Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.98441212.0939
6C1212.000098.900021252.0000
Total33 264.0939
Isotopomer Natural Abundance (%)79.1242


Determined Point Group: C3v








Representation ΓN


Characters of reducible representation
E 2C3 v
33 0 3

Direct sum of irreducible representation
A1 A2 E
7 4 11



Properties of derivatives and isotopomers by single substitution, h(C3v)=6
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 C1 16Cyesyes13C265.09735.2803
2 C1 16Cyesyes13C265.09735.2803
3 C1 16Cyesyes13C265.09735.2803
4 Cs 23Cnoyes13C265.09732.6401
5 Cs 23Hnoyes2H265.10020.037036
6 Cs 23Hnoyes2H265.10020.037036
7 C1 16Hyesyes2H265.10020.074072
Total Number of Atoms:33✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group C3v
***Calculated as h( C3v)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX34
DoubleX21879
DoubleXY6173
TripleX346890
TripleX2Y482.704
TripleXYZ65.453
QuadrupleX41506.745
QuadrupleX3Y9027.235
QuadrupleX2Y230040.770
QuadrupleX2YZ9081.795
QuadrupleWXYZ0163.680
QuintupleX533039.391
QuintupleVWXYZ04.746.720
SextupleX6770184.228
SextupleUVWXYZ0132.908.160

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 v
99 0 3

Direct sum of irreducible representation
A1 A2 E
18 15 33

Molecular motions and force field analysis



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