Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.98442020.1565
6C1212.000098.900011132.0000
Total31 152.1565
Isotopomer Natural Abundance (%)88.2682


Determined Point Group: C3h








Representation ΓN


Characters of reducible representation
E C3 (C3)2 σh S3 (S3)5
31 4 4 9 0 0

Direct sum of irreducible representation
A' E'* A'' E''*
8 6 5 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 23Cnoyes13C153.15992.9452
2 C3 32Cyesyes13C153.15991.9635
3 C3 32Hyesyes2H153.16280.027544
4 C1 16Cyesyes13C153.15995.8905
5 Cs 23Hnoyes2H153.16280.041316
6 Cs 23Hnoyes2H153.16280.041316
7 C1 16Hyesyes2H153.16280.082632
8 C1 16Hyesyes2H153.16280.082632
Total Number of Atoms:31✅ 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
SingleX35
DoubleX21771
DoubleXY24147
TripleX363722
TripleX2Y1172.193
TripleXYZ1684.419
QuadrupleX41935.160
QuadrupleX3Y43220.774
QuadrupleX2Y255431.190
QuadrupleX2YZ76862.550
QuadrupleWXYZ1.008125.364
QuintupleX551928.077
QuintupleVWXYZ5.0403.395.700
SextupleX61.209122.133
SextupleUVWXYZ20.16088.343.640

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
93 0 0 9 0 0

Direct sum of irreducible representation
A' E'* A'' E''*
17 17 14 14

Molecular motions and force field analysis



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