Reduction formula for point group Ih
Your representation
E |
12C5 |
12(C5)2 |
20C3 |
15C2 |
i |
12S10 |
12(S10)3 |
20S6 |
15 |
72 |
6.4721 |
-2.4721 |
0 |
0 |
0 |
0.0000 |
-0.0000 |
0 |
8 |
can be reduced to
Ag |
T1g |
T2g |
Gg |
Hg |
Au |
T1u |
T2u |
Gu |
Hu |
2 |
2 |
0 |
2 |
4 |
0 |
4 |
2 |
2 |
2 |
Substraction of translational and rotational contributions results in
Ag |
T1g |
T2g |
Gg |
Hg |
Au |
T1u |
T2u |
Gu |
Hu |
2 |
1 |
0 |
2 |
4 |
0 |
3 |
2 |
2 |
2 |
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 |
2 |
1 |
0 |
2 |
4 |
0 |
3 |
2 |
2 |
2 |
quadratic |
32 |
44 |
44 |
74 |
106 |
15 |
59 |
58 |
72 |
87 |
cubic |
474 |
1201 |
1200 |
1674 |
2137 |
386 |
1289 |
1288 |
1674 |
2049 |
quartic |
7514 |
21322 |
21322 |
28835 |
36349 |
7052 |
21746 |
21746 |
28798 |
35850 |
Number of independant internal coordinates |
2 |
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