Reduction formula for point group D2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
C2 (y) |
C2 (x) |
i |
 (xy) |
(xz) |
(yz) |
| Cartesian 3N |
324 |
0 |
0 |
0 |
0 |
24 |
12 |
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 |
318 |
2 |
2 |
2 |
0 |
24 |
12 |
8 |
Decomposition into Irreducible representations
| Motion |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Cartesian 3N |
46 |
41 |
38 |
37 |
35 |
40 |
43 |
44 |
324 |
| 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 |
46 |
40 |
37 |
36 |
35 |
39 |
42 |
43 |
318 |
Molecule Parameter
| Number of Atoms (N) |
108 |
| Number of internal coordinates |
318 |
| Number of independant internal coordinates |
46 |
| Number of vibrational modes |
318 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Linear (IR) |
46 |
40 |
37 |
36 |
35 |
39 |
42 |
43 |
124 / 194 |
| Quadratic (Raman) |
46 |
40 |
37 |
36 |
35 |
39 |
42 |
43 |
159 / 159 |
| IR + Raman |
- |
- |
- |
- |
35 |
- |
- |
- |
0* / 35 |
* 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 |
318 |
2 |
2 |
2 |
0 |
24 |
12 |
8 |
| quadratic |
2 |
50.721 |
161 |
161 |
161 |
159 |
447 |
231 |
191 |
| cubic |
3 |
5.410.240 |
320 |
320 |
320 |
0 |
6.128 |
2.200 |
1.360 |
| quartic |
4 |
434.171.760 |
13.040 |
13.040 |
13.040 |
12.720 |
72.528 |
25.080 |
18.000 |
| quintic |
5 |
27.960.661.344 |
25.760 |
25.760 |
25.760 |
0 |
741.552 |
201.432 |
116.112 |
| sextic |
6 |
1.505.215.602.352 |
708.400 |
708.400 |
708.400 |
682.640 |
6.858.544 |
1.748.824 |
1.120.816 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
| linear |
1 |
46 |
40 |
37 |
36 |
35 |
39 |
42 |
43 |
| quadratic |
2 |
6.529 |
6.343 |
6.289 |
6.279 |
6.272 |
6.297 |
6.351 |
6.361 |
| cubic |
3 |
677.611 |
676.561 |
675.579 |
675.369 |
675.189 |
675.919 |
676.901 |
677.111 |
| quartic |
4 |
54.292.401 |
54.275.111 |
54.263.249 |
54.261.479 |
54.260.319 |
54.264.569 |
54.276.431 |
54.278.201 |
| quintic |
5 |
3.495.224.715 |
3.495.132.449 |
3.494.997.419 |
3.494.976.089 |
3.494.959.941 |
3.495.026.447 |
3.495.161.477 |
3.495.182.807 |
| sextic |
6 |
188.153.517.297 |
188.152.445.687 |
188.151.168.257 |
188.151.011.255 |
188.150.914.591 |
188.151.277.801 |
188.152.555.231 |
188.152.712.233 |
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