Reduction formula for point group C2v
Characters for molecular motions
Motion |
E |
C2 (z) |
v(xz) |
v(yz) |
Cartesian 3N |
48 |
-4 |
16 |
4 |
Translation (x,y,z) |
3 |
-1 |
1 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
Vibration |
42 |
-2 |
16 |
4 |
Decomposition into Irreducible representations
Motion |
A1 |
A2 |
B1 |
B2 |
Total |
Cartesian 3N |
16 |
6 |
16 |
10 |
48 |
Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
Vibration |
15 |
5 |
14 |
8 |
42 |
Molecule Parameter
Number of Atoms (N) |
16 |
Number of internal coordinates |
42 |
Number of independant internal coordinates |
15 |
Number of vibrational modes |
42 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A1 |
A2 |
B1 |
B2 |
Total |
Linear (IR) |
15 |
5 |
14 |
8 |
37 / 5 |
Quadratic (Raman) |
15 |
5 |
14 |
8 |
42 / 0 |
IR + Raman |
15 |
- |
14 |
8 |
37 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C2 (z) |
v(xz) |
v(yz) |
linear |
1 |
42 |
-2 |
16 |
4 |
quadratic |
2 |
903 |
23 |
149 |
29 |
cubic |
3 |
13.244 |
-44 |
1.024 |
96 |
quartic |
4 |
148.995 |
275 |
5.735 |
415 |
quintic |
5 |
1.370.754 |
-506 |
27.568 |
1.196 |
sextic |
6 |
10.737.573 |
2.277 |
117.483 |
3.979 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
B1 |
B2 |
linear |
1 |
15 |
5 |
14 |
8 |
quadratic |
2 |
276 |
187 |
250 |
190 |
cubic |
3 |
3.580 |
3.020 |
3.554 |
3.090 |
quartic |
4 |
38.855 |
35.780 |
38.510 |
35.850 |
quintic |
5 |
349.753 |
335.371 |
349.408 |
336.222 |
sextic |
6 |
2.715.328 |
2.654.597 |
2.712.200 |
2.655.448 |
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