Reduction formula for point group D2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
C2 (y) |
C2 (x) |
i |
 (xy) |
(xz) |
(yz) |
| Cartesian 3N |
60 |
0 |
0 |
0 |
0 |
12 |
8 |
0 |
| 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 |
54 |
2 |
2 |
2 |
0 |
12 |
8 |
0 |
Decomposition into Irreducible representations
| Motion |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Cartesian 3N |
10 |
8 |
7 |
5 |
5 |
7 |
8 |
10 |
60 |
| 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 |
6 |
4 |
5 |
6 |
7 |
9 |
54 |
Molecule Parameter
| Number of Atoms (N) |
20 |
| Number of internal coordinates |
54 |
| Number of independant internal coordinates |
10 |
| Number of vibrational modes |
54 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Linear (IR) |
10 |
7 |
6 |
4 |
5 |
6 |
7 |
9 |
22 / 32 |
| Quadratic (Raman) |
10 |
7 |
6 |
4 |
5 |
6 |
7 |
9 |
27 / 27 |
| IR + Raman |
- |
- |
- |
- |
5 |
- |
- |
- |
0* / 5 |
* 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 |
54 |
2 |
2 |
2 |
0 |
12 |
8 |
0 |
| quadratic |
2 |
1.485 |
29 |
29 |
29 |
27 |
99 |
59 |
27 |
| cubic |
3 |
27.720 |
56 |
56 |
56 |
0 |
616 |
304 |
0 |
| quartic |
4 |
395.010 |
434 |
434 |
434 |
378 |
3.234 |
1.434 |
378 |
| quintic |
5 |
4.582.116 |
812 |
812 |
812 |
0 |
14.784 |
5.760 |
0 |
| sextic |
6 |
45.057.474 |
4.466 |
4.466 |
4.466 |
3.654 |
60.830 |
21.542 |
3.654 |
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 |
6 |
4 |
5 |
6 |
7 |
9 |
| quadratic |
2 |
223 |
187 |
177 |
169 |
170 |
177 |
187 |
195 |
| cubic |
3 |
3.601 |
3.497 |
3.419 |
3.343 |
3.371 |
3.419 |
3.497 |
3.573 |
| quartic |
4 |
50.217 |
49.547 |
49.097 |
48.833 |
48.861 |
49.097 |
49.547 |
49.811 |
| quintic |
5 |
575.637 |
573.791 |
571.535 |
570.095 |
570.501 |
571.535 |
573.791 |
575.231 |
| sextic |
6 |
5.645.069 |
5.636.537 |
5.626.715 |
5.622.243 |
5.622.649 |
5.626.715 |
5.636.537 |
5.641.009 |
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