Direct sum of irreducible representation
| Ag |
T1g |
T2g |
Gg |
Hg |
Au |
T1u |
T2u |
Gu |
Hu |
| 2 |
1 |
1 |
3 |
4 |
0 |
3 |
3 |
3 |
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 | C3v |
6 | 20 | C | no | yes | 13C | 961.0034 | 9.1818 |
| 2 | Cs |
2 | 60 | C | no | yes | 13C | 961.0034 | 27.5455 |
| Total Number of Atoms: | 80 | ✅ 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 | 2 | 0 |
| Double | X2 | 17 | 23 |
| Double | XY | 14 | 46 |
| Triple | X3 | 86 | 646 |
| Triple | X2Y | 114 | 1.997 |
| Triple | XYZ | 84 | 4.066 |
| Quadruple | X4 | 440 | 13.066 |
| Quadruple | X3Y | 574 | 52.441 |
| Quadruple | X2Y2 | 950 | 78.799 |
| Quadruple | X2YZ | 714 | 157.801 |
| Quadruple | WXYZ | 420 | 316.106 |
| Quintuple | X5 | 1.778 | 199.452 |
| Quintuple | VWXYZ | 1.680 | 24.039.176 |
| Sextuple | X6 | 7.001 | 2.501.957 |
| Sextuple | UVWXYZ | 5.040 | 1.802.998.680 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N