Reduction formula for point group C2h
Characters for molecular motions
Motion |
E |
C2 (z) |
i |
h |
Cartesian 3N |
120 |
0 |
0 |
8 |
Translation (x,y,z) |
3 |
-1 |
-3 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
3 |
-1 |
Vibration |
114 |
2 |
0 |
8 |
Decomposition into Irreducible representations
Motion |
Ag |
Bg |
Au |
Bu |
Total |
Cartesian 3N |
32 |
28 |
28 |
32 |
120 |
Translation (x,y,z) |
0 |
0 |
1 |
2 |
3 |
Rotation (Rx,Ry,Rz) |
1 |
2 |
0 |
0 |
3 |
Vibration |
31 |
26 |
27 |
30 |
114 |
Molecule Parameter
Number of Atoms (N) |
40 |
Number of internal coordinates |
114 |
Number of independant internal coordinates |
31 |
Number of vibrational modes |
114 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
Ag |
Bg |
Au |
Bu |
Total |
Linear (IR) |
31 |
26 |
27 |
30 |
57 / 57 |
Quadratic (Raman) |
31 |
26 |
27 |
30 |
57 / 57 |
IR + Raman |
- |
- |
- |
- |
0* / 0 |
* Center of inversion: Mutual Exclusion Principle
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C2 (z) |
i |
h |
linear |
1 |
114 |
2 |
0 |
8 |
quadratic |
2 |
6.555 |
59 |
57 |
89 |
cubic |
3 |
253.460 |
116 |
0 |
544 |
quartic |
4 |
7.413.705 |
1.769 |
1.653 |
3.669 |
quintic |
5 |
174.963.438 |
3.422 |
0 |
18.600 |
sextic |
6 |
3.470.108.187 |
35.931 |
32.509 |
96.957 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
Ag |
Bg |
Au |
Bu |
linear |
1 |
31 |
26 |
27 |
30 |
quadratic |
2 |
1.690 |
1.616 |
1.617 |
1.632 |
cubic |
3 |
63.530 |
63.200 |
63.258 |
63.472 |
quartic |
4 |
1.855.199 |
1.852.480 |
1.852.538 |
1.853.488 |
quintic |
5 |
43.746.365 |
43.735.354 |
43.737.065 |
43.744.654 |
sextic |
6 |
867.568.396 |
867.501.952 |
867.503.663 |
867.534.176 |
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