Grouptheoretical Analysis
Composition Input Structure
| Atomic Number |
Atomic Symbol |
Isotope | Isotope Mass |
Isotope Abundance |
Number Atoms |
Mass |
|---|---|---|---|---|---|---|
| 1 | H | 1 | 1.0078 | 99.9844 | 6 | 6.0470 |
| 5 | B | 11 | 11.0093 | 80.1000 | 3 | 33.0279 |
| 7 | N | 14 | 14.0031 | 99.6340 | 3 | 42.0092 |
| Total | 12 | 81.0841 | ||||
| Isotopomer Natural Abundance (%) | 50.7825 | |||||
Determined Point Group: D3h
Representation ΓN
| E | 2C3 | 3C'2 | σh | 2S3 | 3σv |
|---|---|---|---|---|---|
| 12 | 0 | 4 | 12 | 0 | 4 |
| A'1 | A'2 | E' | A''1 | A''2 | E'' |
|---|---|---|---|---|---|
| 4 | 0 | 4 | 0 | 0 | 0 |
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer | ||
|---|---|---|---|---|---|---|---|---|---|
| Isotope | Mass | Abundance**** | |||||||
| 1 | C2v | 4 | 3 | B | no | yes | 10B | 80.0877 | 37.8491 |
| 2 | C2v | 4 | 3 | H | no | yes | 2H | 82.0904 | 0.023770 |
| 3 | C2v | 4 | 3 | N | no | yes | 15N | 82.0811 | 0.5596 |
| 4 | C2v | 4 | 3 | H | no | yes | 2H | 82.0904 | 0.023770 |
| Total Number of Atoms: | 12 | ✅ Correct Number of Atoms found | |||||||
**Subgroup of point group D3h
***Calculated as h( D3h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
| Replacement | Pattern | Achiral Isomers | Chiral Isomer Pairs |
|---|---|---|---|
| Single | X | 4 | 0 |
| Double | X2 | 16 | 0 |
| Double | XY | 28 | 0 |
| Triple | X3 | 48 | 0 |
| Triple | X2Y | 124 | 0 |
| Triple | XYZ | 232 | 0 |
| Quadruple | X4 | 98 | 0 |
| Quadruple | X3Y | 356 | 0 |
| Quadruple | X2Y2 | 528 | 0 |
| Quadruple | X2YZ | 1.020 | 0 |
| Quadruple | WXYZ | 1.992 | 0 |
| Quintuple | X5 | 152 | 0 |
| Quintuple | VWXYZ | 15.840 | 0 |
| Sextuple | X6 | 178 | 0 |
| Sextuple | UVWXYZ | 110.880 | 0 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry