Reduction formula for point group D3h
Characters for molecular motions
Motion |
E |
2C3 (z) |
3C'2 |
h (xy) |
2S3 |
3v |
Cartesian 3N |
216 |
0 |
0 |
72 |
0 |
0 |
Translation (x,y,z) |
3 |
0 |
-1 |
1 |
-2 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
-1 |
2 |
-1 |
Vibration |
210 |
0 |
2 |
72 |
0 |
0 |
Decomposition into Irreducible representations
Motion |
A'1 |
A'2 |
E' |
A''1 |
A''2 |
E'' |
Total |
Cartesian 3N |
24 |
24 |
48 |
12 |
12 |
24 |
144 |
Translation (x,y,z) |
0 |
0 |
1 |
0 |
1 |
0 |
2 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
0 |
1 |
2 |
Vibration |
24 |
23 |
47 |
12 |
11 |
23 |
140 |
Molecule Parameter
Number of Atoms (N) |
72 |
Number of internal coordinates |
210 |
Number of independant internal coordinates |
24 |
Number of vibrational modes |
140 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A'1 |
A'2 |
E' |
A''1 |
A''2 |
E'' |
Total |
Linear (IR) |
24 |
23 |
47 |
12 |
11 |
23 |
58 / 82 |
Quadratic (Raman) |
24 |
23 |
47 |
12 |
11 |
23 |
94 / 46 |
IR + Raman |
- |
23 |
47 |
12 |
- |
- |
47 / 35 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
2C3 (z) |
3C'2 |
h (xy) |
2S3 |
3v |
linear |
1 |
210 |
0 |
2 |
72 |
0 |
0 |
quadratic |
2 |
22.155 |
0 |
107 |
2.697 |
0 |
105 |
cubic |
3 |
1.565.620 |
70 |
212 |
69.792 |
24 |
0 |
quartic |
4 |
83.369.265 |
0 |
5.777 |
1.399.197 |
0 |
5.565 |
quintic |
5 |
3.568.204.542 |
0 |
11.342 |
23.121.576 |
0 |
0 |
sextic |
6 |
127.860.662.755 |
2.485 |
209.827 |
327.363.605 |
323 |
198.485 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A'1 |
A'2 |
E' |
A''1 |
A''2 |
E'' |
linear |
1 |
24 |
23 |
47 |
12 |
11 |
23 |
quadratic |
2 |
2.124 |
2.018 |
4.142 |
1.622 |
1.621 |
3.243 |
cubic |
3 |
136.353 |
136.247 |
272.553 |
124.713 |
124.607 |
249.297 |
quartic |
4 |
7.066.874 |
7.061.203 |
14.128.077 |
6.830.892 |
6.830.786 |
13.661.678 |
quintic |
5 |
299.280.012 |
299.274.341 |
598.554.353 |
295.426.416 |
295.420.745 |
590.847.161 |
sextic |
6 |
10.682.438.076 |
10.682.233.920 |
21.364.670.592 |
10.627.778.125 |
10.627.772.454 |
21.255.549.498 |
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