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 |
1 |
1 |
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 |
1 |
1 |
Decomposition into Irreducible representations
Motion |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
Cartesian 3N |
12 |
12 |
12 |
12 |
12 |
13 |
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 |
12 |
11 |
11 |
11 |
12 |
12 |
12 |
12 |
93 |
Molecule Parameter
Number of Atoms (N) |
33 |
Number of internal coordinates |
93 |
Number of independant internal coordinates |
12 |
Number of vibrational modes |
93 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
Linear (IR) |
12 |
11 |
11 |
11 |
12 |
12 |
12 |
12 |
36 / 57 |
Quadratic (Raman) |
12 |
11 |
11 |
11 |
12 |
12 |
12 |
12 |
45 / 48 |
IR + Raman |
- |
- |
- |
- |
12 |
- |
- |
- |
0* / 12 |
* 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 |
1 |
1 |
quadratic |
2 |
4.371 |
47 |
47 |
47 |
51 |
47 |
47 |
47 |
cubic |
3 |
138.415 |
47 |
47 |
47 |
-145 |
47 |
47 |
47 |
quartic |
4 |
3.321.960 |
1.128 |
1.128 |
1.128 |
1.320 |
1.128 |
1.128 |
1.128 |
quintic |
5 |
64.446.024 |
1.128 |
1.128 |
1.128 |
-3.576 |
1.128 |
1.128 |
1.128 |
sextic |
6 |
1.052.618.392 |
18.424 |
18.424 |
18.424 |
23.128 |
18.424 |
18.424 |
18.424 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
linear |
1 |
12 |
11 |
11 |
11 |
12 |
12 |
12 |
12 |
quadratic |
2 |
588 |
541 |
541 |
541 |
540 |
540 |
540 |
540 |
cubic |
3 |
17.319 |
17.272 |
17.272 |
17.272 |
17.320 |
17.320 |
17.320 |
17.320 |
quartic |
4 |
416.256 |
415.128 |
415.128 |
415.128 |
415.080 |
415.080 |
415.080 |
415.080 |
quintic |
5 |
8.056.152 |
8.055.024 |
8.055.024 |
8.055.024 |
8.056.200 |
8.056.200 |
8.056.200 |
8.056.200 |
sextic |
6 |
131.594.008 |
131.575.584 |
131.575.584 |
131.575.584 |
131.574.408 |
131.574.408 |
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