Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.984422.0157
6C1212.000098.9000112.0000
8O1615.994999.7620115.9949
Total4 30.0106
Isotopomer Natural Abundance (%)98.6338


Determined Point Group: C2v








Representation ΓN


Characters of reducible representation
E C2.(z) σv.(xz) σd.(yz)
4 2 4 2

Direct sum of irreducible representation
A1 A2 B1 B2
3 0 1 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 22Hnoyes2H31.01680.030779
2 C2v 41Cnoyes13C31.01391.0970
3 C2v 41Onoyes18O
17O
32.0148
31.0148
0.1977
0.037570
Total Number of Atoms:4✅ 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
SingleX30
DoubleX240
DoubleXY70
TripleX330
TripleX2Y70
TripleXYZ120
QuadrupleX410
QuadrupleX3Y30
QuadrupleX2Y240
QuadrupleX2YZ70
QuadrupleWXYZ120
QuintupleX500
QuintupleVWXYZ00
SextupleX600
SextupleUVWXYZ00

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)
12 -2 4 2

Direct sum of irreducible representation
A1 A2 B1 B2
4 1 4 3

Molecular motions and force field analysis



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