Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
324 |
0 |
24 |
8 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
318 |
2 |
24 |
8 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
89 |
73 |
85 |
77 |
324 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
88 |
72 |
83 |
75 |
318 |
Molecule Parameter
| Number of Atoms (N) |
108 |
| Number of internal coordinates |
318 |
| Number of independant internal coordinates |
88 |
| Number of vibrational modes |
318 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
88 |
72 |
83 |
75 |
246 / 72 |
| Quadratic (Raman) |
88 |
72 |
83 |
75 |
318 / 0 |
| IR + Raman |
88 |
- |
83 |
75 |
246 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
318 |
2 |
24 |
8 |
| quadratic |
2 |
50.721 |
161 |
447 |
191 |
| cubic |
3 |
5.410.240 |
320 |
6.128 |
1.360 |
| quartic |
4 |
434.171.760 |
13.040 |
72.528 |
18.000 |
| quintic |
5 |
27.960.661.344 |
25.760 |
741.552 |
116.112 |
| sextic |
6 |
1.505.215.602.352 |
708.400 |
6.858.544 |
1.120.816 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
88 |
72 |
83 |
75 |
| quadratic |
2 |
12.880 |
12.561 |
12.704 |
12.576 |
| cubic |
3 |
1.354.512 |
1.350.768 |
1.353.672 |
1.351.288 |
| quartic |
4 |
108.568.832 |
108.523.568 |
108.553.312 |
108.526.048 |
| quintic |
5 |
6.990.386.192 |
6.989.957.360 |
6.990.315.256 |
6.990.002.536 |
| sextic |
6 |
376.306.072.528 |
376.302.082.848 |
376.305.157.920 |
376.302.289.056 |
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