Direct sum of irreducible representation
| A1 |
A2 |
E |
T1 |
T2 |
| 4 |
0 |
2 |
1 |
5 |
Properties of derivatives and isotopomers by single substitution, h(Td)=24
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | C2v |
4 | 6 | C | no | yes | 13C | 137.1286 | 5.9597 |
| 2 | C3v |
6 | 4 | C | no | yes | 13C | 137.1286 | 3.9732 |
| 3 | Cs |
2 | 12 | H | no | yes | 2H | 137.1315 | 0.1672 |
| 4 | C3v |
6 | 4 | H | no | yes | 2H | 137.1315 | 0.055735 |
| Total Number of Atoms: | 26 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group T
d
***Calculated as h( T
d)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
Numbers of isomers by substitution
| Replacement | Pattern | Achiral
Isomers | Chiral
Isomer Pairs |
|---|
| Single | X | 4 | 0 |
| Double | X2 | 19 | 6 |
| Double | XY | 28 | 14 |
| Triple | X3 | 64 | 82 |
| Triple | X2Y | 120 | 268 |
| Triple | XYZ | 168 | 566 |
| Quadruple | X4 | 182 | 547 |
| Quadruple | X3Y | 392 | 2.304 |
| Quadruple | X2Y2 | 498 | 3.508 |
| Quadruple | X2YZ | 672 | 7.142 |
| Quadruple | WXYZ | 840 | 14.530 |
| Quintuple | X5 | 424 | 2.548 |
| Quintuple | VWXYZ | 3.360 | 327.220 |
| Sextuple | X6 | 878 | 9.199 |
| Sextuple | UVWXYZ | 10.080 | 6.901.860 |
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 |
8C3 |
3C2 |
6S4 |
6σd |
| 78 |
0 |
-2 |
0 |
8 |