Direct sum of irreducible representation
| A1 |
A2 |
E |
T1 |
T2 |
| 3 |
0 |
1 |
1 |
3 |
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 | Td |
24 | 1 | C | no | no | 13C | 73.0973 | 1.0504 |
| 2 | C3v |
6 | 4 | C | no | yes | 13C | 73.0973 | 4.2017 |
| 3 | Cs |
2 | 12 | H | no | yes | 2H | 73.1002 | 0.1768 |
| Total Number of Atoms: | 17 | ✅ 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 | 8 | 3 |
| Double | XY | 10 | 7 |
| Triple | X3 | 20 | 21 |
| Triple | X2Y | 30 | 71 |
| Triple | XYZ | 30 | 155 |
| Quadruple | X4 | 42 | 85 |
| Quadruple | X3Y | 70 | 365 |
| Quadruple | X2Y2 | 90 | 557 |
| Quadruple | X2YZ | 90 | 1.145 |
| Quadruple | WXYZ | 60 | 2.350 |
| Quintuple | X5 | 70 | 228 |
| Quintuple | VWXYZ | 60 | 30.910 |
| Sextuple | X6 | 100 | 476 |
| Sextuple | UVWXYZ | 0 | 371.280 |
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 |
| 51 |
0 |
-1 |
-1 |
5 |