Direct sum of irreducible representation
| A1 |
A2 |
E |
T1 |
T2 |
| 2 |
0 |
0 |
0 |
2 |
Properties of derivatives and isotopomers by single substitution, h(Td)=24
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | C3v |
6 | 4 | C | no | yes | 13C | 53.0347 | 4.2537 |
| 2 | C3v |
6 | 4 | H | no | yes | 2H | 53.0376 | 0.059671 |
| Total Number of Atoms: | 8 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group T
d
***Calculated as h( T
d)/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 | 4 | 0 |
| Double | XY | 6 | 0 |
| Triple | X3 | 6 | 0 |
| Triple | X2Y | 10 | 2 |
| Triple | XYZ | 12 | 8 |
| Quadruple | X4 | 8 | 1 |
| Quadruple | X3Y | 14 | 6 |
| Quadruple | X2Y2 | 16 | 11 |
| Quadruple | X2YZ | 18 | 26 |
| Quadruple | WXYZ | 12 | 64 |
| Quintuple | X5 | 6 | 0 |
| Quintuple | VWXYZ | 0 | 280 |
| Sextuple | X6 | 4 | 0 |
| Sextuple | UVWXYZ | 0 | 840 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N
Characters of reducible representation
| E |
8C3 |
3C2 |
6S4 |
6σd |
| 24 |
0 |
0 |
0 |
4 |