Direct sum of irreducible representation
| A1 |
A2 |
B1 |
B2 |
E |
| 3 |
0 |
0 |
2 |
1 |
Properties of derivatives and isotopomers by single substitution, h(D2d)=8
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | D2d |
8 | 1 | C | no | no | 13C | 41.0347 | 1.0753 |
| 2 | C2v |
4 | 2 | C | no | yes | 13C | 41.0347 | 2.1505 |
| 3 | Cs |
2 | 4 | H | no | yes | 2H | 41.0376 | 0.060335 |
| Total Number of Atoms: | 7 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group D
2d
***Calculated as h( D
2d)/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 | 6 | 1 |
| Double | XY | 10 | 1 |
| Triple | X3 | 8 | 2 |
| Triple | X2Y | 18 | 6 |
| Triple | XYZ | 30 | 12 |
| Quadruple | X4 | 8 | 2 |
| Quadruple | X3Y | 20 | 9 |
| Quadruple | X2Y2 | 25 | 17 |
| Quadruple | X2YZ | 40 | 34 |
| Quadruple | WXYZ | 60 | 75 |
| Quintuple | X5 | 6 | 1 |
| Quintuple | VWXYZ | 60 | 285 |
| Sextuple | X6 | 3 | 0 |
| Sextuple | UVWXYZ | 0 | 630 |
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 |
2S4 |
C2 |
2C'2 |
2σd |
| 21 |
-1 |
-3 |
-1 |
5 |