Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.984466.0470
6C1212.000098.9000224.0000
Total8 30.0470
Isotopomer Natural Abundance (%)97.7206


Determined Point Group: D3h








Representation ΓN


Characters of reducible representation
E 2C3 3C'2 σh 2S3 v
8 2 0 0 0 4

Direct sum of irreducible representation
A'1 A'2 E' A''1 A''2 E''
2 0 1 0 2 1



Properties of derivatives and isotopomers by single substitution, h(D3h)=12
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 C3v 62Cnoyes13C31.05032.1738
2 Cs 26Hnoyes2H31.05320.091481
Total Number of Atoms:8✅ 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
SingleX20
DoubleX251
DoubleXY62
TripleX362
TripleX2Y109
TripleXYZ1222
QuadrupleX484
QuadrupleX3Y1417
QuadrupleX2Y21829
QuadrupleX2YZ1861
QuadrupleWXYZ12134
QuintupleX562
QuintupleVWXYZ0560
SextupleX651
SextupleUVWXYZ01.680

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 2C3 3C'2 σh 2S3 v
24 0 0 0 0 4

Direct sum of irreducible representation
A'1 A'2 E' A''1 A''2 E''
3 1 4 1 3 4

Molecular motions and force field analysis



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