Reduction formula for point group C4h
Characters for molecular motions
| Motion |
E |
C4(z) |
C2 |
(C4)3 |
i |
(S4)3 |
 h |
S4 |
| Cartesian 3N |
156 |
0 |
0 |
0 |
0 |
0 |
4 |
0 |
| Translation (x,y,z) |
3 |
1 |
-1 |
1 |
-3 |
-1 |
1 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
1 |
3 |
1 |
-1 |
1 |
| Vibration |
150 |
-2 |
2 |
-2 |
0 |
0 |
4 |
0 |
Decomposition into Irreducible representations
| Motion |
Ag |
Bg |
Eg |
Au |
Bu |
Eu |
Total |
| Cartesian 3N |
20 |
20 |
19 |
19 |
19 |
20 |
117 |
| Translation (x,y,z) |
0 |
0 |
0 |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
1 |
0 |
1 |
0 |
0 |
0 |
2 |
| Vibration |
19 |
20 |
18 |
18 |
19 |
19 |
113 |
Molecule Parameter
| Number of Atoms (N) |
52 |
| Number of internal coordinates |
150 |
| Number of independant internal coordinates |
19 |
| Number of vibrational modes |
113 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
Bg |
Eg |
Au |
Bu |
Eu |
Total |
| Linear (IR) |
19 |
20 |
18 |
18 |
19 |
19 |
37 / 76 |
| Quadratic (Raman) |
19 |
20 |
18 |
18 |
19 |
19 |
57 / 56 |
| IR + Raman |
- |
- |
- |
- |
19 |
- |
0* / 19 |
* Center of inversion: Mutual Exclusion Principle
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C4(z) |
C2 |
(C4)3 |
i |
(S4)3 |
h |
S4 |
| linear |
1 |
150 |
-2 |
2 |
-2 |
0 |
0 |
4 |
0 |
| quadratic |
2 |
11.325 |
3 |
77 |
3 |
75 |
1 |
83 |
1 |
| cubic |
3 |
573.800 |
-4 |
152 |
-4 |
0 |
0 |
312 |
0 |
| quartic |
4 |
21.947.850 |
42 |
3.002 |
42 |
2.850 |
38 |
3.466 |
38 |
| quintic |
5 |
675.993.780 |
-80 |
5.852 |
-80 |
0 |
0 |
12.320 |
0 |
| sextic |
6 |
17.463.172.650 |
118 |
79.002 |
118 |
73.150 |
38 |
97.174 |
38 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
Bg |
Eg |
Au |
Bu |
Eu |
| linear |
1 |
19 |
20 |
18 |
18 |
19 |
19 |
| quadratic |
2 |
1.446 |
1.444 |
1.405 |
1.406 |
1.405 |
1.407 |
| cubic |
3 |
71.782 |
71.784 |
71.667 |
71.704 |
71.706 |
71.745 |
| quartic |
4 |
2.744.666 |
2.744.626 |
2.743.029 |
2.743.068 |
2.743.066 |
2.743.183 |
| quintic |
5 |
84.501.474 |
84.501.514 |
84.496.951 |
84.498.394 |
84.498.434 |
84.500.031 |
| sextic |
6 |
2.182.927.786 |
2.182.927.708 |
2.182.883.703 |
2.182.885.186 |
2.182.885.146 |
2.182.889.709 |
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