Direct sum of irreducible representation
| A'1 |
A'2 |
E' |
A''1 |
A''2 |
E'' |
| 7 |
0 |
5 |
0 |
7 |
5 |
Properties of derivatives and isotopomers by single substitution, h(D3h)=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 | 255.1129 | 5.3373 |
| 2 | C3v |
6 | 2 | C | no | yes | 13C | 255.1129 | 1.7791 |
| 3 | C3v |
6 | 2 | H | no | yes | 2H | 255.1158 | 0.024957 |
| 4 | Cs |
2 | 6 | C | no | yes | 13C | 255.1129 | 5.3373 |
| 5 | Cs |
2 | 6 | C | no | yes | 13C | 255.1129 | 5.3373 |
| 6 | Cs |
2 | 6 | H | no | yes | 2H | 255.1158 | 0.074872 |
| 7 | Cs |
2 | 6 | H | no | yes | 2H | 255.1158 | 0.074872 |
| Total Number of Atoms: | 34 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group D
3h
***Calculated as h( D
3h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
Numbers of isomers by substitution
| Replacement | Pattern | Achiral
Isomers | Chiral
Isomer Pairs |
|---|
| Single | X | 7 | 0 |
| Double | X2 | 54 | 25 |
| Double | XY | 91 | 50 |
| Triple | X3 | 252 | 375 |
| Triple | X2Y | 616 | 1.190 |
| Triple | XYZ | 1.092 | 2.450 |
| Quadruple | X4 | 1.001 | 3.405 |
| Quadruple | X3Y | 2.912 | 14.010 |
| Quadruple | X2Y2 | 4.004 | 21.255 |
| Quadruple | X2YZ | 6.916 | 42.920 |
| Quadruple | WXYZ | 12.012 | 86.750 |
| Quintuple | X5 | 3.136 | 21.630 |
| Quintuple | VWXYZ | 120.120 | 2.722.500 |
| Sextuple | X6 | 8.729 | 107.895 |
| Sextuple | UVWXYZ | 1.081.080 | 80.153.700 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N