Direct sum of irreducible representation
| A |
B |
| 4 |
3 |
Properties of derivatives and isotopomers by single substitution, h(C2)=2
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | C2 |
2 | 1 | C | yes | yes | 13C | 108.9567 | 0.6173 |
| 2 | C1 |
1 | 2 | C | yes | yes | 13C | 108.9567 | 1.2347 |
| 3 | C1 |
1 | 2 | Cl | yes | yes | 37Cl | 109.9504 | 35.5186 |
| 4 | C1 |
1 | 2 | H | yes | yes | 2H | 108.9596 | 0.017320 |
| Total Number of Atoms: | 7 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group C
2
***Calculated as h( C
2)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
Numbers of isomers by substitution
| Replacement | Pattern | Chiral
Isomers |
|---|
| Single | X | 4 |
| Double | X2 | 12 |
| Double | XY | 21 |
| Triple | X3 | 19 |
| Triple | X2Y | 54 |
| Triple | XYZ | 105 |
| Quadruple | X4 | 19 |
| Quadruple | X3Y | 70 |
| Quadruple | X2Y2 | 108 |
| Quadruple | X2YZ | 210 |
| Quadruple | WXYZ | 420 |
| Quintuple | X5 | 12 |
| Quintuple | VWXYZ | 1.260 |
| Sextuple | X6 | 4 |
| Sextuple | UVWXYZ | 2.520 |
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 |
C2 |
| 21 |
-1 |