Reduction formula for point group D4d
Your representation
| E |
2S8 |
2C4 |
2(S8)3 |
C2 |
4C'2 |
4 d |
| 99 |
0.4142 |
1 |
-2.4142 |
-1 |
-1 |
9 |
can be reduced to
| A1 |
A2 |
B1 |
B2 |
E1 |
E2 |
E3 |
| 8 |
4 |
4 |
9 |
13 |
12 |
12 |
Substraction of translational and rotational contributions results in
| A1 |
A2 |
B1 |
B2 |
E1 |
E2 |
E3 |
| 8 |
3 |
4 |
8 |
12 |
12 |
11 |
Force field analysis
Infrared and Raman activities (harmonic approximation)
| Method |
A1 |
A2 |
B1 |
B2 |
E1 |
E2 |
E3 |
| 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 |
| linear |
8 |
3 |
4 |
8 |
12 |
12 |
11 |
| quadratic |
310 |
243 |
266 |
286 |
540 |
552 |
541 |
| cubic |
8801 |
8506 |
8530 |
8778 |
17296 |
17308 |
17296 |
| quartic |
208800 |
206592 |
207156 |
208236 |
415104 |
415380 |
415104 |
| 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