Grouptheoretical Analysis
Composition Input Structure
| Atomic Number |
Atomic Symbol |
Isotope | Isotope Mass |
Isotope Abundance |
Number Atoms |
Mass |
|---|---|---|---|---|---|---|
| 1 | H | 1 | 1.0078 | 99.9844 | 24 | 24.1878 |
| 6 | C | 12 | 12.0000 | 98.9000 | 24 | 288.0000 |
| Total | 48 | 312.1878 | ||||
| Isotopomer Natural Abundance (%) | 76.3985 | |||||
Determined Point Group: D6h
Representation ΓN
| E | 2C6 | 2C3 | C2 | 3C'2 | 3C''2 | i | 2S3 | 2S6 | σh | 3σd | 3σv |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 48 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 8 |
| A1g | A2g | B1g | B2g | E1g | E2g | A1u | A2u | B1u | B2u | E1u | E2u |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 3 | 1 | 1 | 3 | 4 | 4 | 1 | 3 | 3 | 1 | 4 | 4 |
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer | ||
|---|---|---|---|---|---|---|---|---|---|
| Isotope | Mass | Abundance**** | |||||||
| 1 | Cs | 2 | 12 | C | no | yes | 13C | 313.1912 | 10.1968 |
| 2 | Cs | 2 | 12 | C | no | yes | 13C | 313.1912 | 10.1968 |
| 3 | C1 | 1 | 24 | H | yes | yes | 2H | 313.1941 | 0.2861 |
| Total Number of Atoms: | 48 | ✅ Correct Number of Atoms found | |||||||
**Subgroup of point group D6h
***Calculated as h( D6h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
| Replacement | Pattern | Achiral Isomers | Chiral Isomer Pairs |
|---|---|---|---|
| Single | X | 2 | 1 |
| Double | X2 | 22 | 43 |
| Double | XY | 14 | 87 |
| Triple | X3 | 54 | 695 |
| Triple | X2Y | 82 | 2.121 |
| Triple | XYZ | 84 | 4.282 |
| Quadruple | X4 | 320 | 8.028 |
| Quadruple | X3Y | 350 | 32.255 |
| Quadruple | X2Y2 | 710 | 48.451 |
| Quadruple | X2YZ | 490 | 97.045 |
| Quadruple | WXYZ | 420 | 194.370 |
| Quintuple | X5 | 674 | 71.009 |
| Quintuple | VWXYZ | 1.680 | 8.560.680 |
| Sextuple | X6 | 2.818 | 510.505 |
| Sextuple | UVWXYZ | 5.040 | 368.142.840 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry