Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
36 |
-4 |
12 |
4 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
30 |
-2 |
12 |
4 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
12 |
4 |
12 |
8 |
36 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
11 |
3 |
10 |
6 |
30 |
Molecule Parameter
| Number of Atoms (N) |
12 |
| Number of internal coordinates |
30 |
| Number of independant internal coordinates |
11 |
| Number of vibrational modes |
30 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
11 |
3 |
10 |
6 |
27 / 3 |
| Quadratic (Raman) |
11 |
3 |
10 |
6 |
30 / 0 |
| IR + Raman |
11 |
- |
10 |
6 |
27 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
30 |
-2 |
12 |
4 |
| quadratic |
2 |
465 |
17 |
87 |
23 |
| cubic |
3 |
4.960 |
-32 |
472 |
72 |
| quartic |
4 |
40.920 |
152 |
2.112 |
256 |
| quintic |
5 |
278.256 |
-272 |
8.184 |
680 |
| sextic |
6 |
1.623.160 |
952 |
28.336 |
1.904 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
11 |
3 |
10 |
6 |
| quadratic |
2 |
148 |
93 |
128 |
96 |
| cubic |
3 |
1.368 |
1.096 |
1.348 |
1.148 |
| quartic |
4 |
10.860 |
9.676 |
10.656 |
9.728 |
| quintic |
5 |
71.712 |
67.280 |
71.508 |
67.756 |
| sextic |
6 |
413.588 |
398.468 |
412.160 |
398.944 |
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