Reduction formula for point group D2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
C2 (y) |
C2 (x) |
i |
 (xy) |
(xz) |
(yz) |
| Cartesian 3N |
54 |
0 |
0 |
-2 |
0 |
18 |
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 |
48 |
2 |
2 |
0 |
0 |
18 |
2 |
0 |
Decomposition into Irreducible representations
| Motion |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Cartesian 3N |
9 |
9 |
5 |
4 |
4 |
5 |
9 |
9 |
54 |
| 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 |
9 |
8 |
4 |
3 |
4 |
4 |
8 |
8 |
48 |
Molecule Parameter
| Number of Atoms (N) |
18 |
| Number of internal coordinates |
48 |
| Number of independant internal coordinates |
9 |
| Number of vibrational modes |
48 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Linear (IR) |
9 |
8 |
4 |
3 |
4 |
4 |
8 |
8 |
20 / 28 |
| Quadratic (Raman) |
9 |
8 |
4 |
3 |
4 |
4 |
8 |
8 |
24 / 24 |
| IR + Raman |
- |
- |
- |
- |
4 |
- |
- |
- |
0* / 4 |
* 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 |
48 |
2 |
2 |
0 |
0 |
18 |
2 |
0 |
| quadratic |
2 |
1.176 |
26 |
26 |
24 |
24 |
186 |
26 |
24 |
| cubic |
3 |
19.600 |
50 |
50 |
0 |
0 |
1.410 |
50 |
0 |
| quartic |
4 |
249.900 |
350 |
350 |
300 |
300 |
8.670 |
350 |
300 |
| quintic |
5 |
2.598.960 |
650 |
650 |
0 |
0 |
45.594 |
650 |
0 |
| sextic |
6 |
22.957.480 |
3.250 |
3.250 |
2.600 |
2.600 |
211.922 |
3.250 |
2.600 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
| linear |
1 |
9 |
8 |
4 |
3 |
4 |
4 |
8 |
8 |
| quadratic |
2 |
189 |
164 |
124 |
123 |
124 |
124 |
164 |
164 |
| cubic |
3 |
2.645 |
2.620 |
2.280 |
2.255 |
2.280 |
2.280 |
2.620 |
2.620 |
| quartic |
4 |
32.565 |
32.240 |
30.160 |
30.135 |
30.160 |
30.160 |
32.240 |
32.240 |
| quintic |
5 |
330.813 |
330.488 |
319.252 |
318.927 |
319.252 |
319.252 |
330.488 |
330.488 |
| sextic |
6 |
2.898.369 |
2.895.444 |
2.843.276 |
2.842.951 |
2.843.276 |
2.843.276 |
2.895.444 |
2.895.444 |
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