Reduction formula for point group D2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
C2 (y) |
C2 (x) |
i |
 (xy) |
(xz) |
(yz) |
| Cartesian 3N |
156 |
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 |
150 |
2 |
2 |
2 |
0 |
4 |
4 |
4 |
Decomposition into Irreducible representations
| Motion |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Cartesian 3N |
21 |
19 |
19 |
19 |
18 |
20 |
20 |
20 |
156 |
| 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 |
21 |
18 |
18 |
18 |
18 |
19 |
19 |
19 |
150 |
Molecule Parameter
| Number of Atoms (N) |
52 |
| Number of internal coordinates |
150 |
| Number of independant internal coordinates |
21 |
| Number of vibrational modes |
150 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Linear (IR) |
21 |
18 |
18 |
18 |
18 |
19 |
19 |
19 |
57 / 93 |
| Quadratic (Raman) |
21 |
18 |
18 |
18 |
18 |
19 |
19 |
19 |
75 / 75 |
| IR + Raman |
- |
- |
- |
- |
18 |
- |
- |
- |
0* / 18 |
* 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 |
150 |
2 |
2 |
2 |
0 |
4 |
4 |
4 |
| quadratic |
2 |
11.325 |
77 |
77 |
77 |
75 |
83 |
83 |
83 |
| cubic |
3 |
573.800 |
152 |
152 |
152 |
0 |
312 |
312 |
312 |
| quartic |
4 |
21.947.850 |
3.002 |
3.002 |
3.002 |
2.850 |
3.466 |
3.466 |
3.466 |
| quintic |
5 |
675.993.780 |
5.852 |
5.852 |
5.852 |
0 |
12.320 |
12.320 |
12.320 |
| sextic |
6 |
17.463.172.650 |
79.002 |
79.002 |
79.002 |
73.150 |
97.174 |
97.174 |
97.174 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
| linear |
1 |
21 |
18 |
18 |
18 |
18 |
19 |
19 |
19 |
| quadratic |
2 |
1.485 |
1.405 |
1.405 |
1.405 |
1.404 |
1.407 |
1.407 |
1.407 |
| cubic |
3 |
71.899 |
71.667 |
71.667 |
71.667 |
71.665 |
71.745 |
71.745 |
71.745 |
| quartic |
4 |
2.746.263 |
2.743.029 |
2.743.029 |
2.743.029 |
2.742.951 |
2.743.183 |
2.743.183 |
2.743.183 |
| quintic |
5 |
84.506.037 |
84.496.951 |
84.496.951 |
84.496.951 |
84.496.797 |
84.500.031 |
84.500.031 |
84.500.031 |
| sextic |
6 |
2.182.971.791 |
2.182.883.703 |
2.182.883.703 |
2.182.883.703 |
2.182.880.623 |
2.182.889.709 |
2.182.889.709 |
2.182.889.709 |
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