Reduction formula for point group Ih
Your representation
E |
12C5 |
12(C5)2 |
20C3 |
15C2 |
i |
12S10 |
12(S10)3 |
20S6 |
15 |
180 |
0.0000 |
-0.0000 |
0 |
0 |
0 |
0.0000 |
-0.0000 |
0 |
4 |
can be reduced to
Ag |
T1g |
T2g |
Gg |
Hg |
Au |
T1u |
T2u |
Gu |
Hu |
2 |
4 |
4 |
6 |
8 |
1 |
5 |
5 |
6 |
7 |
Substraction of translational and rotational contributions results in
Ag |
T1g |
T2g |
Gg |
Hg |
Au |
T1u |
T2u |
Gu |
Hu |
2 |
3 |
4 |
6 |
8 |
1 |
4 |
5 |
6 |
7 |
Force field analysis
Infrared and Raman activities (harmonic approximation)
Method |
Ag |
T1g |
T2g |
Gg |
Hg |
Au |
T1u |
T2u |
Gu |
Hu |
Infrared |
- |
- |
- |
- |
- |
- |
+ |
- |
- |
- |
Raman |
+ |
- |
- |
- |
+ |
- |
- |
- |
- |
- |
Number of force field parameters
Force field |
No. 1 |
No. 2 |
No. 3 |
linear |
174 |
174 |
2 |
quadratic |
30276 |
15225 |
151 |
cubic |
5268024 |
893200 |
7519 |
quartic |
916636176 |
39524100 |
330468 |
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 |
3 |
4 |
6 |
8 |
1 |
4 |
5 |
6 |
7 |
quadratic |
151 |
361 |
359 |
510 |
661 |
126 |
380 |
379 |
504 |
630 |
cubic |
7519 |
22262 |
22263 |
29784 |
37274 |
7429 |
22352 |
22353 |
29784 |
37184 |
quartic |
330468 |
987131 |
987130 |
1317597 |
1648065 |
329269 |
988075 |
988073 |
1317342 |
1646611 |
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