Reduction formula for point group C2v
Characters for molecular motions
Motion |
E |
C2 (z) |
v(xz) |
v(yz) |
Cartesian 3N |
120 |
0 |
8 |
8 |
Translation (x,y,z) |
3 |
-1 |
1 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
Vibration |
114 |
2 |
8 |
8 |
Decomposition into Irreducible representations
Motion |
A1 |
A2 |
B1 |
B2 |
Total |
Cartesian 3N |
34 |
26 |
30 |
30 |
120 |
Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
Vibration |
33 |
25 |
28 |
28 |
114 |
Molecule Parameter
Number of Atoms (N) |
40 |
Number of internal coordinates |
114 |
Number of independant internal coordinates |
33 |
Number of vibrational modes |
114 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A1 |
A2 |
B1 |
B2 |
Total |
Linear (IR) |
33 |
25 |
28 |
28 |
89 / 25 |
Quadratic (Raman) |
33 |
25 |
28 |
28 |
114 / 0 |
IR + Raman |
33 |
- |
28 |
28 |
89 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C2 (z) |
v(xz) |
v(yz) |
linear |
1 |
114 |
2 |
8 |
8 |
quadratic |
2 |
6.555 |
59 |
89 |
89 |
cubic |
3 |
253.460 |
116 |
544 |
544 |
quartic |
4 |
7.413.705 |
1.769 |
3.669 |
3.669 |
quintic |
5 |
174.963.438 |
3.422 |
18.600 |
18.600 |
sextic |
6 |
3.470.108.187 |
35.931 |
96.957 |
96.957 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
B1 |
B2 |
linear |
1 |
33 |
25 |
28 |
28 |
quadratic |
2 |
1.698 |
1.609 |
1.624 |
1.624 |
cubic |
3 |
63.666 |
63.122 |
63.336 |
63.336 |
quartic |
4 |
1.855.703 |
1.852.034 |
1.852.984 |
1.852.984 |
quintic |
5 |
43.751.015 |
43.732.415 |
43.740.004 |
43.740.004 |
sextic |
6 |
867.584.508 |
867.487.551 |
867.518.064 |
867.518.064 |
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