Direct sum of irreducible representation
| A1 |
A2 |
E1 |
E2 |
| 4 |
2 |
6 |
6 |
Properties of derivatives and isotopomers by single substitution, h(C5v)=10
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | Cs |
2 | 5 | C | no | yes | 13C | 251.0816 | 4.4506 |
| 2 | Cs |
2 | 5 | C | no | yes | 13C | 251.0816 | 4.4506 |
| 3 | C1 |
1 | 10 | C | yes | yes | 13C | 251.0816 | 8.9011 |
| 4 | C1 |
1 | 10 | H | yes | yes | 2H | 251.0845 | 0.1249 |
| Total Number of Atoms: | 30 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group C
5v
***Calculated as h( C
5v)/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 | 2 |
| Double | X2 | 15 | 36 |
| Double | XY | 2 | 86 |
| Triple | X3 | 28 | 392 |
| Triple | X2Y | 28 | 1.204 |
| Triple | XYZ | 0 | 2.436 |
| Quadruple | X4 | 105 | 2.688 |
| Quadruple | X3Y | 28 | 10.948 |
| Quadruple | X2Y2 | 210 | 16.338 |
| Quadruple | X2YZ | 28 | 32.872 |
| Quadruple | WXYZ | 0 | 65.772 |
| Quintuple | X5 | 182 | 14.162 |
| Quintuple | VWXYZ | 0 | 1.710.072 |
| Sextuple | X6 | 455 | 59.150 |
| Sextuple | UVWXYZ | 0 | 42.751.800 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N
Characters of reducible representation
| E |
2C5 |
2(C5)2 |
5σv |
| 90 |
0.000 |
-0.000 |
2 |