Reduction formula for point group D2d
Characters for molecular motions
| Motion |
E |
2S4 |
C2 (z) |
2C'2 |
2 d |
| Cartesian 3N |
99 |
-1 |
-1 |
-1 |
9 |
| Translation (x,y,z) |
3 |
-1 |
-1 |
-1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
-1 |
-1 |
| Vibration |
93 |
-1 |
1 |
1 |
9 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Cartesian 3N |
14 |
10 |
10 |
15 |
25 |
74 |
| Translation (x,y,z) |
0 |
0 |
0 |
1 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
1 |
2 |
| Vibration |
14 |
9 |
10 |
14 |
23 |
70 |
Molecule Parameter
| Number of Atoms (N) |
33 |
| Number of internal coordinates |
93 |
| Number of independant internal coordinates |
14 |
| Number of vibrational modes |
70 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Linear (IR) |
14 |
9 |
10 |
14 |
23 |
37 / 33 |
| Quadratic (Raman) |
14 |
9 |
10 |
14 |
23 |
61 / 9 |
| IR + Raman |
- |
9 |
- |
14 |
23 |
37 / 9 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2S4 |
C2 (z) |
2C'2 |
2d |
| linear |
1 |
93 |
-1 |
1 |
1 |
9 |
| quadratic |
2 |
4.371 |
1 |
47 |
47 |
87 |
| cubic |
3 |
138.415 |
-1 |
47 |
47 |
543 |
| quartic |
4 |
3.321.960 |
24 |
1.128 |
1.128 |
3.288 |
| quintic |
5 |
64.446.024 |
-24 |
1.128 |
1.128 |
16.344 |
| sextic |
6 |
1.052.618.392 |
24 |
18.424 |
18.424 |
77.672 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
E |
| linear |
1 |
14 |
9 |
10 |
14 |
23 |
| quadratic |
2 |
586 |
519 |
542 |
562 |
1.081 |
| cubic |
3 |
17.455 |
17.160 |
17.184 |
17.432 |
34.592 |
| quartic |
4 |
416.496 |
414.288 |
414.840 |
415.920 |
830.208 |
| quintic |
5 |
8.060.256 |
8.051.520 |
8.052.096 |
8.059.704 |
16.111.224 |
| sextic |
6 |
131.603.632 |
131.555.584 |
131.564.784 |
131.594.408 |
263.149.992 |
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