Direct sum of irreducible representation
| A'1 |
A'2 |
E' |
A''1 |
A''2 |
E'' |
| 2 |
0 |
2 |
0 |
2 |
2 |
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 | Cs |
2 | 6 | C | no | yes | 13C | 79.0503 | 6.2391 |
| 2 | Cs |
2 | 6 | H | no | yes | 2H | 79.0532 | 0.087522 |
| Total Number of Atoms: | 12 | ✅ 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 | 2 | 0 |
| Double | X2 | 6 | 4 |
| Double | XY | 6 | 8 |
| Triple | X3 | 10 | 14 |
| Triple | X2Y | 14 | 48 |
| Triple | XYZ | 12 | 104 |
| Quadruple | X4 | 18 | 36 |
| Quadruple | X3Y | 26 | 152 |
| Quadruple | X2Y2 | 38 | 236 |
| Quadruple | X2YZ | 30 | 480 |
| Quadruple | WXYZ | 12 | 984 |
| Quintuple | X5 | 20 | 56 |
| Quintuple | VWXYZ | 0 | 7.920 |
| Sextuple | X6 | 26 | 70 |
| Sextuple | UVWXYZ | 0 | 55.440 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N