Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.98441010.0783
6C1212.000098.900010120.0000
Total20 130.0783
Isotopomer Natural Abundance (%)89.3893


Determined Point Group: C3v








Representation ΓN


Characters of reducible representation
E 2C3 v
20 2 4

Direct sum of irreducible representation
A1 A2 E
6 2 6



Properties of derivatives and isotopomers by single substitution, h(C3v)=6
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 C3v 61Cnoyes13C131.08160.9942
2 C3v 61Hnoyes2H131.08450.013947
3 Cs 23Cnoyes13C131.08162.9827
4 C1 16Cyesyes13C131.08165.9653
5 Cs 23Hnoyes2H131.08450.041841
6 C1 16Hyesyes2H131.08450.083681
Total Number of Atoms:20✅ 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
SingleX42
DoubleX21425
DoubleXY1258
TripleX336174
TripleX2Y44548
TripleXYZ241.128
QuadrupleX477773
QuadrupleX3Y1003.184
QuadrupleX2Y21584.766
QuadrupleX2YZ1089.636
QuadrupleWXYZ2419.368
QuintupleX51442.514
QuintupleVWXYZ0310.080
SextupleX62326.349
SextupleUVWXYZ04.651.200

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
60 0 4

Direct sum of irreducible representation
A1 A2 E
12 8 20

Molecular motions and force field analysis



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