Reduction formula for point group D2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
C2 (y) |
C2 (x) |
i |
 (xy) |
(xz) |
(yz) |
| Cartesian 3N |
18 |
0 |
0 |
-2 |
0 |
6 |
2 |
0 |
| 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 |
12 |
2 |
2 |
0 |
0 |
6 |
2 |
0 |
Decomposition into Irreducible representations
| Motion |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Cartesian 3N |
3 |
3 |
2 |
1 |
1 |
2 |
3 |
3 |
18 |
| 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 |
3 |
2 |
1 |
0 |
1 |
1 |
2 |
2 |
12 |
Molecule Parameter
| Number of Atoms (N) |
6 |
| Number of internal coordinates |
12 |
| Number of independant internal coordinates |
3 |
| Number of vibrational modes |
12 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Linear (IR) |
3 |
2 |
1 |
0 |
1 |
1 |
2 |
2 |
5 / 7 |
| Quadratic (Raman) |
3 |
2 |
1 |
0 |
1 |
1 |
2 |
2 |
6 / 6 |
| IR + Raman |
- |
- |
- |
- |
1 |
- |
- |
- |
0* / 1 |
* 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 |
12 |
2 |
2 |
0 |
0 |
6 |
2 |
0 |
| quadratic |
2 |
78 |
8 |
8 |
6 |
6 |
24 |
8 |
6 |
| cubic |
3 |
364 |
14 |
14 |
0 |
0 |
74 |
14 |
0 |
| quartic |
4 |
1.365 |
35 |
35 |
21 |
21 |
195 |
35 |
21 |
| quintic |
5 |
4.368 |
56 |
56 |
0 |
0 |
456 |
56 |
0 |
| sextic |
6 |
12.376 |
112 |
112 |
56 |
56 |
976 |
112 |
56 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
| linear |
1 |
3 |
2 |
1 |
0 |
1 |
1 |
2 |
2 |
| quadratic |
2 |
18 |
11 |
7 |
6 |
7 |
7 |
11 |
11 |
| cubic |
3 |
60 |
53 |
38 |
31 |
38 |
38 |
53 |
53 |
| quartic |
4 |
216 |
188 |
148 |
141 |
148 |
148 |
188 |
188 |
| quintic |
5 |
624 |
596 |
496 |
468 |
496 |
496 |
596 |
596 |
| sextic |
6 |
1.732 |
1.648 |
1.432 |
1.404 |
1.432 |
1.432 |
1.648 |
1.648 |
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