Direct sum of irreducible representation
| A1 |
A2 |
E |
T1 |
T2 |
| 3 |
0 |
2 |
2 |
5 |
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 | 337.0034 | 3.2640 |
| 2 | Cs |
2 | 12 | C | no | yes | 13C | 337.0034 | 9.7921 |
| 3 | Cs |
2 | 12 | C | no | yes | 13C | 337.0034 | 9.7921 |
| Total Number of Atoms: | 28 | ✅ 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 | 3 | 0 |
| Double | X2 | 13 | 11 |
| Double | XY | 15 | 24 |
| Triple | X3 | 43 | 118 |
| Triple | X2Y | 63 | 378 |
| Triple | XYZ | 60 | 789 |
| Quadruple | X4 | 121 | 807 |
| Quadruple | X3Y | 195 | 3.318 |
| Quadruple | X2Y2 | 265 | 5.009 |
| Quadruple | X2YZ | 255 | 10.110 |
| Quadruple | WXYZ | 180 | 20.385 |
| Quintuple | X5 | 278 | 3.956 |
| Quintuple | VWXYZ | 360 | 491.220 |
| Sextuple | X6 | 578 | 15.466 |
| Sextuple | UVWXYZ | 360 | 11.302.020 |
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 |
| 84 |
0 |
0 |
0 |
6 |