Reduction formula for point group C4v
Characters for molecular motions
| Motion |
E |
2C4 (z) |
C2 |
2 v |
2d |
| Cartesian 3N |
48 |
0 |
0 |
4 |
4 |
| Translation (x,y,z) |
3 |
1 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
-1 |
-1 |
| Vibration |
42 |
-2 |
2 |
4 |
4 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Cartesian 3N |
8 |
4 |
6 |
6 |
12 |
36 |
| Translation (x,y,z) |
1 |
0 |
0 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
1 |
2 |
| Vibration |
7 |
3 |
6 |
6 |
10 |
32 |
Molecule Parameter
| Number of Atoms (N) |
16 |
| Number of internal coordinates |
42 |
| Number of independant internal coordinates |
7 |
| Number of vibrational modes |
32 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Linear (IR) |
7 |
3 |
6 |
6 |
10 |
17 / 15 |
| Quadratic (Raman) |
7 |
3 |
6 |
6 |
10 |
29 / 3 |
| IR + Raman |
7 |
3 |
- |
- |
10 |
17 / 3 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C4 (z) |
C2 |
2v |
2d |
| linear |
1 |
42 |
-2 |
2 |
4 |
4 |
| quadratic |
2 |
903 |
3 |
23 |
29 |
29 |
| cubic |
3 |
13.244 |
-4 |
44 |
96 |
96 |
| quartic |
4 |
148.995 |
15 |
275 |
415 |
415 |
| quintic |
5 |
1.370.754 |
-26 |
506 |
1.196 |
1.196 |
| sextic |
6 |
10.737.573 |
37 |
2.277 |
3.979 |
3.979 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
E |
| linear |
1 |
7 |
3 |
6 |
6 |
10 |
| quadratic |
2 |
131 |
102 |
115 |
115 |
220 |
| cubic |
3 |
1.708 |
1.612 |
1.662 |
1.662 |
3.300 |
| quartic |
4 |
18.870 |
18.455 |
18.655 |
18.655 |
37.180 |
| quintic |
5 |
171.999 |
170.803 |
171.414 |
171.414 |
342.562 |
| sextic |
6 |
1.344.480 |
1.340.501 |
1.342.472 |
1.342.472 |
2.683.824 |
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