Reduction formula for point group D5d
Your representation
E |
2C5 |
2(C5)2 |
5C'2 |
i |
2(S10)3 |
2S10 |
5d |
120 |
0.0000 |
-0.0000 |
0 |
0 |
-0.0000 |
0.0000 |
8 |
can be reduced to
A1g |
A2g |
E1g |
E2g |
A1u |
A2u |
E1u |
E2u |
8 |
4 |
12 |
12 |
4 |
8 |
12 |
12 |
Substraction of translational and rotational contributions results in
A1g |
A2g |
E1g |
E2g |
A1u |
A2u |
E1u |
E2u |
8 |
3 |
11 |
12 |
4 |
7 |
11 |
12 |
Force field analysis
Infrared and Raman activities (harmonic approximation)
Method |
A1g |
A2g |
E1g |
E2g |
A1u |
A2u |
E1u |
E2u |
Infrared |
- |
- |
- |
- |
- |
+ |
+ |
- |
Raman |
+ |
- |
+ |
+ |
- |
- |
- |
- |
Number of force field parameters
Force field |
No. 1 |
No. 2 |
No. 3 |
linear |
114 |
114 |
8 |
quadratic |
12996 |
6555 |
368 |
cubic |
1481544 |
253460 |
12837 |
quartic |
168896016 |
7413705 |
372128 |
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 |
A1g |
A2g |
E1g |
E2g |
A1u |
A2u |
E1u |
E2u |
linear |
8 |
3 |
11 |
12 |
4 |
7 |
11 |
12 |
quadratic |
368 |
294 |
662 |
660 |
318 |
333 |
650 |
649 |
cubic |
12837 |
12507 |
25346 |
25347 |
12565 |
12779 |
25346 |
25347 |
quartic |
372128 |
369409 |
741536 |
741535 |
370128 |
371078 |
741206 |
741204 |
Number of independant internal coordinates |
8 |
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