Reduction formula for point group C2v
Characters for molecular motions
Motion |
E |
C2 (z) |
v(xz) |
v(yz) |
Cartesian 3N |
24 |
-4 |
8 |
4 |
Translation (x,y,z) |
3 |
-1 |
1 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
Vibration |
18 |
-2 |
8 |
4 |
Decomposition into Irreducible representations
Motion |
A1 |
A2 |
B1 |
B2 |
Total |
Cartesian 3N |
8 |
2 |
8 |
6 |
24 |
Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
Vibration |
7 |
1 |
6 |
4 |
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 |
1 |
6 |
4 |
17 / 1 |
Quadratic (Raman) |
7 |
1 |
6 |
4 |
18 / 0 |
IR + Raman |
7 |
- |
6 |
4 |
17 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C2 (z) |
v(xz) |
v(yz) |
linear |
1 |
18 |
-2 |
8 |
4 |
quadratic |
2 |
171 |
11 |
41 |
17 |
cubic |
3 |
1.140 |
-20 |
160 |
48 |
quartic |
4 |
5.985 |
65 |
525 |
133 |
quintic |
5 |
26.334 |
-110 |
1.512 |
308 |
sextic |
6 |
100.947 |
275 |
3.941 |
693 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
B1 |
B2 |
linear |
1 |
7 |
1 |
6 |
4 |
quadratic |
2 |
60 |
31 |
46 |
34 |
cubic |
3 |
332 |
228 |
318 |
262 |
quartic |
4 |
1.677 |
1.348 |
1.578 |
1.382 |
quintic |
5 |
7.011 |
6.101 |
6.912 |
6.310 |
sextic |
6 |
26.464 |
24.147 |
25.980 |
24.356 |
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