Direct sum of irreducible representation
| A1 |
A2 |
B1 |
B2 |
| 5 |
1 |
3 |
2 |
Properties of derivatives and isotopomers by single substitution, h(C2v)=4
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | C2v |
4 | 1 | C | no | yes | 13C | 45.0660 | 1.0746 |
| 2 | Cs |
2 | 2 | C | no | yes | 13C | 45.0660 | 2.1492 |
| 3 | Cs |
2 | 2 | H | no | yes | 2H | 45.0689 | 0.030149 |
| 4 | Cs |
2 | 2 | H | no | yes | 2H | 45.0689 | 0.030149 |
| 5 | C1 |
1 | 4 | H | yes | yes | 2H | 45.0689 | 0.060297 |
| Total Number of Atoms: | 11 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group C
2v
***Calculated as h( C
2v)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
Numbers of isomers by substitution
| Replacement | Pattern | Achiral
Isomers | Chiral
Isomer Pairs |
|---|
| Single | X | 4 | 1 |
| Double | X2 | 10 | 10 |
| Double | XY | 13 | 21 |
| Triple | X3 | 19 | 33 |
| Triple | X2Y | 30 | 110 |
| Triple | XYZ | 33 | 231 |
| Quadruple | X4 | 28 | 71 |
| Quadruple | X3Y | 52 | 304 |
| Quadruple | X2Y2 | 66 | 467 |
| Quadruple | X2YZ | 72 | 954 |
| Quadruple | WXYZ | 60 | 1.950 |
| Quintuple | X5 | 34 | 101 |
| Quintuple | VWXYZ | 60 | 13.830 |
| Sextuple | X6 | 34 | 101 |
| Sextuple | UVWXYZ | 0 | 83.160 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N