Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.98442424.1878
6C1212.000098.9000896.0000
8O1615.994999.762012191.9390
14Si2827.976992.22308223.8154
Total52 535.9422
Isotopomer Natural Abundance (%)46.3703


Determined Point Group: Oh








Representation ΓN


Characters of reducible representation
E 8C3 6C2 6C4 3C2 i 6S4 8S6 h d
52 4 2 0 0 0 0 0 4 14

Direct sum of irreducible representation
A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u
4 0 2 1 5 0 3 1 5 2



Properties of derivatives and isotopomers by single substitution, h(Oh)=48
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 C3v 68Sinoyes29Si
30Si
536.9418
537.9390
18.8452
12.4374
2 C2v 412Onoyes18O
17O
537.9464
536.9464
1.1155
0.2120
3 C3v 68Cnoyes13C536.94554.1260
4 Cs 224Hnoyes2H536.94850.1736
Total Number of Atoms:52✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group Oh
***Calculated as h( Oh)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX40
DoubleX23317
DoubleXY4734
TripleX3170385
TripleX2Y3531.213
TripleXYZ5492.492
QuadrupleX47955.316
QuadrupleX3Y1.90221.627
QuadrupleX2Y22.58532.671
QuadrupleX2YZ3.90565.737
QuadrupleWXYZ6.009132.362
QuintupleX52.97852.747
QuintupleVWXYZ60.0606.467.370
SextupleX610.212419.548
SextupleUVWXYZ540.540305.107.530

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 8C3 6C2 6C4 3C2 i 6S4 8S6 h d
156 0 -2 0 0 0 0 0 4 14

Direct sum of irreducible representation
A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u
5 2 7 8 11 1 5 6 12 8

Molecular motions and force field analysis



Last update April, 29th 2022 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement