Direct sum of irreducible representation
| A1g |
A2g |
B1g |
B2g |
E1g |
E2g |
A1u |
A2u |
B1u |
B2u |
E1u |
E2u |
| 4 |
2 |
0 |
0 |
0 |
6 |
0 |
0 |
4 |
2 |
6 |
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 | C | no | yes | 13C | 301.0973 | 5.1079 |
| 2 | C2v |
4 | 6 | C | no | yes | 13C | 301.0973 | 5.1079 |
| 3 | Cs |
2 | 12 | C | no | yes | 13C | 301.0973 | 10.2159 |
| 4 | Cs |
2 | 12 | H | no | yes | 2H | 301.1002 | 0.1433 |
| Total Number of Atoms: | 36 | ✅ 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 | 4 | 0 |
| Double | X2 | 64 | 0 |
| Double | XY | 108 | 0 |
| Triple | X3 | 614 | 0 |
| Triple | X2Y | 1.804 | 0 |
| Triple | XYZ | 3.576 | 0 |
| Quadruple | X4 | 5.014 | 0 |
| Quadruple | X3Y | 19.684 | 0 |
| Quadruple | X2Y2 | 29.664 | 0 |
| Quadruple | X2YZ | 58.956 | 0 |
| Quadruple | WXYZ | 117.816 | 0 |
| Quintuple | X5 | 31.552 | 0 |
| Quintuple | VWXYZ | 3.769.920 | 0 |
| Sextuple | X6 | 162.924 | 0 |
| Sextuple | UVWXYZ | 116.867.520 | 0 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N