Reduction formula for point group C4v
Characters for molecular motions
| Motion |
E |
2C4 (z) |
C2 |
2 v |
2d |
| Cartesian 3N |
99 |
1 |
-1 |
5 |
5 |
| Translation (x,y,z) |
3 |
1 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
-1 |
-1 |
| Vibration |
93 |
-1 |
1 |
5 |
5 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Cartesian 3N |
15 |
10 |
12 |
12 |
25 |
74 |
| Translation (x,y,z) |
1 |
0 |
0 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
1 |
2 |
| Vibration |
14 |
9 |
12 |
12 |
23 |
70 |
Molecule Parameter
| Number of Atoms (N) |
33 |
| Number of internal coordinates |
93 |
| Number of independant internal coordinates |
14 |
| Number of vibrational modes |
70 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Linear (IR) |
14 |
9 |
12 |
12 |
23 |
37 / 33 |
| Quadratic (Raman) |
14 |
9 |
12 |
12 |
23 |
61 / 9 |
| IR + Raman |
14 |
9 |
- |
- |
23 |
37 / 9 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C4 (z) |
C2 |
2v |
2d |
| linear |
1 |
93 |
-1 |
1 |
5 |
5 |
| quadratic |
2 |
4.371 |
1 |
47 |
59 |
59 |
| cubic |
3 |
138.415 |
-1 |
47 |
255 |
255 |
| quartic |
4 |
3.321.960 |
24 |
1.128 |
1.720 |
1.720 |
| quintic |
5 |
64.446.024 |
-24 |
1.128 |
6.616 |
6.616 |
| sextic |
6 |
1.052.618.392 |
24 |
18.424 |
33.320 |
33.320 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
E |
| linear |
1 |
14 |
9 |
12 |
12 |
23 |
| quadratic |
2 |
582 |
523 |
552 |
552 |
1.081 |
| cubic |
3 |
17.435 |
17.180 |
17.308 |
17.308 |
34.592 |
| quartic |
4 |
416.252 |
414.532 |
415.380 |
415.380 |
830.208 |
| quintic |
5 |
8.059.196 |
8.052.580 |
8.055.900 |
8.055.900 |
16.111.224 |
| sextic |
6 |
131.596.268 |
131.562.948 |
131.579.596 |
131.579.596 |
263.149.992 |
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