Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.984466.0470
5B1111.009380.1000666.0558
Total12 72.1028
Isotopomer Natural Abundance (%)26.3869


Determined Point Group: Oh








Representation ΓN


Characters of reducible representation
E 8C3 6C2 6C4 3C2 i 6S4 8S6 h d
12 0 0 4 4 0 0 0 8 4

Direct sum of irreducible representation
A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u
2 0 2 0 0 0 0 0 2 0



Properties of derivatives and isotopomers by single substitution, h(Oh)=48
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 C4v 86Bnoyes10B71.106439.3333
2 C4v 86Hnoyes2H73.10910.024702
Total Number of Atoms:12✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group Oh
***Calculated as h( Oh)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX20
DoubleX270
DoubleXY100
TripleX3140
TripleX2Y302
TripleXYZ488
QuadrupleX4252
QuadrupleX3Y6214
QuadrupleX2Y28528
QuadrupleX2YZ13462
QuadrupleWXYZ216144
QuintupleX5324
QuintupleVWXYZ8401.560
SextupleX6388
SextupleUVWXYZ2.52012.600

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 8C3 6C2 6C4 3C2 i 6S4 8S6 h d
36 0 0 4 -4 0 0 0 8 4

Direct sum of irreducible representation
A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u
2 0 2 2 2 0 0 0 4 2

Molecular motions and force field analysis



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