Direct sum of irreducible representation
| A1g |
A2g |
Eg |
T1g |
T2g |
A1u |
A2u |
Eu |
T1u |
T2u |
| 2 |
0 |
0 |
0 |
2 |
0 |
2 |
0 |
2 |
0 |
Properties of derivatives and isotopomers by single substitution, h(Oh)=48
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | C3v |
6 | 8 | C | no | yes | 13C | 105.0660 | 8.1342 |
| 2 | C3v |
6 | 8 | H | no | yes | 2H | 105.0689 | 0.1141 |
| Total Number of Atoms: | 16 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group O
h
***Calculated as h( O
h)/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 | 0 |
| Double | X2 | 10 | 0 |
| Double | XY | 14 | 0 |
| Triple | X3 | 22 | 2 |
| Triple | X2Y | 50 | 12 |
| Triple | XYZ | 84 | 32 |
| Quadruple | X4 | 53 | 20 |
| Quadruple | X3Y | 126 | 92 |
| Quadruple | X2Y2 | 174 | 152 |
| Quadruple | X2YZ | 266 | 324 |
| Quadruple | WXYZ | 420 | 704 |
| Quintuple | X5 | 82 | 54 |
| Quintuple | VWXYZ | 1.680 | 10.080 |
| Sextuple | X6 | 130 | 116 |
| Sextuple | UVWXYZ | 5.040 | 117.600 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N