Reduction formula for point group C4v
Characters for molecular motions
Motion |
E |
2C4 (z) |
C2 |
2v |
2d |
Cartesian 3N |
18 |
2 |
-2 |
4 |
2 |
Translation (x,y,z) |
3 |
1 |
-1 |
1 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
-1 |
-1 |
Vibration |
12 |
0 |
0 |
4 |
2 |
Decomposition into Irreducible representations
Motion |
A1 |
A2 |
B1 |
B2 |
E |
Total |
Cartesian 3N |
4 |
1 |
2 |
1 |
5 |
13 |
Translation (x,y,z) |
1 |
0 |
0 |
0 |
1 |
2 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
1 |
2 |
Vibration |
3 |
0 |
2 |
1 |
3 |
9 |
Molecule Parameter
Number of Atoms (N) |
6 |
Number of internal coordinates |
12 |
Number of independant internal coordinates |
3 |
Number of vibrational modes |
9 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A1 |
A2 |
B1 |
B2 |
E |
Total |
Linear (IR) |
3 |
0 |
2 |
1 |
3 |
6 / 3 |
Quadratic (Raman) |
3 |
0 |
2 |
1 |
3 |
9 / 0 |
IR + Raman |
3 |
0 |
- |
- |
3 |
6 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
2C4 (z) |
C2 |
2v |
2d |
linear |
1 |
12 |
0 |
0 |
4 |
2 |
quadratic |
2 |
78 |
0 |
6 |
14 |
8 |
cubic |
3 |
364 |
0 |
0 |
36 |
14 |
quartic |
4 |
1.365 |
3 |
21 |
85 |
35 |
quintic |
5 |
4.368 |
0 |
0 |
176 |
56 |
sextic |
6 |
12.376 |
0 |
56 |
344 |
112 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
B1 |
B2 |
E |
linear |
1 |
3 |
0 |
2 |
1 |
3 |
quadratic |
2 |
16 |
5 |
12 |
9 |
18 |
cubic |
3 |
58 |
33 |
51 |
40 |
91 |
quartic |
4 |
204 |
144 |
185 |
160 |
336 |
quintic |
5 |
604 |
488 |
576 |
516 |
1.092 |
sextic |
6 |
1.668 |
1.440 |
1.612 |
1.496 |
3.080 |
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