Direct sum of irreducible representation
| A1g |
A2g |
Eg |
A1u |
A2u |
Eu |
| 3 |
0 |
3 |
0 |
3 |
3 |
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 | 85.0973 | 6.2332 |
| 2 | Cs |
2 | 6 | H | no | yes | 2H | 85.1002 | 0.087440 |
| 3 | Cs |
2 | 6 | H | no | yes | 2H | 85.1002 | 0.087440 |
| Total Number of Atoms: | 18 | ✅ 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 | 0 |
| Double | X2 | 12 | 9 |
| Double | XY | 15 | 18 |
| Triple | X3 | 28 | 55 |
| Triple | X2Y | 48 | 180 |
| Triple | XYZ | 60 | 378 |
| Quadruple | X4 | 66 | 231 |
| Quadruple | X3Y | 120 | 960 |
| Quadruple | X2Y2 | 162 | 1.467 |
| Quadruple | X2YZ | 180 | 2.970 |
| Quadruple | WXYZ | 180 | 6.030 |
| Quintuple | X5 | 108 | 660 |
| Quintuple | VWXYZ | 360 | 85.500 |
| Sextuple | X6 | 183 | 1.479 |
| Sextuple | UVWXYZ | 360 | 1.113.660 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N