Reduction formula for point group D2h
Characters for molecular motions
Motion |
E |
C2 (z) |
C2 (y) |
C2 (x) |
i |
(xy) |
(xz) |
(yz) |
Cartesian 3N |
78 |
0 |
0 |
-6 |
0 |
26 |
6 |
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 |
72 |
2 |
2 |
-4 |
0 |
26 |
6 |
0 |
Decomposition into Irreducible representations
Motion |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
Cartesian 3N |
13 |
13 |
8 |
5 |
5 |
8 |
13 |
13 |
78 |
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 |
13 |
12 |
7 |
4 |
5 |
7 |
12 |
12 |
72 |
Molecule Parameter
Number of Atoms (N) |
26 |
Number of internal coordinates |
72 |
Number of independant internal coordinates |
13 |
Number of vibrational modes |
72 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
Linear (IR) |
13 |
12 |
7 |
4 |
5 |
7 |
12 |
12 |
31 / 41 |
Quadratic (Raman) |
13 |
12 |
7 |
4 |
5 |
7 |
12 |
12 |
36 / 36 |
IR + Raman |
- |
- |
- |
- |
5 |
- |
- |
- |
0* / 5 |
* 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 |
72 |
2 |
2 |
-4 |
0 |
26 |
6 |
0 |
quadratic |
2 |
2.628 |
38 |
38 |
44 |
36 |
374 |
54 |
36 |
cubic |
3 |
64.824 |
74 |
74 |
-156 |
0 |
3.874 |
254 |
0 |
quartic |
4 |
1.215.450 |
740 |
740 |
970 |
666 |
32.100 |
1.380 |
666 |
quintic |
5 |
18.474.840 |
1.406 |
1.406 |
-3.116 |
0 |
225.030 |
5.466 |
0 |
sextic |
6 |
237.093.780 |
9.842 |
9.842 |
14.364 |
8.436 |
1.381.730 |
22.946 |
8.436 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
linear |
1 |
13 |
12 |
7 |
4 |
5 |
7 |
12 |
12 |
quadratic |
2 |
406 |
363 |
283 |
280 |
281 |
283 |
363 |
369 |
cubic |
3 |
8.618 |
8.575 |
7.670 |
7.549 |
7.586 |
7.670 |
8.575 |
8.581 |
quartic |
4 |
156.589 |
155.650 |
147.970 |
147.849 |
147.886 |
147.970 |
155.650 |
155.886 |
quintic |
5 |
2.338.129 |
2.337.190 |
2.282.299 |
2.279.802 |
2.280.505 |
2.282.299 |
2.337.190 |
2.337.426 |
sextic |
6 |
29.818.672 |
29.804.775 |
29.465.079 |
29.462.582 |
29.463.285 |
29.465.079 |
29.804.775 |
29.809.533 |
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