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
