Reduction formula for point group D2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
C2 (y) |
C2 (x) |
i |
 (xy) |
(xz) |
(yz) |
| Cartesian 3N |
144 |
0 |
0 |
0 |
0 |
0 |
0 |
8 |
| 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 |
138 |
2 |
2 |
2 |
0 |
0 |
0 |
8 |
Decomposition into Irreducible representations
| Motion |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Cartesian 3N |
19 |
17 |
17 |
19 |
17 |
19 |
19 |
17 |
144 |
| 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 |
19 |
16 |
16 |
18 |
17 |
18 |
18 |
16 |
138 |
Molecule Parameter
| Number of Atoms (N) |
48 |
| Number of internal coordinates |
138 |
| Number of independant internal coordinates |
19 |
| Number of vibrational modes |
138 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Linear (IR) |
19 |
16 |
16 |
18 |
17 |
18 |
18 |
16 |
52 / 86 |
| Quadratic (Raman) |
19 |
16 |
16 |
18 |
17 |
18 |
18 |
16 |
69 / 69 |
| IR + Raman |
- |
- |
- |
- |
17 |
- |
- |
- |
0* / 17 |
* 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 |
138 |
2 |
2 |
2 |
0 |
0 |
0 |
8 |
| quadratic |
2 |
9.591 |
71 |
71 |
71 |
69 |
69 |
69 |
101 |
| cubic |
3 |
447.580 |
140 |
140 |
140 |
0 |
0 |
0 |
640 |
| quartic |
4 |
15.777.195 |
2.555 |
2.555 |
2.555 |
2.415 |
2.415 |
2.415 |
4.815 |
| quintic |
5 |
448.072.338 |
4.970 |
4.970 |
4.970 |
0 |
0 |
0 |
25.752 |
| sextic |
6 |
10.679.057.389 |
62.125 |
62.125 |
62.125 |
57.155 |
57.155 |
57.155 |
148.291 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
| linear |
1 |
19 |
16 |
16 |
18 |
17 |
18 |
18 |
16 |
| quadratic |
2 |
1.264 |
1.186 |
1.186 |
1.194 |
1.187 |
1.194 |
1.194 |
1.186 |
| cubic |
3 |
56.080 |
55.850 |
55.850 |
56.010 |
55.920 |
56.010 |
56.010 |
55.850 |
| quartic |
4 |
1.974.615 |
1.971.530 |
1.971.530 |
1.972.130 |
1.971.600 |
1.972.130 |
1.972.130 |
1.971.530 |
| quintic |
5 |
56.014.125 |
56.005.202 |
56.005.202 |
56.011.640 |
56.007.687 |
56.011.640 |
56.011.640 |
56.005.202 |
| sextic |
6 |
1.334.945.440 |
1.334.863.016 |
1.334.863.016 |
1.334.885.800 |
1.334.865.501 |
1.334.885.800 |
1.334.885.800 |
1.334.863.016 |
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