Reduction formula for point group C4v
Characters for molecular motions
Motion |
E |
2C4 (z) |
C2 |
2v |
2d |
Cartesian 3N |
156 |
0 |
0 |
4 |
14 |
Translation (x,y,z) |
3 |
1 |
-1 |
1 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
-1 |
-1 |
Vibration |
150 |
-2 |
2 |
4 |
14 |
Decomposition into Irreducible representations
Motion |
A1 |
A2 |
B1 |
B2 |
E |
Total |
Cartesian 3N |
24 |
15 |
17 |
22 |
39 |
117 |
Translation (x,y,z) |
1 |
0 |
0 |
0 |
1 |
2 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
1 |
2 |
Vibration |
23 |
14 |
17 |
22 |
37 |
113 |
Molecule Parameter
Number of Atoms (N) |
52 |
Number of internal coordinates |
150 |
Number of independant internal coordinates |
23 |
Number of vibrational modes |
113 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A1 |
A2 |
B1 |
B2 |
E |
Total |
Linear (IR) |
23 |
14 |
17 |
22 |
37 |
60 / 53 |
Quadratic (Raman) |
23 |
14 |
17 |
22 |
37 |
99 / 14 |
IR + Raman |
23 |
14 |
- |
- |
37 |
60 / 14 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
2C4 (z) |
C2 |
2v |
2d |
linear |
1 |
150 |
-2 |
2 |
4 |
14 |
quadratic |
2 |
11.325 |
3 |
77 |
83 |
173 |
cubic |
3 |
573.800 |
-4 |
152 |
312 |
1.512 |
quartic |
4 |
21.947.850 |
42 |
3.002 |
3.466 |
11.866 |
quintic |
5 |
675.993.780 |
-80 |
5.852 |
12.320 |
79.492 |
sextic |
6 |
17.463.172.650 |
118 |
79.002 |
97.174 |
490.042 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
B1 |
B2 |
E |
linear |
1 |
23 |
14 |
17 |
22 |
37 |
quadratic |
2 |
1.490 |
1.362 |
1.402 |
1.447 |
2.812 |
cubic |
3 |
72.199 |
71.287 |
71.445 |
72.045 |
143.412 |
quartic |
4 |
2.747.700 |
2.740.034 |
2.741.746 |
2.745.946 |
5.486.212 |
quintic |
5 |
84.522.887 |
84.476.981 |
84.483.181 |
84.516.767 |
168.996.982 |
sextic |
6 |
2.183.053.290 |
2.182.759.682 |
2.182.808.210 |
2.183.004.644 |
4.365.773.412 |
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