Direct sum of irreducible representation
| A1g |
A2g |
B1g |
B2g |
E1g |
E2g |
E3g |
A1u |
A2u |
B1u |
B2u |
E1u |
E2u |
E3u |
| 2 |
0 |
2 |
0 |
0 |
2 |
0 |
0 |
0 |
0 |
0 |
2 |
0 |
2 |
Properties of derivatives and isotopomers by single substitution, h(D8h)=32
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | C2v |
4 | 8 | C | no | yes | 13C | 105.0660 | 8.1342 |
| 2 | C2v |
4 | 8 | H | no | yes | 2H | 105.0689 | 0.1141 |
| Total Number of Atoms: | 16 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group D
8h
***Calculated as h( D
8h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
Numbers of isomers by substitution
| Replacement | Pattern | Achiral
Isomers | Chiral
Isomer Pairs |
|---|
| Single | X | 2 | 0 |
| Double | X2 | 13 | 0 |
| Double | XY | 18 | 0 |
| Triple | X3 | 42 | 0 |
| Triple | X2Y | 114 | 0 |
| Triple | XYZ | 216 | 0 |
| Quadruple | X4 | 136 | 0 |
| Quadruple | X3Y | 474 | 0 |
| Quadruple | X2Y2 | 727 | 0 |
| Quadruple | X2YZ | 1.386 | 0 |
| Quadruple | WXYZ | 2.736 | 0 |
| Quintuple | X5 | 294 | 0 |
| Quintuple | VWXYZ | 32.760 | 0 |
| Sextuple | X6 | 547 | 0 |
| Sextuple | UVWXYZ | 360.360 | 0 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N