Direct sum of irreducible representation
| A1g |
B1g |
B2g |
B3g |
A1u |
B1u |
B2u |
B3u |
| 8 |
5 |
0 |
0 |
0 |
0 |
5 |
8 |
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 | 203.0816 | 1.8608 |
| 2 | Cs |
2 | 4 | C | no | yes | 13C | 203.0816 | 3.7215 |
| 3 | Cs |
2 | 4 | C | no | yes | 13C | 203.0816 | 3.7215 |
| 4 | Cs |
2 | 4 | C | no | yes | 13C | 203.0816 | 3.7215 |
| 5 | C2v |
4 | 2 | C | no | yes | 13C | 203.0816 | 1.8608 |
| 6 | Cs |
2 | 4 | H | no | yes | 2H | 203.0845 | 0.052205 |
| 7 | Cs |
2 | 4 | H | no | yes | 2H | 203.0845 | 0.052205 |
| 8 | C2v |
4 | 2 | H | no | yes | 2H | 203.0845 | 0.026103 |
| Total Number of Atoms: | 26 | ✅ 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 | 8 | 0 |
| Double | X2 | 94 | 0 |
| Double | XY | 170 | 0 |
| Triple | X3 | 670 | 0 |
| Triple | X2Y | 1.980 | 0 |
| Triple | XYZ | 3.930 | 0 |
| Quadruple | X4 | 3.829 | 0 |
| Quadruple | X3Y | 15.040 | 0 |
| Quadruple | X2Y2 | 22.623 | 0 |
| Quadruple | X2YZ | 44.970 | 0 |
| Quadruple | WXYZ | 89.790 | 0 |
| Quintuple | X5 | 16.564 | 0 |
| Quintuple | VWXYZ | 1.973.580 | 0 |
| Sextuple | X6 | 57.937 | 0 |
| Sextuple | UVWXYZ | 41.441.580 | 0 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N