Reduction formula for point group D2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
C2 (y) |
C2 (x) |
i |
 (xy) |
(xz) |
(yz) |
| Cartesian 3N |
99 |
-1 |
-1 |
-1 |
-3 |
1 |
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 |
93 |
1 |
1 |
1 |
-3 |
1 |
9 |
9 |
Decomposition into Irreducible representations
| Motion |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Cartesian 3N |
14 |
10 |
12 |
12 |
10 |
15 |
13 |
13 |
99 |
| 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 |
14 |
9 |
11 |
11 |
10 |
14 |
12 |
12 |
93 |
Molecule Parameter
| Number of Atoms (N) |
33 |
| Number of internal coordinates |
93 |
| Number of independant internal coordinates |
14 |
| Number of vibrational modes |
93 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Linear (IR) |
14 |
9 |
11 |
11 |
10 |
14 |
12 |
12 |
38 / 55 |
| Quadratic (Raman) |
14 |
9 |
11 |
11 |
10 |
14 |
12 |
12 |
45 / 48 |
| IR + Raman |
- |
- |
- |
- |
10 |
- |
- |
- |
0* / 10 |
* 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 |
93 |
1 |
1 |
1 |
-3 |
1 |
9 |
9 |
| quadratic |
2 |
4.371 |
47 |
47 |
47 |
51 |
47 |
87 |
87 |
| cubic |
3 |
138.415 |
47 |
47 |
47 |
-145 |
47 |
543 |
543 |
| quartic |
4 |
3.321.960 |
1.128 |
1.128 |
1.128 |
1.320 |
1.128 |
3.288 |
3.288 |
| quintic |
5 |
64.446.024 |
1.128 |
1.128 |
1.128 |
-3.576 |
1.128 |
16.344 |
16.344 |
| sextic |
6 |
1.052.618.392 |
18.424 |
18.424 |
18.424 |
23.128 |
18.424 |
77.672 |
77.672 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
| linear |
1 |
14 |
9 |
11 |
11 |
10 |
14 |
12 |
12 |
| quadratic |
2 |
598 |
531 |
541 |
541 |
530 |
550 |
540 |
540 |
| cubic |
3 |
17.443 |
17.148 |
17.272 |
17.272 |
17.196 |
17.444 |
17.320 |
17.320 |
| quartic |
4 |
416.796 |
414.588 |
415.128 |
415.128 |
414.540 |
415.620 |
415.080 |
415.080 |
| quintic |
5 |
8.059.956 |
8.051.220 |
8.055.024 |
8.055.024 |
8.052.396 |
8.060.004 |
8.056.200 |
8.056.200 |
| sextic |
6 |
131.608.820 |
131.560.772 |
131.575.584 |
131.575.584 |
131.559.596 |
131.589.220 |
131.574.408 |
131.574.408 |
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