Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.984422.0157
6C1212.000098.9000224.0000
8O1615.994999.7620463.9797
Total8 89.9953
Isotopomer Natural Abundance (%)96.8540


Determined Point Group: C2h








Representation ΓN


Characters of reducible representation
E C2 i σh
8 0 0 8

Direct sum of irreducible representation
Ag Bg Au Bu
4 0 0 4



Properties of derivatives and isotopomers by single substitution, h(C2h)=4
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 Cs 22Cnoyes13C90.99872.1545
2 Cs 22Onoyes18O
17O
91.9996
90.9995
0.3883
0.073785
3 Cs 22Onoyes18O
17O
91.9996
90.9995
0.3883
0.073785
4 Cs 22Hnoyes2H91.00160.030223
Total Number of Atoms:8✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group C2h
***Calculated as h( C2h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX40
DoubleX2160
DoubleXY280
TripleX3280
TripleX2Y840
TripleXYZ1680
QuadrupleX4380
QuadrupleX3Y1400
QuadrupleX2Y22160
QuadrupleX2YZ4200
QuadrupleWXYZ8400
QuintupleX5280
QuintupleVWXYZ3.3600
SextupleX6160
SextupleUVWXYZ10.0800

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 i σh
24 0 0 8

Direct sum of irreducible representation
Ag Bg Au Bu
8 4 4 8

Molecular motions and force field analysis



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