Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.98441818.1409
6C1212.000098.900011132.0000
Total29 150.1409
Isotopomer Natural Abundance (%)88.2957


Determined Point Group: C3h








Representation ΓN


Characters of reducible representation
E C3 (C3)2 σh S3 (S3)5
29 2 2 9 0 0

Direct sum of irreducible representation
A' E'* A'' E''*
7 6 4 3



Properties of derivatives and isotopomers by single substitution, h(C3h)=6
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 Cs 23Cnoyes13C151.14422.9462
2 C3 32Cyesyes13C151.14421.9641
3 C1 16Cyesyes13C151.14425.8923
4 Cs 23Hnoyes2H151.14710.041329
5 Cs 23Hnoyes2H151.14710.041329
6 C1 16Hyesyes2H151.14710.082658
7 C1 16Hyesyes2H151.14710.082658
Total Number of Atoms:29✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group C3h
***Calculated as h( C3h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX34
DoubleX21660
DoubleXY24124
TripleX360582
TripleX2Y1141.770
TripleXYZ1683.570
QuadrupleX41773.876
QuadrupleX3Y40815.636
QuadrupleX2Y252223.490
QuadrupleX2YZ74447.130
QuadrupleWXYZ1.00894.500
QuintupleX545919.566
QuintupleVWXYZ5.0402.372.580
SextupleX61.03278.666
SextupleUVWXYZ20.16056.992.320

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 C3 (C3)2 σh S3 (S3)5
87 0 0 9 0 0

Direct sum of irreducible representation
A' E'* A'' E''*
16 16 13 13

Molecular motions and force field analysis



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