Reduction formula for point group D2d
Characters for molecular motions
| Motion |
E |
2S4 |
C2 (z) |
2C'2 |
2 d |
| Cartesian 3N |
30 |
0 |
-2 |
-2 |
4 |
| Translation (x,y,z) |
3 |
-1 |
-1 |
-1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
-1 |
-1 |
| Vibration |
24 |
0 |
0 |
0 |
4 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Cartesian 3N |
4 |
3 |
2 |
5 |
8 |
22 |
| Translation (x,y,z) |
0 |
0 |
0 |
1 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
1 |
2 |
| Vibration |
4 |
2 |
2 |
4 |
6 |
18 |
Molecule Parameter
| Number of Atoms (N) |
10 |
| Number of internal coordinates |
24 |
| Number of independant internal coordinates |
4 |
| Number of vibrational modes |
18 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Linear (IR) |
4 |
2 |
2 |
4 |
6 |
10 / 8 |
| Quadratic (Raman) |
4 |
2 |
2 |
4 |
6 |
16 / 2 |
| IR + Raman |
- |
2 |
- |
4 |
6 |
10 / 2 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2S4 |
C2 (z) |
2C'2 |
2d |
| linear |
1 |
24 |
0 |
0 |
0 |
4 |
| quadratic |
2 |
300 |
0 |
12 |
12 |
20 |
| cubic |
3 |
2.600 |
0 |
0 |
0 |
60 |
| quartic |
4 |
17.550 |
6 |
78 |
78 |
190 |
| quintic |
5 |
98.280 |
0 |
0 |
0 |
476 |
| sextic |
6 |
475.020 |
0 |
364 |
364 |
1.204 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
E |
| linear |
1 |
4 |
2 |
2 |
4 |
6 |
| quadratic |
2 |
47 |
31 |
37 |
41 |
72 |
| cubic |
3 |
340 |
310 |
310 |
340 |
650 |
| quartic |
4 |
2.272 |
2.138 |
2.174 |
2.230 |
4.368 |
| quintic |
5 |
12.404 |
12.166 |
12.166 |
12.404 |
24.570 |
| sextic |
6 |
59.815 |
59.031 |
59.213 |
59.633 |
118.664 |
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