Reduction formula for point group D2d
Characters for molecular motions
| Motion |
E |
2S4 |
C2 (z) |
2C'2 |
2 d |
| Cartesian 3N |
48 |
0 |
0 |
0 |
8 |
| Translation (x,y,z) |
3 |
-1 |
-1 |
-1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
-1 |
-1 |
| Vibration |
42 |
0 |
2 |
2 |
8 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Cartesian 3N |
8 |
4 |
4 |
8 |
12 |
36 |
| Translation (x,y,z) |
0 |
0 |
0 |
1 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
1 |
2 |
| Vibration |
8 |
3 |
4 |
7 |
10 |
32 |
Molecule Parameter
| Number of Atoms (N) |
16 |
| Number of internal coordinates |
42 |
| Number of independant internal coordinates |
8 |
| Number of vibrational modes |
32 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Linear (IR) |
8 |
3 |
4 |
7 |
10 |
17 / 15 |
| Quadratic (Raman) |
8 |
3 |
4 |
7 |
10 |
29 / 3 |
| IR + Raman |
- |
3 |
- |
7 |
10 |
17 / 3 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2S4 |
C2 (z) |
2C'2 |
2d |
| linear |
1 |
42 |
0 |
2 |
2 |
8 |
| quadratic |
2 |
903 |
1 |
23 |
23 |
53 |
| cubic |
3 |
13.244 |
0 |
44 |
44 |
256 |
| quartic |
4 |
148.995 |
11 |
275 |
275 |
1.095 |
| quintic |
5 |
1.370.754 |
0 |
506 |
506 |
4.056 |
| sextic |
6 |
10.737.573 |
11 |
2.277 |
2.277 |
13.803 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
E |
| linear |
1 |
8 |
3 |
4 |
7 |
10 |
| quadratic |
2 |
135 |
97 |
108 |
123 |
220 |
| cubic |
3 |
1.736 |
1.586 |
1.608 |
1.714 |
3.300 |
| quartic |
4 |
19.004 |
18.319 |
18.451 |
18.861 |
37.180 |
| quintic |
5 |
172.548 |
170.267 |
170.520 |
172.295 |
342.562 |
| sextic |
6 |
1.346.504 |
1.338.464 |
1.339.597 |
1.345.360 |
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