Reduction formula for point group D4
Characters for molecular motions
| Motion |
E |
2C4 (z) |
C2 (z) |
2C'2 |
2C''2 |
| Cartesian 3N |
156 |
0 |
0 |
0 |
-2 |
| Translation (x,y,z) |
3 |
1 |
-1 |
-1 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
-1 |
-1 |
| Vibration |
150 |
-2 |
2 |
2 |
0 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Cartesian 3N |
19 |
20 |
20 |
19 |
39 |
117 |
| Translation (x,y,z) |
0 |
1 |
0 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
1 |
2 |
| Vibration |
19 |
18 |
20 |
19 |
37 |
113 |
Molecule Parameter
| Number of Atoms (N) |
52 |
| Number of internal coordinates |
150 |
| Number of independant internal coordinates |
19 |
| Number of vibrational modes |
113 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Linear (IR) |
19 |
18 |
20 |
19 |
37 |
55 / 58 |
| Quadratic (Raman) |
19 |
18 |
20 |
19 |
37 |
95 / 18 |
| IR + Raman |
- |
- |
- |
- |
37 |
37 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C4 (z) |
C2 (z) |
2C'2 |
2C''2 |
| linear |
1 |
150 |
-2 |
2 |
2 |
0 |
| quadratic |
2 |
11.325 |
3 |
77 |
77 |
75 |
| cubic |
3 |
573.800 |
-4 |
152 |
152 |
0 |
| quartic |
4 |
21.947.850 |
42 |
3.002 |
3.002 |
2.850 |
| quintic |
5 |
675.993.780 |
-80 |
5.852 |
5.852 |
0 |
| sextic |
6 |
17.463.172.650 |
118 |
79.002 |
79.002 |
73.150 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
E |
| linear |
1 |
19 |
18 |
20 |
19 |
37 |
| quadratic |
2 |
1.464 |
1.388 |
1.425 |
1.424 |
2.812 |
| cubic |
3 |
71.781 |
71.705 |
71.783 |
71.707 |
143.412 |
| quartic |
4 |
2.745.330 |
2.742.404 |
2.743.884 |
2.743.808 |
5.486.212 |
| quintic |
5 |
84.501.397 |
84.498.471 |
84.501.437 |
84.498.511 |
168.996.982 |
| sextic |
6 |
2.182.944.524 |
2.182.868.448 |
2.182.907.890 |
2.182.904.964 |
4.365.773.412 |
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