Reduction formula for point group D5d
Your representation
E |
2C5 |
2(C5)2 |
5C'2 |
i |
2(S10)3 |
2S10 |
5d |
180 |
0.0000 |
-0.0000 |
0 |
0 |
-0.0000 |
0.0000 |
4 |
can be reduced to
A1g |
A2g |
E1g |
E2g |
A1u |
A2u |
E1u |
E2u |
10 |
8 |
18 |
18 |
8 |
10 |
18 |
18 |
Substraction of translational and rotational contributions results in
A1g |
A2g |
E1g |
E2g |
A1u |
A2u |
E1u |
E2u |
10 |
7 |
17 |
18 |
8 |
9 |
17 |
18 |
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 |
174 |
174 |
10 |
quadratic |
30276 |
15225 |
812 |
cubic |
5268024 |
893200 |
44793 |
quartic |
916636176 |
39524100 |
1978533 |
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 |
10 |
7 |
17 |
18 |
8 |
9 |
17 |
18 |
quadratic |
812 |
720 |
1532 |
1530 |
756 |
759 |
1514 |
1513 |
cubic |
44793 |
44525 |
89320 |
89321 |
44613 |
44705 |
89320 |
89321 |
quartic |
1978533 |
1974261 |
3952793 |
3952792 |
1975880 |
1976148 |
3952028 |
3952026 |
Number of independant internal coordinates |
10 |
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