Reduction formula for point group D2
Characters for molecular motions
| Motion |
E |
C2 (z) |
C2 (y) |
C2 (x) |
| Cartesian 3N |
216 |
0 |
-8 |
0 |
| Translation (x,y,z) |
3 |
-1 |
-1 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
210 |
2 |
-6 |
2 |
Decomposition into Irreducible representations
| Motion |
A |
B1 |
B2 |
B3 |
Total |
| Cartesian 3N |
52 |
56 |
52 |
56 |
216 |
| Translation (x,y,z) |
0 |
1 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
52 |
54 |
50 |
54 |
210 |
Molecule Parameter
| Number of Atoms (N) |
72 |
| Number of internal coordinates |
210 |
| Number of independant internal coordinates |
52 |
| Number of vibrational modes |
210 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A |
B1 |
B2 |
B3 |
Total |
| Linear (IR) |
52 |
54 |
50 |
54 |
158 / 52 |
| Quadratic (Raman) |
52 |
54 |
50 |
54 |
210 / 0 |
| IR + Raman |
- |
54 |
50 |
54 |
158 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
C2 (y) |
C2 (x) |
| linear |
1 |
210 |
2 |
-6 |
2 |
| quadratic |
2 |
22.155 |
107 |
123 |
107 |
| cubic |
3 |
1.565.620 |
212 |
-668 |
212 |
| quartic |
4 |
83.369.265 |
5.777 |
7.521 |
5.777 |
| quintic |
5 |
3.568.204.542 |
11.342 |
-37.482 |
11.342 |
| sextic |
6 |
127.860.662.755 |
209.827 |
305.731 |
209.827 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A |
B1 |
B2 |
B3 |
| linear |
1 |
52 |
54 |
50 |
54 |
| quadratic |
2 |
5.623 |
5.508 |
5.516 |
5.508 |
| cubic |
3 |
391.344 |
391.572 |
391.132 |
391.572 |
| quartic |
4 |
20.847.085 |
20.840.436 |
20.841.308 |
20.840.436 |
| quintic |
5 |
892.047.436 |
892.060.506 |
892.036.094 |
892.060.506 |
| sextic |
6 |
31.965.347.035 |
31.965.089.256 |
31.965.137.208 |
31.965.089.256 |
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