Reduction formula for point group T
Characters for molecular motions
Motion |
E |
4C3 |
4(C3)2 |
3C2 |
Cartesian 3N |
12 |
0 |
0 |
0 |
Translation (x,y,z) |
3 |
0 |
0 |
-1 |
Rotation (Rx,Ry,Rz) |
3 |
0 |
0 |
-1 |
Vibration |
6 |
0 |
0 |
2 |
Decomposition into Irreducible representations
Motion |
A |
E |
T |
Total |
Cartesian 3N |
1 |
1 |
3 |
5 |
Translation (x,y,z) |
0 |
0 |
1 |
1 |
Rotation (Rx,Ry,Rz) |
0 |
0 |
1 |
1 |
Vibration |
1 |
1 |
1 |
3 |
Molecule Parameter
Number of Atoms (N) |
4 |
Number of internal coordinates |
6 |
Number of independant internal coordinates |
1 |
Number of vibrational modes |
3 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A |
E |
T |
Total |
Linear (IR) |
1 |
1 |
1 |
1 / 2 |
Quadratic (Raman) |
1 |
1 |
1 |
3 / 0 |
IR + Raman |
- |
- |
1 |
1 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
4C3 |
4(C3)2 |
3C2 |
linear |
1 |
6 |
0 |
0 |
2 |
quadratic |
2 |
21 |
0 |
0 |
5 |
cubic |
3 |
56 |
2 |
2 |
8 |
quartic |
4 |
126 |
0 |
0 |
14 |
quintic |
5 |
252 |
0 |
0 |
20 |
sextic |
6 |
462 |
3 |
3 |
30 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A |
E |
T |
linear |
1 |
1 |
1 |
1 |
quadratic |
2 |
3 |
3 |
4 |
cubic |
3 |
8 |
6 |
12 |
quartic |
4 |
14 |
14 |
28 |
quintic |
5 |
26 |
26 |
58 |
sextic |
6 |
48 |
45 |
108 |
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