Reduction formula for point group D2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
C2 (y) |
C2 (x) |
i |
 (xy) |
(xz) |
(yz) |
| Cartesian 3N |
216 |
0 |
-8 |
0 |
0 |
72 |
0 |
8 |
| 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 |
210 |
2 |
-6 |
2 |
0 |
72 |
0 |
8 |
Decomposition into Irreducible representations
| Motion |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Cartesian 3N |
36 |
36 |
16 |
20 |
16 |
20 |
36 |
36 |
216 |
| 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 |
36 |
35 |
15 |
19 |
16 |
19 |
35 |
35 |
210 |
Molecule Parameter
| Number of Atoms (N) |
72 |
| Number of internal coordinates |
210 |
| Number of independant internal coordinates |
36 |
| Number of vibrational modes |
210 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Linear (IR) |
36 |
35 |
15 |
19 |
16 |
19 |
35 |
35 |
89 / 121 |
| Quadratic (Raman) |
36 |
35 |
15 |
19 |
16 |
19 |
35 |
35 |
105 / 105 |
| IR + Raman |
- |
- |
- |
- |
16 |
- |
- |
- |
0* / 16 |
* 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 |
210 |
2 |
-6 |
2 |
0 |
72 |
0 |
8 |
| quadratic |
2 |
22.155 |
107 |
123 |
107 |
105 |
2.697 |
105 |
137 |
| cubic |
3 |
1.565.620 |
212 |
-668 |
212 |
0 |
69.792 |
0 |
928 |
| quartic |
4 |
83.369.265 |
5.777 |
7.521 |
5.777 |
5.565 |
1.399.197 |
5.565 |
9.117 |
| quintic |
5 |
3.568.204.542 |
11.342 |
-37.482 |
11.342 |
0 |
23.121.576 |
0 |
54.120 |
| sextic |
6 |
127.860.662.755 |
209.827 |
305.731 |
209.827 |
198.485 |
327.363.605 |
198.485 |
397.333 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
| linear |
1 |
36 |
35 |
15 |
19 |
16 |
19 |
35 |
35 |
| quadratic |
2 |
3.192 |
3.074 |
2.430 |
2.434 |
2.431 |
2.434 |
3.086 |
3.074 |
| cubic |
3 |
204.512 |
204.394 |
186.726 |
187.178 |
186.832 |
187.178 |
204.406 |
204.394 |
| quartic |
4 |
10.600.973 |
10.593.978 |
10.246.006 |
10.246.458 |
10.246.112 |
10.246.458 |
10.595.302 |
10.593.978 |
| quintic |
5 |
448.920.680 |
448.913.685 |
443.121.085 |
443.146.821 |
443.126.756 |
443.146.821 |
448.915.009 |
448.913.685 |
| sextic |
6 |
16.023.693.256 |
16.023.415.412 |
15.941.648.108 |
15.941.673.844 |
15.941.653.779 |
15.941.673.844 |
16.023.489.100 |
16.023.415.412 |
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