Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
6C1212.000098.900060720.0000
Total60 720.0000
Isotopomer Natural Abundance (%)51.4965


Determined Point Group: Ih








Representation ΓN


Characters of reducible representation
E 12C5 12(C5)2 20C3 15C2 i 12S10 12(S10)3 20S6 15σd
60 0.000 0.000 0 0 0 0.000 0.000 0 4

Direct sum of irreducible representation
Ag T1g T2g Gg Hg Au T1u T2u Gu Hu
1 1 1 2 3 0 2 2 2 2



Properties of derivatives and isotopomers by single substitution, h(Ih)=120
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 Cs 260Cnoyes13C721.003434.3657
Total Number of Atoms:60✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group Ih
***Calculated as h( Ih)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX10
DoubleX2914
DoubleXY328
TripleX329274
TripleX2Y31840
TripleXYZ61.708
QuadrupleX41444.046
QuadrupleX3Y8516.212
QuadrupleX2Y228924.346
QuadrupleX2YZ8748.720
QuadrupleWXYZ697.524
QuintupleX540645.312
QuintupleVWXYZ05.461.512
SextupleX61.464417.006
SextupleUVWXYZ0300.383.160

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 12C5 12(C5)2 20C3 15C2 i 12S10 12(S10)3 20S6 15σd
180 0.000 -0.000 0 0 0 0.000 -0.000 0 4

Direct sum of irreducible representation
Ag T1g T2g Gg Hg Au T1u T2u Gu Hu
2 4 4 6 8 1 5 5 6 7

Molecular motions and force field analysis



Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement