Reduction formula for point group Ih
Your representation
E |
12C5 |
12(C5)2 |
20C3 |
15C2 |
i |
12S10 |
12(S10)3 |
20S6 |
15 |
36 |
3.2361 |
-1.2361 |
0 |
0 |
0 |
0.0000 |
-0.0000 |
0 |
4 |
can be reduced to
Ag |
T1g |
T2g |
Gg |
Hg |
Au |
T1u |
T2u |
Gu |
Hu |
1 |
1 |
0 |
1 |
2 |
0 |
2 |
1 |
1 |
1 |
Substraction of translational and rotational contributions results in
Ag |
T1g |
T2g |
Gg |
Hg |
Au |
T1u |
T2u |
Gu |
Hu |
1 |
0 |
0 |
1 |
2 |
0 |
1 |
1 |
1 |
1 |
Force field analysis
Infrared and Raman activities (harmonic approximation)
Method |
Ag |
T1g |
T2g |
Gg |
Hg |
Au |
T1u |
T2u |
Gu |
Hu |
Infrared |
- |
- |
- |
- |
- |
- |
+ |
- |
- |
- |
Raman |
+ |
- |
- |
- |
+ |
- |
- |
- |
- |
- |
No. 1 : Total number of force constants .
No. 2 : Total number of force constants k.
No. 3 : Total number of nonvanishing force constants k.
Symmetry properties of force field parameters
Force field |
Ag |
T1g |
T2g |
Gg |
Hg |
Au |
T1u |
T2u |
Gu |
Hu |
linear |
1 |
0 |
0 |
1 |
2 |
0 |
1 |
1 |
1 |
1 |
quadratic |
9 |
7 |
7 |
16 |
25 |
3 |
12 |
12 |
15 |
18 |
cubic |
56 |
111 |
111 |
167 |
218 |
38 |
129 |
129 |
167 |
200 |
quartic |
393 |
975 |
975 |
1368 |
1761 |
327 |
1033 |
1033 |
1360 |
1687 |
Number of independant internal coordinates |
1 |
Literature
- J.K.G. Watson, J. Mol. Spec. 41 229 (1972)
The Numbers of Structural Parameters and Potential Constants of Molecules
Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement