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 | 18 | 216.0000 |
| Total | 30 | 228.0939 | ||||
| Isotopomer Natural Abundance (%) | 81.7938 | |||||
Determined Point Group: D2h
Representation ΓN
| E | C2.(z) | C2.(y) | C2.(x) | i | σ.(xy) | σ.(xy) | σ.(xy) |
|---|---|---|---|---|---|---|---|
| 30 | 0 | 0 | 2 | 0 | 30 | 2 | 0 |
| A1g | B1g | B2g | B3g | A1u | B1u | B2u | B3u |
|---|---|---|---|---|---|---|---|
| 8 | 7 | 0 | 0 | 0 | 0 | 7 | 8 |
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer | ||
|---|---|---|---|---|---|---|---|---|---|
| Isotope | Mass | Abundance**** | |||||||
| 1 | C2v | 4 | 2 | C | no | yes | 13C | 229.0973 | 1.8195 |
| 2 | Cs | 2 | 4 | C | no | yes | 13C | 229.0973 | 3.6390 |
| 3 | Cs | 2 | 4 | C | no | yes | 13C | 229.0973 | 3.6390 |
| 4 | Cs | 2 | 4 | C | no | yes | 13C | 229.0973 | 3.6390 |
| 5 | Cs | 2 | 4 | C | no | yes | 13C | 229.0973 | 3.6390 |
| 6 | Cs | 2 | 4 | H | no | yes | 2H | 229.1002 | 0.051047 |
| 7 | Cs | 2 | 4 | H | no | yes | 2H | 229.1002 | 0.051047 |
| 8 | Cs | 2 | 4 | H | no | yes | 2H | 229.1002 | 0.051047 |
| Total Number of Atoms: | 30 | ✅ Correct Number of Atoms found | |||||||
**Subgroup of point group D2h
***Calculated as h( D2h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
| Replacement | Pattern | Achiral Isomers | Chiral Isomer Pairs |
|---|---|---|---|
| Single | X | 8 | 0 |
| Double | X2 | 120 | 0 |
| Double | XY | 218 | 0 |
| Triple | X3 | 1.022 | 0 |
| Triple | X2Y | 3.052 | 0 |
| Triple | XYZ | 6.090 | 0 |
| Quadruple | X4 | 6.930 | 0 |
| Quadruple | X3Y | 27.412 | 0 |
| Quadruple | X2Y2 | 41.265 | 0 |
| Quadruple | X2YZ | 82.222 | 0 |
| Quadruple | WXYZ | 164.430 | 0 |
| Quintuple | X5 | 35.672 | 0 |
| Quintuple | VWXYZ | 4.275.180 | 0 |
| Sextuple | X6 | 148.785 | 0 |
| Sextuple | UVWXYZ | 106.879.500 | 0 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry