Reduction formula for point group C4
Characters for molecular motions
Motion |
E |
C4 |
C2 |
(C4)3 |
Cartesian 3N |
72 |
0 |
0 |
0 |
Translation (x,y,z) |
3 |
1 |
-1 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
1 |
Vibration |
66 |
-2 |
2 |
-2 |
Decomposition into Irreducible representations
Motion |
A |
B |
E |
Total |
Cartesian 3N |
18 |
18 |
18 |
54 |
Translation (x,y,z) |
1 |
0 |
1 |
2 |
Rotation (Rx,Ry,Rz) |
1 |
0 |
1 |
2 |
Vibration |
16 |
18 |
16 |
50 |
Molecule Parameter
Number of Atoms (N) |
24 |
Number of internal coordinates |
66 |
Number of independant internal coordinates |
16 |
Number of vibrational modes |
50 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A |
B |
E |
Total |
Linear (IR) |
16 |
18 |
16 |
32 / 18 |
Quadratic (Raman) |
16 |
18 |
16 |
50 / 0 |
IR + Raman |
16 |
- |
16 |
32 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C4 |
C2 |
(C4)3 |
linear |
1 |
66 |
-2 |
2 |
-2 |
quadratic |
2 |
2.211 |
3 |
35 |
3 |
cubic |
3 |
50.116 |
-4 |
68 |
-4 |
quartic |
4 |
864.501 |
21 |
629 |
21 |
quintic |
5 |
12.103.014 |
-38 |
1.190 |
-38 |
sextic |
6 |
143.218.999 |
55 |
7.735 |
55 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A |
B |
E |
linear |
1 |
16 |
18 |
16 |
quadratic |
2 |
563 |
560 |
544 |
cubic |
3 |
12.544 |
12.548 |
12.512 |
quartic |
4 |
216.293 |
216.272 |
215.968 |
quintic |
5 |
3.026.032 |
3.026.070 |
3.025.456 |
sextic |
6 |
35.806.711 |
35.806.656 |
35.802.816 |
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