Direct sum of irreducible representation
| A1g |
A2g |
B1g |
B2g |
E1g |
E2g |
A1u |
A2u |
B1u |
B2u |
E1u |
E2u |
| 3 |
1 |
1 |
3 |
4 |
4 |
1 |
3 |
3 |
1 |
4 |
4 |
Properties of derivatives and isotopomers by single substitution, h(D6h)=24
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | Cs |
2 | 12 | C | no | yes | 13C | 313.1912 | 10.1968 |
| 2 | Cs |
2 | 12 | C | no | yes | 13C | 313.1912 | 10.1968 |
| 3 | C1 |
1 | 24 | H | yes | yes | 2H | 313.1941 | 0.2861 |
| Total Number of Atoms: | 48 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group D
6h
***Calculated as h( D
6h)/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 | 1 |
| Double | X2 | 22 | 43 |
| Double | XY | 14 | 87 |
| Triple | X3 | 54 | 695 |
| Triple | X2Y | 82 | 2.121 |
| Triple | XYZ | 84 | 4.282 |
| Quadruple | X4 | 320 | 8.028 |
| Quadruple | X3Y | 350 | 32.255 |
| Quadruple | X2Y2 | 710 | 48.451 |
| Quadruple | X2YZ | 490 | 97.045 |
| Quadruple | WXYZ | 420 | 194.370 |
| Quintuple | X5 | 674 | 71.009 |
| Quintuple | VWXYZ | 1.680 | 8.560.680 |
| Sextuple | X6 | 2.818 | 510.505 |
| Sextuple | UVWXYZ | 5.040 | 368.142.840 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N