Direct sum of irreducible representation
| A1g |
B1g |
B2g |
B3g |
A1u |
B1u |
B2u |
B3u |
| 3 |
0 |
1 |
0 |
0 |
1 |
1 |
2 |
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 | B | no | yes | 10B | 27.0692 | 31.8500 |
| 2 | C2v |
4 | 2 | H | no | yes | 2H | 29.0718 | 0.020002 |
| 3 | Cs |
2 | 4 | H | no | yes | 2H | 29.0718 | 0.040005 |
| Total Number of Atoms: | 8 | ✅ 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 | 3 | 0 |
| Double | X2 | 8 | 1 |
| Double | XY | 11 | 2 |
| Triple | X3 | 11 | 3 |
| Triple | X2Y | 23 | 11 |
| Triple | XYZ | 36 | 24 |
| Quadruple | X4 | 14 | 4 |
| Quadruple | X3Y | 31 | 21 |
| Quadruple | X2Y2 | 44 | 35 |
| Quadruple | X2YZ | 63 | 75 |
| Quadruple | WXYZ | 96 | 162 |
| Quintuple | X5 | 11 | 3 |
| Quintuple | VWXYZ | 180 | 750 |
| Sextuple | X6 | 8 | 1 |
| Sextuple | UVWXYZ | 180 | 2.430 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N