Reduction formula for point group D4
Characters for molecular motions
| Motion |
E |
2C4 (z) |
C2 (z) |
2C'2 |
2C''2 |
| Cartesian 3N |
240 |
0 |
0 |
0 |
0 |
| Translation (x,y,z) |
3 |
1 |
-1 |
-1 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
-1 |
-1 |
| Vibration |
234 |
-2 |
2 |
2 |
2 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Cartesian 3N |
30 |
30 |
30 |
30 |
60 |
180 |
| Translation (x,y,z) |
0 |
1 |
0 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
1 |
2 |
| Vibration |
30 |
28 |
30 |
30 |
58 |
176 |
Molecule Parameter
| Number of Atoms (N) |
80 |
| Number of internal coordinates |
234 |
| Number of independant internal coordinates |
30 |
| Number of vibrational modes |
176 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
E |
Total |
| Linear (IR) |
30 |
28 |
30 |
30 |
58 |
86 / 90 |
| Quadratic (Raman) |
30 |
28 |
30 |
30 |
58 |
148 / 28 |
| IR + Raman |
- |
- |
- |
- |
58 |
58 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C4 (z) |
C2 (z) |
2C'2 |
2C''2 |
| linear |
1 |
234 |
-2 |
2 |
2 |
2 |
| quadratic |
2 |
27.495 |
3 |
119 |
119 |
119 |
| cubic |
3 |
2.162.940 |
-4 |
236 |
236 |
236 |
| quartic |
4 |
128.154.195 |
63 |
7.139 |
7.139 |
7.139 |
| quintic |
5 |
6.100.139.682 |
-122 |
14.042 |
14.042 |
14.042 |
| sextic |
6 |
242.988.897.333 |
181 |
287.861 |
287.861 |
287.861 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
E |
| linear |
1 |
30 |
28 |
30 |
30 |
58 |
| quadratic |
2 |
3.512 |
3.393 |
3.451 |
3.451 |
6.844 |
| cubic |
3 |
270.514 |
270.278 |
270.398 |
270.398 |
540.676 |
| quartic |
4 |
16.023.752 |
16.016.613 |
16.020.151 |
16.020.151 |
32.036.764 |
| quintic |
5 |
762.526.206 |
762.512.164 |
762.519.246 |
762.519.246 |
1.525.031.410 |
| sextic |
6 |
30.373.792.125 |
30.373.504.264 |
30.373.648.104 |
30.373.648.104 |
60.747.152.368 |
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