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: D8h








Representation ΓN


Characters of reducible representation
E 2C8 2C4 2(C8)3 C2 4C'2 4C''2 i 2(S8)3 2S4 2S8 σh v d
16 0.000 0 0.000 0 4 0 0 0.000 0 0.000 16 4 0

Direct sum of irreducible representation
A1g A2g B1g B2g E1g E2g E3g A1u A2u B1u B2u E1u E2u E3u
2 0 2 0 0 2 0 0 0 0 0 2 0 2



Properties of derivatives and isotopomers by single substitution, h(D8h)=32
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 C2v 48Cnoyes13C105.06608.1342
2 C2v 48Hnoyes2H105.06890.1141
Total Number of Atoms:16✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group D8h
***Calculated as h( D8h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX20
DoubleX2130
DoubleXY180
TripleX3420
TripleX2Y1140
TripleXYZ2160
QuadrupleX41360
QuadrupleX3Y4740
QuadrupleX2Y27270
QuadrupleX2YZ1.3860
QuadrupleWXYZ2.7360
QuintupleX52940
QuintupleVWXYZ32.7600
SextupleX65470
SextupleUVWXYZ360.3600

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 2C8 2C4 2(C8)3 C2 4C'2 4C''2 i 2(S8)3 2S4 2S8 σh v d
48 0.000 0 -0.000 0 -4 0 0 -0.000 0 0.000 16 4 0

Direct sum of irreducible representation
A1g A2g B1g B2g E1g E2g E3g A1u A2u B1u B2u E1u E2u E3u
2 2 2 2 2 4 2 0 2 0 2 4 2 4

Molecular motions and force field analysis



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