Direct sum of irreducible representation
| Ag |
T1g |
T2g |
Gg |
Hg |
Au |
T1u |
T2u |
Gu |
Hu |
| 1 |
0 |
0 |
1 |
1 |
0 |
1 |
1 |
1 |
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 | 241.0034 | 17.8300 |
| Total Number of Atoms: | 20 | ✅ 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 | 4 | 1 |
| Double | XY | 3 | 2 |
| Triple | X3 | 9 | 6 |
| Triple | X2Y | 11 | 23 |
| Triple | XYZ | 6 | 54 |
| Quadruple | X4 | 20 | 38 |
| Quadruple | X3Y | 25 | 151 |
| Quadruple | X2Y2 | 41 | 233 |
| Quadruple | X2YZ | 27 | 471 |
| Quadruple | WXYZ | 6 | 966 |
| Quintuple | X5 | 36 | 113 |
| Quintuple | VWXYZ | 0 | 15.504 |
| Sextuple | X6 | 61 | 310 |
| Sextuple | UVWXYZ | 0 | 232.560 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N