40 |
80 |
| Translation (x,y,z) |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
| Vibration |
23 |
15 |
38 |
76 |
Molecule Parameter
| Number of Atoms (N) |
40 |
| Number of internal coordinates |
114 |
| Number of independant internal coordinates |
23 |
| Number of vibrational modes |
76 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
Total |
| Linear (IR) |
23 |
15 |
38 |
61 / 15 |
| Quadratic (Raman) |
23 |
15 |
38 |
61 / 15 |
| IR + Raman |
23 |
15 |
38 |
61 / 15 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3v |
| linear |
1 |
114 |
0 |
8 |
| quadratic |
2 |
6.555 |
0 |
89 |
| cubic |
3 |
253.460 |
38 |
544 |
| quartic |
4 |
7.413.705 |
0 |
3.669 |
| quintic |
5 |
174.963.438 |
0 |
18.600 |
| sextic |
6 |
3.470.108.187 |
741 |
96.957 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
| linear |
1 |
23 |
15 |
38 |
| quadratic |
2 |
1.137 |
1.048 |
2.185 |
| cubic |
3 |
42.528 |
41.984 |
84.474 |
| quartic |
4 |
1.237.452 |
1.233.783 |
2.471.235 |
| quintic |
5 |
29.169.873 |
29.151.273 |
58.321.146 |
| sextic |
6 |
578.400.090 |
578.303.133 |
1.156.702.482 |
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