Direct sum of irreducible representation
| A1g |
B1g |
B2g |
B3g |
A1u |
B1u |
B2u |
B3u |
| 5 |
3 |
2 |
0 |
0 |
2 |
3 |
5 |
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 | 109.0973 | 4.0646 |
| 2 | Cs |
2 | 4 | C | no | yes | 13C | 109.0973 | 4.0646 |
| 3 | Cs |
2 | 4 | H | no | yes | 2H | 109.1002 | 0.057018 |
| 4 | Cs |
2 | 4 | H | no | yes | 2H | 109.1002 | 0.057018 |
| 5 | Cs |
2 | 4 | H | no | yes | 2H | 109.1002 | 0.057018 |
| Total Number of Atoms: | 20 | ✅ 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 | 5 | 0 |
| Double | X2 | 31 | 12 |
| Double | XY | 47 | 24 |
| Triple | X3 | 93 | 96 |
| Triple | X2Y | 231 | 312 |
| Triple | XYZ | 414 | 648 |
| Quadruple | X4 | 277 | 484 |
| Quadruple | X3Y | 781 | 2.032 |
| Quadruple | X2Y2 | 1.119 | 3.108 |
| Quadruple | X2YZ | 1.911 | 6.312 |
| Quadruple | WXYZ | 3.390 | 12.840 |
| Quintuple | X5 | 564 | 1.656 |
| Quintuple | VWXYZ | 25.440 | 219.840 |
| Sextuple | X6 | 1.108 | 4.336 |
| Sextuple | UVWXYZ | 171.360 | 3.402.720 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N