Direct sum of irreducible representation
| Ag |
T1g |
T2g |
Gg |
Hg |
Au |
T1u |
T2u |
Gu |
Hu |
| 1 |
1 |
1 |
2 |
3 |
0 |
2 |
2 |
2 |
2 |
Properties of derivatives and isotopomers by single substitution, h(Ih)=120
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | Cs |
2 | 60 | C | no | yes | 13C | 721.0034 | 34.3657 |
| Total Number of Atoms: | 60 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group I
h
***Calculated as h( I
h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
Numbers of isomers by substitution
| Replacement | Pattern | Achiral
Isomers | Chiral
Isomer Pairs |
|---|
| Single | X | 1 | 0 |
| Double | X2 | 9 | 14 |
| Double | XY | 3 | 28 |
| Triple | X3 | 29 | 274 |
| Triple | X2Y | 31 | 840 |
| Triple | XYZ | 6 | 1.708 |
| Quadruple | X4 | 144 | 4.046 |
| Quadruple | X3Y | 85 | 16.212 |
| Quadruple | X2Y2 | 289 | 24.346 |
| Quadruple | X2YZ | 87 | 48.720 |
| Quadruple | WXYZ | 6 | 97.524 |
| Quintuple | X5 | 406 | 45.312 |
| Quintuple | VWXYZ | 0 | 5.461.512 |
| Sextuple | X6 | 1.464 | 417.006 |
| Sextuple | UVWXYZ | 0 | 300.383.160 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N