Reduction formula for point group D2d
Characters for molecular motions
| Motion |
E |
2S4 |
C2 (z) |
2C'2 |
2 d |
| Cartesian 3N |
156 |
0 |
0 |
0 |
14 |
| Translation (x,y,z) |
3 |
-1 |
-1 |
-1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
-1 |
-1 |
| Vibration |
150 |
0 |
2 |
2 |
14 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Cartesian 3N |
23 |
16 |
16 |
23 |
39 |
117 |
| Translation (x,y,z) |
0 |
0 |
0 |
1 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
1 |
2 |
| Vibration |
23 |
15 |
16 |
22 |
37 |
113 |
Molecule Parameter
| Number of Atoms (N) |
52 |
| Number of internal coordinates |
150 |
| Number of independant internal coordinates |
23 |
| Number of vibrational modes |
113 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Linear (IR) |
23 |
15 |
16 |
22 |
37 |
59 / 54 |
| Quadratic (Raman) |
23 |
15 |
16 |
22 |
37 |
98 / 15 |
| IR + Raman |
- |
15 |
- |
22 |
37 |
59 / 15 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2S4 |
C2 (z) |
2C'2 |
2d |
| linear |
1 |
150 |
0 |
2 |
2 |
14 |
| quadratic |
2 |
11.325 |
1 |
77 |
77 |
173 |
| cubic |
3 |
573.800 |
0 |
152 |
152 |
1.512 |
| quartic |
4 |
21.947.850 |
38 |
3.002 |
3.002 |
11.866 |
| quintic |
5 |
675.993.780 |
0 |
5.852 |
5.852 |
79.492 |
| sextic |
6 |
17.463.172.650 |
38 |
79.002 |
79.002 |
490.042 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
E |
| linear |
1 |
23 |
15 |
16 |
22 |
37 |
| quadratic |
2 |
1.488 |
1.363 |
1.401 |
1.449 |
2.812 |
| cubic |
3 |
72.160 |
71.328 |
71.404 |
72.084 |
143.412 |
| quartic |
4 |
2.747.583 |
2.740.149 |
2.741.631 |
2.746.063 |
5.486.212 |
| quintic |
5 |
84.521.290 |
84.478.618 |
84.481.544 |
84.518.364 |
168.996.982 |
| sextic |
6 |
2.183.048.727 |
2.182.764.205 |
2.182.803.687 |
2.183.009.207 |
4.365.773.412 |
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