Reduction formula for point group O
Characters for molecular motions
| Motion |
E |
8C3 |
6C'2 |
6C4 |
3C2 =(C4)2 |
| Cartesian 3N |
240 |
0 |
0 |
0 |
0 |
| Translation (x,y,z) |
3 |
0 |
-1 |
1 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
1 |
-1 |
| Vibration |
234 |
0 |
2 |
-2 |
2 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
T1 |
T2 |
Total |
| Cartesian 3N |
10 |
10 |
20 |
30 |
30 |
100 |
| Translation (x,y,z) |
0 |
0 |
0 |
1 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
0 |
0 |
0 |
1 |
0 |
1 |
| Vibration |
10 |
10 |
20 |
28 |
30 |
98 |
Molecule Parameter
| Number of Atoms (N) |
80 |
| Number of internal coordinates |
234 |
| Number of independant internal coordinates |
10 |
| Number of vibrational modes |
98 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
T1 |
T2 |
Total |
| Linear (IR) |
10 |
10 |
20 |
28 |
30 |
28 / 70 |
| Quadratic (Raman) |
10 |
10 |
20 |
28 |
30 |
60 / 38 |
| IR + Raman |
- |
10 |
- |
- |
- |
0 / 10 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
8C3 |
6C'2 |
6C4 |
3C2 =(C4)2 |
| linear |
1 |
234 |
0 |
2 |
-2 |
2 |
| quadratic |
2 |
27.495 |
0 |
119 |
3 |
119 |
| cubic |
3 |
2.162.940 |
78 |
236 |
-4 |
236 |
| quartic |
4 |
128.154.195 |
0 |
7.139 |
63 |
7.139 |
| quintic |
5 |
6.100.139.682 |
0 |
14.042 |
-122 |
14.042 |
| sextic |
6 |
242.988.897.333 |
3.081 |
287.861 |
181 |
287.861 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
T1 |
T2 |
| linear |
1 |
10 |
10 |
20 |
28 |
30 |
| quadratic |
2 |
1.191 |
1.130 |
2.321 |
3.393 |
3.451 |
| cubic |
3 |
90.236 |
90.120 |
180.278 |
270.278 |
270.398 |
| quartic |
4 |
5.342.451 |
5.338.850 |
10.681.301 |
16.016.613 |
16.020.151 |
| quintic |
5 |
254.177.722 |
254.170.762 |
508.348.484 |
762.512.164 |
762.519.246 |
| sextic |
6 |
10.124.646.409 |
10.124.502.388 |
20.249.145.716 |
30.373.504.264 |
30.373.648.104 |
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