Direct sum of irreducible representation
| A'1 |
A'2 |
E'1 |
E'2 |
A''1 |
A''2 |
E''1 |
E''2 |
| 5 |
3 |
8 |
8 |
2 |
4 |
6 |
6 |
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 | 841.0034 | 5.1279 |
| 2 | C1 |
1 | 20 | C | yes | yes | 13C | 841.0034 | 10.2557 |
| 3 | C1 |
1 | 20 | C | yes | yes | 13C | 841.0034 | 10.2557 |
| 4 | Cs |
2 | 10 | C | no | yes | 13C | 841.0034 | 5.1279 |
| 5 | Cs |
2 | 10 | C | no | yes | 13C | 841.0034 | 5.1279 |
| Total Number of Atoms: | 70 | ✅ 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 | 3 | 2 |
| Double | X2 | 27 | 116 |
| Double | XY | 15 | 234 |
| Triple | X3 | 110 | 2.682 |
| Triple | X2Y | 138 | 8.142 |
| Triple | XYZ | 84 | 16.380 |
| Quadruple | X4 | 563 | 45.712 |
| Quadruple | X3Y | 554 | 183.102 |
| Quadruple | X2Y2 | 1.212 | 274.760 |
| Quadruple | X2YZ | 726 | 549.774 |
| Quadruple | WXYZ | 516 | 1.100.016 |
| Quintuple | X5 | 1.943 | 604.182 |
| Quintuple | VWXYZ | 3.024 | 72.616.572 |
| Sextuple | X6 | 7.343 | 6.553.764 |
| Sextuple | UVWXYZ | 15.120 | 4.720.167.900 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N