Reduction formula for point group D2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
C2 (y) |
C2 (x) |
i |
 (xy) |
(xz) |
(yz) |
| Cartesian 3N |
75 |
-1 |
-1 |
-1 |
-3 |
1 |
1 |
9 |
| 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 |
69 |
1 |
1 |
1 |
-3 |
1 |
1 |
9 |
Decomposition into Irreducible representations
| Motion |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Cartesian 3N |
10 |
8 |
8 |
10 |
8 |
11 |
11 |
9 |
75 |
| 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 |
10 |
7 |
7 |
9 |
8 |
10 |
10 |
8 |
69 |
Molecule Parameter
| Number of Atoms (N) |
25 |
| Number of internal coordinates |
69 |
| Number of independant internal coordinates |
10 |
| Number of vibrational modes |
69 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Linear (IR) |
10 |
7 |
7 |
9 |
8 |
10 |
10 |
8 |
28 / 41 |
| Quadratic (Raman) |
10 |
7 |
7 |
9 |
8 |
10 |
10 |
8 |
33 / 36 |
| IR + Raman |
- |
- |
- |
- |
8 |
- |
- |
- |
0* / 8 |
* 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 |
69 |
1 |
1 |
1 |
-3 |
1 |
1 |
9 |
| quadratic |
2 |
2.415 |
35 |
35 |
35 |
39 |
35 |
35 |
75 |
| cubic |
3 |
57.155 |
35 |
35 |
35 |
-109 |
35 |
35 |
435 |
| quartic |
4 |
1.028.790 |
630 |
630 |
630 |
774 |
630 |
630 |
2.310 |
| quintic |
5 |
15.020.334 |
630 |
630 |
630 |
-2.034 |
630 |
630 |
10.422 |
| sextic |
6 |
185.250.786 |
7.770 |
7.770 |
7.770 |
10.434 |
7.770 |
7.770 |
43.738 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
| linear |
1 |
10 |
7 |
7 |
9 |
8 |
10 |
10 |
8 |
| quadratic |
2 |
338 |
293 |
293 |
303 |
292 |
302 |
302 |
292 |
| cubic |
3 |
7.207 |
7.072 |
7.072 |
7.172 |
7.108 |
7.208 |
7.208 |
7.108 |
| quartic |
4 |
129.378 |
128.328 |
128.328 |
128.748 |
128.292 |
128.712 |
128.712 |
128.292 |
| quintic |
5 |
1.878.984 |
1.875.906 |
1.875.906 |
1.878.354 |
1.876.572 |
1.879.020 |
1.879.020 |
1.876.572 |
| sextic |
6 |
23.167.976 |
23.151.214 |
23.151.214 |
23.160.206 |
23.150.548 |
23.159.540 |
23.159.540 |
23.150.548 |
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