Direct sum of irreducible representation
| A'1 |
A'2 |
E' |
A''1 |
A''2 |
E'' |
| 3 |
0 |
1 |
0 |
1 |
0 |
Properties of derivatives and isotopomers by single substitution, h(D3h)=12
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | D3h |
12 | 1 | P | no | no | - | - | - |
| 2 | C3v |
6 | 2 | F | no | yes | - | - | - |
| 3 | C2v |
4 | 3 | F | no | yes | - | - | - |
| Total Number of Atoms: | 6 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group D
3h
***Calculated as h( D
3h)/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 | 5 | 0 |
| Double | XY | 8 | 0 |
| Triple | X3 | 6 | 0 |
| Triple | X2Y | 11 | 1 |
| Triple | XYZ | 16 | 3 |
| Quadruple | X4 | 5 | 0 |
| Quadruple | X3Y | 11 | 1 |
| Quadruple | X2Y2 | 12 | 3 |
| Quadruple | X2YZ | 16 | 8 |
| Quadruple | WXYZ | 16 | 22 |
| Quintuple | X5 | 3 | 0 |
| Quintuple | VWXYZ | 0 | 60 |
| Sextuple | X6 | 1 | 0 |
| Sextuple | UVWXYZ | 0 | 60 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N