Direct sum of irreducible representation
| A1g |
B1g |
B2g |
B3g |
A1u |
B1u |
B2u |
B3u |
| 7 |
7 |
5 |
5 |
5 |
5 |
7 |
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 | 357.1599 | 3.2538 |
| 2 | Cs |
2 | 4 | H | no | yes | 2H | 357.1628 | 0.045645 |
| 3 | C1 |
1 | 8 | C | yes | yes | 13C | 357.1599 | 6.5077 |
| 4 | C1 |
1 | 8 | C | yes | yes | 13C | 357.1599 | 6.5077 |
| 5 | C1 |
1 | 8 | C | yes | yes | 13C | 357.1599 | 6.5077 |
| 6 | C1 |
1 | 8 | H | yes | yes | 2H | 357.1628 | 0.091290 |
| 7 | C1 |
1 | 8 | H | yes | yes | 2H | 357.1628 | 0.091290 |
| Total Number of Atoms: | 48 | ✅ 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 | 2 | 5 |
| Double | X2 | 30 | 135 |
| Double | XY | 14 | 275 |
| Triple | X3 | 54 | 2.135 |
| Triple | X2Y | 82 | 6.445 |
| Triple | XYZ | 84 | 12.930 |
| Quadruple | X4 | 412 | 24.220 |
| Quadruple | X3Y | 350 | 97.115 |
| Quadruple | X2Y2 | 894 | 145.695 |
| Quadruple | X2YZ | 490 | 291.625 |
| Quadruple | WXYZ | 420 | 583.530 |
| Quintuple | X5 | 674 | 213.701 |
| Quintuple | VWXYZ | 1.680 | 25.683.720 |
| Sextuple | X6 | 3.490 | 1.532.953 |
| Sextuple | UVWXYZ | 5.040 | 1.104.433.560 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N