Reduction formula for point group D8d
Your representation
| E |
2S16 |
2C8 |
2(S16)3 |
2C4 |
2(S16)5 |
2(C8)3 |
2(S16)7 |
C2 |
8C'2 |
8 d |
| 99 |
0.8478 |
2.4142 |
-0.2346 |
1 |
-1.7654 |
-0.4142 |
-2.8478 |
-1 |
-1 |
5 |
can be reduced to
| A1 |
A2 |
B1 |
B2 |
E1 |
E2 |
E3 |
E4 |
E5 |
E6 |
E7 |
| 4 |
2 |
2 |
5 |
7 |
6 |
6 |
6 |
6 |
6 |
6 |
Substraction of translational and rotational contributions results in
| A1 |
A2 |
B1 |
B2 |
E1 |
E2 |
E3 |
E4 |
E5 |
E6 |
E7 |
| 4 |
1 |
2 |
4 |
6 |
6 |
6 |
6 |
6 |
6 |
5 |
Force field analysis
Infrared and Raman activities (harmonic approximation)
| Method |
A1 |
A2 |
B1 |
B2 |
E1 |
E2 |
E3 |
E4 |
E5 |
E6 |
E7 |
| 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 |
A1 |
A2 |
B1 |
B2 |
E1 |
E2 |
E3 |
E4 |
E5 |
E6 |
E7 |
| linear |
4 |
1 |
2 |
4 |
6 |
6 |
6 |
6 |
6 |
6 |
5 |
| quadratic |
165 |
112 |
135 |
141 |
270 |
276 |
270 |
276 |
270 |
276 |
271 |
| cubic |
4402 |
4251 |
4275 |
4379 |
8648 |
8654 |
8648 |
8654 |
8648 |
8654 |
8648 |
| quartic |
104560 |
103136 |
103700 |
103996 |
207552 |
207690 |
207552 |
207696 |
207552 |
207690 |
207552 |
| Number of independant internal coordinates |
4 |
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