Direct sum of irreducible representation
| A1 |
A2 |
B1 |
B2 |
E |
| 3 |
0 |
1 |
0 |
1 |
Properties of derivatives and isotopomers by single substitution, h(C4v)=8
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | C4v |
8 | 1 | Br | no | yes | 81Br | 175.9083 | 49.3100 |
| 2 | C4v |
8 | 1 | F | no | yes | - | - | - |
| 3 | Cs |
2 | 4 | F | no | yes | - | - | - |
| Total Number of Atoms: | 6 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group C
4v
***Calculated as h( C
4v)/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 | 0 |
| Double | X2 | 5 | 0 |
| Double | XY | 7 | 1 |
| Triple | X3 | 6 | 0 |
| Triple | X2Y | 10 | 3 |
| Triple | XYZ | 12 | 9 |
| Quadruple | X4 | 5 | 0 |
| Quadruple | X3Y | 10 | 3 |
| Quadruple | X2Y2 | 12 | 6 |
| Quadruple | X2YZ | 14 | 16 |
| Quadruple | WXYZ | 12 | 39 |
| Quintuple | X5 | 3 | 0 |
| Quintuple | VWXYZ | 0 | 90 |
| Sextuple | X6 | 1 | 0 |
| Sextuple | UVWXYZ | 0 | 90 |
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 |
2C4 |
C2 |
2σv |
2σd |
| 18 |
2 |
-2 |
4 |
2 |