Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
120 |
0 |
12 |
4 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
114 |
2 |
12 |
4 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
34 |
26 |
32 |
28 |
120 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
33 |
25 |
30 |
26 |
114 |
Molecule Parameter
| Number of Atoms (N) |
40 |
| Number of internal coordinates |
114 |
| Number of independant internal coordinates |
33 |
| Number of vibrational modes |
114 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
33 |
25 |
30 |
26 |
89 / 25 |
| Quadratic (Raman) |
33 |
25 |
30 |
26 |
114 / 0 |
| IR + Raman |
33 |
- |
30 |
26 |
89 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
114 |
2 |
12 |
4 |
| quadratic |
2 |
6.555 |
59 |
129 |
65 |
| cubic |
3 |
253.460 |
116 |
976 |
240 |
| quartic |
4 |
7.413.705 |
1.769 |
6.669 |
2.125 |
| quintic |
5 |
174.963.438 |
3.422 |
38.844 |
7.316 |
| sextic |
6 |
3.470.108.187 |
35.931 |
208.845 |
46.669 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
33 |
25 |
30 |
26 |
| quadratic |
2 |
1.702 |
1.605 |
1.640 |
1.608 |
| cubic |
3 |
63.698 |
63.090 |
63.520 |
63.152 |
| quartic |
4 |
1.856.067 |
1.851.670 |
1.854.120 |
1.851.848 |
| quintic |
5 |
43.753.255 |
43.730.175 |
43.747.886 |
43.732.122 |
| sextic |
6 |
867.599.908 |
867.472.151 |
867.558.608 |
867.477.520 |
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