Reduction formula for point group D2d
Characters for molecular motions
Motion |
E |
2S4 |
C2 (z) |
2C'2 |
2d |
Cartesian 3N |
72 |
0 |
0 |
-4 |
4 |
Translation (x,y,z) |
3 |
-1 |
-1 |
-1 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
-1 |
-1 |
Vibration |
66 |
0 |
2 |
-2 |
4 |
Decomposition into Irreducible representations
Motion |
A1 |
A2 |
B1 |
B2 |
E |
Total |
Cartesian 3N |
9 |
9 |
7 |
11 |
18 |
54 |
Translation (x,y,z) |
0 |
0 |
0 |
1 |
1 |
2 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
1 |
2 |
Vibration |
9 |
8 |
7 |
10 |
16 |
50 |
Molecule Parameter
Number of Atoms (N) |
24 |
Number of internal coordinates |
66 |
Number of independant internal coordinates |
9 |
Number of vibrational modes |
50 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A1 |
A2 |
B1 |
B2 |
E |
Total |
Linear (IR) |
9 |
8 |
7 |
10 |
16 |
26 / 24 |
Quadratic (Raman) |
9 |
8 |
7 |
10 |
16 |
42 / 8 |
IR + Raman |
- |
8 |
- |
10 |
16 |
26 / 8 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
2S4 |
C2 (z) |
2C'2 |
2d |
linear |
1 |
66 |
0 |
2 |
-2 |
4 |
quadratic |
2 |
2.211 |
1 |
35 |
35 |
41 |
cubic |
3 |
50.116 |
0 |
68 |
-68 |
144 |
quartic |
4 |
864.501 |
17 |
629 |
629 |
841 |
quintic |
5 |
12.103.014 |
0 |
1.190 |
-1.190 |
2.660 |
sextic |
6 |
143.218.999 |
17 |
7.735 |
7.735 |
11.585 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
B1 |
B2 |
E |
linear |
1 |
9 |
8 |
7 |
10 |
16 |
quadratic |
2 |
300 |
262 |
279 |
282 |
544 |
cubic |
3 |
6.292 |
6.254 |
6.220 |
6.326 |
12.512 |
quartic |
4 |
108.513 |
107.778 |
108.084 |
108.190 |
215.968 |
quintic |
5 |
1.513.393 |
1.512.658 |
1.512.063 |
1.513.988 |
3.025.456 |
sextic |
6 |
17.908.176 |
17.898.516 |
17.902.375 |
17.904.300 |
35.802.816 |
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