Reduction formula for point group D2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
C2 (y) |
C2 (x) |
i |
 (xy) |
(xz) |
(yz) |
| Cartesian 3N |
120 |
0 |
0 |
0 |
0 |
8 |
8 |
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 |
114 |
2 |
2 |
2 |
0 |
8 |
8 |
8 |
Decomposition into Irreducible representations
| Motion |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Cartesian 3N |
18 |
14 |
14 |
14 |
12 |
16 |
16 |
16 |
120 |
| 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 |
18 |
13 |
13 |
13 |
12 |
15 |
15 |
15 |
114 |
Molecule Parameter
| Number of Atoms (N) |
40 |
| Number of internal coordinates |
114 |
| Number of independant internal coordinates |
18 |
| Number of vibrational modes |
114 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
Total |
| Linear (IR) |
18 |
13 |
13 |
13 |
12 |
15 |
15 |
15 |
45 / 69 |
| Quadratic (Raman) |
18 |
13 |
13 |
13 |
12 |
15 |
15 |
15 |
57 / 57 |
| IR + Raman |
- |
- |
- |
- |
12 |
- |
- |
- |
0* / 12 |
* 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 |
114 |
2 |
2 |
2 |
0 |
8 |
8 |
8 |
| quadratic |
2 |
6.555 |
59 |
59 |
59 |
57 |
89 |
89 |
89 |
| cubic |
3 |
253.460 |
116 |
116 |
116 |
0 |
544 |
544 |
544 |
| quartic |
4 |
7.413.705 |
1.769 |
1.769 |
1.769 |
1.653 |
3.669 |
3.669 |
3.669 |
| quintic |
5 |
174.963.438 |
3.422 |
3.422 |
3.422 |
0 |
18.600 |
18.600 |
18.600 |
| sextic |
6 |
3.470.108.187 |
35.931 |
35.931 |
35.931 |
32.509 |
96.957 |
96.957 |
96.957 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
B1g |
B2g |
B3g |
Au |
B1u |
B2u |
B3u |
| linear |
1 |
18 |
13 |
13 |
13 |
12 |
15 |
15 |
15 |
| quadratic |
2 |
882 |
808 |
808 |
808 |
801 |
816 |
816 |
816 |
| cubic |
3 |
31.930 |
31.600 |
31.600 |
31.600 |
31.522 |
31.736 |
31.736 |
31.736 |
| quartic |
4 |
928.959 |
926.240 |
926.240 |
926.240 |
925.794 |
926.744 |
926.744 |
926.744 |
| quintic |
5 |
21.878.688 |
21.867.677 |
21.867.677 |
21.867.677 |
21.864.738 |
21.872.327 |
21.872.327 |
21.872.327 |
| sextic |
6 |
433.817.420 |
433.750.976 |
433.750.976 |
433.750.976 |
433.736.575 |
433.767.088 |
433.767.088 |
433.767.088 |
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