Direct sum of irreducible representation
| A1 |
A2 |
B1 |
B2 |
| 6 |
3 |
6 |
3 |
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 | 85.0973 | 2.0777 |
| 2 | Cs |
2 | 2 | H | no | yes | 2H | 85.1002 | 0.029147 |
| 3 | Cs |
2 | 2 | H | no | yes | 2H | 85.1002 | 0.029147 |
| 4 | C1 |
1 | 4 | C | yes | yes | 13C | 85.0973 | 4.1555 |
| 5 | C1 |
1 | 4 | H | yes | yes | 2H | 85.1002 | 0.058293 |
| 6 | C1 |
1 | 4 | H | yes | yes | 2H | 85.1002 | 0.058293 |
| 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 | 3 | 3 |
| Double | X2 | 15 | 33 |
| Double | XY | 15 | 69 |
| Triple | X3 | 28 | 190 |
| Triple | X2Y | 48 | 588 |
| Triple | XYZ | 60 | 1.194 |
| Quadruple | X4 | 78 | 735 |
| Quadruple | X3Y | 120 | 3.000 |
| Quadruple | X2Y2 | 186 | 4.515 |
| Quadruple | X2YZ | 180 | 9.090 |
| Quadruple | WXYZ | 180 | 18.270 |
| Quintuple | X5 | 108 | 2.088 |
| Quintuple | VWXYZ | 360 | 256.860 |
| Sextuple | X6 | 210 | 4.557 |
| Sextuple | UVWXYZ | 360 | 3.341.340 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N