Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.984466.0470
6C1212.000098.9000672.0000
Total12 78.0470
Isotopomer Natural Abundance (%)93.4913


Determined Point Group: D3h








Representation ΓN


Characters of reducible representation
E 2C3 3C'2 σh 2S3 v
12 0 0 0 0 4

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



Properties of derivatives and isotopomers by single substitution, h(D3h)=12
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 Cs 26Cnoyes13C79.05036.2391
2 Cs 26Hnoyes2H79.05320.087522
Total Number of Atoms:12✅ 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
DoubleX264
DoubleXY68
TripleX31014
TripleX2Y1448
TripleXYZ12104
QuadrupleX41836
QuadrupleX3Y26152
QuadrupleX2Y238236
QuadrupleX2YZ30480
QuadrupleWXYZ12984
QuintupleX52056
QuintupleVWXYZ07.920
SextupleX62670
SextupleUVWXYZ055.440

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
36 0 0 0 0 4

Direct sum of irreducible representation
A'1 A'2 E' A''1 A''2 E''
4 2 6 2 4 6

Molecular motions and force field analysis



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