Direct sum of irreducible representation
| A |
E*
|
T |
| 3 |
1 |
4 |
Properties of derivatives and isotopomers by single substitution, h(T)=12
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | T |
12 | 1 | C | yes | no | 13C | 73.0973 | 1.0504 |
| 2 | C3 |
3 | 4 | C | yes | yes | 13C | 73.0973 | 4.2017 |
| 3 | C1 |
1 | 12 | H | yes | yes | 2H | 73.1002 | 0.1768 |
| Total Number of Atoms: | 17 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group T
***Calculated as h( T)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
Numbers of isomers by substitution
| Replacement | Pattern | Chiral
Isomers |
|---|
| Single | X | 3 |
| Double | X2 | 14 |
| Double | XY | 24 |
| Triple | X3 | 62 |
| Triple | X2Y | 172 |
| Triple | XYZ | 340 |
| Quadruple | X4 | 212 |
| Quadruple | X3Y | 800 |
| Quadruple | X2Y2 | 1.204 |
| Quadruple | X2YZ | 2.380 |
| Quadruple | WXYZ | 4.760 |
| Quintuple | X5 | 526 |
| Quintuple | VWXYZ | 61.880 |
| Sextuple | X6 | 1.052 |
| Sextuple | UVWXYZ | 742.560 |
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 |
4C3 |
4(C3)2 |
3C2 |
| 51 |
0 |
0 |
-1 |