Direct sum of irreducible representation
| A1g |
A2g |
Eg |
A1u |
A2u |
Eu |
| 4 |
1 |
5 |
1 |
4 |
5 |
Properties of derivatives and isotopomers by single substitution, h(D3d)=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 | 163.1442 | 5.8275 |
| 2 | Cs |
2 | 6 | C | no | yes | 13C | 163.1442 | 5.8275 |
| 3 | Cs |
2 | 6 | H | no | yes | 2H | 163.1471 | 0.081748 |
| 4 | C1 |
1 | 12 | H | yes | yes | 2H | 163.1471 | 0.1635 |
| Total Number of Atoms: | 30 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group D
3d
***Calculated as h( D
3d)/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 | 1 |
| Double | X2 | 16 | 32 |
| Double | XY | 15 | 65 |
| Triple | X3 | 46 | 317 |
| Triple | X2Y | 66 | 982 |
| Triple | XYZ | 60 | 2.000 |
| Quadruple | X4 | 148 | 2.236 |
| Quadruple | X3Y | 210 | 9.030 |
| Quadruple | X2Y2 | 326 | 13.592 |
| Quadruple | X2YZ | 270 | 27.270 |
| Quadruple | WXYZ | 180 | 54.720 |
| Quintuple | X5 | 321 | 11.715 |
| Quintuple | VWXYZ | 360 | 1.424.880 |
| Sextuple | X6 | 773 | 49.216 |
| Sextuple | UVWXYZ | 360 | 35.626.320 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N