Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.984466.0470
6C1212.000098.9000336.0000
8O1615.994999.7620347.9847
Total12 90.0317
Isotopomer Natural Abundance (%)95.9572


Determined Point Group: C3v








Representation ΓN


Characters of reducible representation
E 2C3 v
12 0 4

Direct sum of irreducible representation
A1 A2 E
4 0 4



Properties of derivatives and isotopomers by single substitution, h(C3v)=6
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 Cs 23Cnoyes13C91.03503.2018
2 Cs 23Onoyes18O
17O
92.0359
91.0359
0.5771
0.1097
3 Cs 23Hnoyes2H91.03800.044915
4 Cs 23Hnoyes2H91.03800.044915
Total Number of Atoms:12✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group C3v
***Calculated as h( C3v)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX40
DoubleX2106
DoubleXY1216
TripleX32028
TripleX2Y2896
TripleXYZ24208
QuadrupleX43167
QuadrupleX3Y52304
QuadrupleX2Y266462
QuadrupleX2YZ60960
QuadrupleWXYZ241.968
QuintupleX540112
QuintupleVWXYZ015.840
SextupleX644134
SextupleUVWXYZ0110.880

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 2C3 v
36 0 4

Direct sum of irreducible representation
A1 A2 E
8 4 12

Molecular motions and force field analysis



Last update April, 29th 2022 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement