Direct sum of irreducible representation
| Ag |
Bg |
Au |
Bu |
| 3 |
0 |
0 |
3 |
Properties of derivatives and isotopomers by single substitution, h(C2h)=4
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | Cs |
2 | 2 | C | no | yes | 13C | 96.9567 | 1.2484 |
| 2 | Cs |
2 | 2 | H | no | yes | 2H | 96.9596 | 0.017513 |
| 3 | Cs |
2 | 2 | Cl | no | yes | 37Cl | 97.9504 | 35.9137 |
| Total Number of Atoms: | 6 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group C
2h
***Calculated as h( C
2h)/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 | 9 | 0 |
| Double | XY | 15 | 0 |
| Triple | X3 | 10 | 0 |
| Triple | X2Y | 30 | 0 |
| Triple | XYZ | 60 | 0 |
| Quadruple | X4 | 9 | 0 |
| Quadruple | X3Y | 30 | 0 |
| Quadruple | X2Y2 | 48 | 0 |
| Quadruple | X2YZ | 90 | 0 |
| Quadruple | WXYZ | 180 | 0 |
| Quintuple | X5 | 3 | 0 |
| Quintuple | VWXYZ | 360 | 0 |
| Sextuple | X6 | 1 | 0 |
| Sextuple | UVWXYZ | 360 | 0 |
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 |
i |
σh |
| 18 |
0 |
0 |
6 |