Direct sum of irreducible representation
| A1 |
A2 |
B1 |
B2 |
E |
| 2 |
2 |
2 |
2 |
4 |
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 | C1 |
1 | 8 | C | yes | yes | 13C | 105.0660 | 8.1342 |
| 2 | C1 |
1 | 8 | H | yes | yes | 2H | 105.0689 | 0.1141 |
| Total Number of Atoms: | 16 | ✅ 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 | 0 | 2 |
| Double | X2 | 4 | 16 |
| Double | XY | 0 | 30 |
| Triple | X3 | 0 | 70 |
| Triple | X2Y | 0 | 210 |
| Triple | XYZ | 0 | 420 |
| Quadruple | X4 | 16 | 230 |
| Quadruple | X3Y | 0 | 910 |
| Quadruple | X2Y2 | 28 | 1.372 |
| Quadruple | X2YZ | 0 | 2.730 |
| Quadruple | WXYZ | 0 | 5.460 |
| Quintuple | X5 | 0 | 546 |
| Quintuple | VWXYZ | 0 | 65.520 |
| Sextuple | X6 | 28 | 1.008 |
| Sextuple | UVWXYZ | 0 | 720.720 |
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 |
| 48 |
0 |
0 |
0 |
0 |