Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.98441010.0783
6C1212.000098.900020240.0000
Total30 250.0783
Isotopomer Natural Abundance (%)80.0292


Determined Point Group: C5v








Representation ΓN


Characters of reducible representation
E 2C5 2(C5)2 v
30 0.000 0.000 2

Direct sum of irreducible representation
A1 A2 E1 E2
4 2 6 6



Properties of derivatives and isotopomers by single substitution, h(C5v)=10
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 Cs 25Cnoyes13C251.08164.4506
2 Cs 25Cnoyes13C251.08164.4506
3 C1 110Cyesyes13C251.08168.9011
4 C1 110Hyesyes2H251.08450.1249
Total Number of Atoms:30✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group C5v
***Calculated as h( C5v)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX22
DoubleX21536
DoubleXY286
TripleX328392
TripleX2Y281.204
TripleXYZ02.436
QuadrupleX41052.688
QuadrupleX3Y2810.948
QuadrupleX2Y221016.338
QuadrupleX2YZ2832.872
QuadrupleWXYZ065.772
QuintupleX518214.162
QuintupleVWXYZ01.710.072
SextupleX645559.150
SextupleUVWXYZ042.751.800

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 2C5 2(C5)2 v
90 0.000 -0.000 2

Direct sum of irreducible representation
A1 A2 E1 E2
10 8 18 18

Molecular motions and force field analysis



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