Reduction formula for point group C2v
Characters for molecular motions
Motion |
E |
C2 (z) |
v(xz) |
v(yz) |
Cartesian 3N |
144 |
0 |
8 |
0 |
Translation (x,y,z) |
3 |
-1 |
1 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
Vibration |
138 |
2 |
8 |
0 |
Decomposition into Irreducible representations
Motion |
A1 |
A2 |
B1 |
B2 |
Total |
Cartesian 3N |
38 |
34 |
38 |
34 |
144 |
Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
Vibration |
37 |
33 |
36 |
32 |
138 |
Molecule Parameter
Number of Atoms (N) |
48 |
Number of internal coordinates |
138 |
Number of independant internal coordinates |
37 |
Number of vibrational modes |
138 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A1 |
A2 |
B1 |
B2 |
Total |
Linear (IR) |
37 |
33 |
36 |
32 |
105 / 33 |
Quadratic (Raman) |
37 |
33 |
36 |
32 |
138 / 0 |
IR + Raman |
37 |
- |
36 |
32 |
105 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C2 (z) |
v(xz) |
v(yz) |
linear |
1 |
138 |
2 |
8 |
0 |
quadratic |
2 |
9.591 |
71 |
101 |
69 |
cubic |
3 |
447.580 |
140 |
640 |
0 |
quartic |
4 |
15.777.195 |
2.555 |
4.815 |
2.415 |
quintic |
5 |
448.072.338 |
4.970 |
25.752 |
0 |
sextic |
6 |
10.679.057.389 |
62.125 |
148.291 |
57.155 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
B1 |
B2 |
linear |
1 |
37 |
33 |
36 |
32 |
quadratic |
2 |
2.458 |
2.373 |
2.388 |
2.372 |
cubic |
3 |
112.090 |
111.770 |
112.020 |
111.700 |
quartic |
4 |
3.946.745 |
3.943.130 |
3.944.260 |
3.943.060 |
quintic |
5 |
112.025.765 |
112.012.889 |
112.023.280 |
112.010.404 |
sextic |
6 |
2.669.831.240 |
2.669.728.517 |
2.669.771.600 |
2.669.726.032 |
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