Reduction formula for point group D2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
C2 (y) |
C2 (x) |
i |
 (xy) |
(xz) |
(yz) |
| Cartesian 3N |
252 |
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 |
246 |
2 |
2 |
2 |
0 |
4 |
4 |
4 |
Decomposition into Irreducible representations
| Motion |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Cartesian 3N |
33 |
31 |
31 |
31 |
30 |
32 |
32 |
32 |
252 |
| 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 |
33 |
30 |
30 |
30 |
30 |
31 |
31 |
31 |
246 |
Molecule Parameter
| Number of Atoms (N) |
84 |
| Number of internal coordinates |
246 |
| Number of independant internal coordinates |
33 |
| Number of vibrational modes |
246 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Linear (IR) |
33 |
30 |
30 |
30 |
30 |
31 |
31 |
31 |
93 / 153 |
| Quadratic (Raman) |
33 |
30 |
30 |
30 |
30 |
31 |
31 |
31 |
123 / 123 |
| IR + Raman |
- |
- |
- |
- |
30 |
- |
- |
- |
0* / 30 |
* 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 |
246 |
2 |
2 |
2 |
0 |
4 |
4 |
4 |
| quadratic |
2 |
30.381 |
125 |
125 |
125 |
123 |
131 |
131 |
131 |
| cubic |
3 |
2.511.496 |
248 |
248 |
248 |
0 |
504 |
504 |
504 |
| quartic |
4 |
156.340.626 |
7.874 |
7.874 |
7.874 |
7.626 |
8.626 |
8.626 |
8.626 |
| quintic |
5 |
7.817.031.300 |
15.500 |
15.500 |
15.500 |
0 |
32.000 |
32.000 |
32.000 |
| sextic |
6 |
327.012.476.050 |
333.250 |
333.250 |
333.250 |
317.750 |
380.750 |
380.750 |
380.750 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
| linear |
1 |
33 |
30 |
30 |
30 |
30 |
31 |
31 |
31 |
| quadratic |
2 |
3.909 |
3.781 |
3.781 |
3.781 |
3.780 |
3.783 |
3.783 |
3.783 |
| cubic |
3 |
314.219 |
313.843 |
313.843 |
313.843 |
313.841 |
313.969 |
313.969 |
313.969 |
| quartic |
4 |
19.549.719 |
19.541.469 |
19.541.469 |
19.541.469 |
19.541.343 |
19.541.719 |
19.541.719 |
19.541.719 |
| quintic |
5 |
977.146.725 |
977.122.975 |
977.122.975 |
977.122.975 |
977.122.725 |
977.130.975 |
977.130.975 |
977.130.975 |
| sextic |
6 |
40.876.866.975 |
40.876.509.975 |
40.876.509.975 |
40.876.509.975 |
40.876.501.975 |
40.876.525.725 |
40.876.525.725 |
40.876.525.725 |
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