Direct sum of irreducible representation
| A1 |
A2 |
B1 |
B2 |
| 12 |
0 |
12 |
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 | Cs |
2 | 2 | C | no | yes | 13C | 179.0816 | 1.9024 |
| 2 | Cs |
2 | 2 | C | no | yes | 13C | 179.0816 | 1.9024 |
| 3 | Cs |
2 | 2 | C | no | yes | 13C | 179.0816 | 1.9024 |
| 4 | Cs |
2 | 2 | H | no | yes | 2H | 179.0845 | 0.026687 |
| 5 | Cs |
2 | 2 | C | no | yes | 13C | 179.0816 | 1.9024 |
| 6 | Cs |
2 | 2 | C | no | yes | 13C | 179.0816 | 1.9024 |
| 7 | Cs |
2 | 2 | C | no | yes | 13C | 179.0816 | 1.9024 |
| 8 | Cs |
2 | 2 | C | no | yes | 13C | 179.0816 | 1.9024 |
| 9 | Cs |
2 | 2 | H | no | yes | 2H | 179.0845 | 0.026687 |
| 10 | Cs |
2 | 2 | H | no | yes | 2H | 179.0845 | 0.026687 |
| 11 | Cs |
2 | 2 | H | no | yes | 2H | 179.0845 | 0.026687 |
| 12 | Cs |
2 | 2 | H | no | yes | 2H | 179.0845 | 0.026687 |
| Total Number of Atoms: | 24 | ✅ 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 | 12 | 0 |
| Double | X2 | 144 | 0 |
| Double | XY | 276 | 0 |
| Triple | X3 | 1.012 | 0 |
| Triple | X2Y | 3.036 | 0 |
| Triple | XYZ | 6.072 | 0 |
| Quadruple | X4 | 5.346 | 0 |
| Quadruple | X3Y | 21.252 | 0 |
| Quadruple | X2Y2 | 31.944 | 0 |
| Quadruple | X2YZ | 63.756 | 0 |
| Quadruple | WXYZ | 127.512 | 0 |
| Quintuple | X5 | 21.252 | 0 |
| Quintuple | VWXYZ | 2.550.240 | 0 |
| Sextuple | X6 | 67.408 | 0 |
| Sextuple | UVWXYZ | 48.454.560 | 0 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N