Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
90 |
0 |
30 |
0 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
84 |
2 |
30 |
0 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
30 |
15 |
30 |
15 |
90 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
29 |
14 |
28 |
13 |
84 |
Molecule Parameter
| Number of Atoms (N) |
30 |
| Number of internal coordinates |
84 |
| Number of independant internal coordinates |
29 |
| Number of vibrational modes |
84 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
29 |
14 |
28 |
13 |
70 / 14 |
| Quadratic (Raman) |
29 |
14 |
28 |
13 |
84 / 0 |
| IR + Raman |
29 |
- |
28 |
13 |
70 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
84 |
2 |
30 |
0 |
| quadratic |
2 |
3.570 |
44 |
492 |
42 |
| cubic |
3 |
102.340 |
86 |
5.770 |
0 |
| quartic |
4 |
2.225.895 |
989 |
53.853 |
903 |
| quintic |
5 |
39.175.752 |
1.892 |
423.516 |
0 |
| sextic |
6 |
581.106.988 |
15.136 |
2.907.424 |
13.244 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
29 |
14 |
28 |
13 |
| quadratic |
2 |
1.037 |
770 |
994 |
769 |
| cubic |
3 |
27.049 |
24.164 |
27.006 |
24.121 |
| quartic |
4 |
570.410 |
543.032 |
569.464 |
542.989 |
| quintic |
5 |
9.900.290 |
9.688.532 |
9.899.344 |
9.687.586 |
| sextic |
6 |
146.010.698 |
144.550.364 |
145.996.508 |
144.549.418 |
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