Reduction formula for point group C6
Characters for molecular motions
Motion |
E |
C6 |
C3 |
C2 |
(C3)2 |
(C6)5 |
Cartesian 3N |
75 |
2 |
0 |
-1 |
0 |
2 |
Translation (x,y,z) |
3 |
2 |
0 |
-1 |
0 |
2 |
Rotation (Rx,Ry,Rz) |
3 |
2 |
0 |
-1 |
0 |
2 |
Vibration |
69 |
-2 |
0 |
1 |
0 |
-2 |
Decomposition into Irreducible representations
Motion |
A |
B |
E1 |
E2 |
Total |
Cartesian 3N |
13 |
12 |
13 |
12 |
50 |
Translation (x,y,z) |
1 |
0 |
1 |
0 |
2 |
Rotation (Rx,Ry,Rz) |
1 |
0 |
1 |
0 |
2 |
Vibration |
11 |
12 |
11 |
12 |
46 |
Molecule Parameter
Number of Atoms (N) |
25 |
Number of internal coordinates |
69 |
Number of independant internal coordinates |
11 |
Number of vibrational modes |
46 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A |
B |
E1 |
E2 |
Total |
Linear (IR) |
11 |
12 |
11 |
12 |
22 / 24 |
Quadratic (Raman) |
11 |
12 |
11 |
12 |
34 / 12 |
IR + Raman |
11 |
12 |
11 |
- |
22 / 12 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C6 |
C3 |
C2 |
(C3)2 |
(C6)5 |
linear |
1 |
69 |
-2 |
0 |
1 |
0 |
-2 |
quadratic |
2 |
2.415 |
2 |
0 |
35 |
0 |
2 |
cubic |
3 |
57.155 |
-1 |
23 |
35 |
23 |
-1 |
quartic |
4 |
1.028.790 |
0 |
0 |
630 |
0 |
0 |
quintic |
5 |
15.020.334 |
0 |
0 |
630 |
0 |
0 |
sextic |
6 |
185.250.786 |
12 |
276 |
7.770 |
276 |
12 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A |
B |
E1 |
E2 |
linear |
1 |
11 |
12 |
11 |
12 |
quadratic |
2 |
409 |
396 |
397 |
408 |
cubic |
3 |
9.539 |
9.528 |
9.516 |
9.528 |
quartic |
4 |
171.570 |
171.360 |
171.360 |
171.570 |
quintic |
5 |
2.503.494 |
2.503.284 |
2.503.284 |
2.503.494 |
sextic |
6 |
30.876.522 |
30.873.924 |
30.873.792 |
30.876.378 |
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