Reduction formula for point group D3d
Characters for molecular motions
| Motion |
E |
2C3 |
3C'2 |
i |
2S6 |
3 d |
| Cartesian 3N |
324 |
0 |
0 |
0 |
0 |
8 |
| Translation (x,y,z) |
3 |
0 |
-1 |
-3 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
3 |
0 |
-1 |
| Vibration |
318 |
0 |
2 |
0 |
0 |
8 |
Decomposition into Irreducible representations
| Motion |
A1g |
A2g |
Eg |
A1u |
A2u |
Eu |
Total |
| Cartesian 3N |
29 |
25 |
54 |
25 |
29 |
54 |
216 |
| Translation (x,y,z) |
0 |
0 |
0 |
0 |
1 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
0 |
0 |
0 |
2 |
| Vibration |
29 |
24 |
53 |
25 |
28 |
53 |
212 |
Molecule Parameter
| Number of Atoms (N) |
108 |
| Number of internal coordinates |
318 |
| Number of independant internal coordinates |
29 |
| Number of vibrational modes |
212 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1g |
A2g |
Eg |
A1u |
A2u |
Eu |
Total |
| Linear (IR) |
29 |
24 |
53 |
25 |
28 |
53 |
81 / 131 |
| Quadratic (Raman) |
29 |
24 |
53 |
25 |
28 |
53 |
82 / 130 |
| IR + Raman |
- |
24 |
- |
25 |
- |
- |
0* / 49 |
* Center of inversion: Mutual Exclusion Principle
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 |
3C'2 |
i |
2S6 |
3d |
| linear |
1 |
318 |
0 |
2 |
0 |
0 |
8 |
| quadratic |
2 |
50.721 |
0 |
161 |
159 |
0 |
191 |
| cubic |
3 |
5.410.240 |
106 |
320 |
0 |
0 |
1.360 |
| quartic |
4 |
434.171.760 |
0 |
13.040 |
12.720 |
0 |
18.000 |
| quintic |
5 |
27.960.661.344 |
0 |
25.760 |
0 |
0 |
116.112 |
| sextic |
6 |
1.505.215.602.352 |
5.671 |
708.400 |
682.640 |
53 |
1.120.816 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1g |
A2g |
Eg |
A1u |
A2u |
Eu |
| linear |
1 |
29 |
24 |
53 |
25 |
28 |
53 |
| quadratic |
2 |
4.328 |
4.152 |
8.480 |
4.206 |
4.221 |
8.427 |
| cubic |
3 |
451.291 |
450.451 |
901.689 |
450.611 |
451.131 |
901.689 |
| quartic |
4 |
36.189.800 |
36.174.280 |
72.364.080 |
36.178.680 |
36.181.160 |
72.359.840 |
| quintic |
5 |
2.330.090.580 |
2.330.019.644 |
4.660.110.224 |
2.330.032.524 |
2.330.077.700 |
4.660.110.224 |
| sextic |
6 |
125.435.148.674 |
125.434.234.066 |
250.869.379.878 |
125.434.474.475 |
125.434.680.683 |
250.869.152.349 |
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