Reduction formula for point group C2v
Characters for molecular motions
Motion |
E |
C2 (z) |
v(xz) |
v(yz) |
Cartesian 3N |
216 |
-8 |
72 |
8 |
Translation (x,y,z) |
3 |
-1 |
1 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
Vibration |
210 |
-6 |
72 |
8 |
Decomposition into Irreducible representations
Motion |
A1 |
A2 |
B1 |
B2 |
Total |
Cartesian 3N |
72 |
32 |
72 |
40 |
216 |
Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
Vibration |
71 |
31 |
70 |
38 |
210 |
Molecule Parameter
Number of Atoms (N) |
72 |
Number of internal coordinates |
210 |
Number of independant internal coordinates |
71 |
Number of vibrational modes |
210 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A1 |
A2 |
B1 |
B2 |
Total |
Linear (IR) |
71 |
31 |
70 |
38 |
179 / 31 |
Quadratic (Raman) |
71 |
31 |
70 |
38 |
210 / 0 |
IR + Raman |
71 |
- |
70 |
38 |
179 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C2 (z) |
v(xz) |
v(yz) |
linear |
1 |
210 |
-6 |
72 |
8 |
quadratic |
2 |
22.155 |
123 |
2.697 |
137 |
cubic |
3 |
1.565.620 |
-668 |
69.792 |
928 |
quartic |
4 |
83.369.265 |
7.521 |
1.399.197 |
9.117 |
quintic |
5 |
3.568.204.542 |
-37.482 |
23.121.576 |
54.120 |
sextic |
6 |
127.860.662.755 |
305.731 |
327.363.605 |
397.333 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
B1 |
B2 |
linear |
1 |
71 |
31 |
70 |
38 |
quadratic |
2 |
6.278 |
4.861 |
6.148 |
4.868 |
cubic |
3 |
408.918 |
373.558 |
408.788 |
374.356 |
quartic |
4 |
21.196.275 |
20.492.118 |
21.187.956 |
20.492.916 |
quintic |
5 |
897.835.689 |
886.247.841 |
897.827.370 |
886.293.642 |
sextic |
6 |
32.047.182.356 |
31.883.301.887 |
32.046.830.824 |
31.883.347.688 |
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