Reduction formula for point group D2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
C2 (y) |
C2 (x) |
i |
 (xy) |
(xz) |
(yz) |
| Cartesian 3N |
48 |
0 |
-4 |
-4 |
0 |
16 |
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 |
42 |
2 |
-2 |
-2 |
0 |
16 |
4 |
4 |
Decomposition into Irreducible representations
| Motion |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Cartesian 3N |
8 |
8 |
4 |
4 |
2 |
6 |
8 |
8 |
48 |
| 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 |
8 |
7 |
3 |
3 |
2 |
5 |
7 |
7 |
42 |
Molecule Parameter
| Number of Atoms (N) |
16 |
| Number of internal coordinates |
42 |
| Number of independant internal coordinates |
8 |
| Number of vibrational modes |
42 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Linear (IR) |
8 |
7 |
3 |
3 |
2 |
5 |
7 |
7 |
19 / 23 |
| Quadratic (Raman) |
8 |
7 |
3 |
3 |
2 |
5 |
7 |
7 |
21 / 21 |
| IR + Raman |
- |
- |
- |
- |
2 |
- |
- |
- |
0* / 2 |
* 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 |
42 |
2 |
-2 |
-2 |
0 |
16 |
4 |
4 |
| quadratic |
2 |
903 |
23 |
23 |
23 |
21 |
149 |
29 |
29 |
| cubic |
3 |
13.244 |
44 |
-44 |
-44 |
0 |
1.024 |
96 |
96 |
| quartic |
4 |
148.995 |
275 |
275 |
275 |
231 |
5.735 |
415 |
415 |
| quintic |
5 |
1.370.754 |
506 |
-506 |
-506 |
0 |
27.568 |
1.196 |
1.196 |
| sextic |
6 |
10.737.573 |
2.277 |
2.277 |
2.277 |
1.771 |
117.483 |
3.979 |
3.979 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
| linear |
1 |
8 |
7 |
3 |
3 |
2 |
5 |
7 |
7 |
| quadratic |
2 |
150 |
124 |
94 |
94 |
93 |
96 |
126 |
126 |
| cubic |
3 |
1.802 |
1.776 |
1.522 |
1.522 |
1.498 |
1.568 |
1.778 |
1.778 |
| quartic |
4 |
19.577 |
19.232 |
17.902 |
17.902 |
17.878 |
17.948 |
19.278 |
19.278 |
| quintic |
5 |
175.026 |
174.681 |
167.835 |
167.835 |
167.536 |
168.387 |
174.727 |
174.727 |
| sextic |
6 |
1.358.952 |
1.355.824 |
1.327.448 |
1.327.448 |
1.327.149 |
1.328.000 |
1.356.376 |
1.356.376 |
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