Direct sum of irreducible representation
| A'1 |
A'2 |
E' |
A''1 |
A''2 |
E'' |
| 9 |
5 |
13 |
4 |
8 |
11 |
Properties of derivatives and isotopomers by single substitution, h(D3h)=12
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | C3v |
6 | 2 | C | no | yes | 13C | 889.0034 | 0.9812 |
| 2 | Cs |
2 | 6 | C | no | yes | 13C | 889.0034 | 2.9436 |
| 3 | C1 |
1 | 12 | C | yes | yes | 13C | 889.0034 | 5.8871 |
| 4 | Cs |
2 | 6 | C | no | yes | 13C | 889.0034 | 2.9436 |
| 5 | C1 |
1 | 12 | C | yes | yes | 13C | 889.0034 | 5.8871 |
| 6 | Cs |
2 | 6 | C | no | yes | 13C | 889.0034 | 2.9436 |
| 7 | C1 |
1 | 12 | C | yes | yes | 13C | 889.0034 | 5.8871 |
| 8 | C1 |
1 | 12 | C | yes | yes | 13C | 889.0034 | 5.8871 |
| 9 | Cs |
2 | 6 | C | no | yes | 13C | 889.0034 | 2.9436 |
| Total Number of Atoms: | 74 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group D
3h
***Calculated as h( D
3h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
Numbers of isomers by substitution
| Replacement | Pattern | Achiral
Isomers | Chiral
Isomer Pairs |
|---|
| Single | X | 5 | 4 |
| Double | X2 | 39 | 215 |
| Double | XY | 33 | 434 |
| Triple | X3 | 198 | 5.307 |
| Triple | X2Y | 260 | 16.076 |
| Triple | XYZ | 188 | 32.318 |
| Quadruple | X4 | 942 | 95.589 |
| Quadruple | X3Y | 1.244 | 382.928 |
| Quadruple | X2Y2 | 2.034 | 574.629 |
| Quadruple | X2YZ | 1.544 | 1.149.854 |
| Quadruple | WXYZ | 900 | 2.300.802 |
| Quintuple | X5 | 3.740 | 1.340.531 |
| Quintuple | VWXYZ | 3.480 | 161.085.900 |
| Sextuple | X6 | 13.778 | 15.432.665 |
| Sextuple | UVWXYZ | 10.200 | 11.115.042.060 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N