Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.984466.0470
5B1111.009380.1000222.0186
Total8 28.0656
Isotopomer Natural Abundance (%)64.1001


Determined Point Group: D2h








Representation ΓN


Characters of reducible representation
E C2.(z) C2.(y) C2.(x) i σ.(xy) σ.(xy) σ.(xy)
8 0 2 2 0 4 6 2

Direct sum of irreducible representation
A1g B1g B2g B3g A1u B1u B2u B3u
3 0 1 0 0 1 1 2



Properties of derivatives and isotopomers by single substitution, h(D2h)=8
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 C2v 42Bnoyes10B27.069231.8500
2 C2v 42Hnoyes2H29.07180.020002
3 Cs 24Hnoyes2H29.07180.040005
Total Number of Atoms:8✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group D2h
***Calculated as h( D2h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX30
DoubleX281
DoubleXY112
TripleX3113
TripleX2Y2311
TripleXYZ3624
QuadrupleX4144
QuadrupleX3Y3121
QuadrupleX2Y24435
QuadrupleX2YZ6375
QuadrupleWXYZ96162
QuintupleX5113
QuintupleVWXYZ180750
SextupleX681
SextupleUVWXYZ1802.430

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) C2.(y) C2.(x) i σ.(xy) σ.(xy) σ.(xy)
24 0 -2 -2 0 4 6 2

Direct sum of irreducible representation
A1g B1g B2g B3g A1u B1u B2u B3u
4 3 3 2 1 4 3 4

Molecular motions and force field analysis



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