Reduction formula for point group C2v
Characters for molecular motions
Motion |
E |
C2 (z) |
v(xz) |
v(yz) |
Cartesian 3N |
24 |
-2 |
4 |
6 |
Translation (x,y,z) |
3 |
-1 |
1 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
Vibration |
18 |
0 |
4 |
6 |
Decomposition into Irreducible representations
Motion |
A1 |
A2 |
B1 |
B2 |
Total |
Cartesian 3N |
8 |
3 |
6 |
7 |
24 |
Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
Vibration |
7 |
2 |
4 |
5 |
18 |
Molecule Parameter
Number of Atoms (N) |
8 |
Number of internal coordinates |
18 |
Number of independant internal coordinates |
7 |
Number of vibrational modes |
18 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A1 |
A2 |
B1 |
B2 |
Total |
Linear (IR) |
7 |
2 |
4 |
5 |
16 / 2 |
Quadratic (Raman) |
7 |
2 |
4 |
5 |
18 / 0 |
IR + Raman |
7 |
- |
4 |
5 |
16 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C2 (z) |
v(xz) |
v(yz) |
linear |
1 |
18 |
0 |
4 |
6 |
quadratic |
2 |
171 |
9 |
17 |
27 |
cubic |
3 |
1.140 |
0 |
48 |
92 |
quartic |
4 |
5.985 |
45 |
133 |
273 |
quintic |
5 |
26.334 |
0 |
308 |
714 |
sextic |
6 |
100.947 |
165 |
693 |
1.715 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
B1 |
B2 |
linear |
1 |
7 |
2 |
4 |
5 |
quadratic |
2 |
56 |
34 |
38 |
43 |
cubic |
3 |
320 |
250 |
274 |
296 |
quartic |
4 |
1.609 |
1.406 |
1.450 |
1.520 |
quintic |
5 |
6.839 |
6.328 |
6.482 |
6.685 |
sextic |
6 |
25.880 |
24.676 |
24.940 |
25.451 |
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