Reduction formula for point group D2
Characters for molecular motions
Motion |
E |
C2 (z) |
C2 (y) |
C2 (x) |
Cartesian 3N |
324 |
0 |
0 |
0 |
Translation (x,y,z) |
3 |
-1 |
-1 |
-1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
Vibration |
318 |
2 |
2 |
2 |
Decomposition into Irreducible representations
Motion |
A |
B1 |
B2 |
B3 |
Total |
Cartesian 3N |
81 |
81 |
81 |
81 |
324 |
Translation (x,y,z) |
0 |
1 |
1 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
Vibration |
81 |
79 |
79 |
79 |
318 |
Molecule Parameter
Number of Atoms (N) |
108 |
Number of internal coordinates |
318 |
Number of independant internal coordinates |
81 |
Number of vibrational modes |
318 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A |
B1 |
B2 |
B3 |
Total |
Linear (IR) |
81 |
79 |
79 |
79 |
237 / 81 |
Quadratic (Raman) |
81 |
79 |
79 |
79 |
318 / 0 |
IR + Raman |
- |
79 |
79 |
79 |
237 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C2 (z) |
C2 (y) |
C2 (x) |
linear |
1 |
318 |
2 |
2 |
2 |
quadratic |
2 |
50.721 |
161 |
161 |
161 |
cubic |
3 |
5.410.240 |
320 |
320 |
320 |
quartic |
4 |
434.171.760 |
13.040 |
13.040 |
13.040 |
quintic |
5 |
27.960.661.344 |
25.760 |
25.760 |
25.760 |
sextic |
6 |
1.505.215.602.352 |
708.400 |
708.400 |
708.400 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A |
B1 |
B2 |
B3 |
linear |
1 |
81 |
79 |
79 |
79 |
quadratic |
2 |
12.801 |
12.640 |
12.640 |
12.640 |
cubic |
3 |
1.352.800 |
1.352.480 |
1.352.480 |
1.352.480 |
quartic |
4 |
108.552.720 |
108.539.680 |
108.539.680 |
108.539.680 |
quintic |
5 |
6.990.184.656 |
6.990.158.896 |
6.990.158.896 |
6.990.158.896 |
sextic |
6 |
376.304.431.888 |
376.303.723.488 |
376.303.723.488 |
376.303.723.488 |
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