Grouptheoretical Analysis
Composition Input Structure
| Atomic Number |
Atomic Symbol |
Isotope | Isotope Mass |
Isotope Abundance |
Number Atoms |
Mass |
|---|---|---|---|---|---|---|
| 1 | H | 1 | 1.0078 | 99.9844 | 12 | 12.0939 |
| 6 | C | 12 | 12.0000 | 98.9000 | 6 | 72.0000 |
| Total | 18 | 84.0939 | ||||
| Isotopomer Natural Abundance (%) | 93.4038 | |||||
Determined Point Group: D3d
Representation ΓN
| E | 2C3 | 3C'2 | i | 2S6 | 3σd |
|---|---|---|---|---|---|
| 18 | 0 | 0 | 0 | 0 | 6 |
| A1g | A2g | Eg | A1u | A2u | Eu |
|---|---|---|---|---|---|
| 3 | 0 | 3 | 0 | 3 | 3 |
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer | ||
|---|---|---|---|---|---|---|---|---|---|
| Isotope | Mass | Abundance**** | |||||||
| 1 | Cs | 2 | 6 | C | no | yes | 13C | 85.0973 | 6.2332 |
| 2 | Cs | 2 | 6 | H | no | yes | 2H | 85.1002 | 0.087440 |
| 3 | Cs | 2 | 6 | H | no | yes | 2H | 85.1002 | 0.087440 |
| Total Number of Atoms: | 18 | ✅ Correct Number of Atoms found | |||||||
**Subgroup of point group D3d
***Calculated as h( D3d)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
| Replacement | Pattern | Achiral Isomers | Chiral Isomer Pairs |
|---|---|---|---|
| Single | X | 3 | 0 |
| Double | X2 | 12 | 9 |
| Double | XY | 15 | 18 |
| Triple | X3 | 28 | 55 |
| Triple | X2Y | 48 | 180 |
| Triple | XYZ | 60 | 378 |
| Quadruple | X4 | 66 | 231 |
| Quadruple | X3Y | 120 | 960 |
| Quadruple | X2Y2 | 162 | 1.467 |
| Quadruple | X2YZ | 180 | 2.970 |
| Quadruple | WXYZ | 180 | 6.030 |
| Quintuple | X5 | 108 | 660 |
| Quintuple | VWXYZ | 360 | 85.500 |
| Sextuple | X6 | 183 | 1.479 |
| Sextuple | UVWXYZ | 360 | 1.113.660 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry