Direct sum of irreducible representation
| A |
E*
|
| 4 |
2 |
Properties of derivatives and isotopomers by single substitution, h(C3)=3
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | C3 |
3 | 1 | C | yes | yes | 13C | 132.9334 | 0.4728 |
| 2 | C3 |
3 | 1 | C | yes | yes | 13C | 132.9334 | 0.4728 |
| 3 | C1 |
1 | 3 | H | yes | yes | 2H | 132.9363 | 0.019899 |
| 4 | C1 |
1 | 3 | Cl | yes | yes | 37Cl | 133.9271 | 40.8059 |
| Total Number of Atoms: | 8 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group C
3
***Calculated as h( C
3)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
Numbers of isomers by substitution
| Replacement | Pattern | Chiral
Isomers |
|---|
| Single | X | 4 |
| Double | X2 | 10 |
| Double | XY | 20 |
| Triple | X3 | 20 |
| Triple | X2Y | 56 |
| Triple | XYZ | 112 |
| Quadruple | X4 | 26 |
| Quadruple | X3Y | 96 |
| Quadruple | X2Y2 | 140 |
| Quadruple | X2YZ | 280 |
| Quadruple | WXYZ | 560 |
| Quintuple | X5 | 20 |
| Quintuple | VWXYZ | 2.240 |
| Sextuple | X6 | 10 |
| Sextuple | UVWXYZ | 6.720 |
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 |
C3 |
(C3)2 |
| 24 |
0 |
0 |