Force field analysis for point group D
h
Number of atoms: 3
Your
3N representation
E |
2C |
 v |
i |
2S |
C'2 |
9 |
3+ 6cos( ) |
3 | -3 |
-1+2cos( ) |
-1 |
can be reduced to
A1g= +g |
A2g= -g |
E1g= g |
E2g= g |
E3g= g |
E4g= g |
A1u= +u |
A2u= -u |
E1u= u |
E2u= u |
E3u= u |
E4u= u |
1 |
0 |
1 |
0 |
0 |
0 |
2 |
0 |
2 |
0 |
0 |
0 |
Substraction of translational and rotational contributions results in
A1g= +g |
A2g= -g |
E1g= g |
E2g= g |
E3g= g |
E4g= g |
A1u= +u |
A2u= -u |
E1u= u |
E2u= u |
E3u= u |
E4u= u |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
0 |
Infrared and Raman activities (harmonic approximation)
Method |
A1g= +g |
A2g= -g |
E1g= g |
E2g= g |
E3g= g |
E4g= g |
A1u= +u |
A2u= -u |
E1u= u |
E2u= u |
E3u= u |
E4u= u |
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 |
A1g= +g |
A2g= -g |
E1g= g |
E2g= g |
E3g= g |
E4g= g |
A1u= +u |
A2u= -u |
E1u= u |
E2u= u |
E3u= u |
E4u= u |
linear |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
0 |
quadratic |
3 |
0 |
1 |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
0 |
cubic |
3 |
0 |
3 |
1 |
1 |
0 |
3 |
0 |
1 |
1 |
0 |
0 |
quartic |
6 |
0 |
3 |
3 |
1 |
1 |
3 |
0 |
3 |
1 |
1 |
0 |
Number of independant internal coordinates |
1 |
Literature
- J.K.G. Watson, J. Mol. Spec. 41 229 (1972)
The Numbers of Structural Parameters and Potential Constants of Molecules
Last update November, 21th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement