Grouptheoretical Analysis




Composition Input Structure


Atomic
Number		 Atomic
Symbol		 Isotope Isotope
Mass		 Isotope
Abundance		 Number
Atoms		 Mass
6C1212.000098.900080960.0000
Total80 960.0000
Isotopomer Natural Abundance (%)41.2765


Determined Point Group: Ih







Representation ΓN


Characters of reducible representation
E 12C5 12(C5)2 20C3 15C2 i 12S10 12(S10)3 20S6 15σd
80 0.000 0.000 2 0 0 0.000 0.000 0 8

Direct sum of irreducible representation
Ag T1g T2g Gg Hg Au T1u T2u Gu Hu
2 1 1 3 4 0 3 3 3 2



Properties of derivatives and isotopomers by single substitution, h(Ih)=120
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 C3v 620Cnoyes13C961.00349.1818
2 Cs 260Cnoyes13C961.003427.5455
Total Number of Atoms:80✅ 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
SingleX20
DoubleX21723
DoubleXY1446
TripleX386646
TripleX2Y1141.997
TripleXYZ844.066
QuadrupleX444013.066
QuadrupleX3Y57452.441
QuadrupleX2Y295078.799
QuadrupleX2YZ714157.801
QuadrupleWXYZ420316.106
QuintupleX51.778199.452
QuintupleVWXYZ1.68024.039.176
SextupleX67.0012.501.957
SextupleUVWXYZ5.0401.802.998.680

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
240 0.000 -0.000 0 0 0 0.000 -0.000 0 8

Direct sum of irreducible representation
Ag T1g T2g Gg Hg Au T1u T2u Gu Hu
3 5 5 8 11 1 7 7 8 9

Molecular motions and force field analysis


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