Reduction formula for point group C6v
Characters for molecular motions
| Motion |
E |
2C6 (z) |
2C3 (z) |
C2 (z) |
3 v |
3d |
| Cartesian 3N |
324 |
0 |
0 |
0 |
12 |
8 |
| Translation (x,y,z) |
3 |
2 |
0 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
2 |
0 |
-1 |
-1 |
-1 |
| Vibration |
318 |
-4 |
0 |
2 |
12 |
8 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
E1 |
E2 |
Total |
| Cartesian 3N |
32 |
22 |
28 |
26 |
54 |
54 |
216 |
| Translation (x,y,z) |
1 |
0 |
0 |
0 |
1 |
0 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
1 |
0 |
2 |
| Vibration |
31 |
21 |
28 |
26 |
52 |
54 |
212 |
Molecule Parameter
| Number of Atoms (N) |
108 |
| Number of internal coordinates |
318 |
| Number of independant internal coordinates |
31 |
| Number of vibrational modes |
212 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
E1 |
E2 |
Total |
| Linear (IR) |
31 |
21 |
28 |
26 |
52 |
54 |
83 / 129 |
| Quadratic (Raman) |
31 |
21 |
28 |
26 |
52 |
54 |
137 / 75 |
| IR + Raman |
31 |
21 |
28 |
26 |
52 |
- |
83 / 75 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C6 (z) |
2C3 (z) |
C2 (z) |
3v |
3d |
| linear |
1 |
318 |
-4 |
0 |
2 |
12 |
8 |
| quadratic |
2 |
50.721 |
8 |
0 |
161 |
231 |
191 |
| cubic |
3 |
5.410.240 |
-10 |
106 |
320 |
2.200 |
1.360 |
| quartic |
4 |
434.171.760 |
8 |
0 |
13.040 |
25.080 |
18.000 |
| quintic |
5 |
27.960.661.344 |
-4 |
0 |
25.760 |
201.432 |
116.112 |
| sextic |
6 |
1.505.215.602.352 |
55 |
5.671 |
708.400 |
1.748.824 |
1.120.816 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
E1 |
E2 |
| linear |
1 |
31 |
21 |
28 |
26 |
52 |
54 |
| quadratic |
2 |
4.347 |
4.136 |
4.222 |
4.202 |
8.428 |
8.479 |
| cubic |
3 |
451.786 |
450.006 |
451.056 |
450.636 |
901.634 |
901.744 |
| quartic |
4 |
36.192.838 |
36.171.298 |
36.181.662 |
36.178.122 |
72.359.788 |
72.364.132 |
| quintic |
5 |
2.330.136.644 |
2.329.977.872 |
2.330.074.296 |
2.330.031.636 |
4.660.105.930 |
4.660.114.518 |
| sextic |
6 |
125.435.410.927 |
125.433.976.107 |
125.434.732.434 |
125.434.418.430 |
250.869.148.056 |
250.869.384.171 |
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