Direct sum of irreducible representation
| A |
B |
E*
|
| 5 |
4 |
4 |
Properties of derivatives and isotopomers by single substitution, h(S4)=4
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | S4 |
4 | 1 | C | no | no | 13C | 208.9414 | 0.3463 |
| 2 | C1 |
1 | 4 | C | yes | yes | 13C | 208.9414 | 1.3850 |
| 3 | C1 |
1 | 4 | H | yes | yes | 2H | 208.9443 | 0.019429 |
| 4 | C1 |
1 | 4 | Cl | yes | yes | 37Cl | 209.9351 | 39.8430 |
| 5 | C1 |
1 | 4 | H | yes | yes | 2H | 208.9443 | 0.019429 |
| Total Number of Atoms: | 17 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group S
4
***Calculated as h( S
4)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
Numbers of isomers by substitution
| Replacement | Pattern | Achiral
Isomers | Chiral
Isomer Pairs |
|---|
| Single | X | 1 | 4 |
| Double | X2 | 0 | 36 |
| Double | XY | 0 | 68 |
| Triple | X3 | 0 | 172 |
| Triple | X2Y | 0 | 512 |
| Triple | XYZ | 0 | 1.020 |
| Quadruple | X4 | 4 | 600 |
| Quadruple | X3Y | 0 | 2.380 |
| Quadruple | X2Y2 | 0 | 3.584 |
| Quadruple | X2YZ | 0 | 7.140 |
| Quadruple | WXYZ | 0 | 14.280 |
| Quintuple | X5 | 4 | 1.552 |
| Quintuple | VWXYZ | 0 | 185.640 |
| Sextuple | X6 | 0 | 3.108 |
| Sextuple | UVWXYZ | 0 | 2.227.680 |
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 |
S4 |
C2 |
(S4)3 |
| 51 |
-1 |
-1 |
-1 |