Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.984466.0470
6C1212.000098.9000224.0000
Total8 30.0470
Isotopomer Natural Abundance (%)97.7206


Determined Point Group: D3








Representation ΓN


Characters of reducible representation
E 2C3 3C'2
8 2 0

Direct sum of irreducible representation
A1 A2 E
2 2 2



Properties of derivatives and isotopomers by single substitution, h(D3)=6
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 C3 32Cyesyes13C31.05032.1738
2 C1 16Hyesyes2H31.05320.091481
Total Number of Atoms:8✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group D3
***Calculated as h( D3)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternChiral
Isomers
SingleX2
DoubleX27
DoubleXY10
TripleX310
TripleX2Y28
TripleXYZ56
QuadrupleX416
QuadrupleX3Y48
QuadrupleX2Y276
QuadrupleX2YZ140
QuadrupleWXYZ280
QuintupleX510
QuintupleVWXYZ1.120
SextupleX67
SextupleUVWXYZ3.360

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 2C3 3C'2
24 0 0

Direct sum of irreducible representation
A1 A2 E
4 4 8

Molecular motions and force field analysis



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