Direct sum of irreducible representation
| A1 |
A2 |
B1 |
B2 |
E |
| 5 |
0 |
2 |
1 |
3 |
Properties of derivatives and isotopomers by single substitution, h(C4v)=8
| Atom Set* | Site Symmetry** | h(Site Symmetry) | Identical Atoms*** | Element | Chrial | Polar | Isotopomer |
|---|
| Isotope | Mass | Abundance**** |
|---|
| 1 | C4v |
8 | 1 | B | no | yes | 10B | 63.1206 | 8.1804 |
| 2 | C4v |
8 | 1 | H | no | yes | 2H | 65.1232 | 0.005137 |
| 3 | Cs |
2 | 4 | B | no | yes | 10B | 63.1206 | 32.7215 |
| 4 | Cs |
2 | 4 | H | no | yes | 2H | 65.1232 | 0.020550 |
| 5 | Cs |
2 | 4 | H | no | yes | 2H | 65.1232 | 0.020550 |
| Total Number of Atoms: | 14 | ✅ Correct Number of Atoms found |
|---|
*Atom Orbit
**Subgroup of point group C
4v
***Calculated as h( C
4v)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %
Numbers of isomers by substitution
| Replacement | Pattern | Achiral
Isomers | Chiral
Isomer Pairs |
|---|
| Single | X | 5 | 0 |
| Double | X2 | 15 | 5 |
| Double | XY | 21 | 13 |
| Triple | X3 | 34 | 30 |
| Triple | X2Y | 58 | 109 |
| Triple | XYZ | 72 | 237 |
| Quadruple | X4 | 61 | 98 |
| Quadruple | X3Y | 122 | 441 |
| Quadruple | X2Y2 | 154 | 679 |
| Quadruple | X2YZ | 186 | 1.410 |
| Quadruple | WXYZ | 192 | 2.907 |
| Quintuple | X5 | 91 | 210 |
| Quintuple | VWXYZ | 360 | 29.850 |
| Sextuple | X6 | 115 | 323 |
| Sextuple | UVWXYZ | 360 | 270.090 |
Further Reading
- P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry
Representation Γ3N
Characters of reducible representation
| E |
2C4 |
C2 |
2σv |
2σd |
| 42 |
2 |
-2 |
6 |
4 |