Direct sum of irreducible representation
| A1g |
A2g |
B1g |
B2g |
E1g |
E2g |
A1u |
A2u |
B1u |
B2u |
E1u |
E2u |
| 8 |
4 |
0 |
0 |
0 |
12 |
0 |
0 |
8 |
4 |
12 |
0 |
Properties of derivatives and isotopomers by single substitution, h(D6h)=24
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | C2v |
4 | 6 | H | no | yes | 2H | 601.1941 | 0.054845 |
| 2 | C2v |
4 | 6 | C | no | yes | 13C | 601.1912 | 3.9097 |
| 3 | Cs |
2 | 12 | C | no | yes | 13C | 601.1912 | 7.8194 |
| 4 | Cs |
2 | 12 | C | no | yes | 13C | 601.1912 | 7.8194 |
| 5 | Cs |
2 | 12 | C | no | yes | 13C | 601.1912 | 7.8194 |
| 6 | Cs |
2 | 12 | H | no | yes | 2H | 601.1941 | 0.1097 |
| 7 | C2v |
4 | 6 | C | no | yes | 13C | 601.1912 | 3.9097 |
| 8 | C2v |
4 | 6 | H | no | yes | 2H | 601.1941 | 0.054845 |
| Total Number of Atoms: | 72 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group D
6h
***Calculated as h( D
6h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
Numbers of isomers by substitution
| Replacement | Pattern | Achiral
Isomers | Chiral
Isomer Pairs |
|---|
| Single | X | 8 | 0 |
| Double | X2 | 240 | 0 |
| Double | XY | 440 | 0 |
| Triple | X3 | 5.052 | 0 |
| Triple | X2Y | 15.016 | 0 |
| Triple | XYZ | 29.904 | 0 |
| Quadruple | X4 | 86.308 | 0 |
| Quadruple | X3Y | 343.448 | 0 |
| Quadruple | X2Y2 | 515.616 | 0 |
| Quadruple | X2YZ | 1.029.448 | 0 |
| Quadruple | WXYZ | 2.058.000 | 0 |
| Quintuple | X5 | 1.167.416 | 0 |
| Quintuple | VWXYZ | 139.917.120 | 0 |
| Sextuple | X6 | 13.027.616 | 0 |
| Sextuple | UVWXYZ | 9.374.339.520 | 0 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N