Reduction formula for point group D4
Characters for molecular motions
Motion |
E |
2C4 (z) |
C2 (z) |
2C'2 |
2C''2 |
Cartesian 3N |
48 |
0 |
0 |
0 |
0 |
Translation (x,y,z) |
3 |
1 |
-1 |
-1 |
-1 |
Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
-1 |
-1 |
Vibration |
42 |
-2 |
2 |
2 |
2 |
Decomposition into Irreducible representations
Motion |
A1 |
A2 |
B1 |
B2 |
E |
Total |
Cartesian 3N |
6 |
6 |
6 |
6 |
12 |
36 |
Translation (x,y,z) |
0 |
1 |
0 |
0 |
1 |
2 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
1 |
2 |
Vibration |
6 |
4 |
6 |
6 |
10 |
32 |
Molecule Parameter
Number of Atoms (N) |
16 |
Number of internal coordinates |
42 |
Number of independant internal coordinates |
6 |
Number of vibrational modes |
32 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A1 |
A2 |
B1 |
B2 |
E |
Total |
Linear (IR) |
6 |
4 |
6 |
6 |
10 |
14 / 18 |
Quadratic (Raman) |
6 |
4 |
6 |
6 |
10 |
28 / 4 |
IR + Raman |
- |
- |
- |
- |
10 |
10 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
2C4 (z) |
C2 (z) |
2C'2 |
2C''2 |
linear |
1 |
42 |
-2 |
2 |
2 |
2 |
quadratic |
2 |
903 |
3 |
23 |
23 |
23 |
cubic |
3 |
13.244 |
-4 |
44 |
44 |
44 |
quartic |
4 |
148.995 |
15 |
275 |
275 |
275 |
quintic |
5 |
1.370.754 |
-26 |
506 |
506 |
506 |
sextic |
6 |
10.737.573 |
37 |
2.277 |
2.277 |
2.277 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
B1 |
B2 |
E |
linear |
1 |
6 |
4 |
6 |
6 |
10 |
quadratic |
2 |
128 |
105 |
115 |
115 |
220 |
cubic |
3 |
1.682 |
1.638 |
1.662 |
1.662 |
3.300 |
quartic |
4 |
18.800 |
18.525 |
18.655 |
18.655 |
37.180 |
quintic |
5 |
171.654 |
171.148 |
171.414 |
171.414 |
342.562 |
sextic |
6 |
1.343.629 |
1.341.352 |
1.342.472 |
1.342.472 |
2.683.824 |
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