Direct sum of irreducible representation
| A1g |
B1g |
B2g |
B3g |
A1u |
B1u |
B2u |
B3u |
| 5 |
4 |
0 |
0 |
0 |
0 |
4 |
5 |
Properties of derivatives and isotopomers by single substitution, h(D2h)=8
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | C2v |
4 | 2 | C | no | yes | 13C | 129.0660 | 1.9891 |
| 2 | Cs |
2 | 4 | C | no | yes | 13C | 129.0660 | 3.9781 |
| 3 | Cs |
2 | 4 | C | no | yes | 13C | 129.0660 | 3.9781 |
| 4 | Cs |
2 | 4 | H | no | yes | 2H | 129.0689 | 0.055805 |
| 5 | Cs |
2 | 4 | H | no | yes | 2H | 129.0689 | 0.055805 |
| Total Number of Atoms: | 18 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group D
2h
***Calculated as h( D
2h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
Numbers of isomers by substitution
| Replacement | Pattern | Achiral
Isomers | Chiral
Isomer Pairs |
|---|
| Single | X | 5 | 0 |
| Double | X2 | 45 | 0 |
| Double | XY | 77 | 0 |
| Triple | X3 | 208 | 0 |
| Triple | X2Y | 616 | 0 |
| Triple | XYZ | 1.224 | 0 |
| Quadruple | X4 | 792 | 0 |
| Quadruple | X3Y | 3.064 | 0 |
| Quadruple | X2Y2 | 4.644 | 0 |
| Quadruple | X2YZ | 9.184 | 0 |
| Quadruple | WXYZ | 18.360 | 0 |
| Quintuple | X5 | 2.156 | 0 |
| Quintuple | VWXYZ | 257.040 | 0 |
| Sextuple | X6 | 4.704 | 0 |
| Sextuple | UVWXYZ | 3.341.520 | 0 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N