Reduction formula for point group D2d
Characters for molecular motions
| Motion |
E |
2S4 |
C2 (z) |
2C'2 |
2 d |
| Cartesian 3N |
84 |
0 |
0 |
0 |
6 |
| Translation (x,y,z) |
3 |
-1 |
-1 |
-1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
-1 |
-1 |
| Vibration |
78 |
0 |
2 |
2 |
6 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Cartesian 3N |
12 |
9 |
9 |
12 |
21 |
63 |
| Translation (x,y,z) |
0 |
0 |
0 |
1 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
1 |
2 |
| Vibration |
12 |
8 |
9 |
11 |
19 |
59 |
Molecule Parameter
| Number of Atoms (N) |
28 |
| Number of internal coordinates |
78 |
| Number of independant internal coordinates |
12 |
| Number of vibrational modes |
59 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Linear (IR) |
12 |
8 |
9 |
11 |
19 |
30 / 29 |
| Quadratic (Raman) |
12 |
8 |
9 |
11 |
19 |
51 / 8 |
| IR + Raman |
- |
8 |
- |
11 |
19 |
30 / 8 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2S4 |
C2 (z) |
2C'2 |
2d |
| linear |
1 |
78 |
0 |
2 |
2 |
6 |
| quadratic |
2 |
3.081 |
1 |
41 |
41 |
57 |
| cubic |
3 |
82.160 |
0 |
80 |
80 |
272 |
| quartic |
4 |
1.663.740 |
20 |
860 |
860 |
1.548 |
| quintic |
5 |
27.285.336 |
0 |
1.640 |
1.640 |
6.264 |
| sextic |
6 |
377.447.148 |
20 |
12.300 |
12.300 |
27.420 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
E |
| linear |
1 |
12 |
8 |
9 |
11 |
19 |
| quadratic |
2 |
415 |
366 |
386 |
394 |
760 |
| cubic |
3 |
10.368 |
10.192 |
10.232 |
10.328 |
20.520 |
| quartic |
4 |
208.682 |
207.478 |
207.898 |
208.242 |
415.720 |
| quintic |
5 |
3.412.848 |
3.408.896 |
3.409.716 |
3.412.028 |
6.820.924 |
| sextic |
6 |
47.192.366 |
47.172.506 |
47.178.646 |
47.186.206 |
94.358.712 |
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