Grouptheoretical Analysis
Composition Input Structure
| Atomic Number |
Atomic Symbol |
Isotope | Isotope Mass |
Isotope Abundance |
Number Atoms |
Mass |
|---|---|---|---|---|---|---|
| 1 | H | 1 | 1.0078 | 99.9844 | 4 | 4.0313 |
| 6 | C | 12 | 12.0000 | 98.9000 | 4 | 48.0000 |
| Total | 8 | 52.0313 | ||||
| Isotopomer Natural Abundance (%) | 95.6124 | |||||
Determined Point Group: Td
Representation ΓN
| E | 8C3 | 3C2 | 6S4 | 6σd |
|---|---|---|---|---|
| 8 | 2 | 0 | 0 | 4 |
| A1 | A2 | E | T1 | T2 |
|---|---|---|---|---|
| 2 | 0 | 0 | 0 | 2 |
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer | ||
|---|---|---|---|---|---|---|---|---|---|
| Isotope | Mass | Abundance**** | |||||||
| 1 | C3v | 6 | 4 | C | no | yes | 13C | 53.0347 | 4.2537 |
| 2 | C3v | 6 | 4 | H | no | yes | 2H | 53.0376 | 0.059671 |
| Total Number of Atoms: | 8 | ✅ Correct Number of Atoms found | |||||||
**Subgroup of point group Td
***Calculated as h( Td)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
| Replacement | Pattern | Achiral Isomers | Chiral Isomer Pairs |
|---|---|---|---|
| Single | X | 2 | 0 |
| Double | X2 | 4 | 0 |
| Double | XY | 6 | 0 |
| Triple | X3 | 6 | 0 |
| Triple | X2Y | 10 | 2 |
| Triple | XYZ | 12 | 8 |
| Quadruple | X4 | 8 | 1 |
| Quadruple | X3Y | 14 | 6 |
| Quadruple | X2Y2 | 16 | 11 |
| Quadruple | X2YZ | 18 | 26 |
| Quadruple | WXYZ | 12 | 64 |
| Quintuple | X5 | 6 | 0 |
| Quintuple | VWXYZ | 0 | 280 |
| Sextuple | X6 | 4 | 0 |
| Sextuple | UVWXYZ | 0 | 840 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry