Reduction formula for point group D2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
C2 (y) |
C2 (x) |
i |
 (xy) |
(xz) |
(yz) |
| Cartesian 3N |
180 |
0 |
0 |
0 |
0 |
4 |
4 |
4 |
| Translation (x,y,z) |
3 |
-1 |
-1 |
-1 |
-3 |
1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
3 |
-1 |
-1 |
-1 |
| Vibration |
174 |
2 |
2 |
2 |
0 |
4 |
4 |
4 |
Decomposition into Irreducible representations
| Motion |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Cartesian 3N |
24 |
22 |
22 |
22 |
21 |
23 |
23 |
23 |
180 |
| Translation (x,y,z) |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
3 |
| Vibration |
24 |
21 |
21 |
21 |
21 |
22 |
22 |
22 |
174 |
Molecule Parameter
| Number of Atoms (N) |
60 |
| Number of internal coordinates |
174 |
| Number of independant internal coordinates |
24 |
| Number of vibrational modes |
174 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Linear (IR) |
24 |
21 |
21 |
21 |
21 |
22 |
22 |
22 |
66 / 108 |
| Quadratic (Raman) |
24 |
21 |
21 |
21 |
21 |
22 |
22 |
22 |
87 / 87 |
| IR + Raman |
- |
- |
- |
- |
21 |
- |
- |
- |
0* / 21 |
* Center of inversion: Mutual Exclusion Principle
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
C2 (y) |
C2 (x) |
i |
(xy) |
(xz) |
(yz) |
| linear |
1 |
174 |
2 |
2 |
2 |
0 |
4 |
4 |
4 |
| quadratic |
2 |
15.225 |
89 |
89 |
89 |
87 |
95 |
95 |
95 |
| cubic |
3 |
893.200 |
176 |
176 |
176 |
0 |
360 |
360 |
360 |
| quartic |
4 |
39.524.100 |
4.004 |
4.004 |
4.004 |
3.828 |
4.540 |
4.540 |
4.540 |
| quintic |
5 |
1.407.057.960 |
7.832 |
7.832 |
7.832 |
0 |
16.376 |
16.376 |
16.376 |
| sextic |
6 |
41.977.229.140 |
121.396 |
121.396 |
121.396 |
113.564 |
145.604 |
145.604 |
145.604 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
| linear |
1 |
24 |
21 |
21 |
21 |
21 |
22 |
22 |
22 |
| quadratic |
2 |
1.983 |
1.891 |
1.891 |
1.891 |
1.890 |
1.893 |
1.893 |
1.893 |
| cubic |
3 |
111.851 |
111.583 |
111.583 |
111.583 |
111.581 |
111.673 |
111.673 |
111.673 |
| quartic |
4 |
4.944.195 |
4.939.923 |
4.939.923 |
4.939.923 |
4.939.833 |
4.940.101 |
4.940.101 |
4.940.101 |
| quintic |
5 |
175.891.323 |
175.879.219 |
175.879.219 |
175.879.219 |
175.879.041 |
175.883.313 |
175.883.313 |
175.883.313 |
| sextic |
6 |
5.247.267.963 |
5.247.134.463 |
5.247.134.463 |
5.247.134.463 |
5.247.130.369 |
5.247.142.473 |
5.247.142.473 |
5.247.142.473 |
Literature
- J.K.G. Watson, J. Mol. Spec. 41 229 (1972)
The Numbers of Structural Parameters and Potential Constants of Molecules
- X.F. Zhou, P. Pulay. J. Comp. Chem. 10 No. 7, 935-938 (1989)
Characters for Symmetric and Antisymmetric Higher Powers of Representations:
Application to the Number of Anharmonic Force Constants in Symmetrical Molecules
Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement