Direct sum of irreducible representation
| A1 |
A2 |
B1 |
B2 |
E1 |
E2 |
E3 |
E4 |
E5 |
| 4 |
2 |
2 |
4 |
6 |
6 |
6 |
6 |
6 |
Properties of derivatives and isotopomers by single substitution, h(D6d)=24
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | Cs |
2 | 12 | C | no | yes | 13C | 865.0034 | 6.0188 |
| 2 | Cs |
2 | 12 | C | no | yes | 13C | 865.0034 | 6.0188 |
| 3 | C1 |
1 | 24 | C | yes | yes | 13C | 865.0034 | 12.0376 |
| 4 | C1 |
1 | 24 | C | yes | yes | 13C | 865.0034 | 12.0376 |
| Total Number of Atoms: | 72 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group D
6d
***Calculated as h( D
6d)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
Numbers of isomers by substitution
| Replacement | Pattern | Achiral
Isomers | Chiral
Isomer Pairs |
|---|
| Single | X | 2 | 2 |
| Double | X2 | 20 | 107 |
| Double | XY | 6 | 210 |
| Triple | X3 | 70 | 2.452 |
| Triple | X2Y | 74 | 7.418 |
| Triple | XYZ | 12 | 14.904 |
| Quadruple | X4 | 386 | 42.857 |
| Quadruple | X3Y | 206 | 171.362 |
| Quadruple | X2Y2 | 768 | 257.181 |
| Quadruple | X2YZ | 210 | 514.290 |
| Quadruple | WXYZ | 12 | 1.028.784 |
| Quintuple | X5 | 1.190 | 582.386 |
| Quintuple | VWXYZ | 0 | 69.957.720 |
| Sextuple | X6 | 4.692 | 6.509.715 |
| Sextuple | UVWXYZ | 0 | 4.687.167.240 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N