Reduction formula for point group T
Characters for molecular motions
| Motion |
E |
4C3 |
4(C3)2 |
3C2 |
| Cartesian 3N |
120 |
0 |
0 |
0 |
| Translation (x,y,z) |
3 |
0 |
0 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
0 |
-1 |
| Vibration |
114 |
0 |
0 |
2 |
Decomposition into Irreducible representations
| Motion |
A |
E |
T |
Total |
| Cartesian 3N |
10 |
10 |
30 |
50 |
| Translation (x,y,z) |
0 |
0 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
0 |
0 |
1 |
1 |
| Vibration |
10 |
10 |
28 |
48 |
Molecule Parameter
| Number of Atoms (N) |
40 |
| Number of internal coordinates |
114 |
| Number of independant internal coordinates |
10 |
| Number of vibrational modes |
48 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A |
E |
T |
Total |
| Linear (IR) |
10 |
10 |
28 |
28 / 20 |
| Quadratic (Raman) |
10 |
10 |
28 |
48 / 0 |
| IR + Raman |
- |
- |
28 |
28 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
4C3 |
4(C3)2 |
3C2 |
| linear |
1 |
114 |
0 |
0 |
2 |
| quadratic |
2 |
6.555 |
0 |
0 |
59 |
| cubic |
3 |
253.460 |
38 |
38 |
116 |
| quartic |
4 |
7.413.705 |
0 |
0 |
1.769 |
| quintic |
5 |
174.963.438 |
0 |
0 |
3.422 |
| sextic |
6 |
3.470.108.187 |
741 |
741 |
35.931 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A |
E |
T |
| linear |
1 |
10 |
10 |
28 |
| quadratic |
2 |
561 |
561 |
1.624 |
| cubic |
3 |
21.176 |
21.138 |
63.336 |
| quartic |
4 |
618.251 |
618.251 |
1.852.984 |
| quintic |
5 |
14.581.142 |
14.581.142 |
43.740.004 |
| sextic |
6 |
289.185.159 |
289.184.418 |
867.518.064 |
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