Reduction formula for point group D2h
Characters for molecular motions
Motion |
E |
C2 (z) |
C2 (y) |
C2 (x) |
i |
(xy) |
(xz) |
(yz) |
Cartesian 3N |
90 |
0 |
0 |
-2 |
0 |
30 |
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 |
84 |
2 |
2 |
0 |
0 |
30 |
2 |
0 |
Decomposition into Irreducible representations
Motion |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
Cartesian 3N |
15 |
15 |
8 |
7 |
7 |
8 |
15 |
15 |
90 |
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 |
15 |
14 |
7 |
6 |
7 |
7 |
14 |
14 |
84 |
Molecule Parameter
Number of Atoms (N) |
30 |
Number of internal coordinates |
84 |
Number of independant internal coordinates |
15 |
Number of vibrational modes |
84 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
Linear (IR) |
15 |
14 |
7 |
6 |
7 |
7 |
14 |
14 |
35 / 49 |
Quadratic (Raman) |
15 |
14 |
7 |
6 |
7 |
7 |
14 |
14 |
42 / 42 |
IR + Raman |
- |
- |
- |
- |
7 |
- |
- |
- |
0* / 7 |
* 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 |
84 |
2 |
2 |
0 |
0 |
30 |
2 |
0 |
quadratic |
2 |
3.570 |
44 |
44 |
42 |
42 |
492 |
44 |
42 |
cubic |
3 |
102.340 |
86 |
86 |
0 |
0 |
5.770 |
86 |
0 |
quartic |
4 |
2.225.895 |
989 |
989 |
903 |
903 |
53.853 |
989 |
903 |
quintic |
5 |
39.175.752 |
1.892 |
1.892 |
0 |
0 |
423.516 |
1.892 |
0 |
sextic |
6 |
581.106.988 |
15.136 |
15.136 |
13.244 |
13.244 |
2.907.424 |
15.136 |
13.244 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
linear |
1 |
15 |
14 |
7 |
6 |
7 |
7 |
14 |
14 |
quadratic |
2 |
540 |
497 |
385 |
384 |
385 |
385 |
497 |
497 |
cubic |
3 |
13.546 |
13.503 |
12.082 |
12.039 |
12.082 |
12.082 |
13.503 |
13.503 |
quartic |
4 |
285.678 |
284.732 |
271.516 |
271.473 |
271.516 |
271.516 |
284.732 |
284.732 |
quintic |
5 |
4.950.618 |
4.949.672 |
4.844.266 |
4.843.320 |
4.844.266 |
4.844.266 |
4.949.672 |
4.949.672 |
sextic |
6 |
73.012.444 |
72.998.254 |
72.275.182 |
72.274.236 |
72.275.182 |
72.275.182 |
72.998.254 |
72.998.254 |
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