Grouptheoretical Analysis
Composition Input Structure
| Atomic Number |
Atomic Symbol |
Isotope | Isotope Mass |
Isotope Abundance |
Number Atoms |
Mass |
|---|---|---|---|---|---|---|
| 8 | O | 16 | 15.9949 | 99.7620 | 6 | 95.9695 |
| 15 | P | 31 | 30.9738 | 100.0000 | 4 | 123.8950 |
| Total | 10 | 219.8645 | ||||
| Isotopomer Natural Abundance (%) | 98.5805 | |||||
Determined Point Group: Td
Representation ΓN
| E | 8C3 | 3C2 | 6S4 | 6σd |
|---|---|---|---|---|
| 10 | 1 | 2 | 0 | 4 |
| A1 | A2 | E | T1 | T2 |
|---|---|---|---|---|
| 2 | 0 | 1 | 0 | 2 |
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer | ||
|---|---|---|---|---|---|---|---|---|---|
| Isotope | Mass | Abundance**** | |||||||
| 1 | C2v | 4 | 6 | O | no | yes | 18O 17O | 221.8688 220.8688 | 1.1858 0.2253 |
| 2 | C3v | 6 | 4 | P | no | yes | - | - | - |
| Total Number of Atoms: | 10 | ✅ 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 | 5 | 0 |
| Double | XY | 6 | 1 |
| Triple | X3 | 8 | 3 |
| Triple | X2Y | 12 | 10 |
| Triple | XYZ | 12 | 24 |
| Quadruple | X4 | 12 | 5 |
| Quadruple | X3Y | 20 | 27 |
| Quadruple | X2Y2 | 24 | 43 |
| Quadruple | X2YZ | 24 | 94 |
| Quadruple | WXYZ | 12 | 204 |
| Quintuple | X5 | 12 | 6 |
| Quintuple | VWXYZ | 0 | 1.260 |
| Sextuple | X6 | 12 | 5 |
| Sextuple | UVWXYZ | 0 | 6.300 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry