Reduction formula for point group C2v
Characters for molecular motions
Motion |
E |
C2 (z) |
v(xz) |
v(yz) |
Cartesian 3N |
324 |
0 |
24 |
12 |
Translation (x,y,z) |
3 |
-1 |
1 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
Vibration |
318 |
2 |
24 |
12 |
Decomposition into Irreducible representations
Motion |
A1 |
A2 |
B1 |
B2 |
Total |
Cartesian 3N |
90 |
72 |
84 |
78 |
324 |
Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
Vibration |
89 |
71 |
82 |
76 |
318 |
Molecule Parameter
Number of Atoms (N) |
108 |
Number of internal coordinates |
318 |
Number of independant internal coordinates |
89 |
Number of vibrational modes |
318 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A1 |
A2 |
B1 |
B2 |
Total |
Linear (IR) |
89 |
71 |
82 |
76 |
247 / 71 |
Quadratic (Raman) |
89 |
71 |
82 |
76 |
318 / 0 |
IR + Raman |
89 |
- |
82 |
76 |
247 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C2 (z) |
v(xz) |
v(yz) |
linear |
1 |
318 |
2 |
24 |
12 |
quadratic |
2 |
50.721 |
161 |
447 |
231 |
cubic |
3 |
5.410.240 |
320 |
6.128 |
2.200 |
quartic |
4 |
434.171.760 |
13.040 |
72.528 |
25.080 |
quintic |
5 |
27.960.661.344 |
25.760 |
741.552 |
201.432 |
sextic |
6 |
1.505.215.602.352 |
708.400 |
6.858.544 |
1.748.824 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
B1 |
B2 |
linear |
1 |
89 |
71 |
82 |
76 |
quadratic |
2 |
12.890 |
12.551 |
12.694 |
12.586 |
cubic |
3 |
1.354.722 |
1.350.558 |
1.353.462 |
1.351.498 |
quartic |
4 |
108.570.602 |
108.521.798 |
108.551.542 |
108.527.818 |
quintic |
5 |
6.990.407.522 |
6.989.936.030 |
6.990.293.926 |
6.990.023.866 |
sextic |
6 |
376.306.229.530 |
376.301.925.846 |
376.305.000.918 |
376.302.446.058 |
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