Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
6C1212.000098.900074888.0000
Total74 888.0000
Isotopomer Natural Abundance (%)44.1088


Determined Point Group: D3h








Representation ΓN


Characters of reducible representation
E 2C3 3C'2 σh 2S3 v
74 2 0 6 0 8

Direct sum of irreducible representation
A'1 A'2 E' A''1 A''2 E''
9 5 13 4 8 11



Properties of derivatives and isotopomers by single substitution, h(D3h)=12
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 C3v 62Cnoyes13C889.00340.9812
2 Cs 26Cnoyes13C889.00342.9436
3 C1 112Cyesyes13C889.00345.8871
4 Cs 26Cnoyes13C889.00342.9436
5 C1 112Cyesyes13C889.00345.8871
6 Cs 26Cnoyes13C889.00342.9436
7 C1 112Cyesyes13C889.00345.8871
8 C1 112Cyesyes13C889.00345.8871
9 Cs 26Cnoyes13C889.00342.9436
Total Number of Atoms:74✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group D3h
***Calculated as h( D3h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX54
DoubleX239215
DoubleXY33434
TripleX31985.307
TripleX2Y26016.076
TripleXYZ18832.318
QuadrupleX494295.589
QuadrupleX3Y1.244382.928
QuadrupleX2Y22.034574.629
QuadrupleX2YZ1.5441.149.854
QuadrupleWXYZ9002.300.802
QuintupleX53.7401.340.531
QuintupleVWXYZ3.480161.085.900
SextupleX613.77815.432.665
SextupleUVWXYZ10.20011.115.042.060

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 σh 2S3 v
222 0 0 6 0 8

Direct sum of irreducible representation
A'1 A'2 E' A''1 A''2 E''
21 17 38 16 20 36

Molecular motions and force field analysis



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