Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.984433.0235
5B1111.009380.1000111.0093
8O1615.994999.7620347.9847
Total7 62.0175
Isotopomer Natural Abundance (%)79.4922


Determined Point Group: C3h








Representation ΓN


Characters of reducible representation
E C3 (C3)2 σh S3 (S3)5
7 1 1 7 1 1

Direct sum of irreducible representation
A' E'* A'' E''*
3 2 0 0



Properties of derivatives and isotopomers by single substitution, h(C3h)=6
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 C3h 61Bnono10B61.021219.7490
2 Cs 23Onoyes18O
17O
64.0218
63.0217
0.4781
0.090837
3 Cs 23Hnoyes2H63.02380.037208
Total Number of Atoms:7✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group C3h
***Calculated as h( C3h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX30
DoubleX270
DoubleXY140
TripleX3130
TripleX2Y350
TripleXYZ700
QuadrupleX4130
QuadrupleX3Y480
QuadrupleX2Y2700
QuadrupleX2YZ1400
QuadrupleWXYZ2800
QuintupleX570
QuintupleVWXYZ8400
SextupleX630
SextupleUVWXYZ1.6800

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 C3 (C3)2 σh S3 (S3)5
21 0 0 7 -2 -2

Direct sum of irreducible representation
A' E'* A'' E''*
4 5 3 2

Molecular motions and force field analysis



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