Reduction formula for point group D2
Characters for molecular motions
| Motion |
E |
C2 (z) |
C2 (y) |
C2 (x) |
| Cartesian 3N |
66 |
0 |
0 |
-6 |
| Translation (x,y,z) |
3 |
-1 |
-1 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
60 |
2 |
2 |
-4 |
Decomposition into Irreducible representations
| Motion |
A |
B1 |
B2 |
B3 |
Total |
| Cartesian 3N |
15 |
18 |
18 |
15 |
66 |
| Translation (x,y,z) |
0 |
1 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
15 |
16 |
16 |
13 |
60 |
Molecule Parameter
| Number of Atoms (N) |
22 |
| Number of internal coordinates |
60 |
| Number of independant internal coordinates |
15 |
| Number of vibrational modes |
60 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A |
B1 |
B2 |
B3 |
Total |
| Linear (IR) |
15 |
16 |
16 |
13 |
45 / 15 |
| Quadratic (Raman) |
15 |
16 |
16 |
13 |
60 / 0 |
| IR + Raman |
- |
16 |
16 |
13 |
45 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
C2 (y) |
C2 (x) |
| linear |
1 |
60 |
2 |
2 |
-4 |
| quadratic |
2 |
1.830 |
32 |
32 |
38 |
| cubic |
3 |
37.820 |
62 |
62 |
-132 |
| quartic |
4 |
595.665 |
527 |
527 |
721 |
| quintic |
5 |
7.624.512 |
992 |
992 |
-2.240 |
| sextic |
6 |
82.598.880 |
5.952 |
5.952 |
9.184 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A |
B1 |
B2 |
B3 |
| linear |
1 |
15 |
16 |
16 |
13 |
| quadratic |
2 |
483 |
448 |
448 |
451 |
| cubic |
3 |
9.453 |
9.488 |
9.488 |
9.391 |
| quartic |
4 |
149.360 |
148.736 |
148.736 |
148.833 |
| quintic |
5 |
1.906.064 |
1.906.688 |
1.906.688 |
1.905.072 |
| sextic |
6 |
20.654.992 |
20.647.424 |
20.647.424 |
20.649.040 |
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