Direct sum of irreducible representation
| Ag |
T1g |
T2g |
Gg |
Hg |
Au |
T1u |
T2u |
Gu |
Hu |
| 2 |
0 |
0 |
2 |
2 |
0 |
2 |
2 |
2 |
0 |
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 | 261.1599 | 17.7745 |
| 2 | C3v |
6 | 20 | H | no | yes | 2H | 261.1628 | 0.2493 |
| Total Number of Atoms: | 40 | ✅ 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 | 12 | 4 |
| Double | XY | 14 | 8 |
| Triple | X3 | 46 | 62 |
| Triple | X2Y | 74 | 212 |
| Triple | XYZ | 84 | 456 |
| Quadruple | X4 | 163 | 712 |
| Quadruple | X3Y | 294 | 2.908 |
| Quadruple | X2Y2 | 396 | 4.420 |
| Quadruple | X2YZ | 434 | 8.924 |
| Quadruple | WXYZ | 420 | 18.072 |
| Quintuple | X5 | 478 | 5.258 |
| Quintuple | VWXYZ | 1.680 | 657.168 |
| Sextuple | X6 | 1.288 | 31.504 |
| Sextuple | UVWXYZ | 5.040 | 23.027.760 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N