Reduction formula for point group C6
Characters for molecular motions
Motion |
E |
C6 |
C3 |
C2 |
(C3)2 |
(C6)5 |
Cartesian 3N |
216 |
0 |
0 |
0 |
0 |
0 |
Translation (x,y,z) |
3 |
2 |
0 |
-1 |
0 |
2 |
Rotation (Rx,Ry,Rz) |
3 |
2 |
0 |
-1 |
0 |
2 |
Vibration |
210 |
-4 |
0 |
2 |
0 |
-4 |
Decomposition into Irreducible representations
Motion |
A |
B |
E1 |
E2 |
Total |
Cartesian 3N |
36 |
36 |
36 |
36 |
144 |
Translation (x,y,z) |
1 |
0 |
1 |
0 |
2 |
Rotation (Rx,Ry,Rz) |
1 |
0 |
1 |
0 |
2 |
Vibration |
34 |
36 |
34 |
36 |
140 |
Molecule Parameter
Number of Atoms (N) |
72 |
Number of internal coordinates |
210 |
Number of independant internal coordinates |
34 |
Number of vibrational modes |
140 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A |
B |
E1 |
E2 |
Total |
Linear (IR) |
34 |
36 |
34 |
36 |
68 / 72 |
Quadratic (Raman) |
34 |
36 |
34 |
36 |
104 / 36 |
IR + Raman |
34 |
36 |
34 |
- |
68 / 36 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C6 |
C3 |
C2 |
(C3)2 |
(C6)5 |
linear |
1 |
210 |
-4 |
0 |
2 |
0 |
-4 |
quadratic |
2 |
22.155 |
8 |
0 |
107 |
0 |
8 |
cubic |
3 |
1.565.620 |
-10 |
70 |
212 |
70 |
-10 |
quartic |
4 |
83.369.265 |
8 |
0 |
5.777 |
0 |
8 |
quintic |
5 |
3.568.204.542 |
-4 |
0 |
11.342 |
0 |
-4 |
sextic |
6 |
127.860.662.755 |
37 |
2.485 |
209.827 |
2.485 |
37 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A |
B |
E1 |
E2 |
linear |
1 |
34 |
36 |
34 |
36 |
quadratic |
2 |
3.713 |
3.672 |
3.676 |
3.709 |
cubic |
3 |
260.992 |
260.928 |
260.888 |
260.962 |
quartic |
4 |
13.895.843 |
13.893.912 |
13.893.916 |
13.895.839 |
quintic |
5 |
594.702.646 |
594.698.868 |
594.698.866 |
594.702.648 |
sextic |
6 |
21.310.146.271 |
21.310.076.304 |
21.310.075.080 |
21.310.145.010 |
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