Reduction formula for point group C4v
Characters for molecular motions
| Motion |
E |
2C4 (z) |
C2 |
2 v |
2d |
| Cartesian 3N |
39 |
5 |
-5 |
9 |
5 |
| Translation (x,y,z) |
3 |
1 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
-1 |
-1 |
| Vibration |
33 |
3 |
-3 |
9 |
5 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Cartesian 3N |
9 |
2 |
4 |
2 |
11 |
28 |
| Translation (x,y,z) |
1 |
0 |
0 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
1 |
2 |
| Vibration |
8 |
1 |
4 |
2 |
9 |
24 |
Molecule Parameter
| Number of Atoms (N) |
13 |
| Number of internal coordinates |
33 |
| Number of independant internal coordinates |
8 |
| Number of vibrational modes |
24 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Linear (IR) |
8 |
1 |
4 |
2 |
9 |
17 / 7 |
| Quadratic (Raman) |
8 |
1 |
4 |
2 |
9 |
23 / 1 |
| IR + Raman |
8 |
1 |
- |
- |
9 |
17 / 1 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C4 (z) |
C2 |
2v |
2d |
| linear |
1 |
33 |
3 |
-3 |
9 |
5 |
| quadratic |
2 |
561 |
3 |
21 |
57 |
29 |
| cubic |
3 |
6.545 |
1 |
-55 |
273 |
105 |
| quartic |
4 |
58.905 |
9 |
225 |
1.113 |
385 |
| quintic |
5 |
435.897 |
27 |
-531 |
3.969 |
1.141 |
| sextic |
6 |
2.760.681 |
27 |
1.653 |
12.817 |
3.325 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
E |
| linear |
1 |
8 |
1 |
4 |
2 |
9 |
| quadratic |
2 |
95 |
52 |
79 |
65 |
135 |
| cubic |
3 |
906 |
717 |
853 |
769 |
1.650 |
| quartic |
4 |
7.768 |
7.019 |
7.571 |
7.207 |
14.670 |
| quintic |
5 |
55.705 |
53.150 |
55.121 |
53.707 |
109.107 |
| sextic |
6 |
349.334 |
341.263 |
347.658 |
342.912 |
689.757 |
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