Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.98441010.0783
6C1212.000098.900014168.0000
Total24 178.0783
Isotopomer Natural Abundance (%)85.5206


Determined Point Group: C2v








Representation ΓN


Characters of reducible representation
E C2.(z) σv.(xz) σd.(yz)
24 0 24 0

Direct sum of irreducible representation
A1 A2 B1 B2
12 0 12 0



Properties of derivatives and isotopomers by single substitution, h(C2v)=4
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 Cs 22Cnoyes13C179.08161.9024
2 Cs 22Cnoyes13C179.08161.9024
3 Cs 22Cnoyes13C179.08161.9024
4 Cs 22Hnoyes2H179.08450.026687
5 Cs 22Cnoyes13C179.08161.9024
6 Cs 22Cnoyes13C179.08161.9024
7 Cs 22Cnoyes13C179.08161.9024
8 Cs 22Cnoyes13C179.08161.9024
9 Cs 22Hnoyes2H179.08450.026687
10 Cs 22Hnoyes2H179.08450.026687
11 Cs 22Hnoyes2H179.08450.026687
12 Cs 22Hnoyes2H179.08450.026687
Total Number of Atoms:24✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group C2v
***Calculated as h( C2v)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX120
DoubleX21440
DoubleXY2760
TripleX31.0120
TripleX2Y3.0360
TripleXYZ6.0720
QuadrupleX45.3460
QuadrupleX3Y21.2520
QuadrupleX2Y231.9440
QuadrupleX2YZ63.7560
QuadrupleWXYZ127.5120
QuintupleX521.2520
QuintupleVWXYZ2.550.2400
SextupleX667.4080
SextupleUVWXYZ48.454.5600

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 C2.(z) σv.(xz) σd.(yz)
72 0 24 0

Direct sum of irreducible representation
A1 A2 B1 B2
24 12 24 12

Molecular motions and force field analysis



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