Direct sum of irreducible representation
| A1 |
A2 |
B1 |
B2 |
| 11 |
0 |
7 |
0 |
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 | 129.0660 | 0.9945 |
| 2 | C2v |
4 | 1 | C | no | yes | 13C | 129.0660 | 0.9945 |
| 3 | Cs |
2 | 2 | C | no | yes | 13C | 129.0660 | 1.9891 |
| 4 | Cs |
2 | 2 | C | no | yes | 13C | 129.0660 | 1.9891 |
| 5 | Cs |
2 | 2 | C | no | yes | 13C | 129.0660 | 1.9891 |
| 6 | Cs |
2 | 2 | C | no | yes | 13C | 129.0660 | 1.9891 |
| 7 | C2v |
4 | 1 | H | no | yes | 2H | 129.0689 | 0.013951 |
| 8 | C2v |
4 | 1 | H | no | yes | 2H | 129.0689 | 0.013951 |
| 9 | Cs |
2 | 2 | H | no | yes | 2H | 129.0689 | 0.027903 |
| 10 | Cs |
2 | 2 | H | no | yes | 2H | 129.0689 | 0.027903 |
| 11 | Cs |
2 | 2 | H | no | yes | 2H | 129.0689 | 0.027903 |
| Total Number of Atoms: | 18 | ✅ 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 | 11 | 0 |
| Double | X2 | 83 | 0 |
| Double | XY | 159 | 0 |
| Triple | X3 | 424 | 0 |
| Triple | X2Y | 1.244 | 0 |
| Triple | XYZ | 2.460 | 0 |
| Quadruple | X4 | 1.562 | 0 |
| Quadruple | X3Y | 6.164 | 0 |
| Quadruple | X2Y2 | 9.246 | 0 |
| Quadruple | X2YZ | 18.408 | 0 |
| Quadruple | WXYZ | 36.732 | 0 |
| Quintuple | X5 | 4.340 | 0 |
| Quintuple | VWXYZ | 514.080 | 0 |
| Sextuple | X6 | 9.366 | 0 |
| Sextuple | UVWXYZ | 6.683.040 | 0 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N