Direct sum of irreducible representation
| A'1 |
A'2 |
E'1 |
E'2 |
A''1 |
A''2 |
E''1 |
E''2 |
| 2 |
0 |
2 |
2 |
0 |
2 |
2 |
2 |
Properties of derivatives and isotopomers by single substitution, h(D5h)=20
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | Cs |
2 | 10 | C | no | yes | 13C | 131.0816 | 9.9422 |
| 2 | Cs |
2 | 10 | H | no | yes | 2H | 131.0845 | 0.1395 |
| Total Number of Atoms: | 20 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group D
5h
***Calculated as h( D
5h)/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 | 8 | 8 |
| Double | XY | 6 | 16 |
| Triple | X3 | 18 | 48 |
| Triple | X2Y | 22 | 160 |
| Triple | XYZ | 12 | 336 |
| Quadruple | X4 | 43 | 232 |
| Quadruple | X3Y | 50 | 944 |
| Quadruple | X2Y2 | 88 | 1.432 |
| Quadruple | X2YZ | 54 | 2.880 |
| Quadruple | WXYZ | 12 | 5.808 |
| Quintuple | X5 | 72 | 740 |
| Quintuple | VWXYZ | 0 | 93.024 |
| Sextuple | X6 | 128 | 1.904 |
| Sextuple | UVWXYZ | 0 | 1.395.360 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N