Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.984488.0626
6C1212.000098.9000896.0000
Total16 104.0626
Isotopomer Natural Abundance (%)91.4173


Determined Point Group: Oh








Representation ΓN


Characters of reducible representation
E 8C3 6C2 6C4 3C2 i 6S4 8S6 h d
16 4 0 0 0 0 0 0 0 8

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



Properties of derivatives and isotopomers by single substitution, h(Oh)=48
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 C3v 68Cnoyes13C105.06608.1342
2 C3v 68Hnoyes2H105.06890.1141
Total Number of Atoms:16✅ 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
SingleX20
DoubleX2100
DoubleXY140
TripleX3222
TripleX2Y5012
TripleXYZ8432
QuadrupleX45320
QuadrupleX3Y12692
QuadrupleX2Y2174152
QuadrupleX2YZ266324
QuadrupleWXYZ420704
QuintupleX58254
QuintupleVWXYZ1.68010.080
SextupleX6130116
SextupleUVWXYZ5.040117.600

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
48 0 0 0 0 0 0 0 0 8

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

Molecular motions and force field analysis



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