Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.984466.0470
6C1212.000098.9000448.0000
Total10 54.0470
Isotopomer Natural Abundance (%)95.5826


Determined Point Group: C2v








Representation ΓN


Characters of reducible representation
E C2.(z) σv.(xz) σd.(yz)
10 0 10 0

Direct sum of irreducible representation
A1 A2 B1 B2
5 0 5 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 22Cnoyes13C55.05032.1262
2 Cs 22Cnoyes13C55.05032.1262
3 Cs 22Hnoyes2H55.05320.029826
4 Cs 22Hnoyes2H55.05320.029826
5 Cs 22Hnoyes2H55.05320.029826
Total Number of Atoms:10✅ 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
SingleX50
DoubleX2250
DoubleXY450
TripleX3600
TripleX2Y1800
TripleXYZ3600
QuadrupleX41100
QuadrupleX3Y4200
QuadrupleX2Y26400
QuadrupleX2YZ1.2600
QuadrupleWXYZ2.5200
QuintupleX51260
QuintupleVWXYZ15.1200
SextupleX61100
SextupleUVWXYZ75.6000

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)
30 0 10 0

Direct sum of irreducible representation
A1 A2 B1 B2
10 5 10 5

Molecular motions and force field analysis



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