Reduction formula for point group D2d
Characters for molecular motions
| Motion |
E |
2S4 |
C2 (z) |
2C'2 |
2 d |
| Cartesian 3N |
42 |
0 |
-2 |
-2 |
6 |
| Translation (x,y,z) |
3 |
-1 |
-1 |
-1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
-1 |
-1 |
| Vibration |
36 |
0 |
0 |
0 |
6 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Cartesian 3N |
6 |
4 |
3 |
7 |
11 |
31 |
| Translation (x,y,z) |
0 |
0 |
0 |
1 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
1 |
2 |
| Vibration |
6 |
3 |
3 |
6 |
9 |
27 |
Molecule Parameter
| Number of Atoms (N) |
14 |
| Number of internal coordinates |
36 |
| Number of independant internal coordinates |
6 |
| Number of vibrational modes |
27 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Linear (IR) |
6 |
3 |
3 |
6 |
9 |
15 / 12 |
| Quadratic (Raman) |
6 |
3 |
3 |
6 |
9 |
24 / 3 |
| IR + Raman |
- |
3 |
- |
6 |
9 |
15 / 3 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2S4 |
C2 (z) |
2C'2 |
2d |
| linear |
1 |
36 |
0 |
0 |
0 |
6 |
| quadratic |
2 |
666 |
0 |
18 |
18 |
36 |
| cubic |
3 |
8.436 |
0 |
0 |
0 |
146 |
| quartic |
4 |
82.251 |
9 |
171 |
171 |
561 |
| quintic |
5 |
658.008 |
0 |
0 |
0 |
1.812 |
| sextic |
6 |
4.496.388 |
0 |
1.140 |
1.140 |
5.552 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
E |
| linear |
1 |
6 |
3 |
3 |
6 |
9 |
| quadratic |
2 |
99 |
72 |
81 |
90 |
162 |
| cubic |
3 |
1.091 |
1.018 |
1.018 |
1.091 |
2.109 |
| quartic |
4 |
10.488 |
10.122 |
10.203 |
10.398 |
20.520 |
| quintic |
5 |
82.704 |
81.798 |
81.798 |
82.704 |
164.502 |
| sextic |
6 |
563.864 |
560.518 |
561.088 |
563.294 |
1.123.812 |
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