Reduction formula for point group D2d
Characters for molecular motions
| Motion |
E |
2S4 |
C2 (z) |
2C'2 |
2 d |
| Cartesian 3N |
78 |
0 |
-2 |
-2 |
8 |
| Translation (x,y,z) |
3 |
-1 |
-1 |
-1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
-1 |
-1 |
| Vibration |
72 |
0 |
0 |
0 |
8 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Cartesian 3N |
11 |
8 |
7 |
12 |
20 |
58 |
| Translation (x,y,z) |
0 |
0 |
0 |
1 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
1 |
2 |
| Vibration |
11 |
7 |
7 |
11 |
18 |
54 |
Molecule Parameter
| Number of Atoms (N) |
26 |
| Number of internal coordinates |
72 |
| Number of independant internal coordinates |
11 |
| Number of vibrational modes |
54 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Linear (IR) |
11 |
7 |
7 |
11 |
18 |
29 / 25 |
| Quadratic (Raman) |
11 |
7 |
7 |
11 |
18 |
47 / 7 |
| IR + Raman |
- |
7 |
- |
11 |
18 |
29 / 7 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2S4 |
C2 (z) |
2C'2 |
2d |
| linear |
1 |
72 |
0 |
0 |
0 |
8 |
| quadratic |
2 |
2.628 |
0 |
36 |
36 |
68 |
| cubic |
3 |
64.824 |
0 |
0 |
0 |
376 |
| quartic |
4 |
1.215.450 |
18 |
666 |
666 |
2.010 |
| quintic |
5 |
18.474.840 |
0 |
0 |
0 |
8.856 |
| sextic |
6 |
237.093.780 |
0 |
8.436 |
8.436 |
37.268 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
E |
| linear |
1 |
11 |
7 |
7 |
11 |
18 |
| quadratic |
2 |
359 |
307 |
325 |
341 |
648 |
| cubic |
3 |
8.197 |
8.009 |
8.009 |
8.197 |
16.206 |
| quartic |
4 |
152.688 |
151.350 |
151.674 |
152.346 |
303.696 |
| quintic |
5 |
2.311.569 |
2.307.141 |
2.307.141 |
2.311.569 |
4.618.710 |
| sextic |
6 |
29.649.203 |
29.626.351 |
29.630.569 |
29.644.985 |
59.271.336 |
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