Direct sum of irreducible representation
| A1g |
B1g |
B2g |
B3g |
A1u |
B1u |
B2u |
B3u |
| 8 |
7 |
0 |
0 |
0 |
0 |
7 |
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 | 229.0973 | 1.8195 |
| 2 | Cs |
2 | 4 | C | no | yes | 13C | 229.0973 | 3.6390 |
| 3 | Cs |
2 | 4 | C | no | yes | 13C | 229.0973 | 3.6390 |
| 4 | Cs |
2 | 4 | C | no | yes | 13C | 229.0973 | 3.6390 |
| 5 | Cs |
2 | 4 | C | no | yes | 13C | 229.0973 | 3.6390 |
| 6 | Cs |
2 | 4 | H | no | yes | 2H | 229.1002 | 0.051047 |
| 7 | Cs |
2 | 4 | H | no | yes | 2H | 229.1002 | 0.051047 |
| 8 | Cs |
2 | 4 | H | no | yes | 2H | 229.1002 | 0.051047 |
| Total Number of Atoms: | 30 | ✅ 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 | 120 | 0 |
| Double | XY | 218 | 0 |
| Triple | X3 | 1.022 | 0 |
| Triple | X2Y | 3.052 | 0 |
| Triple | XYZ | 6.090 | 0 |
| Quadruple | X4 | 6.930 | 0 |
| Quadruple | X3Y | 27.412 | 0 |
| Quadruple | X2Y2 | 41.265 | 0 |
| Quadruple | X2YZ | 82.222 | 0 |
| Quadruple | WXYZ | 164.430 | 0 |
| Quintuple | X5 | 35.672 | 0 |
| Quintuple | VWXYZ | 4.275.180 | 0 |
| Sextuple | X6 | 148.785 | 0 |
| Sextuple | UVWXYZ | 106.879.500 | 0 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N