Reduction formula for point group D2d
Characters for molecular motions
Motion |
E |
2S4 |
C2 (z) |
2C'2 |
2d |
Cartesian 3N |
66 |
0 |
-2 |
-2 |
6 |
Translation (x,y,z) |
3 |
-1 |
-1 |
-1 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
-1 |
-1 |
Vibration |
60 |
0 |
0 |
0 |
6 |
Decomposition into Irreducible representations
Motion |
A1 |
A2 |
B1 |
B2 |
E |
Total |
Cartesian 3N |
9 |
7 |
6 |
10 |
17 |
49 |
Translation (x,y,z) |
0 |
0 |
0 |
1 |
1 |
2 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
1 |
2 |
Vibration |
9 |
6 |
6 |
9 |
15 |
45 |
Molecule Parameter
Number of Atoms (N) |
22 |
Number of internal coordinates |
60 |
Number of independant internal coordinates |
9 |
Number of vibrational modes |
45 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A1 |
A2 |
B1 |
B2 |
E |
Total |
Linear (IR) |
9 |
6 |
6 |
9 |
15 |
24 / 21 |
Quadratic (Raman) |
9 |
6 |
6 |
9 |
15 |
39 / 6 |
IR + Raman |
- |
6 |
- |
9 |
15 |
24 / 6 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
2S4 |
C2 (z) |
2C'2 |
2d |
linear |
1 |
60 |
0 |
0 |
0 |
6 |
quadratic |
2 |
1.830 |
0 |
30 |
30 |
48 |
cubic |
3 |
37.820 |
0 |
0 |
0 |
218 |
quartic |
4 |
595.665 |
15 |
465 |
465 |
1.071 |
quintic |
5 |
7.624.512 |
0 |
0 |
0 |
4.032 |
sextic |
6 |
82.598.880 |
0 |
4.960 |
4.960 |
15.456 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
B1 |
B2 |
E |
linear |
1 |
9 |
6 |
6 |
9 |
15 |
quadratic |
2 |
252 |
213 |
228 |
237 |
450 |
cubic |
3 |
4.782 |
4.673 |
4.673 |
4.782 |
9.455 |
quartic |
4 |
74.904 |
74.136 |
74.361 |
74.664 |
148.800 |
quintic |
5 |
954.072 |
952.056 |
952.056 |
954.072 |
1.906.128 |
sextic |
6 |
10.330.584 |
10.320.376 |
10.322.856 |
10.328.104 |
20.648.480 |
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