Direct sum of irreducible representation
| A1g |
B1g |
B2g |
B3g |
A1u |
B1u |
B2u |
B3u |
| 8 |
5 |
4 |
3 |
2 |
5 |
6 |
7 |
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 | Cs |
2 | 4 | C | no | yes | 13C | 261.1599 | 3.5549 |
| 2 | C1 |
1 | 8 | C | yes | yes | 13C | 261.1599 | 7.1098 |
| 3 | Cs |
2 | 4 | C | no | yes | 13C | 261.1599 | 3.5549 |
| 4 | Cs |
2 | 4 | H | no | yes | 2H | 261.1628 | 0.049868 |
| 5 | Cs |
2 | 4 | H | no | yes | 2H | 261.1628 | 0.049868 |
| 6 | Cs |
2 | 4 | C | no | yes | 13C | 261.1599 | 3.5549 |
| 7 | Cs |
2 | 4 | H | no | yes | 2H | 261.1628 | 0.049868 |
| 8 | C1 |
1 | 8 | H | yes | yes | 2H | 261.1628 | 0.099736 |
| Total Number of Atoms: | 40 | ✅ 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 | 6 | 2 |
| Double | X2 | 42 | 84 |
| Double | XY | 50 | 170 |
| Triple | X3 | 162 | 1.154 |
| Triple | X2Y | 302 | 3.554 |
| Triple | XYZ | 420 | 7.200 |
| Quadruple | X4 | 650 | 11.170 |
| Quadruple | X3Y | 1.306 | 45.042 |
| Quadruple | X2Y2 | 1.866 | 67.752 |
| Quadruple | X2YZ | 2.438 | 135.866 |
| Quadruple | WXYZ | 3.396 | 272.472 |
| Quintuple | X5 | 1.890 | 81.306 |
| Quintuple | VWXYZ | 25.440 | 9.857.400 |
| Sextuple | X6 | 5.546 | 477.452 |
| Sextuple | UVWXYZ | 171.360 | 345.368.520 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N