Direct sum of irreducible representation
| A1 |
A2 |
E |
T1 |
T2 |
| 4 |
4 |
6 |
10 |
10 |
Properties of derivatives and isotopomers by single substitution, h(O)=24
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | C3 |
3 | 8 | N | yes | yes | 15N | 449.3972 | 2.1721 |
| 2 | C1 |
1 | 24 | C | yes | yes | 13C | 449.4035 | 19.7300 |
| 3 | C1 |
1 | 24 | H | yes | yes | 2H | 449.4065 | 0.2768 |
| 4 | C1 |
1 | 24 | H | yes | yes | 2H | 449.4065 | 0.2768 |
| Total Number of Atoms: | 80 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group O
***Calculated as h( O)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
Numbers of isomers by substitution
| Replacement | Pattern | Chiral
Isomers |
|---|
| Single | X | 4 |
| Double | X2 | 147 |
| Double | XY | 264 |
| Triple | X3 | 3.432 |
| Triple | X2Y | 10.270 |
| Triple | XYZ | 20.540 |
| Quadruple | X4 | 66.214 |
| Quadruple | X3Y | 263.614 |
| Quadruple | X2Y2 | 395.980 |
| Quadruple | X2YZ | 790.790 |
| Quadruple | WXYZ | 1.581.580 |
| Quintuple | X5 | 1.001.676 |
| Quintuple | VWXYZ | 120.200.080 |
| Sextuple | X6 | 12.524.655 |
| Sextuple | UVWXYZ | 9.015.006.000 |
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 |
6C2 |
6C4 |
3C2 |
| 240 |
0 |
0 |
0 |
0 |