Direct sum of irreducible representation
| Ag |
Au |
| 4 |
4 |
Properties of derivatives and isotopomers by single substitution, h(Ci)=2
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | C1 |
1 | 2 | C | yes | yes | 13C | 254.7934 | 0.3208 |
| 2 | C1 |
1 | 2 | H | yes | yes | 2H | 254.7963 | 0.004500 |
| 3 | C1 |
1 | 2 | Br | yes | yes | 81Br | 255.7880 | 28.0559 |
| 4 | C1 |
1 | 2 | Cl | yes | yes | 37Cl | 255.7871 | 9.2279 |
| Total Number of Atoms: | 8 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group C
i
***Calculated as h( C
i)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
Numbers of isomers by substitution
| Replacement | Pattern | Achiral
Isomers | Chiral
Isomer Pairs |
|---|
| Single | X | 0 | 4 |
| Double | X2 | 4 | 12 |
| Double | XY | 0 | 28 |
| Triple | X3 | 0 | 28 |
| Triple | X2Y | 0 | 84 |
| Triple | XYZ | 0 | 168 |
| Quadruple | X4 | 6 | 32 |
| Quadruple | X3Y | 0 | 140 |
| Quadruple | X2Y2 | 12 | 204 |
| Quadruple | X2YZ | 0 | 420 |
| Quadruple | WXYZ | 0 | 840 |
| Quintuple | X5 | 0 | 28 |
| Quintuple | VWXYZ | 0 | 3.360 |
| Sextuple | X6 | 4 | 12 |
| Sextuple | UVWXYZ | 0 | 10.080 |
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 |
i |
| 24 |
0 |