Reduction formula for point group C2
Characters for molecular motions
| Motion |
E |
C2 |
| Cartesian 3N |
90 |
30 |
| Translation (x,y,z) |
3 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
| Vibration |
84 |
32 |
Decomposition into Irreducible representations
| Motion |
A |
B |
Total |
| Cartesian 3N |
60 |
30 |
90 |
| Translation (x,y,z) |
1 |
2 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
| Vibration |
58 |
26 |
84 |
Molecule Parameter
| Number of Atoms (N) |
30 |
| Number of internal coordinates |
84 |
| Number of independant internal coordinates |
58 |
| Number of vibrational modes |
84 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A |
B |
Total |
| Linear (IR) |
58 |
26 |
84 / 0 |
| Quadratic (Raman) |
58 |
26 |
84 / 0 |
| IR + Raman |
58 |
26 |
84 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 |
| linear |
1 |
84 |
32 |
| quadratic |
2 |
3.570 |
554 |
| cubic |
3 |
102.340 |
6.816 |
| quartic |
4 |
2.225.895 |
66.439 |
| quintic |
5 |
39.175.752 |
543.808 |
| sextic |
6 |
581.106.988 |
3.874.748 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A |
B |
| linear |
1 |
58 |
26 |
| quadratic |
2 |
2.062 |
1.508 |
| cubic |
3 |
54.578 |
47.762 |
| quartic |
4 |
1.146.167 |
1.079.728 |
| quintic |
5 |
19.859.780 |
19.315.972 |
| sextic |
6 |
292.490.868 |
288.616.120 |
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