Direct sum of irreducible representation
| Ag |
Eg*
|
Tg |
Au |
Eu*
|
Tu |
| 4 |
4 |
10 |
3 |
3 |
11 |
Properties of derivatives and isotopomers by single substitution, h(Th)=24
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | C1 |
1 | 24 | C | yes | yes | 13C | 2615.0435 | 0.00000114 |
| 2 | C1 |
1 | 24 | C | yes | yes | 13C | 2615.0435 | 0.00000114 |
| 3 | Cs |
2 | 12 | C | no | yes | 13C | 2615.0435 | 0.00000057 |
| 4 | C1 |
1 | 24 | Br | yes | yes | 81Br | 2616.0381 | 0.00009957 |
| Total Number of Atoms: | 84 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group T
h
***Calculated as h( T
h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
Numbers of isomers by substitution
| Replacement | Pattern | Achiral
Isomers | Chiral
Isomer Pairs |
|---|
| Single | X | 1 | 3 |
| Double | X2 | 15 | 143 |
| Double | XY | 3 | 289 |
| Triple | X3 | 41 | 3.959 |
| Triple | X2Y | 43 | 11.889 |
| Triple | XYZ | 6 | 23.818 |
| Quadruple | X4 | 327 | 80.340 |
| Quadruple | X3Y | 121 | 321.523 |
| Quadruple | X2Y2 | 655 | 482.263 |
| Quadruple | X2YZ | 123 | 964.689 |
| Quadruple | WXYZ | 6 | 1.929.498 |
| Quintuple | X5 | 820 | 1.285.924 |
| Quintuple | VWXYZ | 0 | 154.360.080 |
| Sextuple | X6 | 4.616 | 16.935.984 |
| Sextuple | UVWXYZ | 0 | 12.194.446.320 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N