Direct sum of irreducible representation
| A1 |
A2 |
E |
T1 |
T2 |
| 3 |
0 |
2 |
1 |
4 |
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 | 141.1096 | 6.1425 |
| 2 | C3v |
6 | 4 | N | no | yes | 15N | 141.1032 | 1.3525 |
| 3 | Cs |
2 | 12 | H | no | yes | 2H | 141.1125 | 0.1723 |
| Total Number of Atoms: | 22 | ✅ 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 | 3 | 0 |
| Double | X2 | 12 | 5 |
| Double | XY | 15 | 12 |
| Triple | X3 | 34 | 52 |
| Triple | X2Y | 54 | 168 |
| Triple | XYZ | 60 | 355 |
| Quadruple | X4 | 84 | 272 |
| Quadruple | X3Y | 150 | 1.149 |
| Quadruple | X2Y2 | 193 | 1.746 |
| Quadruple | X2YZ | 210 | 3.555 |
| Quadruple | WXYZ | 180 | 7.225 |
| Quintuple | X5 | 167 | 1.025 |
| Quintuple | VWXYZ | 360 | 131.490 |
| Sextuple | X6 | 301 | 2.986 |
| Sextuple | UVWXYZ | 360 | 2.238.210 |
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 |
| 66 |
0 |
-2 |
0 |
6 |