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 | 5 | 60.0000 |
| Total | 17 | 72.0939 | ||||
| Isotopomer Natural Abundance (%) | 94.4427 | |||||
Determined Point Group: T
Representation ΓN
| E | 4C3 | 4(C3)2 | 3C2 |
|---|---|---|---|
| 17 | 2 | 2 | 1 |
| A | E* | T |
|---|---|---|
| 3 | 1 | 4 |
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer | ||
|---|---|---|---|---|---|---|---|---|---|
| Isotope | Mass | Abundance**** | |||||||
| 1 | T | 12 | 1 | C | yes | no | 13C | 73.0973 | 1.0504 |
| 2 | C3 | 3 | 4 | C | yes | yes | 13C | 73.0973 | 4.2017 |
| 3 | C1 | 1 | 12 | H | yes | yes | 2H | 73.1002 | 0.1768 |
| Total Number of Atoms: | 17 | ✅ Correct Number of Atoms found | |||||||
**Subgroup of point group T
***Calculated as h( T)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
| Replacement | Pattern | Chiral Isomers |
|---|---|---|
| Single | X | 3 |
| Double | X2 | 14 |
| Double | XY | 24 |
| Triple | X3 | 62 |
| Triple | X2Y | 172 |
| Triple | XYZ | 340 |
| Quadruple | X4 | 212 |
| Quadruple | X3Y | 800 |
| Quadruple | X2Y2 | 1.204 |
| Quadruple | X2YZ | 2.380 |
| Quadruple | WXYZ | 4.760 |
| Quintuple | X5 | 526 |
| Quintuple | VWXYZ | 61.880 |
| Sextuple | X6 | 1.052 |
| Sextuple | UVWXYZ | 742.560 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry