Direct sum of irreducible representation
| A'1 |
A'2 |
E' |
A''1 |
A''2 |
E'' |
| 5 |
5 |
10 |
0 |
0 |
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 | Cs |
2 | 6 | C | no | yes | 13C | 229.0973 | 5.4584 |
| 2 | Cs |
2 | 6 | C | no | yes | 13C | 229.0973 | 5.4584 |
| 3 | Cs |
2 | 6 | C | no | yes | 13C | 229.0973 | 5.4584 |
| 4 | Cs |
2 | 6 | H | no | yes | 2H | 229.1002 | 0.076571 |
| 5 | Cs |
2 | 6 | H | no | yes | 2H | 229.1002 | 0.076571 |
| Total Number of Atoms: | 30 | ✅ 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 | 5 | 0 |
| Double | X2 | 80 | 0 |
| Double | XY | 145 | 0 |
| Triple | X3 | 680 | 0 |
| Triple | X2Y | 2.030 | 0 |
| Triple | XYZ | 4.060 | 0 |
| Quadruple | X4 | 4.620 | 0 |
| Quadruple | X3Y | 18.270 | 0 |
| Quadruple | X2Y2 | 27.510 | 0 |
| Quadruple | X2YZ | 54.810 | 0 |
| Quadruple | WXYZ | 109.620 | 0 |
| Quintuple | X5 | 23.751 | 0 |
| Quintuple | VWXYZ | 2.850.120 | 0 |
| Sextuple | X6 | 99.205 | 0 |
| Sextuple | UVWXYZ | 71.253.000 | 0 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N