Reduction formula for point group D2d
Characters for molecular motions
| Motion |
E |
2S4 |
C2 (z) |
2C'2 |
2 d |
| Cartesian 3N |
51 |
-1 |
-1 |
-1 |
5 |
| Translation (x,y,z) |
3 |
-1 |
-1 |
-1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
-1 |
-1 |
| Vibration |
45 |
-1 |
1 |
1 |
5 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Cartesian 3N |
7 |
5 |
5 |
8 |
13 |
38 |
| Translation (x,y,z) |
0 |
0 |
0 |
1 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
1 |
2 |
| Vibration |
7 |
4 |
5 |
7 |
11 |
34 |
Molecule Parameter
| Number of Atoms (N) |
17 |
| Number of internal coordinates |
45 |
| Number of independant internal coordinates |
7 |
| Number of vibrational modes |
34 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Linear (IR) |
7 |
4 |
5 |
7 |
11 |
18 / 16 |
| Quadratic (Raman) |
7 |
4 |
5 |
7 |
11 |
30 / 4 |
| IR + Raman |
- |
4 |
- |
7 |
11 |
18 / 4 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2S4 |
C2 (z) |
2C'2 |
2d |
| linear |
1 |
45 |
-1 |
1 |
1 |
5 |
| quadratic |
2 |
1.035 |
1 |
23 |
23 |
35 |
| cubic |
3 |
16.215 |
-1 |
23 |
23 |
135 |
| quartic |
4 |
194.580 |
12 |
276 |
276 |
580 |
| quintic |
5 |
1.906.884 |
-12 |
276 |
276 |
1.876 |
| sextic |
6 |
15.890.700 |
12 |
2.300 |
2.300 |
6.300 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
E |
| linear |
1 |
7 |
4 |
5 |
7 |
11 |
| quadratic |
2 |
147 |
118 |
129 |
135 |
253 |
| cubic |
3 |
2.069 |
1.990 |
2.002 |
2.058 |
4.048 |
| quartic |
4 |
24.574 |
24.146 |
24.278 |
24.430 |
48.576 |
| quintic |
5 |
238.930 |
237.854 |
237.998 |
238.798 |
476.652 |
| sextic |
6 |
1.988.778 |
1.984.478 |
1.985.622 |
1.987.622 |
3.972.100 |
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