Reduction formula for point group D2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
C2 (y) |
C2 (x) |
i |
 (xy) |
(xz) |
(yz) |
| Cartesian 3N |
39 |
-5 |
-5 |
-5 |
-3 |
9 |
9 |
9 |
| 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 |
33 |
-3 |
-3 |
-3 |
-3 |
9 |
9 |
9 |
Decomposition into Irreducible representations
| Motion |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Cartesian 3N |
6 |
4 |
4 |
4 |
0 |
7 |
7 |
7 |
39 |
| 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 |
6 |
3 |
3 |
3 |
0 |
6 |
6 |
6 |
33 |
Molecule Parameter
| Number of Atoms (N) |
13 |
| Number of internal coordinates |
33 |
| Number of independant internal coordinates |
6 |
| Number of vibrational modes |
33 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Linear (IR) |
6 |
3 |
3 |
3 |
0 |
6 |
6 |
6 |
18 / 15 |
| Quadratic (Raman) |
6 |
3 |
3 |
3 |
0 |
6 |
6 |
6 |
15 / 18 |
| IR + Raman |
- |
- |
- |
- |
0 |
- |
- |
- |
0* / 0 |
* 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 |
33 |
-3 |
-3 |
-3 |
-3 |
9 |
9 |
9 |
| quadratic |
2 |
561 |
21 |
21 |
21 |
21 |
57 |
57 |
57 |
| cubic |
3 |
6.545 |
-55 |
-55 |
-55 |
-55 |
273 |
273 |
273 |
| quartic |
4 |
58.905 |
225 |
225 |
225 |
225 |
1.113 |
1.113 |
1.113 |
| quintic |
5 |
435.897 |
-531 |
-531 |
-531 |
-531 |
3.969 |
3.969 |
3.969 |
| sextic |
6 |
2.760.681 |
1.653 |
1.653 |
1.653 |
1.653 |
12.817 |
12.817 |
12.817 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
| linear |
1 |
6 |
3 |
3 |
3 |
0 |
6 |
6 |
6 |
| quadratic |
2 |
102 |
63 |
63 |
63 |
54 |
72 |
72 |
72 |
| cubic |
3 |
893 |
784 |
784 |
784 |
702 |
866 |
866 |
866 |
| quartic |
4 |
7.893 |
7.224 |
7.224 |
7.224 |
7.002 |
7.446 |
7.446 |
7.446 |
| quintic |
5 |
55.710 |
53.991 |
53.991 |
53.991 |
52.866 |
55.116 |
55.116 |
55.116 |
| sextic |
6 |
350.718 |
343.483 |
343.483 |
343.483 |
340.692 |
346.274 |
346.274 |
346.274 |
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